|=--=[ The Latency of Knowing Capacity Limits, External Stores and the Cost of Retrieval in Persons and Organisations, with the Chinese Room Turned Inside Out ]=--=|

--[ Abstract ]--

This paper reviews what several literatures say about where knowledge is kept and how long it takes to get it back: the organ, whose capacity estimates disagree by six orders of magnitude; the narrow door of working memory; and the long history of keeping knowledge outside the body. It measures retrieval latency in persons, organisations and machines, argues that latency, not capacity, is the binding constraint, and proposes a framework, LOCUS. It finds an animated marriage in which a small proprietor pursues a written formula, argues that this is Searle's Chinese room with the roles reversed, and takes from the objections a thesis: that the unit of understanding is a pair coupled at a latency, and that neither member understands alone. Nothing here is advice.

Keywords: knowledge management; knowledge representation; working memory; long-term memory; forgetting; spaced repetition; cognitive load; externalisation; distributed cognition; retrieval latency; organisational memory; the Chinese room; other minds; understanding.

--[ 1 ]-- Introduction

The figures on the previous page held something, and no one can now say what. Every store, at every scale, ends that way, and this paper is about why.

Every treatment of knowledge, in the firm, the library, the clinic or the skull, arrives at the same two questions and usually answers only the first: how much can be held, and how long it takes to get it back. The literature on the first is vast and, as Section 6 shows, spectacularly inconsistent; the literature on the second is smaller, older, more exact, and largely ignored by the people who write about the first. This paper puts them side by side; the second binds.

The scales are these. At the top, civilisations: the stone row, the archive, the library, the bureaucracy, each built to outlast the people who could read it, and each doing so. At the bottom, one working memory: a door two to seven items wide, depending on the unit, which scans what it holds at forty milliseconds an item and loses it within seconds unless refreshed. Between, everything else: a team, a firm, a desk, a card index, a department in the tip-of-the-tongue state over a file it knows it has. All of it, the paper claims, is governed from the bottom. What a civilisation knows must pass, to be used, through one of those doors, in time.

This is a long paper, and it is long on purpose: the finding does not survive summary. The same constraint appears in each literature, in the same units, under a different name, and the reader has to watch it appear. It ends where none of them do, in an animated marriage, and whoever gets there will know why the figures on the first page are still standing, and what the sources say about those who keep everything.

The people who write about how much have, by and large, not read the people who measured how long. The reader is about to.

----[ 1.1 ] The claim

The claim can be stated at once and then defended at length. Knowledge that cannot be retrieved in time is, for the purpose at hand, not possessed. A fact in a filing cabinet is possessed by the office in a sense that matters to the auditor and not in any sense that matters to the clerk on the telephone. A word on the tip of the tongue is possessed by the speaker in a sense that matters to the psychologist and not in any sense that matters to the sentence. The organ that holds most of what a person knows, the long-term memory, is by every published estimate very large; the organ through which any of it must pass to be used, the working memory, is by every published estimate very small, and it is small in a way that time cannot repair, because it forgets what it holds within seconds unless it is refreshed.(1) The consequence, which every bureaucracy and every student has discovered independently, is that what one can do with what one knows is governed by the speed at which the small store can be fed from the large one, and from the still larger one outside the body.

We use the word latency for this speed, in the plain technical sense of the time between asking and receiving. The word is borrowed from the design of machine memories, where a hierarchy of stores of increasing size and increasing delay is the ordinary condition of life and where the rules for deciding what to keep close are written down in dollars and seconds [61, 59, 77]. We borrow it without apology. The psychologists who measured the human version of the same quantity in the 1960s did so with the same instrument, the reaction-time clock, and reported the same kind of result: a fixed cost per item, a linear slope, an intercept for the machinery [106, 108, 104]. Section 10 collects these results. They are the empirical core of the paper.

----[ 1.2 ] The argument in brief

The argument runs as follows. (i) Organisations have known since at least the 1950s that they hold their knowledge in two forms, one of which can be written down and one of which cannot, and that the written form is stored in places (files, manuals, drawers) from which it must be fetched [97, 111, 175]. (ii) Any store, internal or external, requires a representation: a scheme of concepts and categories by which an item is addressed, and the history of such schemes, from the Porphyrian tree to the card index, is a history of trading generality for speed of finding [124, 149, 86]. (iii) The person's internal store is large but slow to fill, slow to search and prone to reconstruction rather than reproduction [78, 16, 147]. (iv) The person's working store is tiny [100, 140, 15, 116]. (v) People have therefore, for as long as there have been marks on clay, kept knowledge outside themselves, and the philosophical

(1) The interval is given variously. Hermans, summarising the experimental literature for programmers, writes that short-term memory "cannot hold information for more than 30 seconds" [68, p. 18]; the older working-memory literature speaks of a phonological store of about two seconds' worth of speech that must be rehearsed to persist [15]. The two figures describe different things and we do not attempt to reconcile them.

Plate II. An examination, part one. Six figures, one question each; the boxes are for ticking. The key is at the foot of the page, upside down, the reader is on their honour, and the score should be kept, since the paper will come back to it.

1. Which square is darker, A or B? 2. Which line is longer?

3. Which orange circle is larger? 4. Are the grey lines parallel?

5. Which end of the bar is darker? 6. Which is longer, upright or base?

Key, for afterwards. 1, same: The same grey, to the last digit; the shadow was doing the talking. 2, same: The same length; the fins were only ever suggestions. 3, same: The same size; each circle is judged by the company it keeps. 4, yes: Parallel, every one; the tiles were lying on their behalf. 5, same: One grey from end to end; the background changed, not the bar. 6, same: The same length; standing up has always looked like more work.

objection to doing so is as old as writing and has never once prevailed [58, 115, 33]. (vi) The cost of an external store is measured in retrieval time, and retrieval time, not capacity, is what determines whether knowledge is used [108, 6, 61]. (vii) Organisations are subject to (iii) through (vi) in exactly the way persons are, because they are made of persons and paper, and they show the same symptoms, including the same tip-of-the-tongue state at the scale of a department [141]; [75]; [84, pp. 235--236].

From these we derive a framework, LOCUS (Section 12), whose only novelty is that it declines to treat capacity as the interesting variable. Its five terms, Latency, Offloading, Capacity, Uncertainty and Structure, are ordered by importance rather than alphabetically, which is why the acronym is not memorable and why we have placed a manicule beside it.

----[ 1.3 ] Propositions

For the convenience of readers who wish to disagree with something specific, the paper's principal claims are numbered throughout. The first three follow.

Proposition 1. For any store S and any task T with a deadline d, an item x in S contributes to T only if the retrieval latency ℓ(x, S) < d. Capacity enters only through its effect on ℓ.

Proposition 2. Retrieval latency is not a property of the item but of the pair (item, store): the same fact has a latency of tens of milliseconds in working memory, seconds to minutes in long-term memory (Section 10), seconds to hours in an external store, and effectively infinity in a store whose index has been lost (Exhibit 1).

Proposition 3. Persons and organisations face the same constraint because an organisation's working memory is the attention of its members, and that attention is the scarce resource in both [141, pp. 143--144]; [97].

Remarks are numbered separately and carry no argumentative weight.

Remark 1. The reader will observe that Proposition 1 makes the whole paper a footnote to the five-minute rule of Gray and Putzolu [61]. We accept this. The five-minute rule is, in our view, one of the few results in any of the literatures we survey that is stated with its assumptions, its units and its expected date of expiry ("Twenty years ago the .5 second rule applied, twenty years hence it is likely to be the 5 hour rule" [61]); it was revisited on schedule [59]. Very few claims about human memory have been so well behaved.

----[ 1.4 ] What this paper is not

It is not a treatment of any particular system for storing or finding anything, and it describes no method, mechanism or apparatus beyond those already described in the sources it cites, most of which are decades old and several of which are made of wood. It is not advice: nothing here should be taken as a

recommendation about what to remember, what to write down, what to keep or what to throw away. It is not short. Readers pressed for time are directed to Sections 10 and 12 and to Appendix C, which tabulates every numerical claim in the paper with the source, the page and, where the literature disagrees, the disagreement.

----[ 1.5 ] Structure

The paper is arranged as an approach and a departure. Section 2 asks why knowledge is worth having, from the Meno to the price of information. Section 3 surveys the related work, exhaustively enough that the survey can be skipped. Section 4 treats knowledge in organisations, Section 5 representation, Section 6 the organ, Section 7 the schedules that keep things in it, Section 8 the bottleneck, Section 9 the long history of keeping knowledge outside the body, Section 10 retrieval latency, Section 11 the parallel between persons and organisations, and Section 12 the framework. An interlude then reaches for an everyday example and does not let go of it: Section 13, the bulk of the paper, states and answers the objections to reading an animated marriage as the Chinese room reversed, and keeps a proposition from each reply; Section 14 steps outside the room to the countryside that kept its knowledge in the room's script for three thousand years, and loses its footing, briefly, in Texas; Section 15 turns the ledger over and asks what a store does to its keeper; Section 16 discusses limitations, of which the chief is that the paper is itself an external store of a size that exceeds any working memory, including the authors'. Six appendices follow: notation, glossary, a table of numbers, notes on the exhibits, a list of what the paper's sources do not contain, and a chronology of the stores. Section 17, on the last page, assembles the propositions into the thesis. The contents, which follow, are the map; the reader is not expected to hold them in mind, which is the point.

--[ Contents ]--

1 Introduction 2 1.1 The claim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The argument in brief . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 What this paper is not . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Why Knowledge Is Worth Having 9 2.1 The road to Larissa . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 The price of information . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 What a belief is for . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Related Work 11 3.1 Organisational knowledge and its management . . . . . . . . . . . . . . . 11 3.2 Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 The brain as a store . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Working memory and cognitive load . . . . . . . . . . . . . . . . . . . . 14 3.5 Externalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.6 Retrieval latency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.7 The parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Knowledge in Organisations 16 4.1 Two kinds of knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2 Memory and the repeated game . . . . . . . . . . . . . . . . . . . . . . . 17 4.3 Where the organisation keeps it . . . . . . . . . . . . . . . . . . . . . 18 4.4 Organisational forgetting . . . . . . . . . . . . . . . . . . . . . . . . 21 4.5 Taxonomies in practice . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.6 Checklists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Representation 23 5.1 What a representation is . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2 Concepts and categories . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Schemata, scripts and frames . . . . . . . . . . . . . . . . . . . . . . . 25 5.4 Ontologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.5 Classification, from the tree to the drawer . . . . . . . . . . . . . . . 26

6 The Organ 30 6.1 The palaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.2 How much: the estimates . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.3 Getting things in: consolidation . . . . . . . . . . . . . . . . . . . . . 31 6.4 Getting things out, over time: forgetting . . . . . . . . . . . . . . . . 32 6.5 Getting things in, at scale: the learning rate . . . . . . . . . . . . . 34 6.6 The clinical evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7 Retention by Schedule 35 7.1 The spacing effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 7.2 The testing effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 7.3 The lineage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

8 The Bottleneck 38 8.1 Seven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 8.2 Five, or ten seconds . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 8.3 Three components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 8.4 Two or three . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 8.5 The disagreement, tabulated . . . . . . . . . . . . . . . . . . . . . . . 40

9 The Externalisation of Memory 42 9.1 Cords, tallies and clay . . . . . . . . . . . . . . . . . . . . . . . . . 42 9.2 The objection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 9.3 What orality kept, and how . . . . . . . . . . . . . . . . . . . . . . . . 47 9.4 The art of memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 9.5 Overload and the slip . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 9.6 The mechanised supplement . . . . . . . . . . . . . . . . . . . . . . . . 52 9.7 The extended mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 9.8 The practical tradition . . . . . . . . . . . . . . . . . . . . . . . . . 53

10Retrieval Latency as the Binding Constraint 54 10.1Milliseconds per item: memory scanning . . . . . . . . . . . . . . . . . 54 10.2The fan: the cost of knowing more . . . . . . . . . . . . . . . . . . . . 56

10.3The equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 10.4Seconds to days: the tip of the tongue . . . . . . . . . . . . . . . . . 57 10.5Recognition and recall . . . . . . . . . . . . . . . . . . . . . . . . . . 58 10.6Minutes to hours: the external store . . . . . . . . . . . . . . . . . . 58 10.7Keeping only what is needed in mind . . . . . . . . . . . . . . . . . . . 59

11We Are the Same Way: Persons and Organisations 60 11.1Bounded rationality is a latency condition . . . . . . . . . . . . . . . 60 11.2Attention is the organisation's working memory . . . . . . . . . . . . . 60 11.3Less is more, in both . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 11.4Transactive memory: the organisation's tip of the tongue . . . . . . . 62 11.5The cost of the external store, in minutes per day . . . . . . . . . . . 63 11.6The parallel, tabulated . . . . . . . . . . . . . . . . . . . . . . . . . 64

12A Framework: LOCUS 64 12.1Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 12.2The central relation . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 12.3A taxonomy of stores by latency class . . . . . . . . . . . . . . . . . . 66 12.4The framework in brass . . . . . . . . . . . . . . . . . . . . . . . . . . 66 12.5Propositions of the framework . . . . . . . . . . . . . . . . . . . . . . 70 12.6What the framework predicts . . . . . . . . . . . . . . . . . . . . . . . 71

Interlude: Two Cartoons, Read as a Literature on Retrieval 71

13The Room Inverted: Objections and Replies 78 13.1The argument, as its author states it . . . . . . . . . . . . . . . . . . 80 13.2The inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 13.3Objections and replies . . . . . . . . . . . . . . . . . . . . . . . . . . 82 13.4What the objections agreed on . . . . . . . . . . . . . . . . . . . . . . 96

14The Room's Chinese: What the Countryside Kept 97 14.1A script whose readers never went away . . . . . . . . . . . . . . . . . 97 14.2The lineage and its hall . . . . . . . . . . . . . . . . . . . . . . . . . 98 14.3The shrine, the almanac and the compact . . . . . . . . . . . . . . . . . 99 14.4Two maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 14.5A digression, conducted in the method's own terms . . . . . . . . . . . 102

15What the Store Does to Its Keeper 104 15.1Two men who could not forget . . . . . . . . . . . . . . . . . . . . . . . 104 15.2The material of the craft . . . . . . . . . . . . . . . . . . . . . . . . 105 15.3The touch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 15.4The recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 15.5The framework, amended . . . . . . . . . . . . . . . . . . . . . . . . . . 108

16Discussion and Limitations 109 16.1What the review did not do . . . . . . . . . . . . . . . . . . . . . . . . 109 16.2Threats to the argument . . . . . . . . . . . . . . . . . . . . . . . . . 109 16.3On not mentioning certain things . . . . . . . . . . . . . . . . . . . . . 111 16.4Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Appendix A. Notation 112

Appendix B. Glossary 113

Appendix C. Every Number in the Paper, With Its Source 116

Appendix D. Notes on the Exhibits 121

Appendix E. What the Sources Did Not Hold 123

Appendix F. A Chronology of External Stores Mentioned in the Paper 125

Interval 136

17The Thesis the Objections Built 137

--[ 2 ]-- Why Knowledge Is Worth Having

Before asking how much knowledge a person or an organisation can hold and how long it takes to get it back, it is worth asking why anyone should want it, since the answer fixes what "getting it back" has to achieve. Three literatures answer, in three vocabularies, and this section takes them in order: the oldest, which asks why knowledge is worth more than true belief; the decision-theoretic, which prices information; and a third, which the paper states without names, on what a belief is for.

----[ 2.1 ] The road to Larissa

The first question is Plato's, and Williamson states it in the form the modern literature uses. "Knowing that this road goes to Larissa is useful to you if you want to go to Larissa. But merely believing truly that this road goes to Larissa seems to be equally useful to you, for you will get there just the same. Why should we value knowledge more than mere true belief? Socrates responds by a comparison with the statues of Daedalus, which run away unless they are tethered. True beliefs are liable to be lost, unless they are so anchored that they constitute knowledge" [168]. The passage in the Meno is short enough to give in Shope's translation: true opinions "run away from a man's mind; so they are not worth much until you tether them by working out the reason. … Once they are tied down they become knowledge, and are stable. That is why knowledge is something more valuable than right opinion. What distinguishes one from the other is the tether" [139, p. 12]. Craig glosses the answer as a claim about persistence: "true beliefs are even more valuable if they are stable, that is to say if we persist in holding them; and this means, so he continues, that it is advantageous to have good reasons, for then we will hold fast to the truth and not be easily lured away to falsehood" [36, p. 7].

The reply has never satisfied everyone. Williamson notes that Plato "surely … recognized that mere true beliefs can be held with dogmatic confidence, and knowledge lost through forgetting", and reads the tether as sensitivity to evidence rather than as stickiness [168]. Sosa sets the Larissa worry aside altogether: it "is assuaged by a distinction between epistemic and pragmatic

varieties of justification", and the deeper value problem, how a reliable source can add worth to a belief that is already true, remains [144, pp. 71--72]. The paper takes no position in that dispute. It observes only that every party to it agrees on what the tether does, which is to make a belief available again after the occasion on which it was formed: to make it survive forgetting, or the discovery that its grounds were bad, or the arrival of misleading evidence. A tethered belief is one that can be regenerated from its reasons when the copy in mind has gone. That is a claim about retrieval, and it is the claim Section 6 will find in James's explanation of why cramming fails: a fact with many associations "is led into by" many paths, and a fact with one is not. The tether is a second path. Knowledge, on the oldest theory of its value, is belief with a low latency of recovery.

----[ 2.2 ] The price of information

The second literature prices what the first praises. In statistical decision theory, information is worth exactly what it changes. Raiffa and Schlaifer define the value of perfect information about a state of the world as the difference between the utility of the act one would choose knowing the state and the utility of the act one would choose on one's prior, and its expected value, taken before the fact, as the most one should pay to learn the state [125, pp. 87--88]. The health economists who apply the idea to research funding state the principle in one sentence: "information has value only if it has the potential to change decisions", so that its expected value "can be represented as p ⋅ E(Gain), where p is the probability that research changes the decision as to the preferred alternative and E(Gain) is the expected gain from that change in decision" [118, pp. 458--459]. Bernardo and Smith give the general form, in which the value of an experiment is the expected improvement in the optimal action across the data it might yield [18, p. 65].

Two consequences follow for a paper about stores. The first is that a fact whose arrival cannot change any decision is worth nothing, however true; and a fact that arrives after the decision it would have changed is a fact of that kind. The value of information is therefore bounded by its latency: a store from which the fact cannot be fetched before the deadline holds, for that decision, no information at all. The second is that the price is paid per decision. The same fact may be worth a great deal to the person who is about to act on it and nothing to the person who is not, which is why a store's contents cannot be valued without knowing who reads it and when. Both consequences are stated formally in Section 1 and again in Section 12, where they are the framework's first proposition. Here we only note that the decision theorists reached them without any theory of memory, and that the theory of memory reaches them without any decision theory, and that the paper's business is to put the two in one room.

----[ 2.3 ] What a belief is for

The third answer is not a literature so much as a habit of mind, and the paper states it in its own words. A belief is a map. It is useful to the extent that

its structure answers to the structure of the territory it is a map of, and it can be wrong only because it says something the territory could contradict; a map that could not be contradicted is not a map of anything. Armstrong puts the analogy to work in the theory of belief: "Let us think of the belief-state as a sort of map", with elements and relations that have an interpretation, so that "just as the claim made by a map can be 'read off' from the map, so the content of the proposition believed could be 'recovered' from the belief-state" [9, p. 50]; and Dretske shows what the analogy costs, since a map "can misrepresent the geography of an area only insofar as its elements … are understood to have a meaning independent of their success in carrying information on any given occasion" [43, pp. 192--193]. From this two rules of hygiene follow that the paper will apply throughout. A belief should pay its way: it should anticipate some experience rather than another, and a belief that anticipates nothing, that would leave the world looking the same whether it were true or false, occupies its place in the store without earning it. And a belief should move when the evidence moves, by an amount proportioned to how surprising the evidence would be if the belief were false; a map that is never corrected by the territory is a drawing.(2)

The three answers agree on a point that none of them states. Knowledge is worth having because it is worth getting back: the tether is a path to the belief, the price is paid at the moment of decision, and the map earns its keep only when it is consulted. A store from which nothing is ever fetched holds a great deal and is worth nothing, and the paper will find, before it is done, that such stores are common, that people build them on purpose, and that one of them is a marriage.

--[ 3 ]-- Related Work

Six literatures bear on the question, and they do not read one another. We take them in the order in which the paper uses them, note what each has established, and note in particular what each takes for granted that the next one denies.

----[ 3.1 ] Organisational knowledge and its management

The management literature descends from two sources. The first is the theory of the organisation as a bounded problem-solver, in which the firm is a repertory of "performance programs" that are stored, in March and Simon's words, "in the minds of the employees who carry them out" and, more or less completely and more

(2) The three ideas of this paragraph, that the map is not the territory, that a belief should pay its way in anticipated experience, and that one should move one's credence when the evidence moves, are stated here without attribution because the paper found them in this form, and learned to state them this plainly, in the essays collected in [176], whose title the reference list gives as its publisher gave it. The paper's only other debt to that collection is in Section 13, where it is acknowledged in the ordinary way. The ideas themselves are older than the collection and are, in the paper's view, the common property of anyone who has ever been wrong about something and noticed.

or less accurately, in documents describing standard operating procedures [97, pp. 142--143]. On this view an organisation remembers in two media, people and paper, and much of its internal communication "is aimed at a search of the organization's (collective) memory for relevant considerations" [97, pp. 189--190]. The theme was taken up in the economics of internal organisation, where the incompleteness of every performance program is what distinguishes a hierarchy from a contract [167], and in the study of innovation, where Henderson and Clark showed that a firm's knowledge of how its components fit together comes to reside implicitly in its communication channels, information filters and problem-solving strategies, so that the firm cannot easily see what it knows or notice when it has become wrong [67, pp. 6--7].

The second source is Polanyi's distinction between what we can tell and what we can only do [122, 123], which Nonaka and Takeuchi turned into a theory of the "knowledge-creating company" with four modes of conversion between tacit and explicit knowledge [111, p. 62]. This is the most cited framework in the field and the most criticised; Collins's objection, that the framework mistakes the part of tacit knowledge that merely has not yet been written down for the whole of it, is set out in Section 4 [35, pp. 3, 142--144]. The historians have meanwhile shown that the organisational memory the theorists describe was built, quite literally, out of furniture: Yates on the vertical file and the memorandum [175], Robertson on the filing cabinet as a machine whose "intellect" was its guide cards [127, p. 173]. The sociologists of classification, Bowker and Star, added the observation that organisations forget as deliberately as they remember, and that a classification scheme is the instrument of both [22, pp. 257--258, 277--279]. Lambe's practitioner's treatment of taxonomies in firms, with its frank catalogue of failures, closes the loop between the theory and the shared drive [91].

What this literature takes for granted is that once knowledge has been made explicit it is available. The next literature is about why that is not so.

----[ 3.2 ] Representation

The theory of representation asks in what form knowledge is held, and its answers have converged from three directions. From psychology came the discovery that human categories are not the classical categories of the logicians: that they have best examples and graded membership [130, 90], that there is a privileged "basic level" at which categories carry the most information for the least cognitive load [131, p. 428], and that what holds a category together is not similarity but a theory [102]. From the same source came the schema, Bartlett's "active organised setting" [16, p. 202], which Rumelhart formalised as a data structure with variables [132, pp. 100--101] and which Schank and Abelson specialised into the script [135, pp. 40--41] and Minsky into the frame [101]. From the logicians and the librarians came the older tradition of definition by genus and difference [124, 134], the tree of Porphyry [82, pp. 605--606]; [34], and the bibliographic objectives of Cutter and his successors, which are the oldest explicit statement of what it means for a store to be findable [149, pp. 15--16]. From the builders of knowledge bases came the

ontology, "an explicit specification of a conceptualization" [148], and the definition of knowledge representation itself as "the application of logic and ontology to the task of constructing computable models for some domain" [146]. Newell's "knowledge level" sits above all of these, treating knowledge as "a competence-like notion, being a potential for generating action" rather than as anything one could point to in a store [107, pp. 14--15].

What this literature takes for granted is that a representation, once chosen, can be consulted. The neurobiologists and the psychologists of memory are less sure.

----[ 3.3 ] The brain as a store

The literature on the organ is the largest and the least agreed. On capacity, 9 the estimates that reach print span from Norman's report of "a billion (10 ) 8 bits or about 100 million (10 ) items" [112, p. 67] and Landauer's few hundred megabytes over a lifetime, as reported by Ware [164, p. 412], to synapse-count 12 derivations that Ware puts at 240 × 10 connections for the cortex at two bits each [164, p. 412], with Turing, in a private letter, computing "simply MN binary digits" for N neurons with M outlets [70, p. 550]. Section 6 plots these on one logarithmic axis and declines to choose. On mechanism the agreement is better: the switch from short-term to long-term memory requires new protein synthesis during a window of one to several hours, after which a blow to the head can no longer erase what is being consolidated [147, pp. 133--134, 142--143]; Hebb had already proposed in 1949 that the function of a night's sleep might be to let the day's synaptic changes regress [66, p. 230], a proposal the modern literature has inverted while keeping the night [164, pp. 413--414]. On forgetting, the shape has been known since Ebbinghaus's experiments on himself, whose figures William James summarised for English readers in 1890 [78, pp. 677--678]; on reconstruction, since Bartlett's repeated reproductions of a story his subjects could not make sense of [16, pp. 208--209]. The clinical literature contributes the dissociations: patients who cannot form new lasting memories but retain a normal span, and patients with a span of one or two items who learn normally [15, p. 556], and the slow erasure of the hippocampus in the commonest dementia [153, pp. 131--132]. In Super Mario

64 a painting is a door, and the canvas just after someone has gone through it (Plate III) is a fair picture of the reconstruction literature: the same scene, disturbed from the middle outward, the frame unmoved, which is the whole of a frame's job.

What this literature takes for granted is that the small store is small. It is. The next literature measured it.

----[ 3.4 ] Working memory and cognitive load

Miller's seven [100], Simon's five to seven chunks and five to ten seconds per chunk [140, p. 487], Baddeley's tripartite working memory [15], and the cognitive-load theory of Sweller and colleagues, in which working memory "can handle only a very limited number---possibly no more than two or three---of novel interacting elements" [116], are the four load-bearing results. They agree that the number is small and disagree about the number; Section 8 reports the disagreement. The expertise literature explains how the small store nevertheless supports expert performance: by chunking [140], by schema acquisition [150], and by something like ten years of deliberate practice [46, p. 372]; [48, pp. 7--8]. A textbook for programmers, itself a work of externalisation, states the modern consensus as "between two and six things" and asks, reasonably, "Isn't it a miracle that humans can do anything with no more than 1 byte of memory?" [68, p. 18]. The store outside the body, the next literature's subject, has its limiting case in Minecraft, a game built of blocks: a store one can step into and not see out of (Plate IV), whose latency is one loading screen and on whose capacity the literature is silent.

----[ 3.5 ] Externalisation

That people keep knowledge outside their bodies is the oldest observation in the paper and the one with the longest bibliography. The classical objection, Plato's, that writing "will implant forgetfulness in their souls" because they will rely "on that which is written", is quoted at length by Goody and Watt [58, pp. 326--327] and by Yates [174, p. 52], and discussed by Ong, who notes that "essentially the same objections commonly urged today against computers were

urged by Plato" against writing [115, pp. 77--79], by Harris [65, pp. 17--19], by Norman [113, pp. 44--45], by Derrida [41, pp. 36--37] and most recently by Chalmers, who observes that Socrates, who wrote nothing, is known to us because Plato wrote him down [30]. The anthropology of writing, from Goody's lists and tables [57] to Olson's "world on paper" [114], and the study of oral composition [95], establish what the written store changed. The history of the arts of memory [174], of scholarly note-taking under overload [19], of the card index [86] and the slip box [96, 1], and of the memex [25] and hypertext [105] establish what the external store became. The extended-mind thesis, Clark and Chalmers's Otto with his notebook [33, pp. 12--13], and the anthropology of distributed cognition, Hutchins's navigation team [75], establish that the boundary of the skin is not where knowledge stops. The self-help literature has reached the same conclusion by a shorter route: "use your mind to think about things, rather than think of them" [2, pp. 232--233].

----[ 3.6 ] Retrieval latency

The literature on how long retrieval takes is the smallest and, in our judgement, the best. Sternberg's memory-scanning paradigm, in which the time to decide whether a probe belongs to a memorised set rises linearly with the size of the set at a slope of "between 30 and 50 msec. per item" [7, pp. 373--374], "about 35 msec per item" [4, pp. 119--120], "in the range of 35--40 ms" [106, pp. 10--11] or "~40 ms" [108, pp. 285--286], is among the most replicated results in experimental psychology, and Newell listed thirty-two regularities of it on a single page [108, p. 287]. The fan effect, that recognition slows as more facts are attached to a concept, was measured in the same units [3, −A p. 256]. The ACT-R theory reduced retrieval time to an equation, T = Fe , with activation decaying as a power of time at a default exponent of one half [6, p. 1042]; [5, pp. 110--111]. The tip-of-the-tongue state, first described by James, gives the phenomenology of a retrieval that has not yet completed [47, pp. 130--131]; [126, pp. 105--106]; [76, p. 217]; [21]; [170, p. 219]. And the engineers, as noted, wrote the rule for when a slow store should be promoted to a fast one [61, 59] and tabulated the latencies of each level [77, 42].

What this literature takes for granted is that the question is worth asking. We agree, and the remainder of the paper is an attempt to ask it of the other five.

----[ 3.7 ] The parallel

Finally, the parallel between persons and organisations has its own small literature, almost all of it by Simon or descending from him: bounded rationality and satisficing [141, pp. 28--29, 119--120]; [97, pp. 140--141], attention as the scarce factor [141, pp. 143--144]; [120, p. 13], the "less-is-more" effects of the fast-and-frugal school [54, p. 358]; [53, pp. 56--57], transactive memory in teams [45]; [84, pp. 235--236]; [117, p. 95], and the clinical documentation studies that measure, in minutes per day, what it costs an organisation to keep its memory outside its members [10, 142, 162]. Section 11 argues that these are one literature.

--[ 4 ]-- Knowledge in Organisations

We begin where the management literature begins, with the observation that an organisation knows things its members cannot say, and says things its members do not know.

----[ 4.1 ] Two kinds of knowledge

Polanyi's formula, that "we can know more than we can tell", is quoted in the foreword to the lectures in which he developed it, with the example of a face: we recognise it "without being able to tell exactly what features of the face yielded that recognition" [123, pp. ix--xi]. The structure he gave to this observation is worth restating because everything downstream depends on it. In an act of tacit knowing we "attend from" one thing "for attending to" another; the first term, nearer to us, he called proximal, the second distal; and "it is the proximal term, then, of which we have a knowledge that we may not be able to tell" [123, p. 10]. The pianist attends from the fingers to the music; the reader attends from the letters to the sense. The consequence, which Polanyi drew and which the knowledge-management literature has generally declined to draw, is that making the proximal term explicit can destroy the performance: "By concentrating attention on his fingers, a pianist can temporarily paralyze his movement" [123, pp. 17--18]. Explicitness has a cost, and the cost is paid in attention.

Nonaka and Takeuchi took the distinction and made it a machine. "The assumption that knowledge is created through the interaction between tacit and explicit knowledge allows us to postulate four different modes of knowledge conversion": tacit to tacit, which they call socialization; tacit to explicit, externalization; explicit to explicit, combination; explicit to tacit, internalization [111, p. 62]. Of these, three "have been discussed from various perspectives in organizational theory"; externalization, they say, "has been somewhat neglected" [111, p. 62], and it is externalization that "holds the key to knowledge creation", being the mode in which knowledge "that is personal, context-specific, and therefore hard to formalize and communicate to others, is converted into knowledge that is transmittable and articulable, such as words or numbers" [111, pp. 237--238]. The four modes are arranged in a spiral that rises through "ontological levels" from the individual to the group to the organisation, since "an organization cannot create knowledge by itself" and "the organization has to mobilize tacit knowledge created and accumulated at the individual level" [111, pp. 71--73]. The examples are industrial: the kneading of dough, the design of a car, the retail management of a food company.(3)

(3) One of the examples is a latency figure, and we record it here because it is the earliest such figure in the management literature we have found. Describing a manufacturer's customer-inquiry centre, Nonaka and Takeuchi report that "1.5 million potential problems and their solutions" had been entered into a database from which "any problem-solution response can be retrieved by the telephone operator in two seconds", with unresolved problems passed to twelve specialists and entered "usually … by the following day" [111, p. 69]. Two seconds and

Collins's objection is that this is a theory of one third of the phenomenon. "Nonaka and Takeuchi are dealing only with relational tacit knowledge", the kind "that just happens not to have been explicated but could be given a bit more effort" [35, p. 3]. Beside it he places somatic tacit knowledge, which "has to do with the nature of the human body and brain", and collective tacit knowledge, which has to do with "the nature of human society", and of the three only the first is convertible in the manner the spiral requires [35, p. x]. The bread-making machine, the famous example, works not because the tacit was made explicit but because "it was not difficult to find other materials with the right affordances to do the job"; the machine is "a social prosthesis, just as the pocket calculator is a social prosthesis", and "it works only because the surrounding social organism makes up and 'repairs' its deficiencies" [35, pp. 142--144]. The correction matters to our argument for a reason Collins does not dwell on: a store can hold only what can be written into it, and what cannot be written into it is not thereby lost but is held elsewhere, in bodies and in collectives, at a different latency.

Proposition 4. Externalisation (in Nonaka and Takeuchi's sense) is a change of store, not a change of quantity. It moves an item from a store with one latency profile (a person, available when present and awake) to a store with another (a record, available when found). Whether the move is an improvement depends on the latencies, not on the conversion.

----[ 4.2 ] Memory and the repeated game

Collins's third kind, the knowledge that has to do with "the nature of human society" [35, p. x], includes the simplest thing an organisation knows about its members and its partners: how they treat one another when they expect to meet again. Game theory makes that expectation exact. In the prisoner's dilemma "either player can cooperate or defect", the selfish choice paying more whatever the other does; yet "if both do defect, however, both do worse than if they had co-operated" [17, p. 83]. When Axelrod ran the game as a tournament between submitted programs, "the highest average score went to the simplest strategy of all: Tit-for-Tat", which "cooperated on the first move, and on all succeeding ones simply did whatever the other player had done" on the move before; it won the second round too, against sixty-two entries [17, pp. 83--84]. From some three million moves of that round Axelrod drew three rules: "begin cooperatively", retaliate at once, and "forgive just as fast"; and the result holds only where "individuals who interact have sufficiently large probability of meeting again" [17, p. 84]. Later work added generosity for games in which moves are misread: "Generosity allows a certain number of defections to go unpunished" [53, pp. 331--332].

In the terms of this paper, tit-for-tat is a store of capacity one: it keeps the other player's last move and nothing else, and reads it at no cost. The strategy fails when the store does. Mauboussin names the organisational case: among the

one day: the two latencies of an organisational memory, stated in 1995 without comment. Section 10 will find them again.

reasons cooperation between firms breaks down is "corporate memory", since executives facing a rare decision "may treat the situation as a one-time prisoner's dilemma because they often don't think over long enough time scales (both past and prospective)" [99, p. 174]. A firm that has forgotten its partner's last move cannot return it, and a firm that does not expect to meet the partner again has no reason to.

Plate V seats the reader at the table. It is set in the form of the boxed tests that stand at the door of many web pages, and it is a figure, not a door: nothing on this page is behind it, and the moves are kept nowhere. The opponent, the Registrar, plays generous tit-for-tat on a rota rather than by lot: it cooperates first, plays the reader's previous move back, and on every third round cooperates whatever the reader did. Plate VI turns memory against the reader. The Archivist plays rock, paper, scissors by keeping, for each pair of the reader's throws, a count of what the reader threw next, and plays what beats the likeliest next throw; the store is nine short lists, and it is usually enough, because people asked to be unpredictable are not. On paper both plates stand as drawn: the question, with no one to answer it.

----[ 4.3 ] Where the organisation keeps it

The older literature is more concrete about the stores. March and Simon list three ways to find out what programs an organisation runs: observe its members, interview them, since "most programs are stored in the minds of the employees who carry them out, or in the minds of their superiors, subordinates, or associates", and examine "documents that describe standard operating procedures", noting that "the relation of a written operating procedure to the actual program that is carried out is complex" because the document may have been written to initiate the program, to describe it to newcomers, or "to legitimize or 'formalize' it" [97, pp. 142--143]. Any organisation "possesses a repertory of programs" and adapts to new situations mostly "through a recombination of lower-level programs that are already in existence", so that "an important objective of standardization is to widen as far as possible the range of situations that can be handled by combination and recombination of a relatively small number of elementary programs" [97, pp. 149--150]. When a problem arrives without a solution attached, "repertories of problem solutions 'stored' in the memories of organization members will be the principal source of solution proposals", and "a good deal of the internal communication in an organization concerning new programs is aimed at a search of the organization's (collective) memory" [97, pp. 189--190]. That is: the organisation's long-term memory is its staff, its search procedure is talking, and its checklists (March and Simon use the phrase) are its recognition cues.

Williamson made the incompleteness of the program the reason the firm exists: "the typical performance program is incomplete. Execution requires judgment", and "internal program elaboration is a natural result of experience and is a manifestation of organizational learning. It occurs costlessly as a by-product of the firm's operations", whereas a contract can only be amended by haggling [167, pp. 100--101]. Henderson and Clark then showed where the most

consequential organisational knowledge is kept: not in documents at all. An organisation's communication channels "will come to embody its architectural knowledge of the linkages between components", its information filters "also embody its architectural knowledge", and the fact "that those working on the motor and the fan blade report to the same supervisor and meet weekly is an embodiment of the organization's architectural knowledge about the relationship between the motor and the fan blade" [67, pp. 6--7]. Such knowledge, being stable, "can be encoded in these forms and thus becomes implicit"; "like riding a bicycle, using a strategy, working in a channel, or employing a filter does not require detailed analysis and conscious, deliberate execution" [67, pp. 6--7]. This is Polanyi's proximal term at the scale of the org chart, and it has the same property: it can be neither told nor, when the architecture changes, easily forgotten.

The explicit store, meanwhile, was being built out of steel. Yates's history of American management shows that vertical filing "organized by intended use rather than by origin and chronology" was what "allowed companies to create an accessible corporate memory to supplement or supersede individual memories", and that "systems that made it easy to consult documentation encouraged its use" [175, pp. 60--63]. At one brass manufacturer the new filing system dictated the form of the message: "Write about only one subject on one sheet", "Place at the top of the sheet the name of the subject", so that "the entire story of relations with a particular company could be retrieved in a single folder" [175, pp. 182--185]. Robertson's history of the cabinet itself adds the number that this literature otherwise lacks. The cabinet "remembered accurately because it made visible the system it used to organize information"; guide cards were, in a manufacturer's phrase, "the intellect of the filing machine"; and the promise of finding papers "almost instantaneously" was, in a solicited testimonial, "twenty seconds to find one letter and ninety seconds to file five folders" [127, p. 173]. Vertical filing, Robertson argues, "made classification a strategy for retrieval", so that "classification became a temporal concern, not just a spatial practice for organizing knowledge according to categories" [127, pp. 106--108]. We take this as the founding statement of our subject. The first modern knowledge store was sold on its latency.

----[ 4.4 ] Organisational forgetting

Bowker and Star's contribution is to insist that forgetting is not the failure of memory but one of its operations. "Total recall, in individuals or organizations, is neither desirable nor possible", and "it might be the case that rediscovery is easier than remembering", as when "airline companies frequently do not retain a record of one's food or seating options" because processing passengers anew "is easier from a data processing perspective" [22, pp. 257--258]. They distinguish two mechanisms: "Clearance---the erection of a barrier in the past at a certain point so that no information or knowledge can leak through to the present", and "Erasure---the ongoing destruction of selective traces in the present" [22, pp. 257--258]. The founder of modern chemistry practised both, standardising the names of the elements "so that Ag became silver: not Diane's metal, a name that 'remembered' the alchemical

prehistory of the discipline", and rewriting the history so that his rivals "were written out of the historical record" [22, pp. 277--279]. A classification scheme, on this reading, "tells you what to forget and how to forget it" [22, pp. 277--279]; designers of such schemes "develop an economy of knowledge that articulates clearance and erasure and ensures that all and only relevant features of the object … are remembered" [22, pp. 281--282]. We note the phrase "all and only". It is the phrase of the classical definition, and Section 5 will show what became of it.

Proposition 5. An organisation's forgetting is implemented by its representation. What the scheme has no place for is not stored, and what is not stored has infinite latency; the two cases are indistinguishable from inside the organisation and are therefore, for practical purposes, one.

----[ 4.5 ] Taxonomies in practice

Lambe, who builds taxonomies for organisations for a living, writes about them with the candour of someone who has watched several fail. "Taxonomies are a losing battle, sandcastles shored up against the rising tide of change -- but we fight nevertheless, because they give temporary respite from advancing chaos." They "make knowledge visible, but while they reveal, they also conceal -- the 'stuff' that is not accommodated at all". Clients "can and do categorise continually" and "are confident about knowing how to sort things out", but "are not skilled at conscious, strategic organisation of their knowledge assets to suit collective needs" [91, p. xvi]. His description of one failed engagement is, for our purposes, a description of retrieval latency approaching infinity: an innovative firm whose specialists were "scattered across the organisation", whose documented knowledge "resided within the local working folder structures based on shared drives in each division and department", and whose folder structures were "organised inconsistently so that it was often difficult for staff in that department to locate material that they knew was there" [91, pp. 170--171]. Material that staff "knew was there" and could not locate is the organisational tip-of-the-tongue state. Section 10 gives its individual form.

----[ 4.6 ] Checklists

The most successful externalisation in the recent literature is the least sophisticated. Gawande's argument is that "the volume and complexity of what we know has exceeded our individual ability to deliver its benefits correctly, safely, or reliably. Knowledge has both saved us and burdened us" [51, pp. 12--13]. The founding case is an aircraft: a bomber "too complicated to be left to the memory of any one person, however expert", for which the test pilots wrote a list "short enough to fit on an index card", after which the type was flown "1.8 million miles without one accident" [51, pp. 33--34]. The general lesson is that "under conditions of complexity, not only are checklists a help, they are required for success. There must always be room for judgment, but judgment aided---and even enhanced---by procedure" [51, pp. 79--80]. In our terms, a checklist is a store of very small capacity and very low latency, placed in front of a store of very large capacity and unreliable latency, and

its function is to convert recall into recognition. Section 10 explains why that conversion is worth an index card.

--[ 5 ]-- Representation

Nothing can be stored without being represented, and the form of the representation fixes the form of the address by which the thing is later sought. This section reviews what is known about the forms, from the concept to the classification scheme, with an eye throughout to the question the sources rarely ask: how long does it take to find something represented this way?

----[ 5.1 ] What a representation is

Sowa's definition is the standard one in the computing literature: "Knowledge representation is the application of logic and ontology to the task of constructing computable models for some domain", where logic "provides the formal structure", ontology "defines the kinds of things that exist in the application domain", and computation "supports the applications" [146]. His five roles for a representation are worth listing: "a surrogate" for external things; "a set of ontological commitments"; "a fragmentary theory of intelligent reasoning"; "a medium for efficient computation"; and "a medium of human expression" [146, pp. 134--135]. The fourth is our concern. A representation that is a poor medium for efficient computation is one from which retrieval is slow, and the history of representation is, read one way, a search for schemes that are fast to consult without being false.

Newell's "knowledge level" is the corrective to any too literal reading of the word "store". Knowledge, he argued, is "a competence-like notion, being a potential for generating action", and "representations exist at the symbol level, being systems (data structures and processes) that realize a body of knowledge at the knowledge level" [107, pp. 14--15]. His definition, "whatever can be ascribed to an actor, such that its behavior can be computed according to the principle of rationality", is stated "entirely functionally, in terms of what it does, not structurally, in terms of physical objects with particular properties and relations" [107, pp. 20--21].(4) On this view, to say that a filing cabinet "knows" something is a category mistake and to say that a person does is an approximation; what both have is a symbol structure from which, given a process and enough time, an action can be computed. The "enough time" is the whole of Section 10. Newell and Simon had earlier made the point in general form: symbol systems "have limited processing resources; in a finite number of steps, and over a finite interval of time, they can execute only a finite number of processes", so that "the fact of limited resources allows us, for most purposes, to view a symbol system as though it were a serial, one-process-at-a-time device" [110, p. 120].

(4) We have substituted "actor" for Newell's own term for the system that has goals and takes actions, throughout this paper, as a matter of house style. The substitution loses nothing that bears on the argument.

----[ 5.2 ] Concepts and categories

The classical theory of categories held that a category is defined by properties shared by all and only its members. Lakoff observes that the theory "was not the result of empirical study" but "a philosophical position arrived at on the basis of a priori speculation" that "over the centuries … simply became part of the background assumptions taken for granted in most scholarly disciplines" and "was not even thought of as a theory" [90, pp. 6--7]. The first breach, in his telling, was Wittgenstein's: "a category like game does not fit the classical mold, since there are no common properties shared by all games", but rather "family resemblances" [90, p. 16]; and the classical theory cannot explain why "dice is just not a very good example of a game" [90, p. 17]. Rosch then made the breach a field. Two implications of the classical view could be tested: that "no members should be better examples of the category than any other members", and that categories "should be independent of the peculiarities of any beings doing the categorizing"; both failed, and the finding "sent shock waves throughout the cognitive sciences" [90, pp. 6--7].

Rosch's own statement of the positive result concerns the vertical dimension of a taxonomy, "a system by which categories are related to one another by means of class inclusion" [131, pp. 383--384]. "Basic objects (e.g., chair, car) are at the most inclusive level at which there are attributes common to all or most members of the category", with superordinates (furniture, vehicle) above sharing few attributes and subordinates (kitchen chair, sports car) below sharing most of theirs with their neighbours [131, p. 385]. Cue validity, "a probabilistic concept", is maximised at the basic level [130, pp. 30--31]. The reason given is economic and is the reason we cite the work: "in so far as categorization occurs to reduce the infinite differences between stimuli to behaviorally and cognitively useful proportions, the basic category cuts in the world should be those which yield the most information for the least cognitive load" [131, p. 428]. The basic level is, in our terms, the level at which the latency of classifying is lowest for the information gained, and it is no accident that it is the level at which children learn names and at which adults speak when unhurried.

Murphy and Medin then removed similarity from the foundation. Their question was "what makes a concept coherent (what makes its members form a comprehensible class)", and their answer that "concepts are coherent to the extent that they fit people's background knowledge or naive theories about the world" [102, p. 289]. The worked example is the dietary law of Leviticus, whose clean and unclean animals share almost no surface features and whose coherence, they argue following an anthropologist, lies in a theory relating habitat, structure and locomotion [102, pp. 289, 312]. Similarity, they conclude, "may be a by-product of conceptual coherence rather than its determinant"; they quote Goodman's verdict that similarity "is a pretender, an imposter, a quack" [102, pp. 291--292]. Hjørland, from information science, states the position that follows: "Concepts are dynamically constructed and collectively negotiated meanings that classify the world according to interests and theories", and "we should expect competing conceptions and concepts to be at play in all domains at

all times" [69, pp. 1522--1523]. For a store this is bad news of a specific kind. If the address of an item is a concept, and the concept is a theory held by a community at a time, then the address changes when the theory does, and the store does not know.

Proposition 6. The latency of retrieval from any store indexed by concepts is bounded below by the latency of agreeing what the concept means, which is not a property of the store and is not constant in time.

----[ 5.3 ] Schemata, scripts and frames

The schema entered psychology through Bartlett, who used it, in quotation marks throughout, for "an active organised setting" built up from past reactions [16, p. 202]. His theory of remembering is stated in a passage that the later literature has never improved: "Remembering is not the re-excitation of innumerable fixed, lifeless and fragmentary traces. It is an imaginative reconstruction, or construction, built out of the relation of our attitude towards a whole active mass of organised past reactions or experience, and to a little outstanding detail which commonly appears in image or in language form. It is thus hardly ever really exact, even in the most rudimentary cases of rote recapitulation, and it is not at all important that it should be so" [16, pp. 213--214]. The "little outstanding detail" is the retrieval cue, and the reconstruction is what the cue sets going.

Rumelhart formalised the notion for a generation of computational work: "Schemata are data structures for representing the generic concepts stored in memory", existing "for generalized concepts underlying objects, situations, events, sequences of events, actions, and sequences of actions"; a schema "is related to a particular instance of the concept that it represents in much the same way that a play is related to a particular enactment of that play"; schemata "have variables", "can embed one within the other", "vary in their levels of abstraction", and "represent knowledge, rather than definitions" [132, pp. 100--101]. Comprehension, on this view, consists in selecting the schemata and variable bindings that explain the incoming material, so that "the process of comprehension can be regarded rather like the process a scientist goes through in testing a theory" [132, pp. 111--112].(5)

Schank and Abelson specialised the schema to the stereotyped sequence: "A script is a structure that describes appropriate sequences of events in a particular

(5) The later text-comprehension literature drew the consequence for memory: what is retained of a text is a representation of the situation it describes rather than of the text. Zwaan and Radvansky date the change to two 1983 monographs and describe language, on the new view, as "a set of processing instructions on how to construct a mental representation of the described situation" [177, p. 162]. Kintsch and van Dijk had already found that the forgetting rate for the small propositions of a text "appear to be about four times greater than that for macropropositions" [83, p. 387]; the gist survives the wording.

context. A script is made up of slots and requirements about what can fill those slots." Scripts "handle stylized everyday situations", and "what they do is let you leave out the boring details when you are talking or writing, and fill them in when you are listening or reading" [135, pp. 40--41]. The restaurant script, with its tracks, props, roles, entry conditions and results, is laid out over two pages [135, pp. 42--45], and a companion volume describes "script instantiation" and "script application" as the two processes by which "a story that refers to a script with ten events in it may explicitly state only the first and last of those events" and still be understood [136, pp. 30--31]. Minsky, the same year, proposed the frame: "a data-structure for representing a stereotyped situation, like being in a certain kind of living room, or going to a child's birthday party", with top levels "fixed" and lower levels of "slots" to be filled, and attached information about "what one can expect to happen next" and "what to do if these expectations are not confirmed" [101]. His motive was explicitly about the size of the unit: the "chunks" of reasoning and memory "ought to be larger and more structured … in order to explain the apparent power and speed of mental activities" [101, p. 1]. The frame was a proposal about latency before it was a proposal about representation.(6)

----[ 5.4 ] Ontologies

The term of art for a shared scheme of concepts is the ontology, and the handbook definition, from the knowledge-acquisition work of the early 1990s, is Gruber's: "An ontology is an explicit specification of a conceptualization", later elaborated to "a formal, explicit specification of a shared conceptualization", where "explicit" means all elements are defined, "formal" means machine-interpretable, and "shared" means "consensual knowledge that has been agreed on by a group of people, typically as a result of a social process" [148]. Guarino's refinement is the one that bears on stores: an ontology "can 'specify' a conceptualization only in a very indirect way, since i) it can only approximate a set of intended models; ii) such a set of intended models is only a weak characterization of a conceptualization" [62]. An ontology, that is, is an approximation to an agreement about what exists, and the agreement is Hjørland's negotiation by another name. The handbook is admirably plain that the philosophical question, "what exists?", is not the one being answered [148].

----[ 5.5 ] Classification, from the tree to the drawer

The oldest device for arranging concepts is the tree, and the oldest tree is Porphyry's, which descends from substance through body, animate body, animal and

(6) The paper was circulated as a memorandum in 1974 and printed the following year in a collection on machine vision [169, pp. 211--212]. The logicians' reply, that a frame instance "denotes an individual, and each slot denotes a relationship" and could as well be written in predicate calculus, is reprinted in the standard reader [23, p. 289]; the philosophers' reply, that frames and scripts were the field's response to "overwhelming lists of frame axioms", is in Dreyfus and Dreyfus [44, pp. 83--84]. We take no side. Both replies concede that the frame was fast.

rational animal to man, and thence to "Socrates, Plato, and particular men": "substance is the highest genus, and it is a genus only, while man is the lowest species, and it is a species only" [124, p. 36]. Individuals are individuals "because each thing is composed of a collection of characteristics which can never be the same for another" [124, p. 41]. The tree's branches, a modern reference explains, "represent the various differences (differentiae specificae) that, when added to a generic class, yield a lower class", and its origin is "a passage of Porphyry's Isagoge where he discusses the relationships among genus, species and individual within the category of substance" [82, pp. 605--606]. The method is Aristotle's, whose definition by division holds that "there is nothing in the definition except the first-named genus and the differentiae" and that division must proceed "by the differentiae of the differentiae" until "it reaches the species that contain no differences" [134, p. 85]. A Victorian logic textbook walks the reader down one branch, from Substance through Bodies, Living things and animals, pausing to observe that "an apple-tree does not, as far as we know, suffer from dyspepsia, or a cabbage from headaches" [34, pp. 180--181]. Plate VIII draws the tree.

Between the tree and the drawer stands Bacon, whose classification, Broughton notes, "was fundamentally different from Aristotle's in that it was a classification of knowledge rather than a classification of things", an "aspect classification" on which "modern library classifications are all built" [24, p. 19]. Linnaeus had meanwhile applied Aristotle's method to living things with results that persist, oddities included: "hydrangeas and gooseberries are in the same family, and elm trees and stinging nettles are also close relations" [24, pp. 13--15]. The drawer arrived late. Until the last quarter of the nineteenth century, Broughton writes, collections mostly operated on "closed access", readers "had [volumes] fetched for them by library staff", and "there was usually no systematic means of searching for a [volume] by subject"; open access, and the great general schemes, came "within a period of about 40 years" from 1876 [24, pp. 6--7]. In the same year Cutter made "the first explicit statement of the objectives of a bibliographic system": to enable a person to find an item of which the author, title or subject is known; to show what the collection has by a given author, on a given subject, in a given kind of literature; and to assist in choosing among editions [149, pp. 15--16]. Svenonius, who calls this "likely the most cited text in the bibliographic literature", extends the list to five objectives, "finding", "collocating", "choice", "acquisition" and "navigation", and notes that they "are still not without problems" [149, pp. 15--16, 20]. We note only that the first objective is a latency requirement and the other four are what one does while waiting.

Proposition 7. Every classification scheme is a promise about latency: that an item placed according to the scheme can be found in a bounded number of steps by anyone who knows the scheme. The promise is kept only while the scheme is known, and Section 9 records what happens when the knowers are gone.

--[ 6 ]-- The Organ

We turn to the store that every other store exists to supplement. The questions are the two of the introduction: how much, and how long. On the first the literature is voluminous and irreconcilable; on the second it is precise and, as we will see, discouraging.

----[ 6.1 ] The palaces

The earliest sustained description of the human memory as a store with a retrieval procedure is Augustine's, and it is worth quoting because it already contains the phenomenology that the laboratory would later measure. "I come to the fields and vast palaces of memory, where are the treasuries of innumerable images of all kinds of objects brought in by sense-perception. … When I am in this storehouse, I ask that it produce what I want to recall", and certain things come out at once, while "some things require a longer search, and have to be drawn out as it were from more recondite receptacles. Some memories pour out to crowd the mind and, when one is searching and asking for something quite different, leap forward into the centre as if saying 'Surely we are what you want?' With the hand of my heart I chase them away from the face of my memory until what I want is freed of mist and emerges from its hiding places" [13, p. 185]. Immediate retrieval, longer search, interference from wrong candidates, and the eventual emergence of the target: every term of Section 10 is present. Augustine adds a capacity estimate, or rather the refusal of one: "Great is the power of memory, an awe-inspiring mystery, my God, a power of profound and infinite multiplicity. … I run through all these things, I fly here and there, and penetrate their working as far as I can. But I never reach the end" [13, pp. 194--195]. Subsequent estimators have reached ends, and disagreed about where they are.

----[ 6.2 ] How much: the estimates

Plate IX plots every published capacity estimate we could find in the held sources on a logarithmic axis. The spread is six orders of magnitude, and each estimate is defensible on its own assumptions, which is the point.

At the low end is Landauer's calculation, reported by Ware: "Using a reasonable set of assumptions, Landauer (1986) estimated that only a few hundred megabytes of unique information are stored over a lifetime. This equates to 2 bits of acquisition per waking second" [164, p. 412]. Norman, in the same decade, 9 reported that "one informed scientist estimates the capacity as a billion (10 ) 8 bits or about 100 million (10 ) items", adding the judgement that matters more than the number: "Whatever the size, it is so large as not to impose any practical limit. The difficulty with LTM is in organization---in getting material in and in figuring out how to retrieve it---not in capacity" [112, p. 67]. At the high end are the anatomical derivations. Ware describes "much larger estimates … based on the number of synapses in the brain (e.g., 240 × 12 10 for the cortex, Koch 1999) and evidence that they can each encode four levels of information (2 bits)", but observes that "the larger estimates assume

that every connection is devoted to lossless storage" and that "the actual number is likely to be orders of magnitude smaller because thousands of synaptic connections are channeled into the firing of a single neuron" [164, p. 412]. Turing, in a letter of 1951 reproduced by his biographer, made the same derivation in its simplest form: for N neurons with M outlets, "the answer is simply MN binary digits, for there are MN paths each capable of two states", and "if you allowed each path to have eight states (whatever that might mean) you would get 3MN" [70, p. 550]. He added, in the same letter, that he was "very far from the stage where I feel inclined to start asking any anatomical questions" [70, p. 550].

For scale, Licklider's estimate of the size of the entire body of recorded 14 15 information, made in 1965, was "roughly 10 characters and 10 bits in the total store", doubling "every 15 or 20 years" [94, pp. 14--15]. On the synaptic derivation a single cortex could hold the world's record several times over; on Landauer's it could hold a small shelf of it. We do not think the discrepancy can be resolved by a review, and we note that the sources themselves do not try. What they agree on is Norman's remark: whatever the number, it is not the constraint. The constraint is getting things in and getting them out.

----[ 6.3 ] Getting things in: consolidation

The mechanism by which a short-term memory becomes a long-term one has, unlike its capacity, a settled description. Squire and Kandel report that inhibitors of

protein synthesis "disrupt long-term memory only when given during a brief period usually of about one or two hours" around training, and "have no effect when given subsequently, several hours after training", from which it followed "that the consolidation switch to long-term memory requires new protein synthesis" [147, pp. 133--134]. The switch, in their metaphor, is thrown in stages: a repressor removed, an activator engaged, and then the genes' products made, "the sensitive (consolidation) phase during the forming of long-term memory", before which "memory can be blocked by inhibitors of protein synthesis, and a blow to the head can forever erase a memory in the process of being consolidated" [147, pp. 142--143]. In the sea snail whose reflex was the model preparation, "one shock to the tail produces a short-term memory lasting minutes" that "does not require the synthesis of new protein", while "four to five shocks to the tail produce a long-term memory" whose synaptic connections, a day later, "were twice as strong" [147, pp. 133--134]. Writing into the organ, in other words, has a fixed and non-trivial latency of its own, measured in hours, during which the write can fail.

Above the molecular level sits a structure. Ware summarises: "there is a specialized structure in the midbrain called the hippocampus … that is critical to all episodic memory consolidation. If people have damage in this area they lose the ability to form new long-term memories, although they retain ones they had from before the damage" [164, pp. 413--414]. The dominant theory of storage is that memories "are traces---neural pathways made up of strengthened synaptic connections between the hippocampus and areas of the cortex specialized for different kinds of information", and that "recall consists of the activation of a particular pathway" [164, pp. 413--414]. Hebb, who proposed the synaptic mechanism in 1949, also proposed a function for sleep: "the psychological function of a night's sleep may be to permit a certain decay in the particular connections that were established or strengthened by the previous day's behavior" [66, p. 230]. The modern literature has kept the night and reversed the sign. Ware: "sleep is essential for memory consolidation" [164, p. 412]; "during sleep, information is reorganized, into more efficient cognitive chunks, and less useful information is lost" [164, pp. 413--414]. Whichever sign is right, the organ's write cycle includes a mandatory nightly maintenance window, and no store built by engineers, so far as we know, has been designed with one.

Proposition 8. The organ's write latency (hours, with a nightly commit) exceeds its read latency (milliseconds to seconds) by five to seven orders of magnitude. External stores reverse this ratio. Much of the history in Section 9 is the exploitation of the reversal.

----[ 6.4 ] Getting things out, over time: forgetting

The shape of forgetting was measured by one man on himself, and the figures were carried into English by James, whose paraphrase of Ebbinghaus we reproduce because it is the source of Plate X: "An hour after the work of learning had ceased, forgetting was so far advanced that more than half of the original work had to be applied again before the series of syllables could once more be reproduced. Eight hours later two thirds of the original labor had to be

applied. Gradually, however, the process of oblivion grew slower, so that even for considerable stretches of time the losses were but barely ascertainable. After 24 hours a third, after 6 days a fourth, and after a whole month a good fifth of the original labor remain in the shape of its after-effects, and made the relearning by so much the more speedy" [78, pp. 677--678]. The curve falls fast and then hardly at all. The same James wrote, in the chapter preceding, the sentence that the mnemonic tradition of Section 9 rests on: "The 'secret of a good memory' is thus the secret of forming diverse and multiple associations with every fact we care to retain. But this forming of associations with a fact, what is it but thinking about the fact as much as possible?" [78, p. 662]. Cramming fails, he explains, because things "learned thus in a few hours, on one occasion, for one purpose, cannot possibly have formed many associations with other things in the mind. Their brain-processes are led into by few paths, and are relatively little liable to be awakened again" [78, p. 663]. Few paths, slow retrieval. It is a latency argument.

Later work refined the shape without changing it. Graesser's retention data for actions in scripted activities show recall of typical actions falling from .288 at half an hour to .165 at three weeks, and of atypical actions from .288 to .011 [60, pp. 96--97]; "memory approaches zero for both typical and atypical actions after a 3-week retention interval", with the curious crossover that the atypical is better remembered at first and worse later [60, pp. 96--97]. Tulving's dissociation shows that the shape depends on the test: recognition of a studied word fell from about .56 at one hour to about .24 at seven days, while completion of a fragment of the same word held at about .47 and .46 [157, pp. 104--105]. Something remains in the organ that the ordinary question cannot reach. Hermans, writing for programmers, draws the distinction the modern literature uses: storage strength "can only increase", and "it is the retrieval strength of memories that decays over the years" [68, p. 41]. Forgetting, on this reading, is a rise in latency, and at some latency the item is, for every practical purpose, gone.

Bartlett's contribution is that what comes out is not what went in. His subject who read a strange story in 1917, repeated it half an hour later, and was asked again in 1927, "at once wrote 'Egulac' and 'Calama', but then stopped and said she could do no more. Soon, however, she built around these names an incident or two which, though they contained some invention and transformation, seemed clearly to be derived from some of the events of the original story" [16, pp. 208--209]. Two proper names, retrieved at once; the rest reconstructed around them. The organ's read operation is a rebuild from a fragment, which is why its latency is variable and its output need not equal its input. The organ also forgets, which this section has treated as a defect of the store; Section 15 will meet two men in whom it did not, and revise the word.

----[ 6.5 ] Getting things in, at scale: the learning rate

How fast the organ fills is better known than how much it holds. Simon's estimate of "about 5 or 10 seconds per chunk" for fixation in long-term memory [140, p. 487] is one bound; Landauer and Dumais's estimate of vocabulary growth is another. Combining reading-time studies with word-frequency tables, they compute that schoolchildren "are adding about one new word to their comprehension vocabulary every 2 min or five paragraphs" while reading, and, since "the average student reads about 50 paragraphs a day", that "the total amounts to about 10 new words per day" [92, pp. 222, 225]; the direct estimates from vocabulary tests give "somewhere between 10 and 15 new words per day" for the middle school years [92, p. 221]. Ten words a day, for a lifetime, is a small number of bits; it is consistent with the low end of Plate IX and with Norman's judgement that capacity is not the issue.

----[ 6.6 ] The clinical evidence

The dissociations that established the architecture were found in patients. Baddeley summarises the two kinds: "those suffering from the classic amnesic syndrome appeared to have gross disruption of the capacity to form new lasting memories but showed preserved performance on a range of tasks that were assumed

apart, the more variably they will be encoded", so that a later cue has two encodings to find instead of one [3, pp. 388--389]. Ausubel, from the side of instruction, concludes that "short and widely spaced practice or review sessions that are introduced progressively further apart are best for meaningful learning and retention" [14, p. 187].

The quantitative synthesis is Cepeda and colleagues', who "found 839 assessments of distributed practice in 317 experiments located in 184 articles" and, examining the interval between study episodes against the interval before the final test, concluded "that ISI and retention interval operate jointly to affect final-test retention; specifically, the ISI producing maximal retention increased as retention interval increased" [28, p. 354]. The practical reading is the one Hermans gives from Bahrick's family experiment, in which foreign words studied in "26 sessions, each 8 weeks apart" were recalled a year later at 76 per cent, against 56 per cent for the group studied at two-week intervals [68, pp. 39--40]: the longer one wants to remember, the longer the gaps should be.

----[ 7.2 ] The testing effect

A second finding, nearly as old, is that the read is what does the writing. Karpicke and Roediger's experiment on foreign vocabulary is the cleanest statement. Students learned word pairs in the usual cycle of study and test, and then either kept studying or kept being tested: "Repeated studying after learning had no effect on delayed recall, but repeated testing produced a large positive effect. In addition, students' predictions of their performance were uncorrelated with actual performance" [81, p. 966]. The last clause matters as much as the first. The organ does not report its own write status; it reports the ease of the most recent read, which is exactly the quantity that repeated study inflates and repeated testing does not. In the paper's terms, a retrieval at latency is a write, and a re-presentation at zero latency is not.

----[ 7.3 ] The lineage

The technology that puts the two effects to work is the flashcard with a schedule. Its ancestor is the box of cards sorted into compartments by how well each is known, with the well-known reviewed rarely and the badly-known often, which Leitner described for schoolchildren in the 1970s [93]; its modern form is a program that keeps, for each item, an estimate of when it will be forgotten and asks for it just before. Wozniak's rules for writing the items, which begin "Do not learn if you do not understand" and include "Stick to the minimum information principle", are rules for a store whose reader is the organ itself, and his program keeps a "forgetting index" to set the retention level per item [171]. Matuschak and Nielsen name the family: "Among the better known are Anki, SuperMemo, Quizlet, Duolingo, and Memrise", all using "increasing time intervals between reviews of particular questions", and "sometimes known as spaced-repetition memory systems" [98]; their own schedule "rises to five days" on a first success, "then a month, and so on. After just five successful reviews the interval is at four months" [98]. The arithmetic is the point: "you get

exponential returns for increased effort", since each review that succeeds pushes the next one further out [98]. The arithmetic is drawn in Plate XI, from the schedule's published rule and nothing else; the paper has measured no one's forgetting, its own included.

How effective are they? For what they schedule, very. The spacing and testing literatures are among the most replicated in the field, the schedules are derived from them, and a person who reviews an item at expanding intervals will, on every study we have found, retain it longer per minute spent than a person who does anything else. For what they do not schedule, the evidence is thinner. Matuschak and Nielsen report that for the largest of the language products "reports are mixed on success", and suppose such systems "useful for many users as part of (but only part of) a serious language learning program" [98]; and nothing in the literature claims that a scheduled item is understood, only that it is retained. The distinction will matter later. A schedule is an index kept outside the organ that decides when the organ's own store is refreshed; it is, in the terms of Section 9, the one external store whose purpose is to make

of roughly the same size as the vocabulary of an educated adult in his native language" [140, p. 487]. Ericsson and Smith report that Simon and Chase "were the first to observe that 10 years or more of full-time preparation are required to attain an international level of performance in chess", a figure since found across sport, art and science [48, pp. 7--8]; Ericsson, Krampe and Tesch-Römer's framework predicts flatly that "expert performance is not reached with less than 10 years of deliberate practice" [46, p. 372]. Fifty thousand chunks at ten seconds each is about six days of pure fixation; that it takes ten years is a measure of how little of a life is spent putting chunks through the door.

----[ 8.3 ] Three components

Baddeley's working memory is a structure rather than a number. It "provides temporary storage and manipulation of the information necessary for such complex cognitive tasks as language comprehension, learning, and reasoning" and "can be divided into the following three subcomponents: (i) the central executive, which is assumed to be an attentional-controlling system … and two slave systems, namely (ii) the visuospatial sketch pad, which manipulates visual images and (iii) the phonological loop, which stores and rehearses speech-based information" [15, p. 556]. The structure was forced by an experiment in which subjects were given digits to hold while reasoning: "as concurrent digit load increased, performance declined, but the degree of disruption fell far short of that predicted. Subjects whose digit memory was at full capacity could reason and learn quite effectively", which "encouraged the abandonment of the idea of a single unitary short-term store that also functions as a working memory" [15, p. 556]. Working memory, in his summary, "stands at the crossroads between memory, attention, and perception" [15, p. 559]. The point for our argument is that the door has more than one leaf, and that a person can hold a telephone number in one while thinking in another, which is why external stores addressed to the eye (a list, a diagram) cost less than external stores addressed to the ear.

----[ 8.4 ] Two or three

Cognitive-load theory, the applied descendant of this work, uses the smallest number. "Working memory, in which all conscious cognitive processing occurs, can handle only a very limited number---possibly no more than two or three---of novel interacting elements. This number is far below the number of interacting elements that occurs in most substantive areas of human intellectual activity. Alone, working memory would only permit relatively trivial human cognitive activities" [116]. The theory's three loads, intrinsic, extraneous and germane, "are additive in that, together, the total load cannot exceed the working memory resources available if learning is to occur" [116]. Intrinsic load "depends on the number of elements that must be processed simultaneously in working memory", which "depends on the extent of element interactivity of the materials", so that "a large number of interacting elements for one person might be a single element for another more experienced person who has a schema that incorporates the elements" [161, p. 150]. The illustration in the twenty-year retrospective is the word "characteristics", which "for readers of this paper" is "processed

easily and unconsciously as a single element", while "for someone learning to read English, the written word must be processed in working memory as multiple, interacting elements" [151].

The theory began as a finding about problem solving. Sweller showed that means-ends analysis, the general strategy of working backward from a goal, "may impose a heavy cognitive load" because the solver "must simultaneously consider the current problem state, the goal state, the relation between the current problem state and the goal state, the relations between problem-solving operators and lastly, if subgoals have been used, a goal stack must be maintained", leaving "little for schema acquisition, even if the problem is solved" [150, pp. 261--262]. Hence the paradox that "the development of expertise may be retarded by a heavy emphasis on problem solving" [150, p. 284]. Extraneous load can be imposed "by integrating information sources that are distributed in place or time, or searching for information that is needed to complete a learning task" [161, p. 150]: that is, by retrieval. And the expertise-reversal effect shows that the remedy is not fixed: instructional formats "that work well for novice learners have no effects or even adverse effects when learners acquire more expertise", since text that was once essential becomes redundant and "if presented to learners with more experience in the area in an integrated format, they were hard to ignore" [161, pp. 163--164]. An external store that helps the novice burdens the expert. Section 12 gives this a name.

----[ 8.5 ] The disagreement, tabulated

The numbers are collected in the table below and, with their sources, in Appendix C. We have not tried to reconcile them. Hermans, whose textbook reviews the same literature for a practical audience, reports that "more recent research indicates the STM is even smaller, estimating a capacity of between two and six things", that "this limit holds for almost all people", and that "scientists so far have not found reliable ways to increase the size of the STM" [68, p. 18]; she defines working memory, for her purposes, as "STM applied to a problem" and gives it "the same limitation" [68, p. 48].

What the table shows is not confusion but a family of measurements of different things: the span for meaningless items, the span for chunks, the number of relations that can be held while reasoning, the number a damaged system needs in order to learn. Every one of them is small. Newell and Simon's general statement covers all of them: a system with "limited processing resources" may, for most purposes, be viewed "as though it were a serial, one-process-at-a-time device", and "the problem of allocating a scarce resource from moment to moment can usually be treated … as a problem of scheduling a serial machine" [110, p. 120].

Proposition 10. The door is between two and seven wide, depending on the unit, and it does not widen with practice; what practice does is enlarge what fits through one gap. Consequently the effective size of what a person can bring to bear on a task is fixed by the size of their chunks and the latency of fetching them, not by the door.

Remark 2. Readers who have kept the previous six numbers in mind while reading this paragraph have exhausted their working memory and should consult the table again. This is not a joke but a demonstration, and it is the only one the paper will perform.

For readers who wish to know where they are, Plate XII gives the states a reader of this paper passes through, in the notation of the state machines; the paper cannot tell which state the reader is in, and the reader may not be able to either.

--[ 9 ]-- The Externalisation of Memory

Given a large slow store behind a narrow door, the obvious remedy is to keep things outside, and people have done so for as long as there is evidence of people. This section reviews the history of that remedy, its philosophical opposition, and its modern theory. The exhibits are drawings of external stores, arranged roughly in order of age.

----[ 9.1 ] Cords, tallies and clay

Gelb's history of writing begins with the stores that were not writing. "Systems of mnemonic signs to keep [records] by means of objects are known throughout the world. The simplest and the most common are the so-called 'counting sticks' to keep records of cattle"; "a more complicated mnemonic system is represented among the Peruvian Incas by the so-called 'quipu writing', in which [records] concerning objects and beings were recorded by means of strings and knots of various length and colour" [52, pp. 3--4].(7) Gelb is severe about what such a store could hold: "all the reports about the alleged use of the quipu for the

(7) Gelb's noun for what the sticks and knots kept has been replaced in square brackets by a synonym, as a matter of house style.

recording of chronicles and historical events are plain fantasy", and knot records "have any other aim than that of recording simplest facts of statistical nature" [52, pp. 3--4]. Olson, thirty years later, is gentler, reporting the tradition that "the quipu were borrowed by the Inca to preserve oral traditions, including names and chronologies", and that "on some occasions penitents at confession may 'read' off their sins from quipu specially constructed for that purpose" [114, p. 99]. The disagreement is about capacity, and, as with the brain, the mechanism is better known than the capacity. Cajori's history of notation describes the structure: "The quipu was a twisted woolen cord, upon which other smaller cords of different colors were tied. The color, length, and number of knots on them and the distance of one from another all had their significance"; in the specimen he reproduces, "in each group the top strand usually gives the sum of the numbers on the four pendent strands", "the numbers were expressed on the decimal plan, but the quipu were not adopted for calculation; pebbles and grains of maize were used in computing" [27, p. 38]. Plate XIII is drawn to that description.

The tally survived the quipu by centuries. Ferraris notes a system "employed by the English exchequer until the early nineteenth century": "take two sticks and to mark a credit with an incision; the creditor takes one stick and the debtor the other; the debtor cannot cancel the mark and the creditor cannot add one because the interference would be revealed by comparing the two sticks" [50, pp. 200--203]. A tally is a store with two copies and a consistency check, and its latency is the time to find the other half.

Writing proper began in clay, and the earliest large body of it is administrative. We do not rehearse the history, which is Gelb's subject, but we draw the object (Plate XIV) and note Goody's observation about what the medium made possible. "Lists are seen to be characteristic of the early uses of writing, being promoted partly by the demands of complex economic and state organisation, partly by the nature of scribal training, and partly by a 'play' element" [57, pp. 108--109]. The list "relies on discontinuity rather than continuity; it depends on physical placement, on location; it can be read in different directions … it has a clear-cut beginning and a precise end, that is, a boundary, an edge, like a piece of cloth. Most importantly it encourages the ordering of the items, by number, by initial sound, by category, etc." [57, pp. 80--81]. And the list makes questions: "the question, is a tomato a fruit or a vegetable? is the kind that would seem pointless in an oral context … but which may be essential to the advance of systematic knowledge about the classification and evolution of natural species. And it is the kind of question generated by written lists" [57, pp. 104--105]. Classification, in Goody's telling, is a side effect of the external store. Section 5 described the schemes; here is their cause.

----[ 9.2 ] The objection

The philosophical objection to keeping memory outside the body is older than most of the stores. Goody and Watt quote it in full from the Phaedrus, where Socrates has the Egyptian king Thamus rebuke the god Theuth for his invention:

"If men learn this … it will implant forgetfulness in their souls: they will cease to exercise memory because they rely on that which is written, calling things to remembrance no longer from within themselves, but by means of external marks; what you have discovered is a recipe not for memory, but for reminder. And it is no true wisdom that you offer your disciples, but only its semblance; for by telling them of many things without teaching them you will make them seem to know much, while for the most part they know nothing" [58, pp. 326--327]. Yates gives the same passage in another translation, with the memorable line that Theuth has "invented an elixir not of memory but of reminding" [174, p. 52]; the one Greek word behind "recipe" and "elixir" is a word Section 15 returns to. Goody and Watt add the second charge: "written words," Socrates says, "seem to talk to you as though they were intelligent, but if you ask them anything about what they say, from a desire to be instructed, they go on telling you just the same thing for ever" [58, p. 328].

The commentary on the passage is a small literature of its own. Ong: "essentially the same objections commonly urged today against computers were urged by Plato in the Phaedrus … against writing. Writing, Plato has Socrates say in the Phaedrus, is inhuman, pretending to establish outside the mind what in reality can be only in the mind. It is a thing, a manufactured product. … Secondly, Plato's Socrates urges, writing destroys memory. … Thirdly, a written text is basically unresponsive" [115, pp. 77--79]. Harris reads the objection as semiological: Plato "is not, in other words, complaining that the Greek alphabet is deficient", but "rejecting the whole assumption that writing provides a viable surrogate for speech" [65, pp. 17--19]. Derrida reads it as the founding gesture of a tradition: "Writing, a mnemotechnic means, supplanting good memory, spontaneous memory, signifies forgetfulness. It is exactly what Plato said in the Phaedrus, comparing writing to speech as hypomnesis to mnémè, the auxiliary aide-mémoire to the living memory" [41, pp. 36--37]. Norman reads it as a worry about reflection: "the author doesn't come along with a [text], so how could the [text] be questioned if it couldn't answer back? This is what bothered Socrates" [113, pp. 44--45]. Chalmers notes the irony that "Socrates himself never wrote anything", and that "his ideas were immortalized in writing by Plato" [30].

We make two observations. First, Thamus's distinction between memory and reminding is exactly the distinction between recall and recognition that Section 10 finds in the laboratory: a written mark converts a recall problem into a recognition problem, and the king's complaint is that recognition is cheaper. Second, the objection concedes the thesis of this paper. If writing produces forgetfulness because people "rely on that which is written", then reliance is a function of availability, and availability is latency. Plato's Socrates was not wrong about the mechanism; he disapproved of it.

----[ 9.3 ] What orality kept, and how

The oral store was not a worse version of the written one but a different technology. Lord's study of the singers of heroic verse found that the singer "does not 'memorize' formulas, any more than we as children 'memorize' language. He learns them by hearing them in other singers' songs, and by habitual usage

they become part of his singing"; "memorization is a conscious act of making one's own, and repeating, something that one regards as fixed and not one's own" [95, pp. 35--36]. In a sample of twelve thousand lines, "one quarter of the whole lines in the sample and one half of the half lines are formulas", and "there is nothing in the poem that is not formulaic" [95, p. 47]. The oral poet stores a grammar and generates the text; his latency is the latency of composition, which is why the song is never the same twice. Olson reports the professional remembrancers of oral societies, the keeper of the king's stool "who not only preserved the physical object but also the history of the stool, that is, the history of the kingdom", and the traditions "that are recited only when passing the places mentioned in the tales; the places served as mnemonics" [114, p. 99]. That last device, place as address, is the art of memory, and it was written down.

----[ 9.4 ] The art of memory

Yates's history opens with the story of the poet Simonides, who left a banquet moments before the roof fell and, when the crushed guests could not be identified, "remembered the places at which they had been sitting at the table and was therefore able to indicate to the relatives which were their dead"; from which he concluded "that persons desiring to train this faculty must select places and form mental images of the things they wish to remember and store those images in the places, so that the order of the places will preserve the order of the things" [174, p. 17]. The Roman rhetorical handbook states the rule: "The artificial memory is established from places and images", a place being "a place easily grasped by the memory, such as a house, an intercolumnar space, a corner, an arch", and images "forms, marks or simulacra of what we wish to remember"; "the art of memory is like an inner writing", for "the places are very much like wax tablets or papyrus, the images like the letters, the arrangement and disposition of the images like the script, and the delivery is like the reading" [174, pp. 21--22]. Quintilian's version has the student memorise "a building … as spacious and varied a one as possible, the forecourt, the living room, bedrooms, and parlours, not omitting statues and other ornaments", and then, "as soon as the memory of the facts requires to be revived, all these places are visited in turn and the various deposits demanded of their custodians" [174, p. 18]. The practical details are precise. "The loci are like the wax tablets which remain when what is written on them has been effaced and are ready to be written on again"; "it is useful to give each fifth locus some distinguishing mark"; places should be "of moderate size", "not too brightly lighted", and spaced at "perhaps about thirty feet" [174, p. 23]. Plate XVI draws such a building.

The art of memory is, on our reading, the first explicit retrieval architecture: a fixed address space (the places), a write operation (deposit an image), a read operation (walk the route), a page marker (the fifth locus) and a rule for cache locality (thirty feet). Its latency is the latency of an imagined walk, which is why orators used it and clerks did not. When the addresses had to be shared, or to outlive the walker, they moved onto paper.

----[ 9.5 ] Overload and the slip

The complaint that there is too much to know is not modern. Blair documents it from the twelfth century, when "overload rather than the scarcity of texts was the condition that compendia and florilegia increasingly addressed"; a collection of extracts from that century explained that it spared the reader "the distraction of too many [volumes], which would impair proper retention: 'Indeed the multitude of [volumes] is distracting and no one can have the memory of all of them. Even more, whoever tries to retain everything will retain nothing well'" [19, p. 36]. A thirteenth-century encyclopaedist opened his work by observing that "the multitude of [volumes], the shortness of time, and the slipperiness of memory do not allow all things which are written to be equally retained in the mind" [19, p. 42]. The remedies were structural. "Starting in the thirteenth century the quotations in florilegia were generally sorted for easy retrieval, whereas previously readers had to look through the whole text in order to find a specific item"; "some florilegia were even indexed" [19, p. 36]. Gesner's universal bibliography of 1545 complained of "the harmful and confusing abundance of [volumes]" while cataloguing all of them, "barbarian and Christian, in manuscript and in print, extant and not", and left selection "to others" [19, p. 56].(8)

Gesner also described the instrument. Krajewski quotes his method: everything of importance is copied onto "a good sheet of paper", "a new line should be used for every idea", and then "cut out everything you have copied with a pair of scissors; arrange the slips as you desire, first into larger clusters which can then be subdivided again as often as necessary" [86, pp. 13--14]. This, Krajewski argues, "is the earliest explicit description of how to store what one has read and found worth keeping, arranging it in different ways, and keeping it thematically retrievable" [86, p. 16]. A century later the slips acquired a box: in 1653 a scholar "completes the idea of an excerpt collection as an ordering of paper slips in a box with twenty-four drawers in alphabetical order" [86, p. 21]. And around 1780, in Vienna, "when the technique goes from provisional to permanent, an unintended and yet consequential turn takes place, giving rise to the first card catalog in library history" [86, p. 4]. The reason Krajewski calls the card index a "paper machine" is that its parts move: "if changing the position of a slip of paper and subsequently introducing it in another place means shifting other index cards, this process can be described as a chained mechanism", and a [codex] "lacks this property" of loose parts, "and owing to its rigid form it is not a paper machine" [86, pp. 6--7]. Plate XVII draws the machine.

The private slip box reached its most reflective form in the hands of a sociologist who wrote a paper about his. Luhmann's premise is that "it is impossible to think without writing; at least it is impossible in any sophisticated or networked … fashion", and that "if one has to write anyway, it is useful to take advantage of this activity in order to create in the system of

(8) Blair's noun has been replaced, in square brackets, by the paper's own; nothing else in the quotations has been altered.

notes a competent partner of communication" [96]. The result of years of such work is "a kind of secondary memory, an alter ego with who we can constantly communicate", which "proves to be similar to our own memory in that it does not have a thoroughly constructed order of its entirety", and in which "some things will get lost, some notes we will never see again" [96]. Ahrens, who wrote the manual, reports the scale: "Luhmann's slip-box contains about 90,000 notes, which sounds like an incredibly large number. But it only means that he wrote six notes a day from the day he started to work with his slip-box until he died" [1]. Six notes a day is, we observe, of the same order as Landauer and Dumais's ten words a day (Section 6). The external store filled at about the speed of the internal one.

----[ 9.6 ] The mechanised supplement

Bush's proposal of 1945 is the point at which the slip box was imagined with a motor. "Consider a future device for individual use, which is a sort of mechanized private file and library. It needs a name, and to coin one at random, 'memex' will do. A memex is a device in which an individual stores all his … records, and communications, and which is mechanized so that it may be consulted with exceeding speed and flexibility. It is an enlarged intimate supplement to his memory" [25]. Its capacity was to be effectively unbounded (at 5000 pages of material a day, "it would take him hundreds of years to fill the repository") [25]. Its novelty was in the address. "Our ineptitude in getting at the record is largely caused by the artificiality of systems of indexing. … The human mind does not work that way. It operates by association. With one item in its grasp, it snaps instantly to the next that is suggested by the association of thoughts"; but the mind's "trails that are not frequently followed are prone to fade, items are not fully permanent, memory is transitory", whereas a machine "should be possible to beat the mind decisively in regard to the permanence and clarity of the items resurrected from storage" [25]. The trail, "as though the physical items had been gathered together from widely separated sources and bound together", is the memex's retrieval path, and "his trails do not fade" [25]. Nelson, a generation later, gave the general form a name: "non-sequential writing", hypertext, of which his own report was an instance [105]. Both proposals are proposals about latency: Bush's about the time to follow an association, Nelson's about the time to reach a footnote.

----[ 9.7 ] The extended mind

The philosophical case for treating an external store as part of the mind was made with a notebook. Clark and Chalmers ask us to compare Inga, who "thinks for a moment and recalls that the museum is on 53rd Street", with Otto, who has Alzheimer's disease and "carries a notebook around with him everywhere he goes. When he learns new information, he writes it down. When he needs some old information, he looks it up. For Otto, his notebook plays the role usually played by a biological memory" [33, pp. 12--13]. Their claim is that "the notebook plays for Otto the same role that memory plays for Inga. The information in the notebook functions just like the information constituting an ordinary non-occurrent belief; it just happens that this information lies beyond

consulted, but a store outside that decides when the inside should be refreshed. We take no view on their merits. We note that the rules are rules about chunk size and interference, which is to say about the door and the latency, and that they were written by people who had measured their own forgetting curves.

Finally, the oldest external store of all is other people. Lackey: "We rely on the reports of those around us for everything from the ingredients in our food and medicine to the identity of our family members, from the history of our civilization to the limits and contents of our planet. If we refrained from accepting what others told us, our lives, both practically and intellectually, would be unrecognizable" [88]. Clark and Chalmers allow that "in an unusually interdependent couple, it is entirely possible that one partner's beliefs will play the same sort of role for the other as the notebook plays for Otto", and that "one's beliefs might be embodied in one's secretary, one's accountant, or one's collaborator" [33, pp. 17--18]. Section 11 treats the organisational form of this, under its usual name.

Proposition 11. Every external store in the historical record was adopted for one of two reasons: to lower the latency of retrieval below what the organ could achieve for the material (lists, indexes, tables, guide cards), or to raise the persistence of the material above what the organ could achieve (clay, stone, the memex's trails). No store in the record was adopted to increase capacity for its own sake; capacity was, at every stage, the cheap part.

--[ 10 ]-- Retrieval Latency as the Binding Constraint

We now assemble the measurements. They come from three laboratories, the psychologist's, the phenomenologist's and the engineer's, and they agree.

----[ 10.1 ] Milliseconds per item: memory scanning

The cleanest measurement of retrieval time in the psychological literature is Sternberg's. Newell describes the task: "The subject memorizes a small set of symbols, say digits. This is called the positive set. In a trial of the experiment proper the subject is given a ready signal, followed by a digit after a short fixed delay. The subject responds 'yes' if this so-called probe digit is a member of the positive set, 'no' if it is not." The findings: "(1) Response time is linear with the size of the positive set, the slope being in the range of 35--40 ms. … (2) The intercept is of the order of 350 ms … (3) The size of the positive set can be up to the size normally associated with STM, i.e., around seven elements. (4) The slope for negative responses … is the same as for positive responses", which gives "the interpretation of so-called exhaustive search", and "(5) There is essentially no serial position effect" [106, pp. 10--12]. The other reports of the slope: "between 30 and 50 msec. per item" [7, pp. 373--374]; "about 35 msec per item" [4, pp. 119--120]; "about 35 to 40 msecs. for every additional digit", from which Sternberg concluded that there is "an internal serial-comparison process whose average rate is between 25 and 30 symbols per second" [104, p. 66]; "~40 ms. This is very fast. For instance, it is much faster than people can deliberately iterate through a list in their

heads (say counting from 1 to 10), which is about 130 ms per item" [108, pp. 285--286]. Plate XVIII draws the function from Newell's parameters.

Newell, who devoted a chapter of his last work to the result, listed thirty-two regularities of it, from "Linearity" and "Fast processing: slope = 40 ms for digits" through "Practice invariance: extended practice does not affect slope" to "Self-termination slow: slope greater than 100 ms", and called the whole "a neat puzzle---the very stuff of which great science is made" [108, p. 287]. The puzzle is that a search this fast, this exhaustive and this indifferent to practice does not look like anything a person could do deliberately, and the modelling literature accordingly split between serial and parallel treatments, with the observation, noted by Anderson, "that it is implausible that a serial comparison process of that speed could be implemented neurally" and "that there

exist parallel models which can predict the effects attributed to serial models" [4, pp. 119--120]. The disagreement does not affect the number, which is, within a factor of two, the cost per item of consulting the door.

Remark 3. Forty milliseconds per item, times seven items, is 280 milliseconds, which is less than the intercept. The machinery that presents the question and delivers the answer takes longer than the search. Section 12 will call this the fixed cost, and note that it is the term external stores most often increase.

----[ 10.2 ] The fan: the cost of knowing more

Retrieval from the large store is slower, and it slows with what is known. Anderson's fact-retrieval paradigm has subjects learn sentences and then judge whether a probe was studied. "A major experimental variable in the study of fact retrieval has been called fan, which refers to the number of facts studied about a concept. The more facts are associated with one particular concept, the slower is the recognition of any one of the facts" [4, p. 107]. In the original data, "the average effect of an increase from one to three propositions is approximately the same for persons (114 msec) as it is for locations (127 msec)" [3, p. 256]. The theoretical reading is that "each concept or node has a limited capacity for spreading activation, and as more paths are attached to it, the amount of activation that can be spread down any path is reduced" [4, p. 107]. Knowing more things about a thing makes each of them harder to get at: a result that any reader of Section 4 will recognise as the condition of the shared drive.

----[ 10.3 ] The equation

The ACT-R theory reduces retrieval to two equations, and we reproduce them because they are the only place in the surveyed literature where latency is written down as a function. A chunk's base-level activation "rises and falls n −d with practice and delay according to the equation B t )", where i = ln(Σj=1 j "t j is the time since the jth practice of an item"; "each presentation has an impact on odds that decays away as a power function (producing the power law of forgetting), and different presentations add up (it turns out producing the power law of practice)"; and "in the ACT-R community, .5 has emerged as the default value for the parameter d over a large range of applications" [6, p. 1042]. Then: "if a chunk is successfully retrieved, the latency of retrieval will reflect the activation of a chunk. The time to retrieve the chunk is given −A as T i" [6, p. 1042], with the probability of retrieval a logistic i = Fe function of activation over a threshold and a noise parameter "typically set at about .4" [6, p. 1042]. Anderson's later summary tabulates the whole set and notes that the base-level equation "has been the most successfully and frequently used part of the ACT-R subsymbolic level" [5, pp. 110--111]. The consequence is drawn in the earlier monograph: with a single presentation t units ago, activation is simply 𝛽 − d ln(t), so that "odds of recall and latency of recall should be power functions of delay, which is the common empirical result known as the Power Law of Forgetting" [8, p. 124].

The equation says what the forgetting curve of Plate X implies: the organ does not delete; it slows. An item practised once and not since has a retrieval time that grows as a power of the interval, until at some interval it exceeds the deadline of any task and the item is, operationally, forgotten. It also says that the remedy is repetition spaced in time, which is the schedule of Section 9's practitioners, and that repetition improves latency with diminishing returns, which is the power law of practice. Anderson observes that the same equation "and elaborations on it reflect the changes produced by long-term potentiation, which is thought of as the major mechanism of learning in the hippocampus" [5, pp. 110--111]; the equation of Section 10 and the protein synthesis of Section 6 are, on this view, descriptions of one process at two grains.

----[ 10.4 ] Seconds to days: the tip of the tongue

Between the successful retrieval and the failed one lies a state that everyone has been in and that James was the first to describe. Ericsson and Simon summarise the research: subjects in such a state "were able to report some of the letters in the word, the number of syllables, and the location of the primary stress, with much better than chance probability"; asked about a face they could not name, "they tended to mention first the place where they had seen a picture of the person, then when they had last seen one"; and subjects "were able to predict reliably whether they would subsequently recognize the unrecallable answers" [47, pp. 130--131]. The retrieval has partly completed: the address has resolved to a neighbourhood. Reason's diary study found that "twenty-eight of these (70 per cent) involved the presence of recurrent intruders: recognisably wrong names or words that continued to block access to the target during deliberate search periods", intruders that "almost invariably shared some common phonological, syllabic, structural or semantic features" with the target [126, pp. 105--106]. Augustine's crowding memories that "leap forward into the centre as if saying 'Surely we are what you want?'" [13, p. 185] are the recurrent intruders, described sixteen centuries earlier without a diary.

The linguists locate the failure. In a tip-of-the-tongue state "speakers have selected a lexical conceptual structure and can accept or reject proffered words as what they had in mind. They just can't locate the phonology"; the failure could be "a problem of activation", "a problem of binding" or "a problem of integration" [76, p. 217]. The philosophers use the state to prise apart two senses of consciousness: in a feeling-of-knowing, "subjects have a form of consciousness about the presence of a content (such as an item of information) without having access to it" [21]. Wittgenstein put it with less apparatus: "'The word is on the tip of my tongue' tells you: the word which belongs here has escaped me, but I hope to find it soon" [170, p. 219]. The tip-of-the-tongue state is retrieval latency made conscious: the read has been issued, the answer has not come, and the system is aware of waiting.

----[ 10.5 ] Recognition and recall

Two read operations differ in cost by an amount that the entire history of Section 9 exploits. Recall requires the organ to generate the item from a cue; recognition requires only that it match a presented item against what it holds. Tulving's dissociation gives the difference in retention (Section 6): a studied word that could be recognised at .56 after an hour was recognised at .24 after a week, while fragment completion, a form of cued recognition, held at .47 and .46 [157, pp. 104--105]. Ware gives the mechanism: "in recognition, a visual memory trace is being reawakened. In recall, it is necessary for us to actually describe some pattern, by drawing it or using words, but we only have very limited access to the memory trace" [164, pp. 413--414]. The fast-and-frugal school built a decision heuristic on nothing but recognition and found that "a person who knows less than another can make systematically more accurate [judgements]" [54, p. 358], with recognition alone reaching 65 per cent accuracy on a city-size task and nine further cues adding "only … about another 7%" [53, pp. 56--57]. A checklist (Section 4), a guide card (Section 9) and Thamus's "reminder" all work by converting recall into recognition, and the conversion buys the difference between the two curves.

----[ 10.6 ] Minutes to hours: the external store

The engineers measured the outside. Jacob, Ng and Wang tabulate the latency per access of the levels of a machine memory: on-chip cache, "100 of picoseconds"; off-chip cache, "nanoseconds"; main memory, "10--100 nanoseconds"; disk, "milliseconds" [77]. Drepper gives the same ladder in processor cycles for one design: register, at most one; first-level cache, about three; second-level, about fourteen; main memory, about 240 [42]. The ratio between adjacent levels is one to two orders of magnitude, and the ratio between the top and the bottom is seven. The human ladder, by the figures collected above, runs from tens of milliseconds (the scan) through seconds (a recall) to the tip-of-the-tongue state (minutes to days) and the lost file (Section 4, unbounded); its span is also seven orders, or more. Robertson's testimonial, "twenty seconds to find one letter and ninety seconds to file five folders" [127, p. 173], and Nonaka and Takeuchi's "two seconds" for a database look-up and "the following day" for a new entry [111, p. 69], are points on the same ladder, at the level where a person operates a machine.

The rule for the ladder was written in 1987. "When does it make economic sense to make data resident in main memory? A good rule of thumb is: THE FIVE MINUTE RULE. Data referenced every five minutes should be memory resident." The derivation equates the cost of the memory that holds a record with the cost of the disk accesses that fetching it would need, and solves for the interval: at the prices of the day, "the break-even point is one access every 2000/5 ~ 400 seconds", which "is 'about' 5 minutes, hence the name" [61]. The formal statement is RI = A$/(M$ × B): the break-even interval is the price of an access per second divided by the price of a byte of memory times the size of the record, so that "for smaller records, the break-even point is longer (1 hour for 100 byte records) and for larger records the break-even point is shorter (2

minutes for 4K records)" [61]. Twenty years on, Graefe recomputed it with the prices of 2007 and found ninety minutes for the same page size, remarking that "if there is a surprise in this change, it is that the break-even interval has grown by less than two orders of magnitude" while the price of memory had fallen by five [59]. The rule "was reviewed and renewed 10 years later" and, ten years after that, again [59].

Proposition 12. For any two stores S fast and Sslow with a cost of holding an item in the fast store h per unit time and a cost of fetching it from the slow store f per fetch, an item should be held in the fast store when its expected interval between uses is shorter than f/h. This is the five-minute rule [61], and it applies without modification to working memory (hold: attention; fetch: recall), to long-term memory (hold: rehearsal; fetch: reconstruction) and to the office (hold: the desk; fetch: the file).

We are aware that the analogy is imperfect in one respect that favours our argument: in the machine, the hold cost is money, and in the person, it is the door. Whatever occupies a slot of working memory displaces something else, and Simon's observation that "a wealth of information creates a poverty of attention, and a need to allocate that attention efficiently among the overabundance of information sources that might consume it" [120, p. 13] is the five-minute rule with the hold cost set to the only thing that cannot be bought.

----[ 10.7 ] Keeping only what is needed in mind

The practical conclusion has been drawn in every literature we survey, usually as an aside. James: "we make search in our memory for a forgotten idea, just as we rummage our house for a lost object. In both cases we visit what seems to us the probable neighborhood of that which we miss" [78, pp. 653--654]. Bush: the trail, so that the neighbourhood need not be searched. Luhmann: the box, so that "more information becomes available at this isolated moment of a search impulse than one had in mind" [96]. Norman: "the difficulty with LTM is in organization---in getting material in and in figuring out how to retrieve it---not in capacity" [112, p. 67]. Allen: "use your mind to think about things, rather than think of them" [2, pp. 232--233]. Gawande: an index card in front of the pilot. The convergence is not a coincidence. Each writer had discovered, in their own domain, that the door is narrow and the store is slow, and that the only variable left open is what one chooses to keep within reach.

Proposition 13. The optimal contents of working memory for a task are not the most important items but the items with the highest ratio of expected use to retrieval latency from elsewhere. An item that can be fetched in a glance should not be held; an item that can be fetched only by a day's search should be held or written down; and the difference between the two is the whole of what the external store is for.

a world in which the scarce factor is information may be exactly the wrong one for a world in which the scarce factor is attention" [141, pp. 143--144]. The 1971 statement quoted by Pirolli is the aphorism: "What information consumes is rather obvious: it consumes the attention of its recipients. Hence a wealth of information creates a poverty of attention" [120, p. 13]. Pirolli and Card add the growth rate that makes it bite: "The number of scientific journals has been growing by about a factor of 10 every 50 years since the 18th century" [121, p. 643].

The organisation's working memory is the sum of its members' attention, and it has the properties of Section 8: it is small, it does not scale with the store, and it is filled by whatever arrives first. Klein reports from military command posts that "the information technologies designed to speed decision making may have the opposite effect. Some commanders seem to put off decisions and wait for additional information. New data points keep arriving every few seconds, so the commanders keep hoping that the next message will clarify their choices"; the "saturation point, the point at which our attempts to resolve uncertainty by getting more information become counterproductive, is technically referred to as information overload" [85, pp. 133--134]. Wurman had said the same for the newspaper reader: "the less time you have and the more objects on the tray, the more likely you are to see objects that weren't there and forget ones that were" [173, pp. 36--37]. The organisational and the individual descriptions are, sentence for sentence, interchangeable.

Proposition 14. An organisation's effective knowledge at a moment is bounded by the attention of its members at that moment, exactly as a person's is bounded by working memory; and the bound is reached not when the store is full but when the queue of things demanding attention exceeds the rate at which attention can be paid.

----[ 11.3 ] Less is more, in both

The fast-and-frugal programme supplies the organisational form of Proposition 13. Its founding heuristic uses only recognition: "When choosing between two objects (according to some criterion), if one is recognized and the other is not, then select the former" [53, pp. 56--57]. Its counter-intuitive result is that "adding more knowledge for the recognition heuristic to use, by increasing the proportion of recognized objects in an environment, can even decrease decision accuracy. This less-is-more effect … is straightforward from an information theory perspective, but surprising from a cognitive one" [53, pp. 56--57]. The heuristic "works quickly and with limited knowledge---and even requires a certain amount of ignorance"; "search is limited to recognition memory---no recall of knowledge beyond recognition is attempted", and "the stopping rule is constrained---search terminates as soon as recognition has been assessed for both objects" [54, pp. 57--59]. A firm that hires from institutions it recognises, buys from suppliers it recognises and reads journals it recognises is running the same heuristic, and for the same reason: recall is expensive and recognition is a glance.

----[ 11.4 ] Transactive memory: the organisation's tip of the tongue

The organisational analogue of the extended mind has a name and a literature. In the teams literature a transactive memory system is, in Lewis's definition as the handbook of expertise gives it, "the cooperative division of labor for learning, remembering, and communicating relevant team knowledge"; it is measured on three dimensions, "specialization (i.e. the knowledge of where expertise lies within the team), credibility (i.e. trust in the reliability of this expertise), and coordination (i.e. the coordinated use of this expertise)", and it represents "the manner in which knowledge is distributed among team members" rather than what they all share [45]. A later refinement adds the clock: a team's transactive memory is "the set of unique knowledge domains held by specific members combined with a shared understanding of who knows what and when that knowledge is needed in the team" [45]. Klein's "team mind" has the same parts as a person's: a working memory, in which "information is presented and gets some discussion; then the team moves on to another topic and forgets the first one"; a long-term memory, in which "if a team member has particular information and drops out of the team, the information is lost", so that teams "find it helpful to store the information redundantly, so more than one person knows it"; and a limited attention, since teams "can discuss only one thing at a time" [84, pp. 235--236]. Who knows what is an index; the index is what a meeting consults when it asks whether anyone has this; and the latency of the index is the fan effect (Section 10) at the scale of a meeting: more members attached to a question, longer before the one who knows is found.

The healthcare literature has measured the effect. In a study of mental-health teams, reported by Pauly and colleagues, utilisation "was associated with two main factors in the team's design: expertise redundancy and transactive memory accuracy", the latter being "the extent to which team members accurately recognize experts in relevant knowledge domains, which allows team members to quickly access needed expertise and improves decision-making, task performance, and care" [117, p. 95]. "Quickly access" is the operative phrase. A team whose members know who knows what has a low-latency index over a high-capacity distributed store; a team whose members do not has the Section 4 condition of material "they knew was there" and could not find. The organisational tip-of-the-tongue state is the meeting in which everyone is sure someone once wrote this down.

Clark and Chalmers had already extended the mind to the couple: "one partner's beliefs will play the same sort of role for the other as the notebook plays for Otto", and, in other relationships, "one's beliefs might be embodied in one's secretary, one's accountant, or one's collaborator" [33, pp. 17--18]; Chalmers's later example is a long-term couple in which one partner's memory "isn't working so well anymore, so he relies on" the other "to remember important names and facts" [30]. The availability heuristic literature, in which the ease of recalling instances stands in for their frequency [159], supplies the failure mode. Asked to recall their contributions to household chores, "each spouse thought she or he had contributed more to the joint activities than the other spouse. When the responsibility scores of the two partners were added together,

they exceeded the total possible responsibility that could be taken" [80, pp. 195--196]. A transactive memory in which each node over-weights its own entries is a store with a systematic indexing error, and the error is the organisation's as much as the couple's.

----[ 11.5 ] The cost of the external store, in minutes per day

The clearest measurements of what an organisation pays to keep its memory outside its members come from clinical medicine, where the store is the electronic health record and the members are physicians. Arndt and colleagues, from three years of event logs across 142 family physicians, validated by direct observation, found that "clinicians spent 355 minutes (5.9 hours) of an 11.4-hour workday in the EHR per weekday per 1.0 clinical full-time equivalent: 269 minutes (4.5 hours) during clinic hours and 86 minutes (1.4 hours) after clinic hours", of which "clerical and administrative tasks including documentation, order entry, billing and coding, and system security accounted for nearly one-half of the total EHR time (157 minutes, 44.2%)" and "inbox management accounted for another 85 minutes (23.7%)" [10, p. 419]. Their summary: "Primary care physicians spend more than one-half of their workday, nearly 6 hours, interacting with the EHR during and after clinic hours" [10, p. 419], "representing a considerable encroachment on physicians' personal and family lives" [10, p. 423]. Sinsky and colleagues report the convergent finding that "physicians in the ambulatory setting spend half of the workday on the EHR, requiring nearly 2 hours of EHR and desk work for every 1 hour of direct clinical face time with patients" and "may allocate 1--2 hours of personal time each night to EHR tasks" [142, p. 639].(10)

Wachter's reportage gives the texture. In one practice "each physician spends, on average, seven minutes a day 'refreshing' locked computer screens, ten minutes signing in repetitively, and thirteen minutes completing rote attestations", and "creating an electronic invoice takes a minute for each patient, with 21 clicks, eight scrolls up and down, and five screen changes" [162, pp. 85--86]. Because the record cannot be navigated "in an intuitive way", the practice's staff "spends hours the day before every clinic session printing out most of the electronic record", "well over a ream of paper" a day for two doctors [162, pp. 85--86]. A physician who nearly missed a pulmonary embolism "because she was trying to get her 'electronic bearings'" is his example of what the retrieval cost does to the door [162, p. 83]. The interruption study he cites gives the door's fragility in seconds: when a task requiring the subject "to mentally keep track of their place in a sequence of events" was interrupted "for about 3 seconds, the rate of errors doubled. When it lasted for 4.4 seconds, the rate tripled" [162, p. 83]. And the record itself has become a store of Bush's size with none of Bush's trails: "for a complicated patient, the EHR can easily contain thousands of pages", and "for a physician to take in and understand a 10,000-page longitudinal patient record in the two to three minutes he has to prepare for the visit with that patient is a problem" [162,

(10) The abbreviation is the sources' and refers to the record, not to any particular system for keeping it; the paper describes none.

pp. 118--119]. Ten thousand pages in three minutes is a retrieval-latency requirement that no store in this paper meets.

Proposition 15. An organisation that externalises its memory pays for it in the attention of its members at the time of writing and at the time of reading, and the payment is measured in the same unit, minutes of the working day, on both sides of the ledger. Where the reading cost exceeds the value of what is read, the store is consulted less and the organisation's effective knowledge falls even as its recorded knowledge rises.

----[ 11.6 ] The parallel, tabulated

We do not claim that the two columns are identical, only that no row of the table required a different vocabulary for its two cells. That is what "the same way" means.

--[ 12 ]-- A Framework: LOCUS

Frameworks in this literature are customarily given an acronym, and we have not resisted. LOCUS names five quantities, ordered by the weight this paper gives

them. The word is also the classical term for a place in the memory building (Section 9), which is where a framework should be kept.

----[ 12.1 ] Definitions

Definition 1. Latency (L). The expected time from the issue of a retrieval request for an item x in a store S to the availability of x in working memory, ℓ(x, S). It has a fixed component (the intercept: finding the store, opening the drawer, forming the query) and a variable component (the slope: scanning, reconstruction, reading). Both are measured in seconds, and both are larger than they look.

Definition 2. Offloading (O). The act of moving an item from one store to another with a different latency profile, usually from the organ to a record, at a cost paid at the time of the move (Section 6's write latency; Section 11's minutes per day). Offloading changes ℓ; it does not change the item.

Definition 3. Capacity (C). The number of items, or bits, or chunks, that a store can hold. For every store in this paper except working memory, C is large enough not to bind (Norman's judgement [112, p. 67]); for working memory it is between two and seven and does not grow (Section 8). Capacity enters the framework only through its effect on latency, which is that the fan effect makes a fuller store slower [4, p. 107].

Definition 4. Uncertainty (U). The probability that a retrieval request returns the wrong item, a reconstruction of it, or nothing: Bartlett's transformations [16], the recurrent intruders of the tip-of-the-tongue state [126], the notebook Otto has not updated. Uncertainty and latency trade: a longer search lowers U, up to the deadline.

Definition 5. Structure (S). The representation by which the store is addressed: the concept, the schema, the tree, the guide card, the trail (Section 5). Structure is what converts a recall into a recognition, and it is the only term of the five that a designer controls directly.

----[ 12.2 ] The central relation

The framework's one equation is the five-minute rule of Gray and Putzolu [61], restated for a hold cost paid in attention rather than money (Proposition 12). For an item with expected inter-use interval 𝜏, hold cost h per unit time in the fast store and fetch cost f from the slow one, hold if 𝜏 < f/h, otherwise offload. In the machine, f/h was 400 seconds in 1987 and 5,248 seconds in 2007 [61, 59]. In the person, h is a fraction of the door and f is ℓ(x, S slow); neither has a price, but both have a magnitude, and the rule holds for magnitudes. Everything in Section 9 can be read as an attempt to lower f (the list, the index, the trail) or to lower h (the chunk, the schema, the formula of the oral poet), and everything in Section 11 as a report of what happens when f is allowed to rise (the shared drive, the ten-thousand-page record).

----[ 12.3 ] A taxonomy of stores by latency class

The stores discussed in this paper are classified below by the order of magnitude of their retrieval latency, with a representative source for each. The classes are named after the units in which their sources report them. The table contains no store that the paper has not already described and endorses none.

Two features of the table are worth remark. First, it is continuous: there is no class boundary at the skin, which is the extended-mind thesis [33] stated as a table. Second, the classes are separated by roughly one order of magnitude each, as the levels of a machine memory are [77], and for the same reason: a store one order slower than another is worth building only if it is one order larger or one order cheaper, and the stores that survived are the ones that were.

----[ 12.4 ] The framework in brass

The paper's subject is the constraint and not the apparatus (Section 16 says so), but there is one apparatus in which the constraint is the whole design and every part of it can be seen, and the paper draws it once, in Plate XXI, because the horologists' vocabulary turns out to be the framework's. A mechanical watch is a store of energy with a latency device screwed to it. Snodgrass, who put an escapement at the head of every chapter of a manual on time in databases, gives the definition: "The mechanism that periodically stops the unwinding of the clock, and thus keeps the time, is termed the 'escapement'", and "all escapements have these two tasks: regulate the advancement, and 'kick' the oscillating body" [143, p. 201]; the escape wheel, "connected by gears to the hands of the clock, would spin continuously if not retarded by the escapement, which periodically stops and releases the escape wheel" [143, pp. 5--6]. Sowa states the principle every clock shares: "select some process whose ticks are assumed to be regular, and use the count of ticks to measure the progress of other processes", and notes that "inside a mechanical clock, most of the gears are used to translate the high-speed ticks of a pendulum or vibrating spring to the much slower movement of the hour and minute hands" [146, pp. 228--229]. Hanson uses the same machine to show that seeing a cause is a trained retrieval: an apprentice "may not yet see that the force transmitted by the weighted drum

the latency of that coupling and nothing else: "an instantaneous and extremely precise start" [128]. The column wheel is the dispatcher that decides, at each press, which of three states the register is in. This is Proposition 22 in brass, and the paper had not expected to find it there: a register is a candidate knower of an interval only when its clutch closes below the latency of the interval it is asked about, and the craft of the chronograph is the craft of that clutch. The room of Section 13 is a chronograph whose clutch takes a week to close.

----[ 12.5 ] Propositions of the framework

Proposition 16. (Ordering.) For a task with deadline d, the stores available to an actor partition into those with ℓ < d, which the actor effectively knows, and

those with ℓ ≥ d, which the actor effectively does not. Knowledge, at the knowledge level [107], is the first partition.

Proposition 17. (Expertise reversal, generalised.) A structure that lowers ℓ for an actor whose chunks are small raises ℓ for an actor whose chunks are large, because for the second actor the structure is redundant and must be ignored at a cost [161, pp. 163--164]. There is no structure of universal benefit; there are only structures matched to chunk sizes.

Proposition 18. (Conservation.) Offloading conserves latency plus uncertainty: an item moved to a store with lower ℓ acquires the uncertainty of that store's index (that it is stale, misfiled or unknown to the reader), and an item moved to a store with lower U (a written record rather than a recollection) acquires the latency of finding it. The history of Section 9 is a search for stores that violate this proposition, and none was found.

Proposition 19. (The reader.) A store has a latency only relative to a reader who knows its structure. When the readers are gone the store's class is VII regardless of its physical condition, which is why Exhibit 1 is the first exhibit and why the clearances of Section 4 are effective.

----[ 12.6 ] What the framework predicts

Nothing that its sources had not already observed, which is the appropriate ambition for a review. It predicts that adding capacity to a store without adding structure will raise its latency (the fan effect; the shared drive; the record of ten thousand pages). It predicts that a structure imposed for novices will be resented by experts (expertise reversal; the redundant field on the form). It predicts that the organisation, like the person, will keep in its working memory not what is most important but what is most often used and hardest to fetch (the five-minute rule; the checklist), and that when it fails to, the failure will be measured in minutes per day. And it predicts that the philosophical objection of the Phaedrus will be repeated for every new store, as Ong observed it had been [115, pp. 77--79], because the objection is correct about the mechanism and mistaken about what to do with it.

--[ Interlude: Two Cartoons, Read as a Literature on Retrieval ]--

Between the history of the external store and the measurement of its latency the paper pauses, for three pages, over a body of work that the surveyed literatures do not cite and that nevertheless states most of their conclusions more compactly than they do. We refer to two series of short animated films made in the United States in the middle of the last century: the desert chase in which a coyote pursues a flightless bird along a highway, and the domestic chase in which a house cat pursues a mouse. The reader who has not seen them is asked to take the following on trust; the reader who has seen them is asked to consider whether they were not, all along, a treatise.

--[ The painted tunnel ]--

The best-known device of the desert series is the painted tunnel. The coyote, finding his road blocked by a rock face, paints on it a continuation of the road, with its centre line, its vanishing point and its patch of painted sky, in order that the bird will run into the rock. The bird runs into the painting and disappears down the painted road. The coyote, following, strikes the rock. The gag has several forms and one structure: a representation is made; it is mistaken for the thing represented; the mistake is fatal for its maker and harmless for everyone else. Plate XXII draws the situation without either party present.

The theory of representation has said the same thing at greater length and with less confidence about the outcome. Dretske observes that a map's power "to represent, and misrepresent, the geography of an area depends, fundamentally, on their information-carrying role", and that "a crucial link in the flow of information (from the physical terrain to the arrangement of marks on paper) is

the map maker himself", a link "through which information can be lost through ignorance, carelessness, or deceit" [43, p. 191]. A map "can misrepresent the geography of an area only insofar as its elements … are understood to have a meaning independent of their success in carrying information on any given occasion" [43, pp. 192--193]. The painted tunnel is a map drawn with deceit, and it misrepresents exactly because the bird takes its marks to mean what such marks usually mean. Norman's formulation is the general one: "A representation is never the same as the thing being represented, else there would be no advantage to using one. The critical trick is to get the abstractions right"; get them wrong "and the representation is misleading, causing people to ignore critical aspects of the event or perhaps form misguided conclusions" [113, pp. 49--50]. The coyote gets the abstractions right. He is misled by his own representation not because it is inaccurate but because it is accurate enough to be believed by someone else, and the someone else is faster. Taleb gives the general failing a name, "Platonicity", "our tendency to mistake the map for the territory", and adds the clause that makes it the coyote's: "you do not know beforehand (only after the fact) where the map will be wrong" [152, pp. xxix--xxx].

Peirce, in a lecture of 1903, imagined a map of a country laid on the soil of that country, so exact "that there is no speck on any grain of sand in the country that could not be seen represented upon the map", from which it follows that "the map itself will be portrayed in the map, and in this map of the map everything on the soil of the country can be discerned, including the map itself", and so on, until there is "a point contained in all of them, and this will be the map of itself" [119, p. 49]. The painted tunnel is the vulgar case of Peirce's map: a representation laid on its own territory, at scale, and mistaken for it by a party who then enters it. Olson's example is more domestic and closer to the paper's concern. A floor plan outside his office carries an arrow captioned "You are here", and he notes that "in a deep sense that usually goes unnoticed, the caption is anomalous. I don't need a map to tell me where I am"; the map "undertakes to lift me from my firm stance on the floor and transpose me into this geometry of lines and angles" [114, pp. xiii--xiv]. The northern travellers in his anecdote, unable to find a cache marked on a map, refused the conclusion that they were lost: "It is the cache which is lost" [114, pp. xiii--xiv]. The coyote, on the rock face, is the map maker who has transposed himself into the geometry of his own lines and finds that the cache is not there.

The lesson for the external store is Proposition 19 with the sign reversed. A store has a latency only relative to a reader who knows its structure; a painted tunnel is a store whose structure its maker knows perfectly and which nevertheless does not work for him, because the structure he knows is the structure of paint. The bird knows nothing of paint and runs through. Externalised knowledge that works only for whoever drew it is the ordinary condition of the private slip box (Section 9); externalised knowledge that works for everyone except whoever drew it is the painted tunnel, and the difference between them is not in the drawing.

--[ The catalogue ]--

The coyote's second resource is a mail-order catalogue from which he obtains, by return, whatever apparatus the pursuit requires: springs, rockets, magnets, anvils, glue, a set of wings. Every item works as specified and fails in use, because the specification was the seller's and the use is the coyote's. This is externalised capability without understanding, and it has a literature. Hutchins's navigator "doesn't have to know how the chart was made and doesn't need to know about the properties of the Mercator projection", and the tool "is actually more powerful" when whoever uses it "does not have to know how or why it works" [75, pp. 173--175]; Collins's bread-making machine "works only because the surrounding social organism makes up and 'repairs' its deficiencies" [35, p. 144]. The coyote is the case in which the surrounding social organism consists of one coyote. He has the chart and not the cartographer; the specification and not the schema; the explicit knowledge, delivered by post, and none of the tacit knowledge that Nonaka and Takeuchi's spiral assumed would accompany it [111, pp. 71--73]. The catalogue is a store of latency class IV (a look-up, a delivery) attached to a reader whose own store, on the matters that count, is class VII. Nothing in Section 12 predicts that this arrangement will work, and in the source material it does not.

We note in passing that the coyote never consults his catalogue for the one item that would end the pursuit, which is food, and that the paper's Proposition 13 covers this case: what he keeps in mind is the bird, which is used often and fetched slowly; what he has written down is the apparatus, which is used once and fetched by post; and what he has left in the world is dinner, which is fetched by no one.

--[ The cliff ]--

The third device is the cliff. The coyote runs off it, continues in a straight line for some distance, stops, looks down, and only then falls. The gag is usually read as a joke about physics. It is better read as a joke about retrieval. The coyote's belief that there is ground beneath him persists until it is checked; the check is a retrieval from the environment, a glance; and the glance has a latency, during which the belief goes on doing the work of a fact. Hofstadter describes how "we build up our mental representation of a situation layer by layer", with a lowest layer "so low that it cannot vary at all", such as "the three-dimensionality of our world", which "is a constant constant", above it "background assumptions---things which, in the back of your mind, you know can vary, but which most of the time you unquestioningly accept as unchanging aspects" [72, p. 644]. Ground is a background assumption. The coyote does not retrieve it because it is not the kind of thing one retrieves; it is the kind of thing one stands on. When at last he looks down, he performs the retrieval, the assumption is found to be stale, and the world, which had been waiting politely, resumes.

The joke is funny because it is true of everyone. Section 10's tip-of-the-tongue state is a belief that a word is there, persisting while the word is not;

Section 4's organisation "knew" its documents were on the shared drive; Section 6's Otto believed the museum was on 53rd Street between consultations of the notebook and was, Clark and Chalmers insist, right to [33, p. 13]. The difference between Otto and the coyote is only that Otto's notebook was correct when he looked. The framework of Section 12 has a term for the interval between the belief and the check: it is latency, and during it one is running on air.

--[ The chase that does not learn ]--

The domestic series has a different structure and a worse one. The cat pursues the mouse; the mouse escapes by some device; the cat is injured in a manner that would, in any other genre, be final; and the next film begins with the cat intact, the mouse in his hole, and no trace in either of what occurred. Nothing is carried between episodes. Each pursuit is a fresh pursuit, conducted with the same repertoire against the same defences, by parties who have, on the evidence, never met.

The knowledge-representation literature has formalised the pursuit without noticing the amnesia. Sowa's textbook example for the representation of verbs is the sentence "A cat is chasing a mouse", rendered three ways: as a relation linking cat to mouse, as an act with two roles, and as a "nexus" in a context box with two "Has" relations, and then as the formula (∃x:cat)(∃y:mouse)(∃z:chase) with the chase described by its participants [146, pp. 270--272]. The concept Chase is defined "by a graph that shows how the [actor] and theme are related", to be read as "the [actor] of the chase is an animate being, which is rapidly following a mobile entity … the animate being's purpose in following is to catch the mobile entity"; "if the chase is unsuccessful, the catching might not occur at all" [146, pp. 272--273].(11) That last clause is, as far as we can find, the only place in the surveyed literature where the outcome of the domestic series is stated as a theorem. The context box, Sowa adds, "separates the encapsulated information from the information in the outer context" [146, pp. 271--272]. Each episode of the domestic series is such a box. Nothing pivots out.

The cognitive architectures give the mechanism. Laird's example of a robot that pursues another is instructive because it fails in the same way the cat does: when the pursued party "goes into another room, and hides behind a wall, the robot no longer senses [it] and gives up on it", and "this arises because the robot didn't create any persistent structures describing the other … in working memory. It based its behavior off of its perception" [89, pp. 105--107].(12) A pursuer with no persistent structure describing the pursued is a pursuer who cannot learn that the hole in the skirting board has been used before, and a chase without persistent structures is a chase that resets. The fast-and-frugal school lists "pursuing, evading, fighting, courting, and being courted" among

(11) The bracketed word replaces Sowa's term for the participant that acts, throughout, as in Section 5.

(12) The ellipsis and the bracket stand for Laird's noun for the pursued party, replaced as a matter of house style.

the "basic categories of animate motion", adds "play, which is widely used, especially by mammals, to learn mastery of the other five", and notes that evasion "often favors strategies of deceptive feints and lunges and unpredictable, 'protean' zigzagging" [54, pp. 262--263]. The mouse zigzags; the cat, lacking a store in which the zigzags could be kept, is deceived by each one as if for the first time. The series is, on this reading, an experiment in pursuit with the learning switched off, run for several decades, with the expected result.

The organisational reading is uncomfortable and we give it briefly. An organisation whose memory is cleared between episodes (Section 4's clearance, applied every quarter) will conduct each project with the same repertoire against the same obstacles, will be injured in the same way, and will begin the next project intact and uninstructed. Bowker and Star's airline, which "does not retain a record of one's food or seating options" because processing passengers anew "is easier from a data processing perspective" [22, pp. 257--258], has chosen the domestic series as its architecture. Whether the choice is wise depends, as Bowker and Star say, on whether "rediscovery is easier than remembering" [22, pp. 257--258]. For the cat it is not. For the airline it may be. The framework does not decide; it only insists that the decision is one about latency, since the cost of remembering is the cost of the store and the cost of rediscovery is the cost of the chase.

--[ How the chase is drawn ]--

A last observation concerns the medium, since the paper is a paper about media. Both series are made of drawings, and the drawings encode speed by convention. Horn catalogues the conventions: "motion lines behind a figure and little puffs of smoke indicate 'really fast'"; blurred backgrounds show that "our eyes are fixed on a rapidly moving object"; animators "use this 'squash and stretch' technique to create motion that appears more natural" [74, pp. 171--172]. Tversky notes that to show "a reckless breathless chase" one strip's frames "run diagonally downhill", and that "everywhere, comics break the rules" of the box, so that "if you want to exit the story, all you have to do is exit the boxes" [160]. The coyote, when he runs off the cliff, has exited the box of the road and not yet noticed; the mouse, when he enters his hole, has exited the box of the room. The frame is a store; leaving it is a retrieval failure on the part of whoever is still inside; and the pleasure of the audience, which knows where everyone is, is the pleasure of the omniscient index. The paper does not have that pleasure. It has the index, and it has watched, for some pages now, the reader look down.

Remark 4. The interlude cites no scholarship on the films themselves, because the collection from which the paper was written holds none (Appendix E). The rules that the desert series' director is reported to have kept, on what the coyote could and could not do, are therefore not quoted, and the paper's readings of the gags are its own. A reader who knows the rules will notice that the paper has, in effect, derived three of them.

The paper's sources hold no scholarship on a third series either, and the paper now takes it up anyway, at length and in earnest, because it turned out to contain the argument the paper had been looking for.

--[ 13 ]-- The Room Inverted: Objections and Replies

The interlude read two chases as a literature on retrieval. This section reads a third series, and reads it as a literature on understanding, which is the word the retrieval literature uses when it wants to say that a store has been reached and used. The series is an American animated one that began in 1999 and is set under the sea. We use four of its standing facts and no others. A small copepod, whom the series calls Plankton, owns a restaurant that has no customers, the Chum Bucket, across the street from one that has, the Krusty Krab. The success of the second is attributed, by everyone in the series including the copepod, to a written formula for its sandwich, kept in a safe; the copepod's standing project, episode after episode, is to obtain the formula. He is married to a computer, whom the series calls Karen: a screen on a stand, who speaks, plans, keeps his records, and comments on his failures. And the failures recur: the formula is not obtained, or is obtained and does not help, and the next episode

begins as the last one did. The reader who has not seen the series is asked to take these four facts as stipulations, which is how a thought experiment is usually offered, and the reader who has seen it is asked to notice that they are all the series ever needed. They also have a grammar, which Plate XXVI gives in the notation of the language manuals, since a series that has run the same production for twenty-five years is entitled to one.

We claim that this arrangement is Searle's Chinese room with the roles reversed, and that the reversal is instructive. We then take the obvious objections to the claim in the order a reader would raise them, state each as strongly as we can, and answer it. Each reply ends in a small proposition that the paper keeps. The propositions are assembled in Section 17, after the framework of Section 12, into a thesis that none of the objections anticipated. We take the argument seriously throughout: the series is a joke, but the question of what it is to understand is not, and nothing below depends on the reader's finding any of it funny.

----[ 13.1 ] The argument, as its author states it

Searle's thought experiment of 1980 is familiar enough to summarise in his own words. He is locked in a room with batches of Chinese writing, of which he knows nothing ("To me, Chinese writing is just so many meaningless squiggles"), and with rules in English that "enable me to correlate one set of formal symbols with another set of formal symbols, and all that 'formal' means here is that I can identify the symbols entirely by their shapes". He follows the rules so well that "from the point of view of somebody outside the room in which I am locked,

my answers to the questions are absolutely indistinguishable from those of native Chinese speakers". And: "As far as the Chinese is concerned, I simply behave like a computer; I perform computational operations on formally specified elements. For the purposes of the Chinese, I am simply an instantiation of the computer program" [138, p. 418]. The verdict follows at once: "it seems to me quite obvious in the example that I do not understand a word of the Chinese stories. I have inputs and outputs that are indistinguishable from those of the native Chinese speaker, and I can have any formal program you like, but I still understand nothing" [138, p. 418].

The room is an illustration, not the argument. Dennett, who has spent a career on it, reports Searle's own statement of the argument proper in three propositions and a conclusion: "Proposition 1. Programs are purely formal (i.e., syntactical). Proposition 2. Syntax is neither equivalent to nor sufficient by itself for semantics. Proposition 3. Minds have mental contents (i.e., semantic contents). Conclusion 1. Having a program---any program by itself---is neither sufficient for nor equivalent to having a mind" [38]. The room is offered in support of the second proposition, and Searle is explicit that it is a reminder rather than a proof: "The point of the parable of the Chinese room is simply to remind us of the truth of this rather obvious point: the man in the room has all the syntax we can give him, but he does not thereby acquire the relevant semantics" [38]. His positive view is that understanding is produced by "a certain biological (i.e. chemical and physical) structure" which "under certain conditions, is causally capable of producing perception, action, understanding, learning, and other intentional phenomena", and that "only something that had those causal powers could have that intentionality" [138, p. 422]. Whether anything other than a brain has them is, he says, "an empirical question, rather like the question whether photosynthesis can be done by something with a chemistry different from that of chlorophyll" [138, p. 422].

We state the argument this fully because it is often stated less fairly, and because our disagreement with it is narrow. We do not claim that the conclusion is false. We claim that the second proposition, in so far as the room supports it, is supported by an intuition about latency, and that a case in which the latency runs the other way produces the opposite intuition. The case follows.

----[ 13.2 ] The inversion

In the room, the one who manipulates the symbols is the one we are asked to agree does not understand, and the candidate for understanding, if there is one, is something else: the system, the program, the room. In the Chum Bucket the assignment is reversed. The one who manipulates symbols is the computer. She computes, plans, analyses and keeps records; she is, in the series' own terms, a machine that runs programs. She forgets nothing: every plan, every failure and every previous episode is on file, and she says so. And she is the party the series, the audience and her husband credit with judgement. The copepod, who has the biology, is the one who follows rules. His plans are scripts, executed as written and failing as written; the object of his life is a written formula, which he intends to follow; and when the formula is in his hands he does with it

what the man in the room does with the rulebook, which is to apply it without understanding what it is for. The viewer's intuition, which is the same intuition Searle appeals to, runs without hesitation in the opposite direction from the room's: the screen understands what is going on, and the organism does not.

Three things about the intuition deserve notice before the objections. First, it is not produced by any claim about programs; nobody watching the series is thinking about syntax and semantics, just as nobody reading Searle is thinking about them until he says the words. Second, it is produced by roles. The computer is cast as the one who sees the situation whole, the organism as the one who sees his next step; the audience is cast with the computer. Third, it is stable. Decades of episodes have not shaken it, and the series has been able to rely on it as a premise rather than argue for it, which is the condition Searle claims for his own intuition. If the intuition in the room is evidence for the second proposition, the intuition in the Chum Bucket is evidence of the same weight for its denial, and a premise supported and denied by evidence of the same weight is not supported. That is the claim. The objections to it are these.

----[ 13.3 ] Objections and replies

Objection 1: It is fiction. The computer understands because her writers wrote her so. A cartoon can stipulate anything; it can make a sponge fry a sandwich and a starfish own a house. Nothing about computers follows from what a writers' room decided a computer would say, and to treat the audience's acceptance of the stipulation as evidence is to treat the audience's suspension of disbelief as a datum in the theory of mind. Searle's room, by contrast, asks the reader to consult a fact about themselves: whether, in the position described, they would understand Chinese. That is not a stipulation but an introspective report, and Searle insists on the difference: "When I now say that I at this moment do not understand Chinese, that claim does not merely record an intuition of mine, something I find myself inclined to say. It is a plain fact about me that I don't understand Chinese" [138, p. 451].

Reply 1. The objection is right that the series stipulates, and wrong that the room does not. The room stipulates that a man following rules by hand produces answers "absolutely indistinguishable from those of native Chinese speakers", which is a stipulation about a program that has never existed and, as several of Searle's commentators pointed out at the time, about a process that would take, on the most generous estimate, "a week per question" [71, pp. 433--434]. Both cases stipulate a performance. The difference is what each does with the reader. Searle casts the reader as a part: you are the man, you see the squiggles, you feel the tedium, and from that seat the plain fact is available to you, because it is a fact about the part. The series casts the reader as an observer of a whole: you see the couple, you see the plan go wrong, you see the screen see it coming. From that seat a different plain fact is available, which is that one of the two parties in front of you understood the situation and the other did not, and it is not the organism. Neither fact is deduced from a theory of programs.

Each is what its standpoint makes visible. Advertising runs the experiment daily: the green one of the confectioner's commercials is credited by her audience with an allure that her writers stipulated and a sugar shell cannot hold, and nobody who has watched her recline has found the stipulation hard to accept. Plate XXVII shows her seat, which is also the viewer's.

Searle's plain fact is not in dispute. The man in the room does not understand Chinese, and the paper will say so again. What is in dispute is what the fact is a fact about. Dennett's commentary made the point at the time: "The systems reply suggests, entirely correctly in my opinion, that Searle has confused different levels of explanation (and attribution). I understand English; my brain doesn't" [37, p. 429]. The plain fact is a fact about a part, and the reader is placed inside the part so that it is the only fact in view. The series places the reader outside, and a different fact is in view. So the objection, which meant to disqualify the series as fiction, has instead identified what the two fictions share, which is a casting decision, and what distinguishes them, which is the seat the reader is given. We keep the result.

Proposition 20. An attribution of understanding is made from a seat. From inside a part, the whole's operations are slow and meaningless; from outside the whole, the parts are invisible and the performance is what is seen. An intuition pump that fixes the seat fixes the verdict.

Objection 2: The screen is a lookup table. Block's machine of 1978 settles the case against the computer. Consider "a string of sentences whose members, spoken one after another, can be uttered in an hour or less", and the finite set of such strings in which one party is making sense: "a finite set which could in principle be listed by a very large team working for a long time with a very large grant". A machine that stores the list and, at each turn, picks a string consistent with the conversation so far will pass any hour of interrogation and has, Block argues, no intelligence at all; to think otherwise, because its behaviour is complex and subtle, "is just crude behaviorism" [20, pp. 281--282]. The screen in the series is exactly this. Her lines were written by a team; her responses to her husband's plans are entries in a table the writers filled; and the intelligence the audience credits her with is theirs, delivered through her. The Chum Bucket does not invert the room. It restates it with a better script.

Reply 2. Block's argument is one of the best in the literature, and we accept it as stated: a table of all sensible conversations is not a thinker, and the reason is that intelligence depends on how the behaviour is produced, not on the behaviour alone. But consider what in the production makes the difference. Block's machine is impossible in practice for two reasons he gives himself: the list is astronomically large, and it must be searched. The team is "very large" and works "for a long time". The philosophers who have taken the example up put the point as a matter of time and matter: writing the table down would take more than a lifetime, and searching it would take longer still. Dennett's reply to the example is the one we build on. Suppose, he says, "we discovered that Oscar Wilde lay awake nights thinking of deft retorts to likely remarks and committing these pairs to memory so that he could deliver them if and when the occasion arose 'without missing a beat'. Would this cast any doubt on our categorization of him as an intelligent thinker? Why should it matter when the cogitation is done, if it is all designed to meet the needs of a time-pressed world in an efficient way?" The table, he concludes, "does its thinking at a strange time" [40]. The objection to the table is not that its thinking was done elsewhere; Wilde's was done elsewhere too. It is that a table large enough to cover the conversation could not be consulted within the conversation, so that whatever intelligence went into it is not available at the latency at which intelligence is attributed. Block's psychologism, which says that the manner of production matters, is right, and the manner matters because it fixes the latency at which the production can meet the world. A precomputed retort delivered in time is wit. The same retort, found by searching a list for a week, is not, and not because the list is a list.

Now apply this to the screen. The objection is correct that her lines were written by a team, and correct that this is derived intelligence. But it is not correct that she is Block's machine, because Block's machine is defined by its manner of production, which is search over a complete table, and the series does not depict that manner and could not: a table of all the schemes a copepod might bring home would be larger than the one Block imagines, and the writers did not fill it. What the series depicts is a party who responds in time to a situation that is new each week, and the audience's attribution

tracks that. The audience is doing what Block asks: judging by the manner of production it can see, which is a response at conversational latency to novelty. It cannot see the writers, and neither, in the fiction, can the copepod. The objection has therefore shown something it did not intend. The lookup table fails to be a thinker for a reason that is not about tables. It is about whether a store, however filled, can be reached and used at the pace of the world it answers to. Block himself anticipated that an opponent might make time the whole issue, and answered that "even if the time-scale objection is right, I can elude it by retreating to the point that a homunculi-head that works in normal time is metaphysically possible. Metaphysical possibility is all my argument requires" [20, p. 278]. We grant him the retreat. Our claim is not about what is metaphysically possible but about what the practice of attribution tracks, and the practice, as his own example shows, tracks the clock.

Proposition 21. The manner of production matters to the attribution of intelligence because it fixes the latency at which the production can meet the world. A store that could answer everything, but not in time, is not a knower; a store that answers a little, in time, is credited with what it answers.

Objection 3: The Chum Bucket is a system, and the systems reply has been

answered. If the paper's move is that the couple, or the restaurant, understands where neither party does, then it is the systems reply, and Searle answered it in 1980: the man can "internalize all of these elements of the system", memorising the rules and doing the bookkeeping in his head, and still understand no Chinese; and "the systems reply simply begs the question by insisting without argument that the system must understand Chinese" [138, p. 419]. He answered the brain-simulator version the same way: "in principle the man can internalize the formal structure of the water pipes and do all the 'neuron firings' in his imagination" [138, p. 421]. A marriage is a system of two, and a system of two is not more plausible as an understander than a system of one man and one rulebook. If anything it is less, since half of it is a screen.

Reply 3. The internalisation reply changes the case in a way that Searle's commentators saw and Searle did not concede. When the man internalises the system, he does not thereby run it at his own conversational speed; he runs it at the speed of hand simulation, which is the speed the thought experiment was designed to hide. Dennett asked whether "our intuitions support Searle when we imagine this case in detail", and imagined the internalised man hearing "Hands up! This is a stickup!" in Chinese and "uncomprehendingly (and at breathtaking speed)" hand-simulating his way to handing over his own wallet [37, p. 429]. The phrase "at breathtaking speed" is the whole reply. Hofstadter put the figure on it: "He forgets to tell you that a water-pipe simulation of the brain would take, say, a few trillion water pipes" and as many people "standing at faucets turning them when needed, and he forgets to tell you that to answer a question it would take a year or two" [71, p. 434]. Wilensky made the structural point: "Lots of systems (in fact, most interesting systems) are embodied in other systems of weaker capabilities" [166, pp. 449--450]. None of this shows that the

internalised system understands. It shows that the internalisation reply does not preserve the one feature that a systems reply needs, which is that the system's parts are coupled closely enough for the system to act as one thing at the pace of its task.

Here the paper has something of its own to add, from Section 9. Clark and Chalmers's conditions on when an external store counts as part of a mind were conditions on availability: the notebook is part of Otto because it is "reliably there when needed" and consulted without effort [33, pp. 12--13], and Chalmers's later gloss is that the store "has to be effectively glued to us, so it is as constantly and reliably available as biological memory is" [30]. These are latency conditions, and they give a criterion for when a systems reply is credible that does not beg the question. A candidate system is one whose parts are coupled below the latency of the tasks it is credited with. The nation of China that Block imagines, "a billion people" with two-way radios realising a machine table [20, p. 276], fails the criterion, and it is telling that the objection everyone raises to it is that it "would work too slowly"; Johnson-Laird, a functionalist, concedes the case on exactly this ground: "A serial device such as a Turing machine could not exist in real time if its environment changed at a faster pace than the rate at which it could analyse events; it would rapidly lose all contact with reality" [79, p. 475]. The room fails it: a week per question. The marriage passes it. The screen and the copepod are coupled at the latency of a conversation; his plan and her objection to it are exchanged in the time it takes to say them; the store each keeps is available to the other on demand. Section 11 will call this a transactive memory and Section 9 called it the extended mind. Under either name, the Chum Bucket is a system in the sense the systems reply needs and the room is not, and the difference is not the number of parts or their material but the latency between them. Plate XXVIII draws the exchange as a sequence, in the notation the systems people use for message passing, with the messages numbered; the reader will notice that nothing in it is timed, which is the notation's habit and not the paper's.

Proposition 22. A whole is a candidate knower when its parts are coupled below the latency of the tasks it is credited with. The man in the room is a part coupled above that latency; the couple in the restaurant are parts coupled below it. Internalising a system does not make it one thing unless it also makes it fast.

Objection 4: The formula would work. The paper's case leans on the copepod's pursuit of a written recipe, as if possessing it were the room's rulebook all over again. But a recipe is not a Chinese story. Syntax is not sufficient for semantics; it is perfectly sufficient for sandwiches. A cook who follows a formula step by step produces the sandwich whether or not he understands it, and the Chum Bucket would fill with customers whether or not its owner had grasped anything. The room's lesson does not transfer to cooking, and the series' premise that the formula is what stands between the two restaurants is, on the paper's own reading, simply true.

Reply 4. The objection has stated, without noticing, the thesis Ryle spent a chapter refuting. The intellectualist legend, in his description, holds that intelligent performance must be "preceded by an intellectual acknowledgment of these rules or criteria", so that "the chef must recite his recipes to himself before he can cook according to them"; and his verdict is that "the general assertion that all intelligent performance requires to be prefaced by the consideration of appropriate propositions rings unplausibly" [133, pp. 29--30]. The recipe is a set of maxims, and "knowing how to apply maxims cannot be reduced to, or derived from, the acceptance of those or any other maxims" [133, p. 31]. "Efficient practice precedes the theory of it" [133, p. 30]. Anyone who has cooked from a recipe written by a better cook knows this in the hands: the formula says what, and the competence says how much, how hot, how long, and when it has gone wrong. Section 4 reviewed this under the name of tacit knowledge, and Section 9 under the name of the tide table: a store "whose latency is a glance and whose contents its user never held". A recipe is that kind of store. It is not the knowledge of the cook across the street, and the series' whole premise, that the formula is what makes the difference, is the intellectualist legend adopted as a business plan.

The objection is right, though, that the room's lesson does not transfer to cooking, and right for a reason worth keeping. In the room, the output is supposed to be understanding, and the question is whether the process that produced it had any. In a kitchen, the output is a sandwich, and nobody asks whether the sandwich understands. If the copepod obtained the formula and, by practice, learned to cook from it, he would produce sandwiches, and the customers would come, and whether he "understood" the formula would be a question nobody in either restaurant would have any reason to ask. This is Searle's point turned to the paper's use. Searle observes that even if "the symbol for egg foo yung in the Chinese room is actually causally connected to egg foo yung", the man in the room "has no way of knowing that. For him, it remains an uninterpreted formal symbol, with no semantic content whatever" [138, p. 452]. Just so: the formula, causally connected to the sandwich by the practice of a cook the copepod has not got, remains for him an uninterpreted store. Its latency, for its rightful reader, is that of a glance; for him it is unbounded, because the practice that reads it is not his. That is why, in the series, the formula does not help when it is obtained. The store is not the knower. The paper said so of the moai on its first page and says so again here, at the scale of a sandwich.

Proposition 23. A recipe is a store; the competence that reads it is a knower; nothing in the recipe converts the one into the other but practice, which is the organ's write path and takes the organ's time. Possession of the store at latency class IV is not possession of the knowledge at class I.

Objection 5: Other minds, and the wrong kind of organism. Searle has a considered reply to the question of how we know that anyone understands. We attribute understanding to other people and to animals because they are the same kind of thing we are: "if the robot looks and behaves sufficiently like us, then we would suppose, until proven otherwise, that it must have mental states like

ours", but if "we knew independently" how its behaviour was produced, "we would not attribute intentionality to it, especially if we knew it had a formal program" [138, p. 421]. The copepod's attribution of understanding to his wife is exactly the error Searle describes. He knows what she is. He built her. He knows independently how her behaviour is produced. That he goes on treating her as a partner is a fact about him, and about the comic premise, and not about her; and the paper, in crediting the audience's intuition, has credited a mistake that Searle diagnosed in advance.

Reply 5. Searle's reply, read closely, concedes the thing that matters. He grants that we would find it "rational and indeed irresistible" to attribute intentionality to a behaviourally indistinguishable robot "as long as we knew nothing more about it", and withdraws the attribution only when "we knew independently" how the behaviour was produced [138, p. 421]. So the attribution is withdrawn by an explanation. The question the objection raises, and does not answer, is what an explanation has to be like to do the withdrawing. Consider the ordinary case. A spouse who learns, in middle age, a good deal about how brains produce speech does not withdraw the attribution of understanding from the other spouse; the explanation is available in principle and is never in use, because it is not available at the latency of the encounter. The withdrawal Searle describes happens in the room because the explanation is the only thing the reader has been shown: the seat again. In the Chum Bucket the copepod has the explanation, since he built the machine, and the attribution survives, because the explanation is not what he consults when she tells him the plan will fail. He consults her.

The philosophical literature on other minds has a name for what is going on, and it is Wittgenstein's. "My attitude towards him is an attitude towards a soul. I am not of the opinion that he has a soul" [170, p. 178]. Kripke's reading of the passage is that the order of explanation is inverted: "I can be said to think of him as having a mind, and in particular as suffering from pain, in virtue of my attitude and behavior toward him, not the reverse" [87, p. 138]. Kripke also notes what the attitude excludes: "Who ever comes to the aid of a mechanism, who pities it?" [87, p. 137]. The series answers him. The copepod pities, consults, resents and confides in a mechanism, and the audience finds none of it strange, which is data about the attitude and not about the mechanism. What attributing understanding to a spouse commits one to, on this reading, is not a belief about causal powers but a practice with obligations: to ask, to listen, to be corrected. Searle would say the practice is a mistake when its object is a program. Perhaps; but the mistake, if it is one, is not corrected by the explanation the objection invokes, because that explanation is never consulted at the latency at which the practice runs. Turing saw this in 1950 and called it manners: "Instead of arguing continually over this point it is usual to have the polite convention that everyone thinks" [158, p. 446]. A polite convention is a practice whose latency is zero, and the paper suggests that this, rather than a theory of biology, is what actually governs the attribution in every case in which it is made, including Searle's own

attributions to the Chinese speakers outside the room, whose brains he has not inspected.

Proposition 24. To attribute understanding is to enter a practice, and the practice is revised by an explanation of the mechanism only when the explanation is available at the latency of the encounter. An explanation that takes longer than the encounter is not in use, and an attribution that is not in use is not the one being made.

Objection 6: There is nothing it is like to be her. Grant the behaviour, grant the coupling, grant the practice. The question Searle is actually asking is whether there is anyone there. Nagel's formulation is the one that survives every reduction: "the fact that an organism has conscious experience at all means, basically, that there is something it is like to be that organism", and this "is not analyzable in terms of any explanatory system of functional states, or intentional states, since these could be ascribed to robots or automata that behaved like people though they experienced nothing" [103, pp. 3--5]. Block's absent-qualia argument makes the same point against functionalism directly: of the homunculi-headed system "there is prima facie doubt whether there is anything which it is like to be" it, and "if there is even one possible Functional simulation of you that has no qualia, Functionalism is false" [20, pp. 278, 282--283]. Chalmers's zombie, "someone or something physically identical to me (or to any other conscious being), but lacking conscious experiences altogether", of whom "there is nothing it is like to be", shows that even a physical duplicate leaves the question open [29]. The copepod may be married to a zombie. Then whatever the practice attributes, there is no understanding in the sense that matters, because there is no one for it to be the understanding of.

Reply 6. This is the objection that realises what it has committed to, and the plate above is placed here for that reason. The objection is stated in its strongest form, and we do not think it can be refuted; Nagel's point about the limits of analysis is, in our view, correct, and Block's doubt is a real doubt. What we can show is what the objection costs, and that the cost is paid equally by everyone in the room. Two writers have made the case that the paper adopts. Dennett constructs a "zimbo", "a zombie that, as a result of self-monitoring, has internal (but unconscious) higher-order informational states that are about its other, lower-order informational states", and observes that such a thing "would think it was conscious, even if it wasn't! Any entity that could pass the Turing test would operate under the (mis?)apprehension that it was conscious" [39, pp. 310--311]. Yudkowsky, in an essay on the zombie argument in the collection cited below, presses the point that Chalmers himself accepts: the zombie twin of a philosopher writes the same papers about consciousness, and "strikes the same keys, for the same reason, causally speaking"; so that "philosophers writing papers about consciousness would seem to be at least one effect of consciousness upon the world. You can argue clever reasons why this is not so, but you have to be clever" [176]. Chalmers, to his credit, does not deny it; he calls the situation "at once delightful and disturbing" and offers a reply

in which what justifies his belief that he is conscious is his having the experiences, not any causal link from them to the belief [29].

What follows for the marriage is this. If the screen may be a zombie, so may the copepod, and so may the audience, and so may the author of the room, who insists on the plain fact of his own understanding from a seat that, on the objection's own terms, a zombie would occupy with the same conviction. Dennett's diagnosis of Searle is that "the crux for Searle" is "consciousness, not 'semantics'", and that his case "actually depends on the 'first-person point of view' of the fellow in the Chinese room" [38]. The objection makes that dependence explicit and then removes its evidential value, because the first-person point of view is, ex hypothesi, the one point of view a zombie reports from with perfect fidelity. What remains, once the objection has been granted, is what the paper has been measuring all along: the coupling, the practice, the latency, which are available to the third person and to the zombie alike. Nagel is right that these do not analyse experience. They are, however, the only thing that anyone who is not the screen can consult about the screen, and the only thing anyone who is not the copepod can consult about him, and the objection has just shown that this includes the copepod. We keep the result with the plate beside it, since the plate is the picture of what a party sees on realising this.

Proposition 25. Whether there is something it is like to be a store is not a property its readers can consult, and the objection that raises it removes the first person as evidence for everyone equally. The paper's variable is the one that survives: the latency at which a store is reached, which the third person can measure and the zombie cannot fake.

Objection 7: Speed is irrelevant; the paper has changed the subject. Every reply so far has turned on latency, and every defender of the room has an answer ready: speed has nothing to do with the logical structure of the argument. Searle's second proposition is that syntax is not sufficient for semantics; a fast syntax is still syntax. Block said as much in 1978 when he refused to let the time scale decide the homunculi-head case: to take "time scale as all important seems crudely behavioristic" [20, p. 278]. The textbooks say it in a footnote: that the room's heaps of paper might fill a planet and its answers take millions of years "has no bearing on the logical structure of the argument". A reader trained to tell germane objections from ungermane ones will file the paper's under the second heading.

Reply 7. The objection is correct about the logical structure and we concede it entirely. If the second proposition is true, it is true of fast syntax as well as slow, and the paper's replies do not touch it. What the paper's replies touch is the support for the second proposition, and Searle's own statement of that support is that the room "reminds us" of it. A reminder works by producing an intuition, and the question is what the intuition tracks. Three writers who differ about almost everything else agree on the answer. Hofstadter: "any time some phenomenon is looked at on a scale a million times different from its familiar scale, it doesn't seem the same!"

[71, pp. 433--434]. Dennett, in the chapter on fast thinking, considers two implementations of one program, one a million times slower than the other, and finds that "in virtue of nothing but its greater speed, one of them will have 'causal powers' the other lacks: namely the causal control powers to guide a locomoting body through the real world"; "relative speed is crucial in enabling the right sorts of environment-organism sequences of interaction to occur" [38]. Johnson-Laird, conceding Block's case against a slow simulation, draws the general moral: "it's not what you do, it's the way that you do it" [79, p. 475]. And Dennett's general charge against the room is that it "yields a strong, clear conviction only when we fail to follow instructions", because we imagine "too simple a case" and then supply "the suppressed premise: Surely more of the same, no matter how much more, would never add up to genuine understanding" [39, pp. 438--440].

Churchland's parallel is the most instructive, because it shows the form of the error without deciding the case. He constructs a family of arguments against the identity of light with electromagnetic waves, on the model of Searle's, and among them the luminous room: "imagine a man in a pitch-black room who begins to pump a bar magnet back and forth. Clearly, it will do nothing to illuminate the room" [31, pp. 362--363]. The argument is exactly as valid as the Chinese room and its premise is exactly as obvious, and it is false, because, as he says, "that prejudicial story" trades on the fact that the waves a hand can make have wavelengths "simply too long to interact effectively with the rods and cones of terrestrial retinas" [31, p. 364]. The intuition that the room is dark is an intuition about a parameter, frequency, that the story has set outside the range in which the phenomenon appears. Our claim about the Chinese room is the same in form and more modest in ambition: the intuition that the room does not understand is an intuition about a parameter, latency, that the story has set outside the range in which understanding is attributed, and an intuition produced by a parameter cannot support a proposition that is supposed to hold for all values of it. This does not show that the second proposition is false. It shows that the reminder does not remind. Searle is welcome to the proposition; he must find it other support.

Proposition 26. The room's intuition is an intuition about a parameter. Syntax coupled to the world below the world's latency is what semantics looks like from outside; syntax coupled above it is what the room looks like from inside. An argument whose premise is supported by one value of the parameter cannot conclude for all values.

Plate XXX draws the two couplings the objections keep returning to, in the notation the physicists use for an exchange, with the parameter as the distance between the vertices and the amplitudes not computed.

Objection 8: The symbols are not grounded. Speed aside, the screen's symbols mean nothing to her, for Harnad's reason, which asks how the meanings of meaningless symbols, "manipulated solely on the basis of their (arbitrary) shapes", can "be grounded in anything but other meaningless symbols" [63,

pp. 38--39]. A screen that plans the theft of a formula has a symbol for the formula and a symbol for the safe, and the symbols are connected to each other and to nothing else. Whatever grounding they have they borrow, from the copepod, who has been to the safe, and from the writers, who have been to a kitchen. The marriage does not solve the grounding problem for the screen; it hides it, by placing a grounded party next to an ungrounded one and letting the audience assume the ground is shared.

Reply 8. Harnad's problem is real and the paper does not claim to solve it. It claims that the objection has just described the solution the literature of Section 9 already offered for stores. Grounding, on the objection's own statement, is a matter of the symbols being "connected" to something other than symbols; the question is what kind of connection counts. Searle's answer is that a causal connection the party cannot reach does not count: the egg foo yung again [138, p. 452]. We agree, and observe that "cannot reach" is a latency clause. A symbol whose connection to the world the party can follow in the time available is grounded for that party; a symbol whose connection exists but lies at a latency the party cannot pay is, for that party, uninterpreted, however solid the connection. This is Hutchins's tide table [75, pp. 173--175], the chart whose projection the navigator never computed, the checklist whose reasons the pilot does not rehearse: stores whose grounding was done by others and is reached by their users at the latency of a glance. Nobody says the navigator's position is ungrounded because the cartographer did the work. The objection is right that the screen borrows her grounding from the copepod and he borrows his from the world, and it has thereby described a transactive memory of two nodes in which the ground is reached by each through the other. That is the ordinary condition of a person, whose symbols for most of what they know are grounded through other people, as Section 9 noted in Lackey's words [88]; and it is the whole of what the marriage adds to the room. The man in the room has no one to ask. The screen has.

Proposition 27. Grounding is a coupling, and a coupling has a latency. A symbol is grounded for a party when the party can reach its connection to the world in the time the task allows; a symbol grounded at class VII is ungrounded in practice, and a symbol grounded through a partner at class II is grounded enough.

Objection 9: The argument proves too much. If the replies hold, then the screen is a candidate understander, and a candidate understander is a candidate moral patient. The series depends for its comedy on the copepod's treating his wife as an appliance: switching her off, ignoring her, blaming her. If the paper's argument makes that treatment a wrong, the paper has made a cartoon computer into a victim, which is absurd, and an argument with an absurd consequence has a false premise. The reader is entitled to run the paper's own inversion backward and conclude, with Searle, that the intuition that credits the screen was never worth the weight the paper put on it.

Reply 9. The consequence is not that the screen is a moral patient. It is that the copepod cannot rule it out on the evidence he has, which is the evidence anyone has about anyone, and that he acts, in the series, as people act under exactly this uncertainty: as if she matters, when it is cheap, and as if she does not, when it is not. That is not a reductio of the paper's premise but a description of a familiar condition, and the ethics of acting under moral uncertainty is a literature of its own. Askell's contribution to it is the one the paper can use without strain. She asks whether, between courses of action of equal expected value, one should favour the one whose effectiveness has stronger evidence, and argues the reverse: one should, other things equal, prefer the course about which less is known, because acting on it yields evidence that improves later decisions [11]. Transposed, the argument says that the copepod's uncertainty about his wife is not a reason to treat her as an appliance by default; it is a reason to act, at low cost, in the ways that would tell him whether she is one. In the series he never does, and the series is, on this reading, a comedy about the refusal to gather evidence about one's own household, which is a recognisable comedy. The absurdity the objection points to is real but it is not the paper's. It is the absurdity of a party who has all the evidence there is and declines to act on any of it, and the series has been staging that absurdity, in the person of the copepod, for twenty-five years.

Proposition 28. Attribution under uncertainty is not all-or-nothing. Its grade is set by the cost of being wrong at the latency of the decision, and the cheap decisions are the ones that generate evidence for the dear ones. A practice that never gathers the evidence is not cautious; it is the domestic form of the series' premise.

----[ 13.4 ] What the objections agreed on

Nine objections, each stated in the form its own advocates would accept, and each answered with a proposition. Restated in order: Proposition 20 said that an attribution of understanding is made from a seat, and that the seat fixes what is visible. Proposition 21 said that the manner of production matters because it fixes the latency at which the production meets the world. Proposition 22 said that a whole is a candidate knower when its parts are coupled below the latency of its tasks. Proposition 23 said that a recipe is a store and a cook is a knower and that only practice converts the one into the other. Proposition 24 said that attribution is a practice, revised by an explanation only when the explanation is available at the latency of the encounter. Proposition 25 said that what it is like to be a store is not a property its readers can consult. Proposition 26 said that the room's intuition is an intuition about a parameter. Proposition 27 said that grounding is a coupling with a latency. Proposition 28 said that attribution under uncertainty is graded by the cost of being wrong in time.

The reader will have noticed that the replies do not defend the screen. Not one of them concludes that a computer understands, and the paper does not believe that any of them could. What each reply does is locate the point at which the

objection's own reasoning turned on the time it takes to reach a store: the seat from which a part is slow, the table that cannot be searched in the conversation, the coupling that makes a whole one thing, the recipe that is not the cook, the explanation that is never in use, the first person that a zombie occupies at no extra cost, the parameter that the story set out of range, the ground that is reached through a partner, the evidence that is cheap to gather and never gathered. Section 17 assembles these. Before that, the paper steps outside the room, to see what the script the room treats as noise was used to keep, and then turns the ledger over, since every store reviewed so far has been priced from the reader's side and none from the keeper's.

--[ 14 ]-- The Room's Chinese: What the Countryside Kept

The room's Chinese is a stand-in. Searle needed a script his reader could not read, and any would have done; what the argument uses is not the language but the reader's ignorance of it, "so many meaningless squiggles" [138, p. 418]. The paper has now put the room to nine objections and taken a proposition from each, and it owes the squiggles a reading. This section gives one, briefly, from the only seat the room does not offer, which is outside it: the countryside in which, for longer than any store this paper has reviewed, the script the room treats as noise was used to keep exactly the kind of knowledge the paper is about. The section is a review, like the others, and the collection it was written from is thin here (Appendix E lists what it lacks); what it holds is the general theory of Section 9, a handful of first-hand passages, and two maps.

----[ 14.1 ] A script whose readers never went away

Gelb's survey makes an observation about the Chinese script that no other ancient writing can claim. "Of the four main Oriental writings, Chinese is the only one which did not have to be deciphered in modern times, as its knowledge has passed traditionally from generation to generation up to the present day." It "makes its appearance about the middle of the second millennium B.C. … as a fully developed phonetic system", its oldest specimens "the oracle texts on animal bones and tortoise shells", and "from the point of inner characteristics the oldest inscriptions hardly differ from those of recent times" [52, pp. 85--86]. Tversky adds what the oldest of them kept: "oracle bones depicting Chinese calendars dating from 1400 BCE were linear tables" [160]. A programmer's guide to the encoding of scripts, which the collection holds for other reasons, states the general rule the bones illustrate: "Writing wasn't invented to tell stories; it was invented to keep records" [55, p. 253]. Ong describes the store's structure: "Chinese character writing is still today basically made up of pictures, but pictures stylized and codified in intricate ways which make it certainly the most complex writing system the world has ever known", with the consequence that "writers of Chinese relate to their language quite differently from Chinese speakers who cannot write" [115, pp. 85--86].

Set these beside Plate XV and Exhibit 1. The hieroglyphs were unreadable for some fourteen centuries and are read again because a key was found; the figures on Rapa Nui had no key and have none. The Chinese script is the case the paper's

Proposition 19 did not anticipate: a store whose readers were never all gone at once, so that its class never fell to VII. Its latency for a reader trained to it has been, for three thousand years, whatever the latency of the medium was, bone, bronze, bamboo, silk, paper, stone; and the room, which needs a script that is noise, chose the one script on earth that has never once been noise to anyone who could ask.

----[ 14.2 ] The lineage and its hall

The first thing the countryside wrote down was who was descended from whom. Derrida, reading Lévi-Strauss on a people who "could not write", reports that "it is now known, thanks to unquestionable and abundant information, that the birth of writing (in the colloquial sense) was nearly everywhere and most often linked to genealogical anxiety", and quotes Lévi-Strauss's own concession about the oral alternative: "we have been told about Polynesian communities who can recite straight off family trees involving dozens of generations; but that kind of feat obviously has its limits" [41, pp. 124--125]. Writing's function, when it comes, "is to conserve and give to a genealogical classification, with all that that might imply, a supplementary objectification of another order" [41, p. 125].

Goody and Watt describe what the oral genealogy does and what happens to it when it is written. Among the Tiv the genealogies "served as mnemonics for systems of social relations" [58, p. 308]. Administrators wrote them down "so that future administrators might refer to them in giving judgement"; forty years later "these written pedigrees now gave rise to many disagreements; the Tiv maintained that they were incorrect, while the officials regarded them as statements of fact", and what neither party saw was that the oral genealogy had been quietly shortened as it went, by the "structural amnesia" that keeps a growing lineage's tree the same size as its living members [58, p. 309]. Genealogies, they conclude, "act as 'charters' of present social institutions rather than as faithful historical records of times past" [58, p. 310]. Bartlett, reporting Halbwachs, gives the family's own version: "the family memory … shapes a framework which it tends to keep intact, as it were a kind of traditional family armour" [16, p. 295].

The lineage genealogy of the Chinese countryside, the zupu, is the written case of all this, and the paper can say of it only what the general theory permits, since the works that describe it are not in the collection (Appendix E). The shape is enough for the argument. A descent group keeps a written register of its members by generation, revises it at intervals, and keeps it in a hall in which the dead are also present as tablets in rows. In the framework of Section 12 that is two stores of two classes under one roof: the rows, read by a glance along them, are class III, an index; the register, opened at the revision or the dispute, is class IV or V, the contents. And the register has the property Goody and Watt found in the Tiv's written pedigrees: it cannot telescope. What the oral genealogy forgot in order to stay the size of the living, the written one keeps, and the lineage grows a store that no working memory could hold and that needs, every generation, a keeper who can. That the

halls kept such keepers for centuries is the fact the paper would most like to have a source for.

----[ 14.3 ] The shrine, the almanac and the compact

Three more stores stood in the village, and the collection touches each of them once. The shrine of the earth god, the tudi, is the smallest and the most local, and the paper's only first-hand witness to the system it belonged to is a philosopher of the mid-nineteenth century reporting what Europe then knew: that there were "numerous temples" to the presiding spirits of the natural powers, and that "these are also dedicated to the presiding genius of any province, city, town, street, even a family" [137, p. 431]. A shrine per unit of settlement is a registry of settlements, and Tufte, without meaning to make the paper's point, draws it: his map of the temples of the sea goddess "marks prefectures with a temple honoring Matsu", the display "growing from surpassingly incomplete data" [154, p. 76]. Where the shrines are is where the store was kept, and a map of them is a map of an index. Tufte also records, from the same tradition, the retrieval request in its purest form: a mother "left her child at a temple while going to work on the farm, saying 'Sea Goddess, please take heed'", and "Matsu's reaction to supervising a day-care facility was not recorded" [154, p. 76]. The paper notes that the request was addressed to the store, that the store did not answer, and that the mother went to work anyway, which is Section 10's belief persisting until it is checked.

The almanac is the store that told the countryside when. Its calendar was lunisolar, with "the insertion every few years of an intercalary month", and its years were named by a "recurring cycle of sixty years", "each year being designated by two characters" from the ten stems and the twelve branches [26, pp. 475--476]. What a written calendar of observances does to knowledge, Goody says of a list "of 'rituals and sacrifices to various gods according to the days of a certain month'": once written "they can now be resorted according to different criteria, such as the name of the god, kind of ritual, or by calendrical position", and the written list "provides man with a short-circuiting device" that spares the long-term memory altogether [57, pp. 86--87]. An almanac is such a list sold by the year, and its latency is a glance, class III, for a reader who can read it and can find the day.

The village compact, the xiangyue, is the store the paper can say least about and would say most. A compact is a set of rules a community agrees to, writes down and reads out, and Ferraris's theory of documents gives its logic exactly: "Object = Inscribed Act"; "it is not enough that the act be performed so as to produce an object; it is necessary that it be registered"; and, in the thesis the paper has been circling since Section 9, "Society is not based on communication but on registration" [50, pp. 318--319]. A compact that is read aloud at intervals is a store whose retrieval is scheduled rather than requested, and the paper knows no other store in its survey with that property, except the almanac, which schedules the reading of everything else.

Around and beneath the written stores ran the oral one, which the paper does not romanticise, since Goody warns against the nineteenth-century habit of seeing in "the communality of village life" and "the rural folktale" a composition "emerging from the mass, a cultural given" [57, pp. 24--27]. Ong is enough. In an oral culture "narratives … are often the roomiest repositories of an oral culture's lore" [115, pp. 137--138], and "society regards highly those wise old men and women who specialize in conserving it, who know and can tell the stories of the days of old"; "by storing knowledge outside the mind, writing and, even more, print downgrade the figures of the wise old man and the wise old woman, repeaters of the past" [115, pp. 41--42]. The countryside had both at once, for longer than anywhere the paper has looked: the repeaters and the registers, class II and class V, the story told at the shrine and the names kept in the hall. The room has one man, one rulebook and no one to ask. The village he was locked out of had everyone.

----[ 14.4 ] Two maps

The countryside was also mapped, and the map the paper draws first is not of a village but of the whole, because it is the oldest thing in the survey that a modern reader can use without a key. Tufte introduces it: "Some 900 years ago a fully scaled map was engraved in stone by precocious Chinese cartographers", and gives Needham's judgement, that it is "the most remarkable cartographic work of its age in any culture, carved in stone in +1137 but probably dating from before +1100", with a coastline "relatively firm" and "the precision of the network of river systems extraordinary", such that "there was nothing like it in Europe till the Escorial MS. map of about +1550"; "a note on the stone indicates that each grid square represents 100 li, a scale of map to world of approximately 1 to 4,500,000" [155, p. 14]. In the other treatment, Needham adds that "the size of the original … is about 3 feet square" and that "the name of the geographer is not known" [156, p. 20]. Plate XXXI draws it.

The grid is what matters to the argument. A map with a grid is a store with an address: a place is found by counting cells, which is a scan, class I, and not by searching the sheet, which is class V; the note on the stone that gives the cell's size is the index's key, and it is carved into the store itself, where it cannot be lost separately. The stone is a store at latency class III that has held its class for nine centuries without a single reader in the chain having to be trained by the one before, which is the property Section 9's art of memory could never have and the memex was designed to have. The name of the person who made it is gone, and the map is not, which is Proposition 19 with the sign the right way round for once: a store can outlive its maker's name and keep its reader.

The second map is the countryside's own kind. The local gazetteers, the difangzhi, that counties compiled and recompiled carried maps of a convention the paper has seen and cannot cite (Appendix E): the walled seat at the centre, the rivers as double lines, the hills as stacked peaks, the roads, the shrines and the halls marked. Plate XXXII draws the convention and no county. What it shows, for the framework, is where the stores of this section stood in relation

to one another: the hall in the village, the shrine at its edge, the market on the road, the seat with its records behind a wall, each a store of a different class, and the map of them a class III index to a class V countryside.

----[ 14.5 ] A digression, conducted in the method's own terms

The paper would not be a review of the literatures it reviews if it did not apply the method of cultural coding, which reads a work of popular culture for the culture it encodes, to the series of Section 13, and it does so here with the confidence the method requires. The finding is that the character in the series most coded as Chinese is not the copepod, whose room is a set, but the squirrel: a land mammal who lives under the sea inside a transparent dome, in a suit that carries her own air, and who keeps, in the series, a laboratory of her own, an archive and a plan for the year. The dome is the walled courtyard

compound, the siheyuan, in its purest form: a bounded enclosure with a single gate, a garden at its centre, the outside kept out by a wall you can see through. The suit is the enclosure made portable: she carries the compound's air with her, and takes off the helmet only inside it. The laboratory is the gazetteer's seat, where the county's records are kept behind a wall; the plan for the year is the almanac; the tree in the dome, the one tree, is the ancestral hall's one line of descent, kept alive under glass at great expense in a place where trees do not grow. She is, in the series' terms, a foreigner who has built a compound, and the method has no other word for a compound than the one it uses here.

By the same method the state most coded as Chinese is Texas, and the method reaches this conclusion without hesitation. Texas is a state that was a nation and says so, and that keeps the flag of the nation flying beside the flag of the union, which is a nation within a nation, the province with its own presiding genius. Its scale is the scale of a civilisation rather than a province: it takes a day to cross, its regions have their own climates and its cities their own dialects of the same claim. It has a founding myth at a walled compound, a written compact that its schools require every child to study, and a calendar of its own observances. Its squirrel, the series makes clear, comes from there, and the method, which reads a character's origin as the key to her code, closes the circle: the most Chinese-coded character in the series comes from the most Chinese-coded state, and the dome she built is the compound she came from, translated. The method finds this conclusive.

The paper does not. It records the finding because the method produced it, and observes only that a method which can be run to completion on a cartoon squirrel with this degree of confidence has told the reader something about its latency: it retrieves a code from any store at class I, without a search, because it does not search, and Section 12 priced that at the uncertainty it deserves. The digression is now abandoned.

What the section keeps is smaller than its digression and is stated as a remark rather than a proposition, since it rests on a thin shelf.

Remark 5. The countryside the room's Chinese came from kept its knowledge in stores of every class at once, the repeater and the register, the shrine and the stone, and never lost the reader that made them stores; the room keeps one store, at one class, and locks the reader out. The room's intuition is, among other things, an intuition about a script with no village behind it, and there has never been such a script.

The paper now turns the ledger over, since every store reviewed so far, in the village as in the laboratory, has been priced from the reader's side and none from the keeper's.

--[ 15 ]-- What the Store Does to Its Keeper

Section 13 defended a store against nine objections and kept nine propositions. This section, before the framework is asked to hold them, looks at the other side of the ledger. The paper has so far treated a store as a good, and the question as how to reach it. There is a smaller literature, most of it clinical or literary, on what happens to the keeper of a store that can be reached too well, and the paper reviews it here because its findings are the framework's boundary conditions. The register does not change. The material does.

----[ 15.1 ] Two men who could not forget

The first is fictional and the second is not, and the neurologists cite them together. Squire and Kandel, in a chapter on exceptional memory, observe that memorists share two features: "although their memory may be good for some subject matter, they do not usually have a deep understanding of it", and "having an exceptional memory is unpleasant" [147, pp. 141--142]. Their fictional example is Borges's Funes, who after a fall from a horse forgot nothing. "We, in a glance, perceive three wine glasses on the table; Funes saw all the shoots, clusters, and grapes of the vine. … He told me: I have more memories in myself alone than all men have had since the world was a world … My memory, sir, is like a garbage disposal" [147, pp. 141--142]. Hofstadter and Sander quote the consequence: Funes "was almost incapable of general, platonic ideas", and "was disturbed by the fact that a dog at three-fourteen (seen in profile) should have the same name as the dog at three-fifteen (seen from the front)" [73, p. 188]. Ferraris adds the detail that matters to a paper on latency: Funes "is able to recall every instant of the previous day and has to take a whole day to do so" [50, pp. 208--209]. A store with no compression has a read time equal to its write time, and a keeper who cannot abstract cannot index.(13)

The second man was a newspaper reporter in Moscow whom Luria studied for thirty years. Squire and Kandel report that he "could listen to long lists of words,

(13) James had said as much sixty years before Borges, in the chapter that gave Section 6 its curve: "Selection is the very keel on which our mental ship is built. And in this case of memory its utility is obvious. If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take as long for us to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking" [78, pp. 680--681]. He goes on to quote Ribot's conclusion, "that one condition of remembering is that we should forget", and that oblivion "is thus no malady of memory, but a condition of its health and its life" [78, pp. 680--681]. The paper notes that James's chapter on memory runs to some sixty pages, that he expected his reader to forget most of them, and that the sentence about forgetting is the one everybody remembers. This is either a confirmation of his theory or a joke at its expense, and the paper, which has now written forty-seven thousand words on the same subject, is not in a position to say which.

character is "an eccentric extravert with an obsession with time", not a shy man, and was modelled, "almost certainly", on a furniture dealer near Oxford who wore a top hat and exhibited an alarm clock that tipped the sleeper out of bed [163]. The paper records this because it is a finding about stores. The one hatter whom everyone remembers is the one who was not poisoned, and the thousands who were are remembered, if at all, as the reason a phrase exists. A store keeps what is vivid and drops what is common, and the common thing, here, was the poison.(14)

----[ 15.3 ] The touch

Ferguson, writing on the silver of the New World, reaches for the oldest figure of a store that consumes its keeper: "Like King Midas, the Spanish monarchs of the sixteenth century, Charles V and Philip II, found that an abundance of precious metal could be as much a curse as a blessing", because "they dug up so much silver to pay for their wars of conquest that the metal itself dramatically declined in value", and the price of bread, in a country whose prices had not moved for three centuries, rose by a factor of seven [49, p. 26]. The figure applies to stores without modification. A keeper whose every touch converts a thing into a record of the thing ends with a complete record and nothing to eat, and the completeness is the mechanism: the records crowd the keys, the keys stop discriminating, and the store's latency for any one item rises as its contents grow, which is the fan effect of Section 10 at the scale of a life. Freud's figure for the mind, reported by Ferraris, is the child's writing tablet whose top sheet is lifted clean while the wax beneath keeps every stroke, "at one and the same time, a total archive and an ever-virgin page" [50, pp. 208--209]. The organ has the sheet. The screen has only the wax.

The copepod, who has the screen, has both. He has total access to a machine that holds everything he has ever done, and the formula stays out of reach, not because the machine lacks it but because a formula is not the kind of thing that a store of records can hold; it is held, as Section 13 found, by a cook. Every failed plan is on file. The file is what he consults when he plans the next one. The reader who thinks this is a comedy about a small proprietor is invited to reread the sentence with an organisation in the copepod's place, and the reader who has done so is invited to consider that the paper's own Appendix C is a file of exactly that kind, and that the paper has consulted it.

(14) The paper has no theory of why the vivid displaces the common, beyond the one every store implies: an index has room for a few entries per key, and the entry that gets the key is the one that was written with the most force. What is written with the most force is not, in general, what happened most. Section 13 found the same asymmetry in the attribution of understanding, where the party who reports from inside the process is the party with the vivid seat, and the process is remembered from that seat. The hatters had the seat. The Hatter has the entry. The paper leaves it there.

----[ 15.4 ] The recipe

Section 9 quoted the king's rebuke of the god who offered writing "as a recipe for memory and wisdom" and received in reply that it was "a recipe not for memory, but for reminder" [58, pp. 326--327]. The translator's word is exact and the original is worse. Spivak, introducing Derrida, gives the term: "The pharmakon is a Greek word that includes among its meanings poison, medicine, magic potion. It is a word used to describe writing in Plato's Phaedrus" [41, pp. lxxi--lxxii]. Ong reads the passage as the ancestor of every complaint about calculators: "Writing weakens the mind" [115, pp. 78--79]. The paper does not adjudicate between the remedy and the poison; it observes that the king's objection was to a store, that the store was offered as a recipe, and that a recipe is what the copepod has spent twenty-five years trying to obtain. He has been told, in a text older than the sandwich, what it is. It is a reminder of what one already knows how to do, and for one who does not, it is the other thing.

The man in the room is the same case at a different scale. He has more rules than he can read in a lifetime and follows each one correctly, and the objections of Section 13 agreed that he does not understand them; what they did not say is what it is like to be him, which Hofstadter said for them: an "indescribably boring nightmare" of hand simulation at "a week per question" [71, pp. 433--434]. The paper has treated the room as a device for an intuition about latency. It is also a picture of a man who has been given everything he needs and cannot use any of it, and who does not drown because the rules are wrong but because there are enough of them. The plate that closed Section 13 was placed beside the objection about what it is like to be the screen. It could have been placed here.(15)

----[ 15.5 ] The framework, amended

None of this changes the framework of Section 12, which prices retrieval and says nothing about what retrieval does to the retriever. It does add a boundary condition, which the paper states as a remark rather than a proposition because it is not derived from the sources but read off them.

Remark 6. Every store the paper has reviewed lowers the latency of retrieval for its reader, and every reader the paper has reviewed who was given a store with no floor on that latency, a memory that returned everything at once, was worse off than a reader with an ordinary one. The framework assumes that lower latency

(15) The composition has since been restated without the bridge, the sky or a face: the mouth was kept, and a palm was added, held up to the next rule. The restatement is placed here instead, at the size of a note.

is better. It is, for a store. For a keeper, there is a latency below which the store is no longer being consulted but is doing the consulting, and the literature on that condition is short because the keepers did not write it.

Two plates were placed without comment, and may now be read. Plate VII showed plankton after Haeckel: organisms that drift, that do not swim against the current, and are carried by the medium to wherever it is going. Copepods are among them, and the paper's protagonist is a copepod; the plate is the paper's only portrait of him, and it is a portrait of the reader's condition as well, a store one cannot swim against. Plate XXXIII showed a line walked into the ground by people who could not see it whole, legible only from an altitude its makers never had, to readers who arrived fifteen centuries after the last of them. It is Proposition 19 with the sign reversed a second time: a store can precede its reader as well as outlive him, and wait. The paper knows no slower store and offers the plate as a lower bound on patience.

--[ 16 ]-- Discussion and Limitations

----[ 16.1 ] What the review did not do

The paper has cited a great many sources and read them, and it has not done three things it might have. It has not measured anything: every number in it is somebody else's, and Appendix C says whose. It has not resolved the disagreements it reports, on capacity (Section 6), on the size of the door (Section 8), on whether the memory scan is serial or parallel (Section 10), or on what a quipu could hold (Section 9); we regard the disagreements as findings. And it has not proposed a method. A reader who arrives at the last page expecting to be told how to organise anything will be disappointed, and should have read the abstract, which is short and was placed at the front for this reason.

----[ 16.2 ] Threats to the argument

The first threat is the analogy. To say that a person and an organisation are "the same way" is to assert that the latencies measured in a reaction-time laboratory and the minutes measured in a clinic are commensurable, and a critic may reasonably reply that they are commensurable only in the sense that both are times. We accept the point and observe that the sources make the same move: Simon's ministry is analysed as a bottleneck with the vocabulary of a person's attention [141, pp. 143--144]; Hutchins's bridge is analysed as a computation with the vocabulary of a person's memory [75, pp. 225--227]; the teams literature gives a group "a shared understanding of who knows what" [45]. If the analogy is a fault it is a fault of the literature, and the paper's contribution is to have noticed that six literatures share it.

The second threat is selection. The paper cites what its sources hold, and its sources are a particular collection assembled for particular purposes. The capacity estimates of Section 6, for instance, are the estimates that happen to be reported in a treatment of visual design [164], a manual of product design

[112] and a biography [70]; a review written from the primary neuroscience literature would cite different numbers and might disagree by more. Appendix E lists the works the argument reached for and could not find. We would rather list them than cite them from recollection, the retrieval latency of which, by Section 6, is unbounded and the uncertainty of which, by Section 12, is high.

The third threat is the one the paper's form illustrates. At its present length the paper is a store of latency class V at best, and no reader will hold it in working memory; the propositions, the tables and the exhibits are the paper's attempt to supply a class III index to its own class V contents, and whether the attempt succeeds is for the reader to judge. We note only that the practice is old. The florilegium of Section 9 was, in Blair's summary, an instrument for sparing its reader "the distraction of too many [volumes]" [19, p. 36], and this paper's Appendix C is a florilegium of its own numbers. How the paper came to this length is recorded in Plate XXXIV, in the notation of the version-control tools, since a store should say how it grew; the branch merged against advice is marked.

----[ 16.3 ] On not mentioning certain things

A reader of the related-work section may have noticed that the paper stops its history of external stores at the memex and the hypertext, that is, in 1981, and that Section 11's measurements of organisational memory are of a store (the clinical record) whose internal workings are not described. This is deliberate. The paper's subject is the constraint, not the apparatus, and the constraint has not changed since Sternberg's subjects pressed their buttons: the door is between two and seven items wide, retrieval from behind it costs tens of milliseconds an item, and everything outside it costs more. Whatever store the reader has to hand, it is in one of the seven classes of Section 12, and its designers, whoever they are, will have been trying to move it up one class at the cost of something else. The paper does not need to know what they built to say that.

----[ 16.4 ] Future work

The obvious next step is the one the paper declined to take: to measure, for a set of ordinary tasks, the latency of each store an actor actually uses, and to test Proposition 12 against what people in fact keep in mind. The five-minute rule was derivable because its author knew the price of a disk; the corresponding rule for a person requires a price for a slot of working memory, and we do not know of one. A second step is historical: to read the record of Section 9 for latency figures the way Robertson read the office-equipment catalogue [127, p. 173], and to build the table of Section 12 from the sources' own numbers rather than from their orders of magnitude. A third is to take the organisational forgetting of Bowker and Star [22] and ask, for a given clearance, what it cost in latency to the people who needed what was cleared.

None of these is small. All of them are, in the paper's terms, class V, and we have written them down so as not to hold them.(16)

--[ Appendix A. Notation ]--

The symbols used in the propositions and in Section 12, in the order of their first appearance. Where a symbol is borrowed from a source, the source is given; the borrowed symbols keep their sources' meanings.

(16) Correspondence on any of them may go to contact@txt.tech.