Archive for October, 2004

Picture: Kangaroo. Walking along one day on the newly-discovered coast of Australia, Captain Cook saw an extraordinary animal leaping through the bush.
“What’s that?” he asked one of the aborigines accompanying him.
“Uh – gangurru.” he replied – or something like that. Captain Cook duly noted down the name of the peculiar beast as ‘Kangaroo’.
Some time later, Cook had the opportunity to compare notes with Captain King, and mentioned the kangaroo.
“No, no, Cook”, said King, “the word for that animal is ‘meenuah’ – I’ve checked it carefully.
“So what does ‘kangaroo’ mean?”
“Well, I think,” said King “it probably means something like ‘I don’t know’…”

But it was too late, and so ever since,  the English word ‘kangaroo’ has been based on a misunderstanding, and really means ‘I don’t know’. At any rate, that’s how the story (probably apocryphal) goes.

It may well have been this story which Quine had in mind when he came up with the ‘Gavagai’ example used in ‘Word and Object’. The word has achieved a kind of fame in itself: there is now a species of beetle named after it, and it was used by Umberto Eco as the name of a minor character in his novel ‘Baudolino’.

Quine was concerned to give a fundamental explanation of how we manage to use words: ‘how surface irritations generate, through language, one’s knowledge of the world’. He addressed in particular the problem of radical translation – how we can find a translation for words in an entirely unknown language which has no known correspondence with our own. Utterances such as ‘ouch’, he suggested, are relatively straightforward – the word properly corresponds with the occurence of pain. But other words, even nouns, do not correspond so exactly to the pattern of stimuli we happen to be experiencing at the time.

Suppose we have a linguistic explorer and a native subject: a rabbit runs past and the native exclaims ‘Gavagai!’. The linguist forms the reasonable hypothesis that ‘Gavagai’ means ‘rabbit’, but how can he be sure? Putting aside some difficulties about ‘yes’ and ‘no’, he can ask the native in a series of different situations the simple question ‘Gavagai?’ and see what responses he gets.

Quine wants to build up from ‘stimulus meaning’, which is equivalent to a list of all the stimuli which would prompt the native to say ‘yes’ in response to the stereotyped question, to more complex and natural kinds of meaning – ‘occasion sentences’ which are true in particular sets of immediate circumstances (eg when a rabbit is present) and ‘standing sentences’ which are true irrespective of what happens to be going on around us at the moment, for example.

But the upward path proves unexpectedly difficult. As a matter of fact, the native’s tendency to agree may be influenced by extraneous factors – he may have seen a rabbit a few minutes before and hence be prepared to accept a mere rustling in the grass as sufficient evidence. Or he may observe a characteristic ‘rabbit fly’ unknown to the linguist which betokens the presence of a rabbit even in the absence of any other evidence. Or perhaps he dissents, not because he thinks there isn’t a rabbit, but because he presumes the linguist to be a hunter and there isn’t at the moment a clear shot available.

But even if we can get round these difficulties, there simply is no guarantee that any finite set of observations pin down the correct meaning of the word ‘gavagai’. Even if we can establish identity if stimulus meanings, we cannot thereby verify ‘intrasubjective synonymy’ of ‘gavagai’ and ‘rabbit’. The native may use the word in exactly those situations in which the linguist would use the word ‘rabbit’, but it could still mean something different: ‘temporal section of a rabbit’ or ‘set of undetached rabbit parts’. For that matter, it could mean ‘rabbit or dalek’ or ‘rabbit before the year 3000 and bear after that’. Ultimately Quine affirms the ‘indeterminacy of translation’ – we cannot provide certain radical translations (and since translation is, for Quine, much the same as understanding, we can never be sure we have correctly understood any linguistic utterance either).

A natural reaction to this disastrous conclusion is incredulity. Yes, of course, some degree of uncertainty attaches to everything; yes, we can always come up with a fantastic alternative meaning for any sentence which is logically consistent with the circumstances, but so what? We just know that in practice translation is possible. There are two things which can be said in reply.

First, problems of translation and misunderstanding are not as exceptional as all that. It would be entirely possible for an Englishman and an American to have lengthy conversations about robins without realising that the word refers to entirely different birds on different sides of the Atlantic (hence, in part, the bemusement which generally creeps over a British audience during one particular scene in ‘Mary Poppins’); or indeed, to talk about turtles without realising that one used the word in a significantly more inclusive sense than the other.

But second, Quine never denied that in ordinary conversation and translation we seem to manage pretty well – the question is how, exactly? It’s not difficult to explain that once you have seen enough examples of the use of ‘gavagai’ the meaning becomes obvious – but stating exactly how it becomes obvious, and how all those implausible alternatives are recognised as implausible, is extremely difficult, as the creators of translation programs have found. One can liken Quine’s attitude to translation to Hume’s puzzlement over induction – it seems to work: indeed, without it we should be in grave difficulty, but why it works is an utter mystery.

To quote one last practical example, we can return to poor old Captain Cook. Although the legend of his misunderstanding still thrives, it appears from more recent research that in fact the word he heard all those years ago probably did mean ‘kangaroo’ in a particular local dialect after all. So what about Captain King’s ‘meenuah’? It turns out that the word he was reporting was probably one that meant, not ‘kangaroo’, but ‘edible animal’…

Picture: Lull. Machines that deal with numbers and perform useful calculations have a long history, gradually increasing in power and flexibility over the course of several centuries. Machines which deal intelligently with words, and produce sensible prose, however, seem like a relatively recent aspiration. There were simple humanoid automata in Descartes’ day, and impressively sophisticated ones during the eighteenth century: such ‘robots’ naturally gave rise to the speculation that they might one day speak as well as mimic human beings in other ways. But surely Turing was the first person to propose in earnest a machine which could produce worthwhile words of its own?

There were, of course, many more or less mechanical ancient systems designed to produce oracles or mystical insights. The I Ching is one interesting example: the basic apparatus is a collection of texts, with the appropriate one for a given occasion to be looked up using randomly-generated patterns. (the patterns are produced by throwing sticks, though coins and other methods can be used). If that was all there was to it, it would seem to be more or less computational in nature, albeit very simple – not very different, in some ways, to the sortes Virgilianae, the Roman system in which a random text from Virgil was taken as oracular. Leibniz took the symbols which identify the I Ching texts, which consist of sets of broken and unbroken lines, to be a binary numbering system, which would strengthen the resemblance to a modern program. In fact, although the symbols do lend themselves to a binary interpretation, that isn’t the way they were designed or understood by the original practitioners. More fundamental, the significance of the results properly requires meditation and interpretation; it isn’t really a purely mechanical business.

It is just conceivable (I think) that Roger Bacon considered the possibility of a talking machine. There is an absurd story of how he and another friar constructed a brass head which would have pronounced words of oracular wisdom had not their servant botched the experiment by ignoring the vital moment when the head first spoke. This tale was perhaps influenced by earlier stories about mechanical talking heads, such as the bull’s head Pope Silvius (an innovative mathematician, interestingly enough) was said to have had, which would return infallible yes or no answers to any question. There is no evidence that Bacon ever contemplated a talking machine, but a procedure for generating intelligible sentences would have been the sort of thing which might have interested him, and I like to think that the brass head story is a distorted echo of some long-lost project along these lines.

In any case, there is one incontrovertible example from about the same time; Ramon Llull’s Ars Magna provides a mechanical process for generating true statements and even proofs. Llull, born around 1232, enjoyed a tremendous reputation in his day, and was famous enough to have had his name anglicised as ‘Raymond Lully’. He was better acquainted with Jewish and Arabic learning than most medieval scholars, and may possibly have been influenced by the Kabbalistic tradition of generating new insights through new permutations of the words and letters of holy texts. He wrote in both Arabic and the vernacular, and among other achievements is regarded as a founding father of Catalan literature.

The Ars Magna has a relatively complex apparatus and uses single words rather than extended texts as its basic unit. The core of the whole thing is the table below.

Questions Subjects Virtues Vices
B Goodness Difference Whether God Justice Avarice
C Greatness Concord What Angel Prudence Gluttony
D Eternity Opposition Whence Heaven Fortitude Luxury
E Power Priority Which Man Temperance Pride
F Wisdom Centrality How many Imaginative Faith Sloth
G Will Finality What kind Sensitive Hope Envy
H virtue Majority When Vegetative Charity Anger
I Truth Equality Where Elemental Patience Untruthfulness
K Glory Minority How – with what Instrumental Piety Inconstancy

Llull provides four figures in the form of circular or tabular diagrams which recombine the elements of this table in different ways. Very briefly, and according to my shaky understanding, the first figure produces combinations of absolute principles – ‘Wisdom is Power’, say. The second figure applies the relative principles – ‘Angels are different from elements’. The third brings in the questions – ‘Where is virtue final?’. The fourth figure is perhaps the most exciting: it take the form of a circular table which is included in the book as a paper wheel which can be rotated to read off results. This extraordinary innovation has led to Llull acquiring yet another group of fans – this is regarded as the forerunner of pop-up books. The fourth figure combines the contents of four different table cells at once to generate complex propositions and questions.

The kind of thinking going on here is not, it seems to me, all that different from what goes into the creation of simple sentence-generating programs today, and it represents a remarkable intellectual feat. But the weaknesses of the system are obvious. First, the apparatus is capable of generating propositions which are false or heretical, or (perhaps more worrying to us) highly opaque, open to various different interpretations. Llull implicitly recognises this: in fact, to perform some of the tasks he proposes – such as the construction of syllogisms – a good deal of interpretation and reasoning outside the system is required: the four figures alone merely give you a start. Second, the Ars Magna is quite narrowly limited in scope – it really only deals with a restricted range of theological and metaphysical issues. Of course, this reflects Llull’s preoccupations, but he also remained unworried by it because of two beliefs which then seemed natural but now are virtually untenable. One is that the truths of Christianity are ultimately as provable as the truths of geometry. The other is that the world is fully categorisable.

Llull’s system, and many others since, is ultimately combinatorial. It simply puts together combinations of elements. In order to deal with the world at large successfully, such a system has to have a set of elements which in some sense exhaust the universe – which cover everything there is or could be. When we put it like that, it seems obvious that there is no way of categorising or analysing the world into a finite set of elements, but the belief is a tenacious one. Even now, some are tempted to believe that with a big enough encyclopaedia, a computer will be able to deal with raw reality. But any such project sends the finite out to do battle with the infinite. Perhaps it would help to realise just how old – how medieval – this particular project really is.

Picture: Richard M. Pico. Roger Penrose and Stuart Hameroff have famously suggested that consciousness is inextricably connected with quantum effects (albeit ones which we don’t yet understand). Richard M Pico, less famously so far, has invoked the other great pillar of modern physics: relativity.

What on earth has relativity got to do with it? If we had to sum up the theory set out in Pico’s book “Consciousness in Four Dimensions”, we might choose the slogan ‘life is a frame of reference’. Pico is not unique in emphasising the temporally-extended nature of life and consciousness – Steven Rose, for example, has put forward a more general version of that perspective, and Locke’s view that ‘Nothing but consciousness can unite remote existences into the same person’ seems very close to Pico’s central insight.

Pico describes the emergence of life in a story of how protocells may have turned into true life. Protocells, on this view, have a simple bubble-like wall inside which certain reactions go on. But the wall is not enough to defend them from changes in the environment; when the right circumstances come along they form, and when the physical or chemical environment, in one of its periodic oscillations, becomes unfavourable, they simply fall apart again. Eventually a lucky protocell comes up with internal reactions which, fortuitously, have a homeostatic effect – they regulate the internal environment of the cell, defending it from external changes to the point where the cell can survive through the regular cycles of change in its immediate environment.

This persistence, on Pico’s view, is what characterises life: more debatably, he characterises it as a ‘frame of reference’. It certainly establishes a kind of physico-chemical baseline within the cell, but that seems to bear only a metaphorical relation to the ‘frames of reference’ proposed by relativity. A frame of reference (if I’ve understood correctly) is a point of view from which a particular set of measurements of the world and a particular perception of the simultaneity of events holds good: but the view from inside the cell is surely much the same as the view from outside. You might, I suppose, say that time passes differently within the cell because the normal external oscillation, which in a sense beats out time, has been dampened or stopped: but that would be a loosely metaphorical version of relativity.

Be that as it may, Pico sees the emergence of consciousness as broadly recapitulating the emergence of life. The neurological details of the theory are set out with admirable clarity, and with a level of detail it is impossible to do full justice to here. Briefly, Pico believes the columnar structures of the prefrontal neocortex provide prefrontal integration modules (PIMs) which bring together a wide and disparate range of sensory inputs. Generally, the patterns formed are transient, each being swept away by a succeeding wave of inputs: but in the course of evolution some of these PIMs acquire new properties in more or less the way the true cells raised themselves above the level of the protocells. They become able to retain an echo of previous states, and hence provide the basis for true perception of time, and consciousness.

This idea has some appeal. It is a common insight that while animal behaviour is generally governed by conditions in the present moment, conscious thought allows us to address goals in the remote future, and adopt chronologically extended plans. It’s also true that if we want to include a Self in our theory, it somehow has to have a continued existence over the full period of the individual’s life. As a third bonus, it allows Pico a neat view about the ontological reality of consciousness, namely, that it is as real as life (and we might add, as elusive).

However, there are two big problems. First, as with life, this doesn’t really look like relativity in any but the loosest of senses. Second, and much worse, it just doesn’t seem to explain the nature of consciousness. All it tells us is that consciousness has homeostatic properties, and retains items from its past: but you could say the same about parts of the digestive system

It is a good and valid point, however, that a lot of scientific thought outside the confines of physics itself still operates on a Newtonian basis. At the back of most our minds is the Laplacean idea that if we could specify all the data about every particle in the Universe at a single instant, the whole future and past would be calculable. This way of thinking, I believe, lies behind the intuitive certainty which some people feel that consciousness must ultimately be a computational phenomenon. After all, if the Universe itself is essentially a discrete-state machine, with one state-of-affairs arising directly from the preceding state-of-affairs, then everything must be computable. But that begs the question; and in fact, relativity denies the possibility, even in principle, of an objectively correct time-slice containing a full description of every point in the Cosmos at a single given moment. There is no such thing as absolute simultaneity, and if we want our determinism to be computable, we really need a more sophisticated version.

All in all then, I think you could say that Pico is on to something; unfortunately the thing he’s on to is not, in the end, The Answer.

Picture: elephant. “I’m leaving.”
“Who is she?”

This is the kind of human exchange which computers, it is said, will never be able to fathom. The computer might be able to decode the literal meaning of the sentences, but never pick up the “relationship crisis” scenario which human beings recognise more or less instantly. This is an example of the exciting subject of conversational implicature, an ugly word invented by H.P.Grice to describe the inferences we make which are vital to understanding each other. Grice proposed that in order to work out what other people are getting at, we take it for granted that when they talk to us they are normally going to follow certain rules, or maxims. There are nine altogether, grouped under four headings:


i) Make your contribution as informative as is required for the current purposes of the exchange.
ii) Do not make your contribution more informative than is required.

i) Do not say what you believe to be false.
ii) Do not say that for which you lack evidence.

Be relevant

i) Avoid obscurity of expression
ii) Avoid ambiguity
iii) Be brief
iv) Be orderly

These maxims help us express ourselves briefly without fear of being misunderstood. If someone tells you your horse came in either first or fourth, for example, you are entitled to assume, without his saying so, that he does not know which it was (unless other evidence suggests he is deliberately being annoying). Or consider this exchange:

A: Smith doesn’t seem to have a girlfriend these days.
B: He has been paying a lot of visits to New York recently.

If B is following the rules, we have to assume that what he says is relevant in some way, so we can legitimately deduce that he means Smith may have a girlfriend in New York. Besides straightforward use like this, the rules can be deliberately broken as a more subtle way of sending messages. If you provide a job reference which merely says that X worked for you and always turned up on time, the recipient may reasonably assume that you are deliberately being uninformative as a way of implying a negative judgement about X which you prefer not to spell out explicitly.

Grice’s work was directed towards philosophical ends, but it has proved unexpectedly fertile in other areas. In particular, it offers a promising-looking angle on the old debate about whether you can get syntax from semantics: maybe you don’t need to, but can look instead to the new field of pragmatics, in which the linguistic consequences of Grice’s original insights are explored. Particularly interesting is Dan Sperber and Deirdre Wilson’s book tackling the mystery of Relevance, a subject which (according to me, at least) is one of the three-and-a-half big problems of consciousness.

Sperber and Wilson describe two models of communication. In the code model, a thought in one brain (perhaps in mentalese, a brain’s private mental language) is encoded into language, transmitted to another brain, and decoded again. In the inferential model, by contrast, the speaker just provides the linguistic evidence from which the auditor, in a more or less Gricean way, can infer the intended message. The code model cannot provide a complete explanation of the process of communication because it can’t deal with the sort of example quoted above: on the other hand, when you examine real conversations, there does seem to be a whole lot of coding going on. Sperber and Wilson maintain that both code and inference have roles to play.

It’s rather as though human communication had started out as a game of charades (the game where one player has to mime a book, play or film title for the others to guess). At first, the players have to think of clues that straightforwardly make the audience think along the right lines – behaving like a whale for Moby Dick, say. But experienced players gradually develop a set of conventions, such as pointing to their nose (=”knows”) with one finger and at someone who has guessed correctly with another. The grammatical and lexical apparatus of ordinary language represents the code, the ultimate development of this kind of helpful convention, and in ordinary communication it now does most of the work, though successful communication still requires occasional resort to inferential methods.

Sperber and Wilson think Grice’s approach can be slimmed down, and most of the work done by the simple criterion of relevance. This means that the inferential component of communication rests very largely on the ability to work out what is and isn’t relevant in what people are saying to you. They offer an analysis of relevance in terms of contextual effect. Roughly speaking, the idea is that a new piece of information is relevant to the extent that it allows you to revise the beliefs you had already, strengthening, weakening or deleting them or allowing new deductions to be added. If it merely duplicates things you already know, or if it has no connection with any of the pieces of information you have already, it isn’t relevant at all. This, in a more formal guise, is how Sperber and Wilson propose the relevance of any given proposition could in principle be rated.

So, on their theory, if someone says “Coffee would keep me awake.”, I am entitled to assume that the utterance has some relevance to something. As a first shot, I try out the simplest hypothesis I can think of – maybe they just think I need to know about the stimulating properties of coffee? But on that interpretation, the relevance of the remark seems negligible – we’re not in a pharmacological seminar, and at best the remark might convey to me something I didn’t know about coffee – it doesn’t change any of my other current beliefs or allow me to draw many new conclusions. So I move on to more complex hypotheses, and eventually (rather quickly, I hope) I reach the correct hypothesis: depending on the circumstances, coffee is either being asked for or refused.

This looks like a promising avenue to explore, but there are some ifs and buts. First, the analysis is all to do with conversations, and whether it can be widened into any general analysis of relevance is unclear. Second, it’s not at all clear how this approach could be reduced to the kind of concrete algorithm you might use in programming a chat-bot or other program. In particular, there seems to be a danger of circularity. In many cases, when we come to tot up the contextual effects of a given remark, there are actually going to be an infinite number of valid new inferences we can make -nearly all of them will be trivial or uninteresting, but how do we weed them out. Ihave theuneasy feeling that at some stage we are going to find ourselves needing to disallow inferences which are (gulp) irrelevant…

Even if that difficulty is a real one, the idea of implicature seems an interesting one. Sperber and Wilson are good at coming up with little snatches of dialogue which exemplify different varieties of implicature, and it is noticeable that many of them have a witty or rhetorical quality. Towards the end of the book, they discuss the way implicatures contribute to poetry, metaphor and other special forms of language. It seems to me that virtually all jokes are based on implicature, too. Consider this example:

G: Last night I shot an elephant in my pyjamas. How he got into my pyjamas I’ll never know.

Surely a fine example of the manipulation of Gricean conversational implicatures..?