Some time back, I wrote about the painting of spirit-dreamtime maps by Australian aboriginal communities as proof of their relationship to specific places:  Only people with traditional rights to the specific place would have the necessary dreamtime knowledge needed to make the painting, an argument whose compelling force has been recognized by Australian courts.  These paintings are a form of map, showing (some of) the spirit relationships of the specific place.  The argument they make is a very interesting one, along the lines of: 

What I am saying is true, by virtue of the mere fact that I am saying it, since only someone having the truth would be able to make such an utterance (ie, the painting).

Another example of this type of argument is given by Rory Stewart, in his account of his walk across Afghanistan.   Stewart does not carry a paper map of the country he is walking through, lest he be thought a foreign spy (p. 211).   Instead, he learns and memorizes a list of the villages and their headmen, in the order he plans to walk through them.  Like the aboriginal dreamtime paintings, mere knowledge of this list provides proof of his right to be in the area.  Like the paintings, the list is a type of map of the territory, a different way of knowing.  And also like the paintings, possession of this knowledge leads others, when they learn of the possession, to act differently towards the possessor.  Here’s Stewart on his map (p. 213):

It was less accurate the further you were from the speaker’s home . . .  But I was able to add details from villages along the way, till I could chant the stages from memory.

Day one:  Commandant Maududi in Badgah.  Day two:  Abdul Rauf Ghafuri in Daulatyar.  Day three:  Bushire Khan in Sang-izard.  Day four:  Mir Ali Hussein Beg of Katlish.  Day five: Haji Nasir-i-Yazdani Beg of Qala-eNau.  Day six:  Seyyed Kerbalahi of Siar Chisme . . .

I recited and followed this song-of-the-places-in-between as a map.  I chanted it even after I had left the villages, using the list as credentials.  Almost everyone recognized the names, even from a hundred kilometres away.  Being able to chant it made me half belong:  it reassured hosts who were not sure whether to take me in and it suggested to anyone who thought of attacking me that I was linked to powerful names. (page 213) 

Because AI is (or should be) about ways of knowing and doing in the world, it therefore has close links to the social sciences, particularly anthropology, and to the humanities.

References:

Seymour Papert [1988]: One AI or Many? Daedalus, 117 (1) (Winter 1988):  1-14.

Rory Stewart [2004]: The Places in Between. London, UK:  Picador, pp. 211-214.

Technorati Tags: Seymour Papert, Artificial Intelligence, dreamtime, Rory Stewart

Proof is supposed to be what sets mathematics apart from the other sciences. Traditionally, the subject has not been an evolutionary one in which the fittest theory survives. New insights don’t suddenly overturn the theorems of the previous generation. The subject is like a huge pyramid, with each generation building on the secure foundations of the past. The nature of proof means that mathematicians, to use Newton’s words, really do stand on the shoulders of giants.

In the past, those shoulders have been extremely steady. After all, in no other science are the discoveries of the Ancient Greeks still as valid today as they were at the time. Euclid’s 2300-year-old proof that there are infinitely many primes is perhaps the first great example of a watertight proof.

The reason for this widespread view is that mathematics uses deduction to reach its conclusions.  At least, that is true of pure mathematics, or was so until computers began to be used in proofs (a topic which du Sautoy discusses in that article).  But all deduction does is to show that, given some assumptions and given some rules of inference, a certain conclusion follows from those assumptions by applying those rules of inference.  If either the assumptions are false or the rules of inference not acceptable, then the stated conclusions will not, in fact, follow.

Du Sautoy is quite wrong to claim that new insights do not overturn the theorems of the previous generation.  The history of pure mathematics is replete with examples where proven conclusions were later revealed to depend on assumptions not made explicit, or on assumptions previously thought to be obvious but which were later shown to be false, or on rules of inference later considered invalid.   For over a century, mathematicians thought that everywhere-continuous functions were also everywhere-differentiable, until shown a counter-example.  For a similar period, they thought that the convergent limit of an infinite sequence of continuous functions was itself also continuous, until shown a counter-example.  They thought that there could not exist a one-to-one and onto mapping between the real unit interval and the real unit square, until shown such a mapping (a so-called space-filling curve).  In fact, there are infinitely-many such mappings; indeed, an uncountable infinity of them.  In all these case, “proofs” of the erroneous conclusions existed, which is why the earlier mathematicians believed those conclusions.  The proofs were later shown to be flawed, because they depended on (usually-implicit) assumptions which were false.   For the differential calculus, the fixing effort was begun by Cauchy and Weierstrauss, using epsilon-delta arguments which were more rigorous than the proofs of the earlier generation of analysts.  

Not only does Du Sautoy have his history wrong, but there is shurely shome mishtake in his mentioning Euclid here.  The 19th century was consumed by a controversy over the truth-status of Euclidean geometry, and the discovery of apparently-logical alternatives to it.   As clever a man as the logician and philosopher Gottlob Frege (an intellectual hero of Wittgenstein) could not get his head around the idea that these different versions of geometry could all simultaneously be true.   Yet that is the conclusion mathematicians came to: that, depending on the assumptions you made about the surface on which you doing geometry, there were in fact valid alternatives to the discoveries of the Greeks:  draw your triangles on the surface of a sphere, instead of on a flat plane, for example, and you could readily draw triangles whose three angles did not sum to 180 degrees.  You choose your assumptions, you gets your geometry!  This is not a secure pyramid of knowledge, but many pyramids, post-modernist style.

And in the first part of the 20th century, pure mathematics was consumed with a bitter argument over whether a particular rule of inference – reductio ad absurdem (RAA), or reasoning from an assumption thought to be false – was valid in deductive proofs of the existence of mathematical objects.   The dissidents created their own school of pure mathematics, constructivism, which is still being studied.  Indeed, it turns out that a closely-related logic, intuitionistic logic, appears naturally elsewhere in mathematics (as part of the internal structure of a topos). Once again, you choose your rules of inference, you gets your mathematical theorems.  

There is no single, massive pyramid of knowledge here, as du Sautoy claims, but lots of smaller pyramids.  Every so often, a great mathematician is able to devise a new conceptual framework which allows some or all of these baby pyramids to appear to be part of some larger pyramid, as Pieri and Hilbert did with geometry in the 1890s, or as Lawvere and others did with category theory as a foundation for mathematics in the 1960s.   But, based on past experience, new baby pyramids will continue to be created by mathematicians arguing about the assumptions or rules of inference used in earlier proofs.    To consider this process of contestation, splitting, and attempted re-unification to be somehow different to what happens in other domains of human knowledge may be comforting to mathematicians, but is myth nonetheless.

Technorati Tags: Marcus du Sautoy, mathematics, deduction, Cauchy, Weierstrauss, epsilon-delta, Euclid, Frege, reductio ad absurdem, Pieri, Hilbert, Lawvere

From the perspective of the national economy and technological progress, these proposals are extremely misguided, and should be opposed by us all.    They demonstrate a profound ignorance of where important ideas come from, of when and where and how they are applied, and of where they end up.  In particular, they demonstrate great ignorance of the multi-disciplinary nature of most socio-economically-impactful research.

One example will demonstrate this vividly.  As more human activities move online, more tasks can be automated or semi-automated.    To enable this, autonomous computers and other machines need to be able to communicate with one using shared languages and protocols, and thus much research effort in Computer Science and Artificial Intelligence these last three decades has focused on designing languages and protocols for computer-to-computer communications.  These protocols are used in various computer systems already and are likely to be used in future-generation mobile communications and e-commerce systems. 

Despite its deep technological nature, research in this area draws fundamentally on past research and ideas from the Humanities, including: 

• Speech Act Theory in the Philosophy of Language (ideas due originally to Adolf Reinach 1913, John Austin 1955, John Searle 1969 and Jurgen Habermas 1981, among others)
• Formal Logic (George Boole 1854, Clarence Lewis 1910, Ludwig Wittgenstein 1922, Alfred Tarski 1933, Saul Kripke 1959, Jaakko Hintikka 1962, etc), and
• Argumentation Theory (Aristotle c. 350 BC, Stephen Toulmin 1958, Charles Hamblin 1970, etc). 

Assessment of the impacts of research over five years is laughable when Aristotle’s work on rhetoric has taken 2300 years to find technological application.   Even Boole’s algebra took 84 years from its creation to its application in the design of electronic circuits (by Claude Shannon in 1938).  None of the humanities scholars responsible were doing their research to promote technologies for computer interaction or to support e-commerce, and most would not have even understood what these terms mean.  Of the people I have listed, only John Searle (who contributed to the theory of AI), and Charles Hamblin (who created one of the first computer languages, GEORGE, and who made major contributions to the architecture of early computers, including invention of the memory stack), had any direct connection to computing.   Only Hamblin was afforded an obituary by a computer journal (Allen 1985).

None of the applications of these ideas to computer science were predicted, or even predictable.  If we do not fund pure research across all academic disciplines without regard to its potential socio-economic impacts, we risk destroying the very source of the ideas upon which our modern society and our technological progress depend. 

Reference:

M. W. Allen [1985]: “Charles Hamblin (1922-1985)”. The Australian Computer Journal, 17(4): 194-195.

Technorati Tags: RAE

For instance, under the direction of John Fox, the Advanced Computation Laboratory at Europe’s largest medical research charity, Cancer Research UK (formerly, the Imperial Cancer Research Fund) applied Toulmin’s model of argument in computer systems they built and deployed in the 1990s to handle conflicting arguments in some domain.  An example was a system for advising medical practitioners with the arguments for and against prescribing a particular drug to a patient with a particular medical history and disease presentation.  One company commercializing these ideas in medicine is Infermed.    Other applications include the automated prediction of chemical properties such as toxicity (see for example, the work of Lhasa Ltd), and dynamic optimization of extraction processes in mining.

For me, Toulmin’s most influential work was was his book Cosmopolis, which identified and deconstructed the main biases evident in contemporary western culture since the work of Descartes:

• A bias for the written over the oral
• A bias for the universal over the particular
• A bias for the general over the local
• A bias for the timeless over the timely.

Formal logic as a theory of human reasoning can be seen as example of these biases at work. In contrast, argumentation theory attempts to reclaim the theory of reasoning from formal logic with an approach able to deal with conflicts and gaps, and with special cases, and less subject to such biases.    Norm’s dispute with Larry Teabag is a recent example of resistance to the puritanical, Descartian desire to impose abstract formalisms onto practical reasoning quite contrary to local and particular sense.

References:

S. E. Toulmin [1958]:  The Uses of Argument.  Cambridge, UK: Cambridge University Press. 

S. E. Toulmin [1990]: Cosmopolis:  The Hidden Agenda of Modernity.  Chicago, IL, USA: University of Chicago Press.

Technorati Tags: Stephen Toulmin, argumentation, logic

As data collection is completed, processing begins. Coding, punching and some simple programming present formidable problems. Consistency checks are too much to contemplate. Funds begin to run out because the costs of this stage have been underestimated. Reports are due before data are ready. There has been an overkill in data collection; there is enough information for a dozen Ph.D. theses but no one to use it. Much of the material remains unprocessed, or if processed, unanalysed, or if analysed, not written-up, or if written-up, not read, or if read, not remembered, or if remembered, not used or acted upon. Only a minuscule proportion, if any, of the findings affect policy and they are usually a few simple totals. These totals have often been identified early on through physical counting of questionnaires or coding sheets and communicated verbally, independently of the main data processing.”

Reference:

Robert Chambers [1983]: Rural Development: Putting the Last First. London, UK: Longman. p. 53.

In her book Yuendumu Everyday, Yashmine Musharbash refers to the Aboriginal notion that knowledge is acquired through ”doing” rather than questions.”

Reference:

Yasmine Musharbash [2009]: Yuendumu Everyday: Contemporary Life in Remote Aboriginal Australia.  Aboriginal Studies Press.

This concern with lingustic purity is clearly inspired by France’s envy of Anglo-Saxon practice, which, as is well known, sets its face like flint against all overseas importations.  Regular visitors to London report with awe on the capacity of the English of all social classes for keeping the language clean.  From the blase habitues of the London clubs – raconteurs, bon viveurs, hommes d’affaires – with their penchant for bonhomie and camaraderie, through the soi-disant bien pensants of the passe liberal press to the demi-monde of the jeunesse doree, where ingenues in risque decolletages dine a deux, tete a tete and a la carte with their louche nouveau riche fiances in brassieries and estaminets, pure English is de rigueur, and the mildest infusion of French considered de trop, deja vu, cliche, devoid of all cachet, a linguistic melange or bouillabaisse, a cultural cul-de-sac.

The English want no part of this outre galere, no role in this farouche charade, no rapprochement with this compote.   They get no frisson from detente with diablerie.  And long may it remain so.  “A bas les neologismes!” as you often hear people cry late at night on the Earl’s Court Road.”

Source:  The Guardian Weekly, 1989-01-08 (London, UK).

I have argued before (and here) that many (perhaps even most) religious adherents have personal encounters which they perceive to be of the divine.   These experiences, despite being widespread (in apparently all human societies, and seemingly across all human history) have so far proven not to be objectively replicable, which therefore invalidates them as evidence for scientific claims.  But this does not invalidate them as evidence for personal beliefs and actions.   Indeed, quite the contrary.   If I prefer the taste of drinking coffee to the taste of drinking tea, it is because of my personal subjective experiences of the two liquids; there is nothing that an explicitly-socially-negotiated activity such as science should have to say on the matter of my personal preferences or tastes.    To argue otherwise is to misunderstand the nature of science as an activity as well as to intrude on my autonomy as a human person.  (In other words, if Richard Dawkins chooses not to believe in a non-material realm, fine.  But he has no moral right to tell other people what they may believe or practice, let alone to assert that they should ignore or discount their own personal experiences in deference to his.)

All the writers here are victims of the bias in our western intellectual culture these last three centuries, a bias which is long-run consequence of the European religious wars of the 17th century.  This bias favours beliefs over actions, favours propositions over other representations of knowledge, and (inter alia) favours written accounts over other forms of communication.  There are many ways of knowing besides beliefs, and other forms of knowledge representation besides propositions.  For example:

• Know-What: We may know what objects there are in the world, what features they have, and what their relationships are to each other.  Such knowledge may be expressed in the form of propositions – statements which are true (or not) of the portion of reality they purport to describe.  On the other hand, not all human communicative utterances are statements with truth values (perhaps, indeed, most utterances are not), and a great part of the meaning of utterances is unrelated to their truth or falsity relative to the world.  Arguably, the mainstream of pure mathematics since Mario Pieri’s and David Hilbert’s work in creating and studying formal axiom systems in the 1890s has been unrelated to truth or falsity.    As Eagleton is trying to argue, many religious actions may be communicative utterances with profound meanings and highly-impactful consequences not associated with their truth values.  And in situations of extreme uncertainty, where the very objects in the domain are unknown, let alone their attributes and relationships, I am not convinced it makes any sense at all to talk of propositional representation of knowledge of the domain.
• Know-How:  We may be able  to perform some activity, or exercise some skill, without our knowledge being expressed, or even expressible, in propositional form.  All of us can breathe, most of us can walk down a staircase, some of us can even hit a 99-mile-per-hour cricket ball over the boundary or improvise jazz on a piano or successfully manage a large software development team, yet every single one of us would be hard-put to express any of these abilities in propositional form.  Indeed, many of us would be hard part to even describe the actions involved  in these activities:  try saying exactly what basic actions, in what precise order, you undertake to walk down stairs, for instance. (And as any sportsman or musician can tell you, the whole point of achieving mastery of some physical skill is to put it out of conscious awareness – to be such a master of the skill that one does not think consciously about it and cannot describe it verbally.)    In any case, representation of  know-how knowledge may be much better undertaken with collections of actions or commands, rather than with propositions, as in computer protocols (such as HTTP).
• Know-Where: We may know our geographic position, relative for instance to the sun or to the directions of the compass, without even necessarily being aware that we have this knowledge, let alone being able to put it into propositional form.   Yet we may use this knowledge even without being aware that we have it.   In an earlier post, I reported on experiments in Australian aboriginal communities which demonstrated that some people maintain a sense of their relative geographic position all the time, and use this knowledge without conscious awareness, in the same way that we all breathe or most of us walk down stairs.   One could easily imagine non-propositional representation of know-where knowledge by means (for instance) of co-ordinates in some manifold, or a directed arrow (a vector) always pointing from the knower to some other point, such as the sun or the north pole.
• Know-Who (or perhaps, in  deference to Huxley, Know-That):  We may know that some entity exists merely by being in its presence.   We may know this without use of any of our so-called “five senses“, but through some other means.  The Sufi school of Illuminationism, founded by Shahab al-Din Suhrawardi (1155-1191), is an example of a mystical tradition based on such knowledge.    Anyone who has been in love or felt the love of another person will have had something like this knowledge.

Wittgenstein famously said, “Whereof one cannot speak, thereof one must remain silent.“  He was certainly not claiming that there is nothing about which one cannot speak.

Reference:

Aldous Huxley [1944]: The Perennial Philosophy.  London, UK:  Chatto and Windus.

Mehdi Amin Razavi [1996]: Suhrawardi and the School of Illumination.  London, UK:  Routledge.

Technorati Tags: Terry Eagleton, Richard Dawkins, Sufi, Illuminationism, Suhrawardi