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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. |
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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. |
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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. |
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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.
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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. |
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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. |
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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. |
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