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CATEGORIES:Artificial Intelligence and Natural Computation se
minars
SUMMARY:Why current AI and neuroscience fail to replicate
or explain ancient forms of spatial reasoning and
mathematical consciousness - Prof Aaron Sloman (Ho
norary Professor of Artificial Intelligence and Co
gnitive Science\, School of Computer Science\, Uni
versity of Birmingham\, UK)
DTSTART:20190902T100000Z
DTEND:20190902T110000Z
UID:TALK3844AT
URL:/talk/index/3844
DESCRIPTION:It is widely\, but erroneously\, believed that Imm
anuel Kant's philosophy of mathematics in his Crit
ique of Pure Reason (1781) was disproved by Einste
in's theory of general relativity (confirmed by Ed
dington's observations of the solar eclipse in 191
9\, establishing that physical space is non-Euclid
ean). My 1962 DPhil thesis (now online) defended a
slightly modified version of Kant's claim that ma
ny important mathematical discoveries are non-empi
rical\, non-contingent\, and non-analytic (i.e. no
t just logical consequences of axioms and definiti
ons)\, but did not explain how brains or machines
could make such discoveries. I later encountered A
I\, learnt to program\, and hoped to show how to b
uild a baby robot that could grow up to be a mathe
matician making discoveries like those of Archimed
es\, Euclid\, Zeno\, etc.\, and many other deep di
scoveries made long before the development of mode
rn logic and formal proof procedures. I think thos
e mathematical abilities are closely related to th
e spatial intelligence of pre-verbal human toddler
s\, and other intelligent animals\, e.g. squirrels
\, elephants\, crows\, apes\, and perhaps octopuse
s[†] -- whose abilities are not yet replicated in
AI/Robotics systems nor explained by current theor
ies in neuroscience or psychology. Insofar as such
mathematical discoveries involve *necessity* or *
impossibility* they *cannot* be substantiated by m
echanisms that collect statistical information and
derive probabilities.\n\nThis version of Kant's t
heory rules out natural and artificial neural nets
and related forms of deep learning\, E.g. they ca
nnot learn that something is impossible\, such as
a largest prime number\, or a finite volume bounde
d by three plane surfaces. I have a large\, and st
eadily growing\, collection of examples to be expl
ained by any adequate theory of mathematical consc
iousness. I'll present a small sample during the t
alk.[‡]\n\nAlan Turing's comments in his PhD thesi
s on the difference between mathematical intuition
and mathematical ingenuity seem to me to echo Kan
t's insights\, and I suspect (though the evidence
is flimsy) that Turing's 1952 paper on chemistry-b
ased morphogenesis (nowadays his *most* cited pape
r) was at least partly motivated by a search for a
new model of computation\, combining continuous a
nd discrete components. The most likely location f
or such a mechanism is sub-neural chemistry\, for
reasons related to Schrodinger's analysis in What
is life? (1944) of the role of chemistry in reprod
uction. A few neuroscientists are exploring relate
d ideas (e.g. Seth Grant in Edinburgh).\n\nI'll pr
esent examples of spatial/mathematical reasoning i
llustrating Kant's claims. E.g. what sorts of brai
n mechanisms enable a child to understand that it'
s *impossible* to separate linked rings made of im
permeable material? Why are you sure that no plana
r triangle can have one side whose length exceeds
the combined lengths of the other two sides?) Curr
ent neurally inspired AI mechanisms cannot discove
r\, or even represent\, necessity or impossibility
\, or understand paragraphs like this. Logic-based
mechanisms don't explain what was going on in mat
hematical brains before the development of logic i
n the last few centuries\, or squirrel brains\, or
human toddler brains\, e.g. this one:\nhttp://www
.cs.bham.ac.uk/research/projects/cogaff/movies/ijc
ai-17/small-pencil-vid.webm\n(Skip the introductio
n.)\n\nThe implications for the current wave of en
thusiasm for deep learning are potentially devasta
ting -- but invisible to people who have never stu
died Kant\, or philosophy of mathematics. Which is
not to deny that deep learning can be very useful
\, if used properly.\n\n[†]\nhttps://www.bbc.co.uk
/iplayer/episode/m0007snt/natural-world-20192020-5
-the-octopus-in-my-house\n\n[‡] A disorganised col
lection of additional examples can be found here\,
\nwith links to many more:\nhttp://www.cs.bham.ac.
uk/research/projects/cogaff/misc/impossible.html (
also pdf)
LOCATION:Computer Science\, The Sloman Lounge (UG)
CONTACT:Hector Basevi
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