BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.bham.ac.uk//v3//EN
BEGIN:VEVENT
CATEGORIES:Theoretical computer science seminar
SUMMARY:Physical/evolutionary foundations for mathematics
vs logico/semantic foundations for mathematics - A
aron Sloman (University of Birmingham)
DTSTART:20161111T110000Z
DTEND:20161111T120000Z
UID:TALK2305AT
URL:/talk/index/2305
DESCRIPTION:Questions about the nature of mathematics\, the na
ture of mathematical\ndiscovery\, the nature of ma
thematical proof\, how humans can make\nmathematic
al discoveries and how mathematics can be applicab
le to a\nphysical world have been raised in the pa
st by many philosophers\,\nscientists\, and mathem
aticians. Some examples are summarised here:\n\nht
tps://en.wikipedia.org/wiki/The_Unreasonable_Effec
tiveness_of_Mathematics_in_the_Natural_Sciences\n\
nA related\, very old\, thread of human history ha
s been concerned with\nattempts to create machines
that can perform mathematical calculations\, and\
nmore recently machines that can find proofs\, mec
hanising processes that had\npreviously been perfo
rmed by humans. There are now machines that will f
ind\nproofs of new theorems.\n\nOne of them will s
ell you a certified new theorem for ?15.00\n htt
p://theorymine.co.uk/?go=overview\n http://theor
ymine.co.uk/?go=about\n [The main author\, Alan
Bundy\, will visit us next term.]\n\n(In a later t
alk I'll discuss some apparent limitations in curr
ent AI\ntheorem proving technology.)\n\nAmong many
questions still under investigation is whether th
ere is a core\nsubset of mathematics from which al
l of mathematics can be rigorously\nderived: e.g.
pure symbolic logic\, or logic with set theory add
ed. The\nsearch for such a subset is often referre
d to as the study of "Foundations\nof mathematics"
\, to which great philosophers and mathematicians
have\ncontributed:\n https://en.wikipedia.org/w
iki/Foundations_of_mathematics\n\n(A possible answ
er is that no matter how powerful any proposed gen
erative\nsystem is\, there are always questions th
at it cannot answer without first\nbeing extended.
Perhaps that also applies to every human brain. D
oes it\nalso apply to the future sequence of human
brains?)\n\nA related but different question is h
ow it came about that humans could\nmake mathemati
cal discoveries\, including the great discoveries
reported\nover 2000 years ago by Euclid\, Archimed
es\, Pythagoras\, and others\, some of\nwhich are
still in daily use by engineers and scientists all
round the\nplanet.\n\nThis talk generalises that
question: long before there were any human\nmathem
aticians natural selection had produced organisms
with mechanisms\nthat (unwittingly) made use of ma
thematical structures and processes\, e.g.\nnegati
ve feedback control loops\, and parametrised contr
ol systems for\ngrowing organisms\, or for use acr
oss species.\n\nErwin Schrodinger in What is life?
(1944) argued that biological\nreproduction made
use of mathematical properties of discrete sequenc
es of\nstable chemical structures made possible by
quantum mechanisms.\n\nAnd before that physical a
nd chemical processes of many kinds conformed to\n
mathematical constraints\, e.g. a liquid flowing o
n a surface will tend to\nminimise its gravitation
al potential energy.\n\nLater evolutionary process
es produced mechanisms making more and more\nsophi
sticated uses of mathematics\, including brains of
many animals\, e.g.\nsquirrels and nest-building
birds.\n\nOnly later did humans not only use mathe
matical features of the\nenvironment: they also be
gan to think about what they were doing: another\n
product of biological evolution. (Human toddlers s
eem to discover and use\ntopological theorems\, un
wittingly.)\n\nThis talk will introduce some quest
ions about the capabilities of the\nuniverse that
made all this possible\, providing a different kin
d of\n"foundation" for mathematics: a foundation f
or mathematical *machinery*.\nThis sort of foundat
ion is different from a part of mathematics that\n
generates the rest.\n\nSuch foundational machinery
must be a kind of "construction kit" with the\nab
ility to grow an increasingly complex and varied c
ollection of derived\n"construction kits" mainly p
rovided by biological evolution\, repeatedly\nusin
g properties of the fundamental construction kit p
rovided by physics\,\nto build new more powerful c
onstruction kits.\n\nSo far nobody has produced a
computer-based system capable of making all\nthe d
iscoveries made by ancient mathematicians. Is that
because we are not\nclever enough\, or could some
of the evolved construction kits have features\nt
hat cannot be replicated\, or accurately simulated
\, in digital computers --\nincluding features use
d by animal brains? Finding an answer may require
a\nmulti-pronged research strategy. I don't have a
n answer\, yet. But I'll\nsuggest a research strat
egy\, within the Turing-insired Meta-Morphogenesis
\nproject.\nhttp://www.cs.bham.ac.uk/research/proj
ects/cogaff/misc/meta-morphogenesis.html\n
LOCATION:Computer Science\, The Sloman Lounge (UG)
CONTACT:Paul Taylor
END:VEVENT
END:VCALENDAR