Why current AI and neuroscience fail to
replicate or explain ancient forms of spatial
reasoning and mathematical consciousness?
ABSTRACT
Most recent discussions of consciousness focus on a tiny subset of loosely
characterized examples of human consciousness, ignoring evolutionary origins and
transitions, the diversity of human and non-human phenomena, the variety of
functions of consciousness, including consciousness of: possibilities for
change, constraints on those possibilities, and implications of the
possibilities and constraints -- together enabling extraordinary spatial
competences in many species (e.g. portia spiders, squirrels, crows, apes) and,
in humans, mathematical consciousness of spatial
possibilities/impossibilities/necessities, discussed by Immanuel Kant (1781).
(James Gibson missed important details.) These are products of evolution's
repeated discovery and use, in evolved construction-kits, of increasingly
complex types of mathematical structure with constrained possibilities, used to
specify increasingly complex organisms with increasingly complex needs and
behaviours, using lower-level impossibilities (constraints) to support higher
level possibilities and necessities, using new biological physical structures
that require more sophisticated information-based control. Such transitions
produce new layers of control requirements: for control of acquisition and use
of nutrients and other resources, of reproductive processes, of physical and
informational development in individual organisms, and recognition and use of
possibilities for action by individuals, as well as risks, using layered
mixtures of possibilities and constraints in the environment, over varying
spatial and temporal scales (e.g. sand-castles to cranes and cathedrals). I'll
try to show how all this relates to aspects of mathematical consciousness
noticed by Kant, that are essential for creative science and engineering as well
as everyday actions, involved in important aspects of spatial cognition used in
ancient mathematical discoveries. In contrast, mechanisms using statistical
evidence to derive probabilities cannot even express, let alone explain these
achievements, and modern logic (unavailable to ancient mathematicians, and
non-human species) lacks powerful heuristic features of spatial mathematical
reasoning. New models of computation may be required, e.g. sub-neural
chemistry-based computation with its mixture of discreteness and continuity
Grant(2018).
Dana Ballard and Chris Brown, 1982,
Computer Vision,
Prentice Hall,
Englewood Cliffs, New Jersey 07632, USA, online at:
http://homepages.inf.ed.ac.uk/rbf/BOOKS/BANDB/bandb.htm
John Seely Brown, Richard R. Burton, and Kathy M. Larkin,
1977,
Representing and using procedural bugs for educational purposes,
Proceedings of the 1977 annual conference, ACM '77,
pp. 247--255, ACM, New York, NY, USA,
http://doi.acm.org/10.1145/800179.810211
S. Barry Cooper and Mariya I. Soskova, editors
2017
The Incomputable: Journeys Beyond the Turing Barrier Springer-Verlag,
http://www.springer.com/gb/book/9783319436678
Richard Dawkins,
1986,
The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design
Norton & Company, Inc,
Brian V. Funt (1980),
Problem-Solving with Diagrammatic Representations, in
Artificial Intelligence 13 (1980), pp201-230
North-Holland
http://www.cs.sfu.ca/~funt/ProblemSolvingWithDiagrammaticRepresentations_AIJournal1980.pdf
Gallistel, C.R. & Matzel, L.D., 2012(Epub),
The neuroscience of learning: beyond the Hebbian synapse,
Annual Revue of Psychology,
Vol 64, pp. 169--200,
https://doi.org/10.1146/annurev-psych-113011-143807
Tibor Ganti, 2003.
The Principles of Life, Eds. E. Szathmáry,
& J. Griesemer,
(Translation of the 1971 Hungarian edition),
OUP, New York.
http://chemoton.com/images/pdf/GantiTiborEletmu_14.pdf
See the very useful summary/review of this book by Gert Korthof:
http://wasdarwinwrong.com/korthof66.htm
J. J. Gibson, The Ecological Approach to Visual Perception, Houghton Mifflin, Boston, MA, 1979.
Seth G.N. Grant, 2010,
Computing behaviour in complex synapses: Synapse proteome complexity and the
evolution of behaviour and disease,
Biochemist 32, pp. 6-9,
http://www.biochemist.org/bio/default.htm?VOL=32&ISSUE=2
Seth G. N. Grant, 2018,
Synapse molecular complexity and the plasticity behaviour problem,
Brain and Neuroscience Advances 2, pp. 1--7,
https://doi.org/10.1177/2398212818810685
Several sample quotes from this remarkable paper are below.
David Hilbert,
The Foundations of Geometry,
1899,
Translated 1902 by E.J. Townsend, from 1899 German edition,
Project Gutenberg, Salt Lake City,
http://www.gutenberg.org/ebooks/17384
Immanuel Kant,
Critique of Pure Reason,
Macmillan, London, 1781. Translated
(1929) by Norman Kemp Smith.
Various online versions are also available now.
I. Lakatos, 1976, Proofs and Refutations, Cambridge University Press, Cambridge, UK,
Tom McClelland, 2017,
The Mental Affordance Hypothesis, in
Minds Online Conference 2017,
http://mindsonline.philosophyofbrains.com/2017/2017-session-1/the-mental-affordance-hypothesis/
Video of presentation:
https://www.youtube.com/watch?v=zBqGC4THzqg
Thomas Nagel, 1974,
What is it like to be a bat?
Philosophical Review,
83, pp. 435--50, Duke Univ. Press,
http://dx.doi.org/10.2307/2183914
(I wrote a semi-serious spoof in 1996
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/like_to_be_a_rock/)
Much of Jean Piaget's work is also relevant, especially his last two (closely related) books written with his collaborators: Possibility and Necessity
Erwin Schrödinger,
What is life?,
CUP, Cambridge, 1944.
Commented extracts available here:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/schrodinger-life.html
Aaron Sloman (1962) Knowing and Understanding: Relations between meaning and truth, meaning and necessary truth, meaning and synthetic necessary truth DPhil thesis, Oxford University, May 1962. (Transcribed and made searchable in 2016, thanks to Luc Beaudoin.) http://www.cs.bham.ac.uk/research/projects/cogaff/62-80.html#1962
A. Sloman, 1984 (extended later)
Experiencing Computation: A Tribute to Max Clowes,
originally in
New horizons in educational computing,
Ellis Horwood Series In AI Ed. Masoud Yazdani,
pp. 207--219,
Chichester,
Online version with expanded obituary and biography
http://www.cs.bham.ac.uk/research/projects/cogaff/81-95.html#61
Aaron Sloman,
1971,
Interactions between philosophy and AI: The
role of intuition and non-logical reasoning in intelligence,
Proc 2nd IJCAI, London, 1971
Reprinted in Artificial Intelligence,
vol 2, 3-4, pp 209-225, 1971,
http://www.cs.bham.ac.uk/research/cogaff/62-80.html#1971-02
Aaron Sloman, 1978 (Revised, .... 2018)
The Computer Revolution in Philosophy: Philosophy, Science and Models of Mind,
Harvester Press.
http://www.cs.bham.ac.uk/research/cogaff/62-80.html#crp
Aaron Sloman (2007-14),
Predicting Affordance Changes (Alternative ways to deal with uncertainty),
Unpublished discussion paper (HTML),
School of Computer Science, University of Birmingham,
(Installed 2007, later updated)
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/changing-affordances.html
Aaron Sloman, 2013--2018,
Jane Austen's concept of information (Not Claude Shannon's)
Online technical report, University of Birmingham,
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/austen-info.html
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/austen-info.pdf
Trettenbrein, Patrick C., 2016, The Demise of the Synapse As the Locus of Memory: A Looming Paradigm Shift?, Frontiers in Systems Neuroscience, Vol 88, http://doi.org/10.3389/fnsys.2016.00088
Aaron Sloman (2018),
Alan Turing's 1938 thoughts on mathematical reasoning
(intuition vs ingenuity). Published in
(his thesis).
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/turing-intuition.html
(also
pdf)
A. M. Turing, 1939,
Systems of Logic Based on Ordinals,
Proc. London Mathematical Society,
pp. 161-228,
https://doi.org/10.1112/plms/s2-45.1.161
Also reprinted in
Alan Turing: His work and impact
Elsevier 2013.
A.M. Turing (1952) The Chemical Basis Of Morphogenesis. Phil Trans R Soc
London
B 237 237:37-72
Note: A presentation of Turing's main ideas for non-mathematicians can be
found in Ball, 2015.
Eds. S. Barry Cooper and J. van Leeuwen, Alan Turing: His Work and Impact, 2013, Elsevier, Amsterdam,
"Furthermore, when considering the molecular machinery of the presynaptic terminal versus the post-synaptic terminal, it was discovered that the postsynaptic protein machinery was the most ancient, having first arisen in prokaryotes."
"The synapse molecular machinery is therefore more ancient than the neuron."
"A striking fact is that these prokaryotic proteins include receptor signalling complexes, which are basic multiprotein machines used by cells to detect the external environment and trigger intracellular adaptive responses."
"These evolutionary observations indicate that the most ancient and fundamental property of the postsynaptic machinery is the integration of temporal information. It also indicates that temporal integration by signalling complexes is a basic and ancient memory mechanism."
"This raises a fascinating and simple alternative to the classical model of synaptic resistance and the LTSS model, namely, that it is temporal detection that is the fundamental property and that the adjustment of strength is a secondary and much later evolved function. It is also worth noting that the capacity to detect patterns of activity is significantly altered in synapses carrying mutations in the scaffold proteins that organise the vertebrate signalling complexes."
Comment by A.S.:
It is not just what the synapses detect that's important but also how such
detection influences control. In very simple organisms control is immediate, but
as organisms, their needs, and the environments they interact with become more
complex, the information processing requirements become more complex, and less
closely tied to requirements for immediate action, or reaction. Examples include
considering and choosing between alternative actions, reasoning about actual or
possible causal influences, assembling actions to achieve a novel goal, or,
later still, rejecting a considered goal after working out that it is impossible
to achieve.
As I believe Kant saw, at least dimly, in 1781, all of this mechanism that evolved initially for fairly direct detection and selection of means to various desired ends, was later used as the basis of mathematical discoveries about spatial structures, processes and their relationships that eventually led to the production of Euclid's Elements and many more mathematical discoveries in geometry and topology not included by Euclid and also not included in Hilbert's Foundations of geometry.
The Turing-inspired Meta-Morphogenesis project studying such transitions in
biological information processing is available here:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/meta-morphogenesis.html
Maintained by
Aaron Sloman
School of Computer Science
The University of Birmingham