Matti Pitkänen (matpitka@pcu.helsinki.fi)
Wed, 1 Dec 1999 10:19:39 +0200
Below is the slightly corrected version of previous message, which contained
stupid error (comment about chess).
****************************************************************************************
Hi all,
Yesterday I ended up with a quantitative prediction about evolution
made possible by the identification of evolution as p-adic evolution.
Before continuing:
a) Does anyone know estimate for the neuron
number for the largest structural units of the
most primitive vertebrate brains? My rough
estimate is that neuron number N=256.000 is a good order of magnitude guess
for the emergence of cognition and possibly of vertebrates with their
brains increasing rapidly in size. I could not however
find from web any data about this and I have no access to literature.
b) Does anyone know whether cortex contains modular
cubical structures such that the side of cube is 4 mm?
Cubes of this side should combine to form cubes/ bilayers with
side/thickness 8 mm. This should be largest modular structure
repeating itself in human brain. Any information?
Below brief exposition of evolution understood as p-adic evolution.
1. Evolution as p-adic evolution
Quantum TGD predicts that evolution reduces to
the gradual increase of p-adic prime characterizing
spacetime sheet of biostructure.
Each revolutionary step corresponds to the emergence
of a new larger p-adic spacetime sheet containing
earlier structures and having minimal size
characterized by p-adic length scale L_p:
L_p= about sqrt(p)*10^4 Planck lengths,
p =about 2^k, k prime of power of prime.
There are not two many interesting values of k in biolength scales.
a) Below neúron length scale k=167 the interesting p-adic primes
correspomd to
k=137,139, k=149,151, k=163 and k=167.
b) Above neuron length scale one has primes
k= 169=13^2, 173, 179, 181,191,193, 197, 199, 211, 223,..
2. Preneural evolution
There are several revolutions preceding the emergence of
cell. The levels preceiding cellular evolution correspond to
k=137,139: DNA and DNA double helix. k=137 corresponds to
atomic length scale.
k=149,151: lipid layers of cell membrane and cell membrane itself.
k=157 and k=163: L(157) correponds to 80 nanometers.
L(163) corresponds to length scale .64 micrometers.
My poor knowledge about cell biology does not allow clearcut
interpretation. Some cell organelles. Nucleus, ribosomes?
Collagen fibres forming the connective tissue of body and
giving rise to body consciousness? Can anyone help?
.
3. Evolutionary steps at critical neuron numbers
This leads to a precise prediction at what critical neuron numbers
evolution of nervous system made dramatic jumps.
Since typical cell size corresponds to the length scale L(k=167),
these jumps occurred when the neuron number for relevant
unit of brain became so large that neurons filled volume of cube
with side L(k). Thus the critical neuron numbers
are given by
N(k) =about (L(k)/L(167)^3 .
If one considers spheres of diameter L(k), the estimate is reduced by
a factor of 1/2.
More concretely, for *cube topology* critical neuron numbers
with suggested evolutionay interpretation are
a) N(169)= 8: epithelial sheets: organs, skin, walls for the nuclei of brain.
Primary sensory experience?
b) N(173)= 512: Larger structures in midbrain consisting of cubes containing 8x8x8
cells. 3-dimensional chess-board or 8-move simulation for ordinary chess game.
Perhaps the structure of chess game is not an accident but reflects the
basic morphology of brain. Does these structures make emotions possible?
Is Cambrian explosion related to this length scale. Neuron number for nematode worm
is about 300. Prediction is consistent with Hameroff-Penrose prediction
(if structure was spherical, N(173)= about 256).
c) N(179)=about 256.000: Ocular dominance columns in cortex and similar
structures. Emergence of cognition? Emergence of vertebrates?
N(181)= 8*N(179): Pairs of ocular dominances columns correspond to k=181.
Integration of left and right cognition to stereocognition, say stereovision.
d) N(191)= (2^18)*N(179). Structures of size 1/2 mm.
N(193)= 2^3* N(191). Cubical structures of side 1 mm. The morphology
of cortex demonstrates decomposition to modules of size (1 mm)^3.
These structures should consist of 8 sub-cubes of side 1/2 mm!
Some kind of comparison modules, novelty detectors?
e) k=197 and 199 form again a pair. Does anyone know
about the structure of the human brain in these length
scales? Is this the level of cognition, which is especially
evolved in the brain of chess-players?
f) k=211: L(211) corresponds to 24 cm length scale. This length scale
seems to be larger than the size of human brain.
Thus, possibly apart from k= 197 case, it seems that p-adic TGD is consistent
with the architecture of brain correctly! Comments?
Best,
MP
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