**Matti Pitkänen** (*matpitka@pcu.helsinki.fi*)

*Wed, 1 Dec 1999 08:21:31 +0200*

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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. Does these structures make emotions possible? Cambrian

explosion. 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!

Three-dimensional chess-boards or 8-move simulation for

ordinary chess! Is it mere accident that chess-board contains

8x8 squares?! Some kind of comparison modules, novelty detectors?

e) k=197 and 199 form again a pair. 8 cubes with side of 4 mm

composing to cubes of side 8 mm. Does anyone know about

3-D-chess-board. 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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