Matti Pitkänen (matpitka@pcu.helsinki.fi)
Thu, 9 Dec 1999 11:24:04 +0200
I have been thinking about ideas related to the realization
of genetic program. In particular, the question about
telomeres was very useful and helped in getting
to the correct track.
Very beautiful general picture
emerges when DNA is generalized to manysheeted DNA
and combined with the earlier idea about
DNA and proteins as a "formal system". The
latter idea was originally inspired by Hofstadter's " Goedel, Escher
Bach". It means that genes are interpreted
as statements constructed from fundamental statements
represented by DNA triplets. and proteins
represent truthness flags for these statements.
One can indeed understand basic numbers of the genetic
code from the model of abstraction hierarchy realized in
terms of Boolean statements leading to Combinatorial
Hierarchy. See the chapter "Quantum model
for intelligent systems" of
" TGD inspired theory of cs..." at
http://www.physics.helsinki.fi/~matpitka/cbook.html.
1. Manysheeted DNA
Manysheeted DNA corresponds to DNA sequence
having besides atomic spacetime sheets also other sheets
labelled by p-adic primes p=about 2^k, k=139,151, 157,163,
167,169,173, 179,181, 191, 193,...
These sheets could originally correspond to cognitive
spacetime sheets and are probably of
size of DNA. Thus body plan would be originally
only an intention! During the growth of organism
these spacetime sheets gradually grow and combine
by join along boundaires contact and give
rise to to various organs in adult. Note that growth occurs
at several spacetime sheets giving rise to
the hierarchical structures characteristic to organism.
One could roughly say that the geometry and topology of
body structures are mapped to manysheeted DNA
by contracting organ in transversal dimensions
to the thickness of DNA.
2. Many-sheeted proteins
Also proteins are manysheeted structures and
the foldings of proteins are probably very sensitive
to the number of spacetime sheets contained
by them. Thus a protein having
same chemical structure can serve as flag for truthness
of several different statements=genes. This makes
possible modularization of genetic programs.
DNA sequence with same chemical structure can have
different meanings according to the structure
of spacetime sheets associated with it.
This modularization allows to avoid huge genome:
note that plants can have genome which is
by orders of magnitude larger than human genome.
3. Is highest level of p-adic hierarchy determined
by body size of em size ?
The body size (or perhaps em size) of organism gives
upper bound for k:s present in the hierarchy of spacetime
sheets. The length of DNA coding primitive organisms is larger
than organism size typically by a factor of hundred.
On the contrary, for humans the length of chromosome is by
factor of 46 smaller than the size of organism! This suggests
that some other scale than body size must determine the number of
levels in case of higher level organisms
This discrepancy suggests that, at least for organisms possessing
EEG, it might be that electromagnetic size of organism determines the
largest value of k present: this would explain why
we are more intelligent than dinosauri. EEG frequencies
could correspond to resonant Schumann frequencices
associated with the cavity between Earth's surface and
ionosphere.
The presence of these levels
would make understable why slow EEG and Schumann
resonances seem to be related with spiritual and
mystic experiences. Most importantly, this
would mean that our growth could transform
to electromagnetic evolution after death: we
would become em subselves of Mother Gaia.
Topological field quanta representing Scumann
resonances perhaps!
In fact, electromagnetic size seems to be a reasonable
criterion also in case of proteins. Proteins oscillate
with frequencies of order 10^9 Hz and this
would correspond to electromagnetic size
of order .1 m. Em size of proteins should
indeed bee this since otherwise manysheeted
proteins having wormhole contacts to
spacetime sheets of body size are not possible.
4. Genes as statements and proteins as truthness flags.
The interpretation of genes and proteins is
following.
a) N-sheeted gene corresponds to a statement
G at the N:th level of statements
about statements hierarchy. Therefore the hierarchy
of spacetime sheets corresponds to an abstraction
hierarchy.
b) When the concentration of protein coded by G is
above critical concentration the statement G is true,
otherwise false. Otherwise G is not true.
c) The statement "If G1 ...Gn then G"
corresponds to situation in which there are present
minimum concentrations of entzymes coded
by G1 ...Gn needed to activate gene G
to code its own protein serving as truth indicator for statement
G. Also external parameters like pH and temperature can affect
the concentrations of proteins and hence the truth values
of the statements represented by them.
Most of these can be represented as truth
values for higher level genes.
d) In TGD based model for simple emotions,
which result from comparisons, hormone
or its absence tells the result of comparison: yes
or not. Hormones are indeed enzymes,
so that this fits nicely with the interpretation
of enzymes as truth flags! Also we would experiences
directly the truthness of at least some statements G.
Perhaps just those G:s which correspond to
the entire body or those parts of body which
correspond to our self. There is entire
hierarchy of emotions unconscious to
us.
5. Genetic programs
The previous assumptions guarantee that genetic
program runs automatically!
a) The structure of genetic program reflects
the evolution of genetic program
ORP suggests strongly that the structure of genetic
program reflects its evolution. This in turn suggests that
the conditions guaranteing the activation of genes
are such that first only the lowest level program
modules are activated and in turn active
more evolved programs which in turn code more
advance programs. Gradually new hierarchy levels
appear and this has interpretation as emergence of
new abstraction levels: statements about statements
are formed.
b) Consistency conditions for statements
Also genes Gi having higher level
than G can appear in " If G1...Gn then G " type
statements for lower level organism but G
but these there must be several statements
"... then G" since otherwise the absence of
the higher level activation would stop
the growth of the organism!
c) Conditions making possible differentiation
The presence of the conditions involving higher
level G:s could explain differentiation since they
reflect dependence of the gene activity on
the organ where it is located.
d) Why telomeres?
WHILE N>0 DO .... N-->N-1
is basic structure of program making possible to avoid
infinite loops, which are nightmare of programmer.
Invididual never dying is typical infinite loop and
the presence of too many indiduals of this kind is
a catastrophe for obvious reasons. Thus crucial
G:s must contain additional condition
WHILE amount of telomre >0 ..... Reduce the amount
of telomere by one unit!
e) Why chromosomes?
Chromosomes are identified as a set of
mutually interacting paralelly running genetic programs.
One possibility is that chromosomes in fact mean
composition of body part to N_c linear structures.
Paralle interacting processing would bind these
structures to single coherent hole.
6. Mendel rules OK
One can understand basic rules of Mendel easily
if the conditions guaranteing the activity of gene
depend on both members of chromosome.
For instance, in case that two traits are such that second
on dominates the output of gene realizing
the property is AND function.
If G1 in chromosome 1 and G2 in its partner chromosome
have coded their particular enzymes then G codes
the enzyme giving rise to the nondominant trait,
otherwise the dominate trait appears.
Second situation is the one in which traits are
not yes/no properties but have continuous spectrum.
Either of both chromosomes could contain gene coding
the trait under conditions which do not depend
on activities of second chromosome.
Best,
MP
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