Re: Adjoint Functor Pairs Preserve Limits and Colimits in Categories of Biological Systems, Automata and (M,R)Systems

["Professor I.C. Baianu" <***>]

Hi, Tim:

I am trying to catch up with your questions before I'd have to take a break
in my responses to the group in a day or two.

>>RE: Tim asked:

>Do these remarks suggest that an organism's development is, in some sense,
anticipatory? Perhaps I am reading too much into this, but it strikes me
that perhaps the organism itself at each developmental stage is also a kind
of model of which particular completions can follow. Also, if possible, can
you speak a bit about "adjoint functors" and their utility? Maybe the
corrected file will make it more clear - it is not a term I've run across
before in my (limited) reading on category theory.
Regards, Tim>>

A qualified "Yes", Tim:

After a certain stage of development of an organism from the fertilized
egg, because of increasing cell specialization during development of a
biological organism, and the larger and larger limits of different
interacting, specialized cells, the adjointness condition will no longer be
satisfied and would ne to be replaced by 'weak adjointness', that is
epimorphic mappings on earlier stages instead on 'isomorphisms', or more
precisely natural equivalences of adjoint factors at the earlier stages of
development when all nuclei are "totipotent' (e.g., mutually
interchangeable without any notable change in phenotypic development or
chromosomal structures; please note that this does not assume either
structural or functional identity, only isomorphism). The nice thing about
this model is that it would apply to most multi-cellular organisms that we
know, and therefore, it is universal in this sense, unlike very complicated
models with lots of specific mechanisms invoked for specific organisms;
e.g., you may call such a model "Rosennean" if you wish and its complexity
instead of being generated by just a few 'impredicativities' it contains
them as part of the adjointness relations and natural equivalence ( that
cannot be however described, or have never been described to my knowledge
as being "impredicative" , even though they preserve the level of complexity
of the developing initial stages, until the transition occurs to 'weak
adjointness'and higher level (s) of complexity associated with the mature
stages of the organism. In this respect, I was surprised to find in
Robert's publications, and in his "Essays..." quite detailed mechanisms of
interacting 'propagating waves of chemical gradients' generating different
'morphogenetic states' (discussed in parallel with Rashevsky-style two-
factor models applied to morphogenesis), the same problem as the one
discussed above in just functional terms--without the restrictions imposed
by the specific molecular mechanisms of "chemical wave propagation in
morphogenesis", such as the model proposed by A. Turing in 1950 and cited
by Robert in his work on morphogenesis. Were we more "catholic than the
Pope" in our nuclear transplant/ morphogenesis paper with adjoint functors?
My educated guess is that Robert's discussion in terms of 'states' was
merely introduced to clarify the distinction between the two quite
different types of models that, nevertheless, converged onto similar
conclusions, e.g. Rashevsky's and Robert's, on the one hand, and Allan
Turing's, on the other hand. There is, of course, the third alternative,
such as the one that I have just described above in terms of adjointness of
dynamic systems and/or developing stages of an organism, that can be
converted without much difficulty into a generalized (M,R)-system
construction as shown in my second posting on natural transformations in
molecular biology. Although one might contrive models with (M,R)-systems
to follow chemical gradients and their propagation during organismic
development, as the sole 'mechanism' responsible for morphogenetic
development, it would seem to me to be just not 'complex' enough in
Robert's sense, and too much automata-like,(which is exactly what Alan
Turing wanted to say in the first place, in 1950). Here complex is not to
be  replaced by 'complicated', because I think one can make quite
complicated  'wave patterns" out of chemical gradients, without necessarily
building a surviving organism, but a sort of a pretty, symmetric "chimera"
that would not "survive in the struggle for Life", or if it did, it would
not succeed to propagate as a stable, or non-terminal, species. If one were
asked the question, "Is such a 'chimera' alive?", one could perhaps answer
it with a qualified yes, close to the meaning of life for a malignant
tumor. This answer relates perhaps to the one partially formulated by
Schrodinger in his book "What is Life?": Schrodinger's surviving hereditary
system  ("quantum genome" in Robert's terms and ours) is part 'chimera' and
part quantum automaton, and therefore, may be ' a superposition of
half-dead and half-alive quantum states'--until observed-- like his
imaginary cat, even though our Boolean / Chryssippian logic does not alow
for the existence of such things.
Hence... there must be a basic flaw in that reasoning, such as the absence
of a defined 'quantum state' at the level of a huge number of interacting
components of different kinds that have all different phases at room
temperature--that do not have coherent dynamics such as Bose-Einstein
condensates, or superconductors at low temperature, or liquid He-3,
or 'high-temperature superconductors', that do possess quantum state even
for huge numbers of such
Bose-Einstein, 'identical' particles forming Macroscopic, quantized, or
quantum, systems.

If one looked at the "Quantum Evolution", book by J.F.,it seems to propose
that somewhat similar mechanisms to the Bose-Einstein condensates must
operate in "quantum genetics", even though the author recognizes the
formidable barriers posed by quantum decoherence processes at the level of
the genome at room temperature. Anyway, his suggested mechanism is far too
complicated and too long to be worth my while to repeat here.

Regards,
Ionel