Re: [Fis] ON MOLECULAR BIONETWORKS (IV) On Number

Dear Jerry:

    I am not sure I understand you correctly. I used mathematical concepts only as a convenient language. There is no mathematics in Nature at large. If we remember Robert Rosen's modeling paradigm (natural phenomenon ->encoding -> model -> mathematical evolution of the model ->decoding -> natural phenomenon evolution), the primary role of mathematics is encoding-decoding. As such, it is a very good tool for creative "co-mingling", because very different phenomena may be encoded into very similar mathematical models. Such similarities enhance our understanding of the models and, through them, of the underlying natural phenomena. Also mathematical language is quite well defined, so when it is used there is less space for ambiguity in understanding.
    As to the continuous versus discrete mathematics, this is again the matter of convenience. Very often discrete results come out of continuous equations. A good example may be recursive Feigenbaum nonlinear equation, which produces a range of solutions -- from discrete stable points and periodic solutions with one or several fixed frequencies to chaotic regimes. Also in many cases the same phenomena may be described by either discrete or continuous mathematics. I can refer you here to the same problem of the sea shell patterns. There were two papers in the Journal of Theoretical Biology with two different models -- one was a system of continuous differential equations, another -- a cell automaton type discrete model. Both yielded virtually identical results, which indirectly supports the point of view I advocate here. The choice is ruled in each case by pure convenience.
      In fact, often our distinction between discrete and continuous comes from the level of description we look at the system from. Each particle is discrete only until one does not go into the quantum sizes, and down there it is more of a continuous wave package (I hope that physicists here will not stone me to death for such a crude statement!). On the other hand, a multiparticle system is described well by continuous medium (and continuous mathematics!) in the hydrodynamic approach. There are well defined mathematical procedures that rule the conversion from discrete to continuous mathematics.
    In my previous post I tried to underline the role of mutual "measurement" and infinite recursion that comes as a result of such. I used mathematical terms just for illustration.

Igor

----- Original Message -----
  From: Jerry LR Chandler
  To: Igor Rojdestvenski ; fis@listas.unizar.es
  Sent: Monday, January 23, 2006 5:04 AM
  Subject: Re: [Fis] ON MOLECULAR BIONETWORKS (IV) On Number

  Dear Igor:

  Your reponse includes many threads of science and philosophy that are co-mingled with mathematical concepts.
  The usage of language co-mingles many concepts that must be kept separate if one is to conceptualize a theory of biological information that includes calculations of the genetic structures and reproductive metabolism.

   A few comments which may provide you some concrete examples that separate our world views, particularly about mathematics. Your philosophy of mathematics is a rather traditional one in the physical world. I have sought to explain why this view of continuous mathematics is not adequate for discrete relations among electro-chemical particles, electrochemical individuals we call the chemical elements.

  If you are serious about understanding the mathematical distinction, I suggest you attempt to use the atomic number in basic arithmetic, such as the distributive law and the commutative law.

  I suggest you demonstrate how your view of mathematics applies to these numbers and report back to the list your conclusions.

  On Dec 25, 2005, at 11:32 AM, Igor Rojdestvenski wrote:

    Dear Jerry,

    I will answer "my part" in green:

    Igor writes (vol. 488, 6)

      A cell mechanism A adapts (measures) to the cell environment, which it is part of. During this adaptation it increases its complexity and changes (by its very presence) the cell environment, which thus also increases its complexity. Given that there are many such mechanisms (enzyme catalyzed chemical reactions, organelles, membranes, etc), each mechanism increases its complexity by reflecting on the presence of the totality of the other mechanisms.

      JLRC:
      Reading your words from a 'big picture' frame of mind, I concur.

      I would prefer to express the concepts in terms of the flow of electrical particles...

          It may be flow of electric particles, e.g. "measurement" as exchange of electrons or radicals in chemical reactions, which leads to saturations of concentrations of products and thus changes the environment;
  The concept of "measurement" is hardly a natural concept of information. Measurement is a concept introduced with the French revolution and the international units of the decimal system. Unfortunately, chemical measures are based firstly on the natural units of elements and only secondarily on the concept of mass. Electrical flows are intrinsic to chemical structures and do not depend on saturation, etc. Flow is merely motion, is it not?

          It may be flow of photons, e.g. photosyntetic apparatus of green plants "measures" the incident light by producing flow of protons further used in ATP production and flow of electrons for NADPH production. These flows change, for example, the pH in certain parts of chloroplast, which, in turn, changes the flows themselves, including the available photon flow by, for example, epoxydation/deepoxydation of xantofills, "screening" photosystems from light;
          It may be flow of ions (changes in the state of the neuron through activity of calcium and potassium channels
          It may be flow of genetic information, e.g. transcription of RNA as a reaction to change in the cell environment, which leads to production of enzymes, which, in turn, modify this cell environment (e.g. reaction to heat shock or to strong light)

      Many more examples possible...

      In all these cases change, occuring as a reaction to a certain flow, is a measurement of this flow, and it, in turn, forces the changes to this flow.

      Yes, one may say that most of these phenomena deal with either flows of charged particles or photons. This is, however, trivial.

  Trivial? If these electrical flows are trivial, perhaps you may wish to write the equations for reproduction of a cell in terms of these flows.
  Are you conflating the possibility of a philosophical narrative with doing science? In the FIS case, we would like to calculate information content in a cell? If this is a trivial matter, please demonstrate how you would address the problem.

      Indeed, there exist only 4 force fields -- electromagnetic, gravity, strong and weak. In case of living matter, at the level of description of biomolecular networks, we deal only with the first one, with electromagnetic field.

  As far as I am aware, no conclusive evidence can be provided that ONLY four force fields exist. Perhaps you mean to say that thus far, physicists have not found a way to view the term "force field" in a unified way and thus create a narrative that justifies a statement that at least four distinctions are necessary.

  I have no idea why you reject a gravitational field in bio networks. For example, our blood pressure adapt when we move from a reclining to an upright position.

      Hence, the only material objects that really matter are those which interact with the electromagnetic field or are produced by it, i.e. photons and charges (ions and electrons)
  This is an intersting philosophy of science. I disagree.

      The term "mechanism" can be used in either a mathematical sense, a chemical sense, or a general sense. In what sense is it being used in this paragraph?

      When I say "mechanism" I mean:
           a chemical system of interactions between the biomolecules, ions and quanta, NECESSARILY in the structural context, i.e. in the organelles and compartments, where such interaction happen.
  (This is not a Newtonian description but rather a jargon or usage defined within chemistry; this usage obscures the relations between matter, electrical flow, time and space and genetics. It is a nice narrative.)

           a mathematical abstraction in the form of system of equations for the biochemical networks, that represents our understanding of the above.
  A foundation question for FIS is precisely the relation between these two sentences. Can you calculate it?

      Nature as such does not know equations and networks,

  Are you placing man outside of nature? Man (scientists) are emergent from chemical systems and as part of nature we know how simple equations and simple networks work.

      these are means of our interpretation of what happens out there. I think that this is more or less in line with Robert Rosen's views.

  My reading of Robert Rosens texts is radically different than yours. I am referring to two texts, "Life Itself" and "Anticipatory Systems". Which texts are you referring to?

      More specifically, in the narrative you provide, how does one create relations between electrical particles and the dynamics of bionetworks? Although only a small number of different electrical particles exist, how does one create the range of organisms in an ecosystem?
         
      As it is known from the theory of systems (examples being Lorentz attractor and other strange attractors, swarm theory, fractal structures, and many many more), it is quite possible to develop very complex systems from very small number of simple elements. The source of this complexity is the nonlinearity and instability of the system, or, in a more mathematical sense, the positive Lyapunov exponential in a finite and bounded phase space. It is, for example, known, that all possible patterns on the sea shells may be reproduced in modeling by means of a system of two simple nonlinear equations (this was in Journal of Theoretical Biology some time in 1987). Please also refer to the works of Karl Simms ("virtual creatures") and works in experimental mathematics of evolution by Chris Langton and other guys from Santa Fe institute.
  A clear example of what you mean would be a calculation.
  For example, calculate the number of isomers of (alpha) NAD to show how the methods work.

      Another argument: One needs only 0 and 1 values for the bit to convey in a string of bits as much information as one needs to.

  If this were true, how much information is in an NAD molecule? Please show how you would start with Shannon information and calculate a value.

      How can we make such concepts EXACT such that they become a meaningful method of scientific prediction? This is the challenge for bionetworks at all levels of perplexity. How does individuality arise from such a narrative?

      The problem is that we are oftentimes dealing here with the unstable non-equilibrium systems which are deterministic but unpredictable.

  Are you aware that chemical structures can not be entered into Thermodynamics? Only the ratio of concentrations of a specified reaction can be transferred from chemical theory into continuous mathematical equations. .

      This means that we cannot predict their behavior but can explain it afterwards.

  A very interesting remark. The remark reminds me of my children when they were teenagers.

      A good example is the game of pool. It is absolutely impossible to predict (before the stroke is made) exactly where each ball lands after the first stroke made into the "triangle" of balls. However, all the interactions, of course, obey Newtonian laws, and backward reconstruction of the process is possible.
      Same with evolution of biological systems and, in a way, with bionetworks.

  I fail to see any meaningful comparison between a game of pool and emergence of life and biological reproduction. For example, what is the correspondence between a genetic system and the forces of a fixed set of inelastic collisions? No generative operations are needed to describe a pool game.

      Only general features of it may be probabilistically predicted. And this is exactly how the individuality comes into picture. Had it not been for these instabilities and extreme sensitivity to small variations in initial and boundary conditions, we would have been all alike and all the same.

  Igor: Your belief in mathematical appears to me to be full, complete and totally classical physics.

  The challenge to you is to tackle some real chemical and biological problems to test your theories, EXACTLY. Narratives are easy to generate but the real test is in calculations. If Poincare was correct, you have some real challenges.

  I would add that chemical theory provides an exact method of calculation of electrical flows as well as the representation of electrical particles in chemical structures. The consequences of chemical calculations is a collection of relations that become the starting point for physical calculations attempting to describe the motion of the electrical particles in time and space. The chemical calculations are antecedent to physical calculations.

  Two other comments:

  1. I use the word 'exactly' to mean EXACTLY, not approximately.

  2. One of the philosophical differences between your world view and mine is that revealed by the ancient distinction between species and genera. It appears that you view mathematical generalities as universally applicable. I view the world as composed from species. Classical mathematical generalities are seldom applicable exactly to chemical or biological species. (or, was Poincare wrong?)

  Of course, I could be wrong... if you can calculate the number of isomers of NAD using classical mathematical combinatorics, I would be forced to reconsider the entire structure of my logic. (And chemical sciences would have to reconsider the nature of valence.)

  Cheers

  Jerry

      Igor

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Received on Mon Jan 23 16:17:50 2006