number of messages vs. number of carrier objects

From: Karl Javorszky <[email protected]>
Date: Mon 03 Jun 2002 - 18:33:48 CEST

Dear Jerry,
thanks for continuing the discussion. Please allow me to answer to your points one after the other.

.. progress in chemistry has given us material descriptions of most "things" in terms of chemical structures and associated chemical agglomerations and often these descriptions are strongly supported by quantum mechanical calculations grounded in physics. Many advances of technology are directly relatable to our new understandings of the dynamical structures of simple components of complex objects.
I present to you a model with some few hundreds of elementar truth values of a rather more complicated truth table than the one we are used to. So far, we have had {.t.,.f.}. Now, we shall have {.1a., .1b., ..., .1k., .2a., .2b., ..., .na., .nb., ...}. These truth values are subsets of a "normally structured" set that are present whenever the set size is above a minimum. (Like we may be sure that on any streetcar with a usual population sample there shall be at least ... persons with the combination of properties "most common hair colour" with "most common marital status" AND at least ... persons with the combination of properties "second most common hair colour" with "most common marital status" etc.} Each of these subsets will have a probability of presence f(n) with p -> 1 f(n).

Could you say more about what you mean by "pre-logical"? I do not understand this usage at all.
In psychologic terms: whatever is experienced by the older regions of the brain than the cortex is pre-logical. In physical terms: what is there without me being able to deny its existence (for a newborn: breast, light, Sun, gravity, solid things, etc.) Logic is produced in the cortex. The subcortically registered impressions constitute the set of pre-logical sensations. What you run into and causes pain irrespective of what you think about it is pre-logical. (In Wittgenstein terms: this is what logic is embedded in.)

Q: A central problem is the irregularity of the mathematics of chemical systems. This implies also the mathematics of living systems. The irregularity of chemical structures and chemical dynamics (living structures and living dynamics) denies me access to "the translation between logical structures and carrier objects on which one can observe the logical structures".
A: The chemical systems are not irregular. Our concepts about how they should be are not in line with pre-logical facts (we cannot question the existence of chemical elements, can we. If it doesn't appear logical, then our ideas on how it should be are faulty, not the facts.) If I decide by logic that the Sun and the Moon have to move in synchron around the Earth, then my logic is faulty, not their movement is irregular.
This goes down to the widely misunderstood axiom by Newton that things are idle or in a continuous linear movement. What Newton has omitted to restrict his axiom to is: "non-living things". This means that - if we believe Newton as he stands now - we are not part of the predictable, rational nature. That sentence of Newton has caused great many confusions. (What he has meant was: "be assured, stay calm, there are no witches and the things dont jump up and run after you.")
As to the relation of messages and carrier objects: this is indeed a trick as least as wondrous as pulling a rabbit out of a hat. How many objects do I need to transmit x messages with? This is the crucial question. Surprisingly, genetics appears to make use of the fact that one needs differently many objects to transmit x messages with in dependence of 2 properties of the objects: a) their number f(x) /this is trivial/, b) whether I use them sequentially or concurrently /this is the invention/. If I send n beads on a necklace, then I can send f[s](n) distinct messages with n objects, if I send n beads in a pouch, then I can send f[c](n) distinct messages with n objects, and f[s](n) <,=,> f[c](n) and this f(n). [s]: subscript for "sequenced", [c]: subscript for "contemporary" or "commutative".
Turning the efficiency question on its head, one will find that in order to send x messages with, one may use n or n-1 objects, in dependence on the density of the logical structures on the set (in common language: whether I use the obejcts as a sequenced media, or I send the objects all at once, or what proportion I send so and what proportion so /this last combination of transmission methods appears to be the trick to the riddle of the human memory with its "packaging" of information/). This allows translating an expected (average) number of logical relations into the existence of 0.0 - 1.0 logical object more or less, all f(n). This idea should sound familiar from physics.

I am denied access to this route by the fact that chemical structures are mathematically expressed in terms of labeled graphs and that these labeled graphs can not be placed in correspondence with the natural numbers. In short, each chemical identity (entity, compound, object, thing) is a unique category.
Please allow me to modify your statement "... these labeled graphs can not be placed in correspondence with natural numbers." by adding the words "to my knowledge" and "so far".
I agree that each chemical identity (entity, compound, object, thing) is a unique category.

I wrote:
the concept of time is intertwined with the concept of number. How do you justify this interrelation? At issue is the nature of continuity.
I find one of the strong suits of my theory that it uses any kind of sequence and relates its information-carrying capacity to the information-carrying capacity of any kind of contempororary assembly. One is free to give a sequence (a mathematical entity) an interpretation as time slices. If you can number it consecutively, then it is a sequence. I look into the interdependence between cross-sectional and longitudinal collections of objects (carriers of symbols /information/). In everyday speak this means: I look into the relations between collections that are here all at the same time and collections that come one after the other. In a heroic allegory about a theoretical living organism: the theoretical cell's constituents are all present at the same time and all (each) of them is relevant at the same moment, while the theoretical DNA gets read off from start till the end, one (triplet) at a time, one after the other. In the sequence, it is the neighbourhood relations that count (this comes after that), while in the contemporary assembly the inclusion relations matter (this is like these and like those). Continuity and discontinuity are discussed at great length and detail also.
Ok. I now understand part of the mathematical approach. The metaphysical issues concerning time are critical. Would it be fair to state that the metaphysical symbol exchange for "time - heat" is simpler than your proposed symbol exchange for "time - matter"?
We discuss matters of cyclicity and neighbourhood here. After how many steps do I find the same unique constellation in the same neighbourhood in a structured set that is linearised? One gets into deep waters here and the use of a flip-chart and drawing sketches would be very helpful. But it is frappantly easy. This all boils down to multidimensional partitions and the linearisations of their overlap structures.

You wrote:
I propose to transcend the gap between well established principles of number theory and the concepts of communication between two collections of message carriers by following steps:
1) extend number theory to include multidimensional partitions, hitherto left undefined;
2) introduce the concept of the structure of a set by discussing properties of multidimensional partitions;
3) introduce the technique of linearisations of structured sets;
4) discuss congruence relations between neighbourhood relations on a sequence and structures in a set.
I'd prefer not to call neither a structured set (a contemporary assembly) nor a sequence a system, but the interplay between these two constitutes a system.
Your agenda is clear. Have you published works concerning these topics? I would be very interested in the details or in receiving electronic copies.
Yes, there is an article in Journal of Theoretical Biology, and 2 or 3 contributions to congresses. There is more. A good introduction is to be found on this FIS page. Literature in different depths, details and lengths is available. Please contact me for details.

Thanks again for your interest. I look forward your enquiries.
Karl
Received on Mon Jun 3 18:38:38 2002

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