Re: Papers on SELF-REPRODUCTION and Entailing in Generalized/Extended (M,R)-Systems, Supercategories and MR-Dynamics

[Ionel <***>]

On Mon, 24 May 2004 21:51:51 -0400, Tim Gwinn <***> wrote:

>Ionel,
>
>Are your two papers you mention below referring to the (M,R)-system (1972 &
>1973) among those you intend to post? It would probably clarify much if I
>could read those.
>
>Regards,
>Tim
>
>> -----Original Message-----
>> From: ROSEN Forum [mailto:*** Behalf Of Ionel
>> Sent: Monday, May 24, 2004 8:34 PM
>> To: ***
>> Subject: Re: SELF-REPRODUCTION and Entailing in Generalized/Extended
>> (M,R)-Systems, Supercategories and MR-Dynamics
>>
>>
>> I believe Tim wrote:
>>
>> 1. >>My question was unclear, I think. In Rosen's (M,R)-system, one of
the
>> key qualities is that it is "closed to efficient causation"; that the
>> functions (f, Phi, Beta) are all entailed from within the diagram - they
>> are each generated by some other function in the diagram. (Phi => f ,
Beta
>> => Phi, f => Beta).
>>
>> 2. My question was in how (or whether) the additional functions (reverse
>> transcriptase, closure map?) are similarly entailed within the diagram,
>> such that it would remain "closed to efficient causation"? >>
>> _____________________________________________________________
>>
>> Q.#1. As demonstrated in our 1972 paper (Baianu and Marinescu,
>> 1972): "On a
>> Functorial Construction of (M,R)-Systems", and also continued in: "Some
>> Algebraic Properties of (M,R)-Systems." published in BMB (Baianu, 1973),
>> the generation from Phi to f and from Beta to Phi, and from f to Beta
>> involves in a fact a functorial construction, and also requires the use
of
>> natural transformations, as explained in the above cited papers
>> that "entail" the diagram to have "closed or efficient causation".
>>
>> Q. #2. Therefore, it does require the use of 2-categories,were
>> functors and
>> natural transformations are being employed, the first type of
>> supercategory
>> higher than 'regular', 1-categories. Moreover, either Eilenberg
>> or MacLane,
>> or both said, that the ONLY reason for introducing categories was to be
>> able to use functors and natural transformations of functors, that is TO
>> USE A  2-CATEGORY; the added emphasis is mine, and it is very
>> unlikely that
>> it will ever be contested by any serious algebraist. The level of
>> complexity increases towards the right hand side of the diagram, either
in
>> the common usage of the word, or in  Robert's use of the word. This is a
>> point that Robert has explained clearly in the same manner as discussed
>> here in his papers on "Dynamic Realizations of (M,R)-Systems." (BMB,
1971,
>> 1973). The same argument leads to extending further the (M,R)-Systems
>> towards higher complexity by adding terms on the right hand side of the
>> diagram- THAT ARE CONSTRUCTED WITH THE SAME 'ENTAILING' process -
>> as in the
>> previous 'stage of development of the (M,R) -systems-the one considered
by
>> Robert Rosen for the simplest MR's, both mathematically as well as in
>> Robert's sense of the use of "complexity", as clearly stated in
>> his "Essays
>> on Life...". Robert also pointed out the possibility of extending
>> the (M,R)-
>> Systems towards the right of the diagram, but did not proceed to actually
>> do so. Perhaps, one of the reasons was that at that time the theories of
>> n-categories, and supercategories, were just beginning to be developed
and
>> there were several fundamental issues that had to be settled about such
>> structures in 'constructivist' and/or logical terms, but not in a
semantic
>> sense, i.e., along the very lines of thought that Robert is looking upon
>> favorably in his :"Essays of Life..." book.
>>
>> Q#3... Not asked directly by Tim, but that is here an important question,
>> nevertheless:
>> What happens after the addition of the Reverse Transcriptase, the hTERT
>> gene, and so on on the right hand side of the diagram? That is, when will
>> be this diagram complete? The answer(s), as hinted at in my second posted
>> paper,  depend(s) on which type of cells, or organisms, does one wish to
>> model: a. Somatic Cells; b. Germ Cells and c. Malignant/Cancer cells,
just
>> to name three of the most prominent types. In other words, you'd
>> need three
>> different, generalized (M,R)-systems to represent such evolved cells or
>> organisms thereof. 'One shoe doesn't fit all',  as one might be
>> inclined to
>> believe if one just stopped at considering only the simplest (M,R)-system
>> which is the one discussed most of the time, because of its apparent
>> mathematical 'simplicity'; that, in fact, is only an illusion of
>> the 'hidden',  underlying complexity in Rosen's sense, as well as in the
>> sense of needing a 2-category to be correctly constructed in order to
>> be 'entailed', that is, in order for the (M,R-system to both
>> FUNCTION/work-
>> in the biological sense- , and also to effect 'finite closure'. On the
>> other hand, since, I hope, we're talking Science NOT Religion, further
>> development of such concepts is not only "permitted" by Robert's work but
>> also very strongly encouraged by my extensive contact with him through
>> letters on this subject. I don't think Robert would have ever wanted
>> a 'Religion' created just for Him alone that doesn't allow for further
>> development of his ideas and concepts. Furthermore,it is important and
>> useful to discuss things both from a semantic as well as technical
>> viewpoints. A 'dogmatic', or very narrow, interpretation of his work was
>> never one of Robert's intentions, and he made that very clear to all who
>> knew him directly.
>>
>> Let me also add, or reassure you, that there is still a great deal of
>> additional work to be done in this area, and we can only say that we are
>> just laying the foundations for future developments of robert's vision,
>> covering both interpretation and molecular representations of generalized
>> (M,R)-systems. Compared with Petri nets, for example, that have been very
>> dramatically developed--still not completed, the theory/ theories
>> of (M,R)-
>> systems still has/ have a long way to go in spite of their attractive
>> features in terms of self-reproduction, 'closure and entailing' that have
>> captured a significant--but not comprehensive-- amount of biological
>> complexity. Not to mention the dynamic representation problems of (M,R)-
>> systems that Robert has opened for further development, hopefully to
occur
>> not too far into the future. New mathematical tools and "generalized
>> spaces" are now available for exploring much further the biological
>> complexity that Robert Rosen has just began unvailing in his books "Life
>> Itself.", "Essays on Life...", and all his previous papers cited therein,
>> as well as papers by several others who significantly contributed to
>> opening up this field of complex biological systems and complex dynamics
>> research. Hope this explanation helps expand on the interpretation of the
>> mathematical construction presented in the second, posted paper.

Tim:

I wish I could do so, e.g. post them for you, but their scanning and
careful corrections are going to take awhile. If you have a fax I could fax
copies to you and other group members who'd request it directly from me so
that one doesn't feel that I am holding something useful back from this
group.

Regards,

Ionel