Re: Realization Solutions through Natural Transformations of Organismic Models and Variable Molecular Structures

[Ionel <***>]

On Sat, 12 Jun 2004 18:13:10 -0400, Ionel <***> wrote:

>Dear Tim:
>
>I could do both. The categorical formulation in Robert Rosen's style--
>using just standard sets is straightforward-- BUT is now no longer up-to-
>date because of the loss of consistency in terms of the use of just Boolean
>Logic and sets to model Life! ([Please see my other posting on "What are
>the Logics ...appropriate for modeling Life?' ; see also the comments
>posted by  John M and my reply to his comments and questions).
>Robert's formulation of my Figure 1 would be (hoping that the diagram would
>post correctly--if not I will have to re-post a pdf) as follows:

>
>   Robert's Model                I__My new 'stuff'____---------->........
>                                 I
>---------------------------------gamma= reverse transcriptase (mine!)
>
>   f   phi      beta            gamma                     delta
>A---->B--->H(A,B)---->H[B,H(A,B)] --->H{H(A,B),H[B,H(A,B)]}--->...delta-->I
>                          I<----------------------I                       I
>                                                  I<----------------------I
>
>___________________________________________________________________________


>All of the objects in capital letters: A, B, H(A,B),etc... are 'sets' in
>the original Robert Rosen's published papers. All lower case letters
>represent functions, or 'set-theroretical mappings': f, phi, beta, gamma,
>etc... Robert's diagrams did NOT include either gamma or delta, but he did
>say that the diagram could be efurther extended, although he did not
>specify, as I do above, and did also in my Figure 1, as well as also back
>in 1969. All , of the above diagram is in the (SMALL) Category of Sets,
SET,
>or Ens (French notation: 'ensemble' = set , in French).
>
>
>Please note, however, that the last two 'closure' cycles with arrows
>running backwards to the left --that were hinted at by Robert Rosen in 1973
>in his BMB  paper on dynamical realizations of MR systems, and that are
>shown explicitely shown in my 1969 work on generalized/ extended (M,R)-
>system, provide both the closure and the entailements for 'immortal',
>perpetual cell division as in either in the germ cell or in the cancer
>cells that are malignant...and unfortunately, often lethal.
>
>-------------> Thus the gamma function-- that was never defined in Robert
>Rosen's papers explicitely-- has as 'input'  "phi" (and also
>implicitely "f", as "f" is contained in the domain of "phi"); the  same
>comment applies to delta. Both gamma and delta functions are necessary to
>model correctly living cells. Also, please note that I did not represent in
>the diagram the closure through beta ('DNA gene')for simplicity's sake--
>there was also no room with the simple typing, very limited means of the
>direct posting tools.
>---------------------------------------------------------------
>But the diagram, ofcourse, also closes at beta (not shown), with beta
>making phi, and phi making "f", the metabolic component, such as an enzyme
>or a protein.
>
>Let's see if the diagram here written/showing up correctly will also post
>correctly?!
>
>Regards,
>
>Ionel

Hi, Tim:
Sorry , Tim . In spite of my valiant efforts, the posting did not correctly
reflect my diagram. See if I can email it to you in the correct form
and than you could try to change it to pdf, if you will. Maybe the corrected
quote will fix the posting problem. Let's see!?

Regards,
Ionel