Tim: You have grasped the first, very important feature of supercategories, meta- categories or n-categories: they provide a great deal of "organizational" and algebraic, functional DEPTH, but also they offer much more as advanced tools for complex system modeling, at least in the manner that they are employed in my paper to represent supercategories of generalized (M,R)- systems endowed with mathematical structures--both topological and algebraic. These tools allow us to CONSTRUCT in detail algebraically, or topologically, generalized (M,R) system models of ANY biological system--of ANY COMPLEXITY desired-- as shown in greater detail under "PROTEIN BIOSYNTHESIS" in the same paper, as well as in our cited 1973 and 1987, full-length published papers. Such constructions are not available by utilizing just categories of sets, or worse, just structureless sets. The 'entailment'/entailing that you are asking for is provided by the constructions that employ the canonical functors (Yoneda?) and natural transformations generalized from the Eilenberg and MacLane (1945) early stage set-mappings, between such special construction functors. This means that 'entailment' is not just a 'magic', Rosennean ("Open Sesame!") wand, but an actual functorial construction followed by natural transformations that are then 'entailing' the objects with functions and morphisms with internal dynamics or functional processes. The essential closure of the self-reproduction is available only as a result of this functorial constructions, and 'entailment' does NOT occur when one employs just structureless sets or simple mappings of sets. When you restrict the (M,R) systems to just a set, there are no 'entailed' colimits or limits, except those simple products/ or union sets provided by the automaton/T-machine equivalent to the FINITE set-only (M,R)-system, that does not self- reproduce, it is digitally computable, and-- as stated by Robert Rosen in his "Essays on Life Itself" -- is then NOT at all a complex system, but merely a classical, standard, discrete input-output device that is subject to the fundamental decomposition theorem of automata theory; in a certain algebraic structure sense,it is just as linear as the entire bunch of linear systems already covered by standard classical theories. The question remains then, as Schrodinger did ask it: What happens when you have a Quantum GENETIC system? This is his question in "What is Life?". Other people thought, and still think, he was getting 'philosophical'... and wandering away from his field, but he was actually still very much in his field, and he has run into the "PARADOX OF LIFE's SELF-REPRODUCTION and CATALYTIC SYSTEM"--that he was unable to figure out fully in Quantum Mechanics terms, as he wished very much to do! How come that observation of such a quantum genetic system does NOT lead to marked, IRREVERSIBLE genetic changes--e.g. genetic mutations --ASKED HE-- in a very short time, and every time, the gene "molecules" (that Dr.Delbruck and Dr.F. Crick considered for such a FUNCTION) are being "observed"/measured in order to be CORRECTLY/PERFECTLY duplicated??? The partial answer to this MATHEMATICAL CORRECTEDNESS/ quantum irreversibility paradox of the gene duplication and heredity he thought it would be a CODING , or encryption method in the genes by 'molecules', and (Dr.F.Crick and Dr. George Gamow , both physicists with a very strong mathematical, physical education and thinking, much later followed this trail of thought.} That's why Schrodinger said, to himself and to others, "What is Life?", what's the Quantum trick that gets around the irreversibility problem in LIVE systems only!!! Thus, Schrodinger cited the well-known example of the Habsburg Imperial family in the former Austro- Hungarian Empire whose heads and noses showed a remarkable degree of head/face and nose "hereditary" conservation over at least four generations, over centuries! The quantum irreversibility should have made that disappear in a giffy, at the first gene duplication that occurred, but it doesn't happen that way, he notes!! Why?! What's this magic trick of life that gets around our well-established QUANTUM IRREVERSIBILITY theory of measurement, said in his booklet "What is Life?" a very puzzled, worried and bothered Schrodinger ? At least part of the "magic trick", as also Robert said in 1996/7, is in the pattern and "construction closure", algebraic-topological/ SUPERCATEGORICAL structure present in the "entailed" Metabolic-Replication-RT-DUPLICATION system showed in my papers; the rest of the story has to do also with the biosystem being "open" for energy and molecular exchanges, as well as some very special , unique, properties of the Hilbert space transformations of certain quantum "automata" that I introduced in my other posted 1971 paper , i.e, eqs. 1 through 3,. and more... But that's a subject that will have to wait for the next postings on "Quantum Topology of Quantum Automata", "Supercategorical Models in Neurophysiology" (Baianu, 1972) and <Brain's Quantum Topology mechanism for Memory as a "pseudo-hollogram"> (the latter part was first thought of by Dr. Gabor, a Nobel Laureate, and published by him in Nature in the late 50's!!). Delivered-To: *** Date: Sat, 22 May 2004 05:46:39 -0400 From: Ionel <***> Subject: Re: SELF-REPRODUCTION: LIVE CELLS vsus AUTOMATA&Turing MACHINES To: Tim Gwinn <***> Cc: "Professor I.C. Baianu" <***> X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on zergling X-Spam-Level: X-Spam-Status: No, hits=0.0 required=3.5 tests=none autolearn=no version=2.63
On Sat, 22 May 2004 00:00:24 -0400, Tim Gwinn <***> wrote:
>Ionel, > >Thanks for showing us this paper. I should probably wait and study it some more....but, I've given it a first read, and I have a few questions: >1) I am not quite sure how the (M,R)-system diagram (Fig. 1) utilizes supercategories rather than sets. >2) I am also not sure what function symbolizes the reverse transcriptase actions on the right of the diagram, and what entails that function. >3) Also, what entails the "closure map" Ð?? > >I am intrigued by the idea of using supercategories, because to me that suggests the ability to have depths of detail and structure and entailments that is not possible using the category of sets. (Is this the same value in it that you see?) But I am not grasping it yet in the paper. I will have to re-read when I am back later this weekend, and maybe your comments will help. > >Regards, >Tim > > -----Original Message----- > From: ROSEN Forum [mailto:*** Behalf Of icb > Sent: Friday, May 21, 2004 8:21 PM > To: *** > Subject: SELF-REPRODUCTION: LIVE CELLS vsus AUTOMATA&Turing MACHINES > > > Tim and Dr. Howard Pattee, > > The file attached here illustrates how, in my opinion, a CATEGORICAL , that is, a non-set, super- or meta- category system with a CLOSED , specified algebraic structure of inter-connected component structures, GENERALIZATION of a simplest (M,R)-System. self-reproduces, unlike any of the AUTOMATON or MACHINE models described so diligently by Allan Turing, Von Neumann, Arbib... and others > > Ionel C. Baianu > >