Louis Kauffman loukau at gmail.com
Wed Sep 22 07:18:52 CEST 2021

Dear Folks,
I am including some information  that is relevant to this issue.
I define ‘recursive distinguishing” written as “recursive distinctoning”.
For more, see:
https://www.dropbox.com/sh/r75m4g81rtyhi6y/AAAamRlGWr9P1zeUgdcTjiNua?dl=0 <https://www.dropbox.com/sh/r75m4g81rtyhi6y/AAAamRlGWr9P1zeUgdcTjiNua?dl=0>
https://www.dropbox.com/sh/dbrfjeqhmpcz7nh/AAC0vUqwXZ0Yl9xHCZzpWSaYa?dl=0 <https://www.dropbox.com/sh/dbrfjeqhmpcz7nh/AAC0vUqwXZ0Yl9xHCZzpWSaYa?dl=0>


Recursive Distinctioning means just what it says. A pattern of distinctions is given in a space based on a graphical structure (such as a line of print or a planar lattice or given graph). Each node of the graph is occupied by a letter from some arbitrary alphabet. A specialized alphabet is given that can indicate distinctions about neighbors of a given node. The neighbors of a node are all nodes that are connected to the given node by edges in the graph. The letters in the specialized alphabet (call it SA) are used to describe the states of the letters in the given graph and at each stage in the recursion, letters in SA are written at all nodes in the graph, describing its previous state. The recursive structure that results from the iteration of descriptions is called Recursive Distinctioning. Here is an example. We use a line graph and represent it just as a finite row of letters. The Special Alphabet is SA = { =, [, ], O} where "=" means that the letters to the left and to the right are equal to the letter in the middle. Thus if we had AAA in the line then the middle A would be replaced by =. The symbol "[" means that the letter to the LEFT is different. Thus in ABB the middle letter would be replaced by [. The symbol "]" means that the letter to the right is different. And finally the symbol "O" means that the letters both to the left and to the right are different. SA is a tiny language of elementary letter-distinctions. Here is an example of this RD in operation where we use the proverbial three dots to indicate a long string of letters in the same pattern. For example,

... AAAAAAAAAABAAAAAAAAAA ... is replaced by
... =========]O[========= ... is replaced by
... ========]OOO[======== ... is replaced by 
... =======]O[=]O[======= ... .
Note that the element ]O[ appears and it has replicated itself in a kind of mitosis. To see this in more detail, here is a link to a page from a mathematica program written by LK that uses a 'blank' or 'unmarked state' instead of the '=" sign. Program and Output <https://www.dropbox.com/s/tkkye8g99tzm0xm/RDL.pdf?dl=0>. Elementary RD patterns are fundamental and will be found in many structures at all levels. To see an cellular automaton example of this phenomenon, look at the next link. Here we see a replicator in 'HighLife' a modification of John Horton Conway's automaton 'Life'. The Highlife Replicator follows the same pattern as our RD Replicator! We can begin to understand how the RD Replicator works. This gives a foundation for understanding how the more complex HighLife Replicator behaves in its context. HighLife Replicator. <https://en.m.wikipedia.org/wiki/Highlife_(cellular_automaton)> Finally, here is an excerpt from a paper by LK about replication in biology and the role of RD. Excerpt. <https://www.dropbox.com/s/zm785d20bma6tb2/KauffmanExcerpt.pdf?dl=0>

Recursive Distinctioning (RD) is the study of those systems that use symbolic alphabetic language that can describe the neighborhood of a locus (in a network) occupied by a given icon or letter or element of language. An icon representing the distinctions between the original icon and its neighbors is formed and replaces the original icon. This process continues recursively. 

RD processes encompass a very wide class of recursive processes in this context of language, geometry and logic. These elements are fundamental to cybernetics and cross the boundaries between what is traditionally called first and second order cybernetics. This is particularly the case when the observer of the RD system is taken to be a serious aspect of that system. Then the elementary and automatic distinctions within the system are integrated with the higher order discriminations of the observer. The very simplest RD processes have dialectical properties, exhibit counting and they exhibit patterns of self-replication. Thus one has in the first RD a microcosm of cybernetics and perhaps, a microcosm of the world.

If you have read the above then you see that this mode of recursion goes between a world in which distinctions can be drawn to a new world that is a description, an encoding, of the previous 
world. The encoded world is again a world of distinctions and can be encoded. The recursion of encoding encoding goes on indefinitely and creates structure of great interest.
The question remains whether this is a description of fundamental process at the physical level, and how it manifests at the biological and cognitive levels.
Very best,
Lou Kauffman

> On Sep 21, 2021, at 6:54 AM, Pedro C. Marijuan <pcmarijuan.iacs at aragon.es <mailto:pcmarijuan.iacs at aragon.es>> wrote:
> Dear FISers!
> It is quite a long time without list activity... As you all know, the IS4SI 2021 event just took place during last week . Many of FIS parties participated, though it was complex to explore all subconference tracks and follow them under the ZOOM scheme. It is a new "virtual" regime that the pandemics has precipitated--and it will stay... In any case, for those who missed the sessions, there will be complete recordings available in due time.
> Anecdotally, one of the discussion themes, biological & computer codes, was raised by me during the final, closing session. I had never thought about codes in that way. Joseph made a quick response and sent later a message which I paste below. I think continuing as an open discussion could be interesting for the list.
> Well, I realized that if we compare biological & computer systems with inanimate systems, codes are one of the most significant differences. Apart of the genetic code, there are many biological others: metabolic codes, degradation codes, adhesion codes, histone codes, sugar codes, cytoskeleton codes, dvelopmental codes, neuronal codes, etc., etc. It is quite interesting that prokaryotes did develop very few codes and so, presumably, could not develop their constructive complexity. Something similar would have occurred in the development of computer architecture layers, based on increasing codes hierarchically arranged in general. 
> I am not aware of any physical system which had created any kind of code (except, hypothetically, in the origins of life). Well, symmetry groups in crystallographic systems could be close, but its constructive complexity is low, quite "flat", directly dictated by the components... 
> Are codes really significant for the information realm? Do they represent the obligatory way of channeling the inner self-construction (dynamic) information flows?
> Could there be a deeper discussion on codes?
> All the best,
> --Pedro
> -----------------------------------------------------------------------------------------------------
> Dear Pedro and All,
> Just as the Conference was closing, Pedro brought out the extremely important subject of codes, and the result of my rushed interaction with him can be summarized as follows: codes are epistemological; dynamics are ontological. 
> This means that codes and dynamics co-exist but are of a different nature. Codes describe the catalysts of change in living systems, but they do not change themselves without an input of energy/informatin. The same is true of codes in non-living systems, say, inorganic catalysts that degrade over time. Computer codes are purely epistemological, as many of you have said in other terms.
> Codes and dynamics can be separated physically but not functionally. They instantiate non-separability as a fundamental principle.
> Thanks and to be continued, I hope.
> Best wishes,
> Joseph 
> -- 
> -------------------------------------------------
> Pedro C. Marijuán
> Grupo de Bioinformación / Bioinformation Group
> pcmarijuan.iacs at aragon.es <mailto:pcmarijuan.iacs at aragon.es>
> http://sites.google.com/site/pedrocmarijuan/ <http://sites.google.com/site/pedrocmarijuan/>
> -------------------------------------------------
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