[Fis] Self-structurizing systems

[Louis Kauffman]

Dear Krassimir,
You never know until you see it.
We have the experience in topology over the last forty years that it is very good idea to see what category structures may be implicit in things we already know.
Amplfiying a nascent category is called “categorification” and has led to amazing new topological invariants and breakthroughs in low dimensional topology and in representation theory. To get a flavor, go the arxiv and search on that term and you will see:
https://urldefense.com/v3/__https://arxiv.org/search/?query=categorification&searchtype=all&source=header__;!!D9dNQwwGXtA!Ts6IUbDm73laGeTMfe164Vxr8No1Lok1o2BNr7Bx5XBAFwjleS0Uzpdc-0QLIsi3lEJf7l0V-EGfUo8l$  <https://urldefense.com/v3/__https://arxiv.org/search/?query=categorification&searchtype=all&source=header__;!!D9dNQwwGXtA!Ts6IUbDm73laGeTMfe164Vxr8No1Lok1o2BNr7Bx5XBAFwjleS0Uzpdc-0QLIsi3lEJf7l0V-EGfUo8l$ >
There are hundreds of papers in this link and I guarantee you that you will not at first understand a word. It all new mathematics growing out of 
categories recognized in older mathematics. 
Best,
Lou


> On Jan 6, 2024, at 3:32 PM, Krassimir Markov <itheaiss at gmail.com> wrote:
> 
> Dear colleagues,
> 
> First, the feeling of agnosticism in the commented third transition does not leave me. I hope I'm wrong...
> 
> Second, many thanks for the interesting opinions and thoughts.
> For me, they are a good reason to go back about 15 years to some projects I was working on back then. The main driver and generator of ideas was Prof. Viktor Gladun. I do not have the opportunity here to tell and present all the models that have been built until working systems and practical results are reached.
> Therefore, I will say a few words about the possibility to discover new subsets of causal features of objects that constitute affordances that can be seized by heritable variation and natural selection.
> Yes, Category Theory can be used in the initial stages of task analysis to achieve a collective understanding of the problem and possible approaches to solving it.
> Work then moves into the areas of classification, clustering, pattern recognition, prediction, feature processing, transformations, data mining, and knowledge discovery.
> It has interesting results and will probably interest you. It's about self-structurizing systems like we're talking about now. This is what Prof. Gladun describes in an article published in ITHEA's scientific journal. There's an example there that's similar to Stu's task, but it's about predicting new properties of new chemical compounds. Here is a link to the article: https://urldefense.com/v3/__http://www.foibg.com/ijita/vol15/ijita15-1-p01.pdf__;!!D9dNQwwGXtA!Ts6IUbDm73laGeTMfe164Vxr8No1Lok1o2BNr7Bx5XBAFwjleS0Uzpdc-0QLIsi3lEJf7l0V-NbB4JBi$  <https://urldefense.com/v3/__http://www.foibg.com/ijita/vol15/ijita15-1-p01.pdf__;!!D9dNQwwGXtA!RqsoCnAuTfddfrbGgU9SCAdwn-hINg9s3zygP1snCzMqLErLrrnoGW1Cx6AL22sm3P-Pa47j8BeS4OySyZw$>
> In conclusion, I will note that it is normal to believe in the impossibility of achieving something until it is achieved by someone who does not know that it could not be achieved.
> With respect,
> Krassimir
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