Notes On Categories

[Jon Awbrey]

Cf: Notes On Categories • 2
https://inquiryintoinquiry.com/2021/07/31/notes-on-categories-2/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229136-theory.3A-category.20theory/topic/The.20relative.2Fmap.20perspective.2Fphilosophy

::: Joe Moeller
https://categorytheory.zulipchat.com/#narrow/stream/229136-theory.3A-category.20theory/topic/The.20relative.2Fmap.20perspective.2Fphilosophy/near/247582684


<QUOTE JM:>
In category theory, we have this perspective that we should focus attention on maps,
on the relationships between objects, rather than on the objects themselves. What's
your favorite examples of people giving a schpiel about this? Blog posts, snippets
from books or papers, or even just giving your own take right now, are all welcome.
</QUOTE>

My first “abstract algebra” course in college (U Mich, 1970), the last project
our instructor assigned us was to “do something creative”, a piece of creative
writing, painting, sculpture, or other objet d'art, reflecting one of the topics
covered in the course.

I wrote a science fiction story about two species of creatures, the “Sets”
and the “Mappings”. No way I can remember all the details but I recall it
explored a theme of duality between the two forms of life and the way ideas
about “things in themselves” evolved over time into ideas about “that which
changes into itself”.

Regards,

Jon

[kall...@gmail.com]

There are many conceptualizations and mis-conceptualizations on the application of (mathematical) Category Theory to the Systems Sciences. This has caused me to opine "There are more ways to misunderstand concepts that to get them basically correct."

The problem can generally be traced to the way certain natural words are used to represent prior concepts, wrongly. IOW, the concept of morphism in Category Theory is not a form of transmogrification - often the so-called state of the art.

While Category Theory is (in some ways) simple in its application to systems science, it is obviously not well understood precisely because of the way the natural language interpretation of prior knowledge is misguided. This extends to meanings of science, itself.

I'm not at all certain this can be corrected in my lifetime.

Kenneth A. Lloyd
Retired Director of Systems Science
Watt Systems Technologies Inc.

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[Aleksandar Malečić]

The approach focused on some history of science doesn't go anywhere. Looking for some theory just because it looks more advanced and "beyond" some other theory is destined to fail. A political ideology (for instance) is a collective behaviour then, when it collides with another ideology, can kill people.A predefined infrastructure can affect chances for development of a different more resilient or useful infrastructure. In other words: a good systems theory is useful and it has either predictive or explanatory power that other approaches don't have. The focus should be more on application than on self-proclaimed "advanced" theories and theorists that we mere mortals can't understand during their lifetimes..A good theory is focused on explaining or solving problems and phenomena https://en.wikipedia.org/wiki/Lists_of_unsolved_problems instead of boosting egos.

Aleksandar

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[kall...@gmail.com]

Aleksandar,

 

A study of the history of science only points to all the wrong turns made in the Philosophy of Science. Specifically, the difference is between the belief of knowledge and actually seeking knowledge, especially wrt systems (again, not that hard). Progress in science is hallmarked by moving from one incorrect, incomplete or paradoxical state to a more correct, more complete and less paradoxical state that is still somewhat incorrect, incomplete, and paradoxical. This gets directly to the nature of what we mean by proof – not an unbounded concept of proof as universal truth, but a more narrowly bounded concept of validity with limited contexts (that Popper saw as falsifiability).

 

When I say that the application of Category Theory to the Science of Systems is simple – it is incredibly simple. Anyone can understand it provided they don’t try to force-fit inadequate prior paradigms (set-theory being one) upon the Category of Categories. That is (was) the great challenge of learning Category Theory, itself. But as long as people “believe” Category Theory is some abstruse, advanced theory, they will have problems.

 

Many Category Theorists compound this problem. I’ve been known to tell them “if you didn’t want others to know Category Theory, why didn’t you just say so.” Got more laughs than you’d imagine.

 

So when I tell people that Category Theory is a practical, useful and valuable way of developing interesting understandings of systems, they only look at me in disbelief. I’m a scientist, not a religious practitioner. Let them believe whatever they want.

 

Ken Lloyd

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