David Jaz Myers: 'Three Realisms and The Idea of Sheaves'

Finding the Right Abstractions Summit 2021

[kaushaltimilsina]

For someone (me) interested in using Category Theory, Algebra and Topology in applications, these examples of using Cohomology and Sheaf Theory are really interesting! Really excited to read more on David's work. Thanks very much for sharing the talk!

[Dth]

These three realisms apply to software engineering pretty well :P

Fixed realism: "There is one spec and one implementation"
Covariant realism: "There is one spec but many possible implementations"
Local realism: "There are many specs, depending on your (bounded) context, each with many possible implementations"

[fireclub]

The market example was great! really enjoyed this talk.

[sandropollastrini]

Very interesting indeed. I liked a lot the examples you gave of sheaves. And I didn't know the cohomology example from Penrose: very clear.
Thank you!!!

[hyperduality]

Categories (form, syntax) are dual to sets (substance, semantics) -- category theory.
Global realism is dual to local realism.
Homology is dual to co-homology.
Objects are dual to subjects.
"Always two there are" -- Yoda.
Thesis is dual to anti-thesis creates the converging or syntropic thesis, synthesis -- the time independent Hegelian dialectic.
The synthesis is a product of duality!
Symmetry is dual to conservation -- the duality of Noether's theorem.

[numoru]

Hi can we please start getting subtitles

[kodfkdleepd]

So, to make something clear which is probably quite important: If you have generalized contradictory you can solve those contradictory by making them more specific. It's, "It is ? raining at ___ where ___, ___, ___". Here ? represents a possible not and the ___'s are specializations that can make the statement true(e.g., find the correct part of the generalization that gives a truth).


Wars have been fought over people miscommunication and almost all of it has been due to the Humanity is the way it is precisely because of the ambiguities in our languages. People develop different languages independent but the are all related. But lots of pitfalls and such which has created many social problems since most people do not really understand the things that this video presents(but does not make more explicit along the social side of things). E.g., Everyone has a different perspective. Everyone is local = "concrete" = "specific" in most of their thinking. "Generalizers" are people who think more freely in "generalizations" of specifics and this can be very difficult for a "specifier" to make sense of and many times they will insert their own for the blanks and hence get a false statement(or true) and think you area moron(and get in to an argument to try to prove to you that you are wrong... when in fact they are wrong since they inserted "hidden assumptions"(they filled in the blanks with things that were likely not what the original thought process had in mind. I experience these issues on a regular bases since a large part of my thinking is very general. Most people don't have the time, patience, discipline, or intelligence to understand that communication, meaning, truth, etc is extremely extremely complex.)).

I think mathematics is starting to uncover how the subconscious mind works. Clearly there is structure in the mind and this structure seems to be mathematical or have a mathematical embedding in it. I think as we all, as a species, learns to deal with generalization and specification better potentially the better off we can be. People get in to all kinds of arguments over things that are meaningless. Untold issues have been seeded by simple miscommunications or interpretations that it's amazing we even have a society.

[grudley]

the problem with this "local realism" is it says that atoms didn't exist before Perrin settled the question of the reality of atoms, and then they existed after. In general, you can't have a sensible notion of "realism" without some world for models to model, but that's exactly what this "local realism" tries to do. It's just a models of models, pure epistemology, no ontology.

[santerisatama]

I like the philosophy of local realism (cf. animistic multinature, relational quantum mechanics etc.), but the technical discussion is somewhat dubious. What if, to begin with, we have a serious disagreement about "real numbers", or other aspects of number theory?

How to make the philosophically sound aspects of sheaf theory less "technical" and more foundationally general? The philosophical approach of the sheaf idea seems as such much more general than Category theory.