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Any body can share a success story of using category theory gainfully to any CS/SWE problem that couldn't have been solved without? No Monads isn't one, you wou

• platz 2y ago
  abstractions never solve problems that couldn't have been solved without them.
  • Koshkin 2y ago
    Sure; it's just that doing calculations with the Roman numerals takes longer.
    • thfuran 2y ago
      Roman numerals are too abstract a representation of counting. I use potatoes.
  • lying4fun 2y ago
    ~”numbers are the abstract notion, the primitive way of counting is a bijection” W. Lawvere so the way people use “abstraction” sounds more like they are saying “a thing we (we think) are not used to”
• Krei-se 2y ago
  You are very close. CT is about structure, not which problem this structure solves. Compilers are closest in what i can think of in this regard: They don't resolve one problem domain, but many. Which one you apply it on is up to you. One tool for one job is a simple rule you can adapt as a systems architect allowing you to build clear structure for the problem domain you come across. esbuild comes to mind as an example - the job was solved before, but keeping one purpose in mind and writing it from scratch solves the problem WAAAY faster. So no, no problem is solved inside the domain of product software development, but outside of it, you as a developer can (if you want and for speed) derive any structure from the absurd function instead of combining foreign frameworks.
  • Koshkin 2y ago
    > CT is about structure No, this is exactly what CT is not about. (It is about morphisms.)
    • Krei-se 2y ago
      From Milewski: "That’s because category theory — rather than dealing with particulars — deals with structure. It deals with the kind of structure that makes programs composable." And he is right, because morphisms may or may not preserve structure. If you want to nitpick and create structure from the absurd function morphism - then yeah, so I think a discussion about this gets tedious. The more you look into the matter the more structure / data and morphisms merge and your point feels more like an invitation for the newbies to have a mental breakdown.
• dambi0 2y ago
  Determining whether something is useful because it’s the only way that a problem can be solved is quite a high bar. We could say the same about computers in general. Admittedly even with a less stringent criteria I don’t have any examples. So I understand your point
  • Krei-se 2y ago
    Brainfuck is turing complete, why would we worry about any other structure preserving compilers? Brainfuck will do just fine /s CT is outside most problem domains in computation, as its outside the time and space constraints of a machine. Knowing whether a program will never finish is part of CT for software developers. So handling this case is a maybe in CT while it's a must in software (running endlessly means crashing).
• School-Cotton 2y ago
  It is really not useful at all in software engineering except possibly in some very niche case.
• j2kun 2y ago
  The closest I know of is the work on UMAP. I interviewed Leland McInnes who explained to me in detail how category theory was a big part of helping him connect the dots, even though the final result does not strictly need it in the actual code. Given the relative improvement over the previous state of the art (t-SNE), it's the only example that really makes me reconsider my poo-pooing the way category theory is discussed in software. https://arxiv.org/abs/1802.03426 https://arxiv.org/abs/1802.03426
  • Koshkin 2y ago
    Fascinating. More on the topological data analysis: http://outlace.com/TDApart1.html http://outlace.com/TDApart1.html
  • k_s_b 2y ago
    I felt UMAP and its limitations were explained in a friendly way here https://topos.site/blog/2024-04-05-understanding-umap/ https://topos.site/blog/2024-04-05-understanding-umap/ - written by someone who understands the category theory but is able to explain it without using any category theory.
  • nextos 2y ago
    For an alternative POV, quite critical of UMAP, see: https://doi.org/10.1371/journal.pcbi.1011288 https://doi.org/10.1371/journal.pcbi.1011288
    • j2kun 2y ago
      Yes, but I think that it can stand as an answer to the OP regardless of the techniques status as useful for particular domains
• rnhmjoj 2y ago
  Reformulating something you already understanding in a more general framework can give more insight into what it really means, isolate the essence from messy details. From my very limited understanding of it, characterising an object with universal properties is an important part of category theory. Another practical utility of category theory is providing a common language for computer scientists, mathematicians and physicists to speak. You can imagine collaboration is not easy when everyone calls the same pattern with different names with slightly incompatible definitions that requires you to understand unfamiliar theories.
  • deleted 2y ago
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  • alde 2y ago
    > is providing a common language for computer scientists, mathematicians and physicists to speak The cat theory framework is too high level to usefully exchange ideas between these fields. The consensus in academia seems to be that it is a nice "party trick" framework that has very limited insights or expressiveness in actual physics/CS problems.
    • Koshkin 2y ago
      Historically, Category Theory was developed to formalize and better understand some deep methods used in mathematics. Like much of mathematics, it "automated" some types of reasoning, opening possibilities that did not (practically) exist before. There are some areas today that cannot even be properly understood without thinking in categorical terms.
      • ogogmad 2y ago
        Yes it did, except all of those examples where it convincingly helped were super-advanced, very hard to comprehend, and lacking in non-niche applications to CS or physics. There is a category theory "school of thought" in certain subjects, but it's usually a speculative belief in the importance of category theory.
• javajosh 2y ago
  My cynical understanding of category theory is that it's the mathy Peter principle: category theory is when meta mathematics starts to lose all value. Except two professional mathematicians, of course, in which case the value is almost purely economic. "He who is employed to teach something that cannot be understood will always have a job."
• funktour 2y ago
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• YetAnotherNick 2y ago
  > any CS/SWE problem that couldn't have been solved without? Any computing problem that could be solved with category could be solved by brainfuck.
• whatshisface 2y ago
  There are no problems that can't be modeled without category theory. One of the most foundational category theorems is the Yoneda Lemma, which directly states that any problem phrased in the language of categories can be translated to the language of sets and functions. The same is true of every mathematical object with a definition in terms of sets - you could always replace the name with its definition. The contribution of category theoretic language to the implicit framework of a theory can't be larger than the definition of a category, which is very small. You could be asking "why use groups when sets with an associative operation exhibiting closure, an identity and an inverse are more approachable?" Abstract algebra is based on a library of definitions that refer to types of operations on sets that are simple enough to be common. A tool or a technique are not the kind of things you can find in a definition. Rings, vector spaces and modules get a sort of instant acceptance for what they are, but categories have believers and disbelievers. I am curious about how that can happen.
  • auggierose 2y ago
    It is because without vector spaces, you could not do linear algebra, which you need for everything. Without categories, you cannot do category theory, which you need for ... what exactly?
    • coffeeaddict1 2y ago
      Of course you can do linear algebra without vector spaces. Leibniz didn't know about vector spaces, yet he was doing linear algebra. It just happens that the use of vector spaces massively helps thinking about linear algebra problems. CT is applied to many domains. For a concrete example look up ZX calculus, which is used to optimize quantum circuits.
      • cg30e 2y ago
        You may be interested to know that I made an earlier comment about the ZX Calculus in the thread.
      • auggierose 2y ago
• carlskevin 2y ago
  At the Topos Institute we're working on some new software that we're hoping will be a lot more transparent to people who haven't drunk the CT Kool-Aid yet; the current pre-alpha is mainly for systems dynamics modeling but the category-theoretic basis is, to my mind, indispensable for the range of tasks we're targeting. I'd be very happy to hear anybody's thoughts! https://topos.site/blog/2024-10-02-introducing-catcolab/ https://topos.site/blog/2024-10-02-introducing-catcolab/
• deleted 2y ago
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• bgavran 2y ago
  "Anybody can share a sucess story of using a car to go places I couldn't have gone on foot"? CT is a language and a tool, meaning anything you can say in the language of CT you can say in other languages. Like cars, if you learn how to drive it (and this one has a very steep learning curve), it gets you places faster, but you there's in principle nothing stopping you from going there walking, i.e. without specifically referring to any CT concepts.
• jiggawatts 2y ago
  I've heard of some database migration tooling that uses category theory to compute robust data transformations that are automatically composable to achieve the desired outcome. There has been seen some research into the fundamentals of machine learning, using category theory approaches for computing the compositions of transformations of expressions. E.g.: simultaneously computing a gradient, the "bounding box" of the error, and other similar derivatives to improve the robustness of gradient descent.