David Spivak is thinking along the same lines of many of us here, it seems. Yay! Thanks @starbright

johncarlosbaez.wordpress.com/2

<< The idea that’s haunted me, and motivated me, for the past seven years or so came to me while reading a book called The Moment of Complexity: our emerging network culture, by Mark C. Taylor. It was a fascinating book about how our world is becoming increasingly networked—wired up and connected—and that this is leading to a dramatic increase in complexity. >>

<< I’m not sure if it was stated explicitly there, but I got the idea that with the advent of the World Wide Web in 1991, a new neural network had been born. The lights had been turned on, and planet earth now had a brain.

I wondered how far this idea could be pushed. Is the world alive, is it a single living thing? If it is, in the sense I meant, then its primary job is to survive.. >>

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<<, and to survive it’ll have to make decisions. So there I was in my living room thinking, “oh my god, we’ve got to steer this thing! ..

Looking back on this endeavor now, I remain concerned. Things are getting increasingly complex, in the sorts of ways predicted by Mark C. Taylor in his book, and we seem to be losing some control: of the NSA, of privacy, of people 3D printing guns or germs, of drones, of big financial institutions, etc. >>

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What's really cool is it seems that Spivak got obsessed with this idea just about the same time that I did. There must have been something in the global water supply circa 2006-2007. And I was sitting there reading the C3 Wiki going "someone needs to be working this problem of how we massively reduce complexity, on the maths / CS end". Looks like someone is!

(well, George W Bush was one big thing that was bugging us all back then.. but social media and surveillance capitalism wasn't quite yet)

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<< dspivak says:
27 March, 2015 at 1:27 pm

While I agree I want something someone might call a “semantic web”, I don’t agree that what is currently called the semantic web, i.e., the W3C Tim Berners Lee version, is going to work. Nor do I think any form of predicate logic is going to work. I’ve worked with some of those guys, and though I think there mission is admirable (as you point out, it is similar to my own), I think their approach is too ad hoc to work in the way I’m looking for. >>

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I wonder why he doesn't think logic will work? I agree that stuff like RDF and OWL was just terrible. But that wasn't logic's fault.

The advantage of predicate logic (eg, in as the core of a query/search language like Prolog) is that it is *small and understandable*. Never underestimate the power of simplicity.

Perhaps the core axioms of category theory can be made that small?

If they can't be made at least as small as the Prolog resolution algorithm, then I don't think it will work.

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Spivak's idea of 'ologs' (which I think from his 2015 comments is a category-theoretic approach to what OWL was trying to be as a schema language for RDF?) is developed in this 2011 paper:

arxiv.org/abs/1102.1889

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I can guess that maybe a big difference between the motivating ideas of category theory and predicate logic is that logic was trying to be 'one perfect true pre-parsed form for all knowledge, to be placed into one big database' while CT is about 'patching one domain of knowledge into another one while not being able to control either'. So the culture of CT - by necessity - is more piecemeal and bricolage, while that of logic was more totalitarian (not polite to say that, but it kinda was)?

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And an immediate end result of that is that Prolog expects everything to be in one unified database. Why? Doesn't make sense for it to be, not even compared with Lisp/Scheme where all knowledge is local, scattered into multiple closures/environments, or Smalltalk which made the idea of 'environment' a bit more concrete as 'object'. But maybe it got that idea from the logic community which just didn't really ever imagine that knowledge could be disconnected and have different rules to it?

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(Prolog did absorb a very NON logic-y idea, from its other day job as being a natural-language parser, by allowing terms to be absolutely untyped, unvalidated, just ... stuff that was there, might not even mean anything, like human language. And that non-logical part - not needing to have every piece of data absolutely nailed down with a type/schema before computing - I think, was key to Prolog actually being able to do serious useful work.)

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Category theory is a very high level tool. Take, for example, the idea of 'universal constructions'. I'd link Wikipedia, but its article comes up with a cat-theoretic description of the idea, which needlessly complicates things. It's a basic technique: Given some constraints, find the most general object (algebra, ...) that satisfies them. It's about interpreting things. It's nonconstructive. Commutative diagrams aren' programs, they're more like equations to be solved.

I'd also like to link a talk by Pierre Deligne about 'equality', but his accent requires you to already know most of the words he's using, and he comes up with some rather sophisticated examples. So let me just paraphrase his initial example.

If we take ZF set theory as a foundation for everything, then all objects are comparable as sets. But, for example, the integers can be defined Frege style

0={}, 1={{}}, 2={{},{{}}}, ... n=n-1 U 1

...

Or in one of countless other, isomorphic ways. Usually, nobody actually states which formailzation he uses. Instead, people use '=' in the sense of 'is isomorphic to', i.e. there's a structure preserving bijection between them. You see, 'being isomorphic to' is not a trivial concept. There may be a number of distinct such isomorphisms. We can go down the rabbit hole and ask about 'equality' between those...

What do we mean by "equal" - Pierre Deligne - youtube.com/watch?v=WfDcrN5_1w

...

I guess what I'm saying is that univalence (what Deligne tries to explain) is supposed to resolve the issues with untyped databases, putting homotopic type systems to work.

I remember a discussion I had in the 90's, when I was much younger and naive, coming from mailbox networks, claiming that tge internet (tcp/ip) was ('like', but I wouldn't make that distinction) a brain, only to be corrected that it's more like a nerve system.

But the web bas a memory!

...

I'm not trying to claim credit, if I can see it, someone else must have before me :*)

Nice thread, @natecull!

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