fishfry

I can't see this. Can you give an example? I didn't understand which side you're agreeing with. Do you think that the meaning of a proof is to be foun...

A neo-Malthusian. Malthus was wrong. Human ingenuity wins. We crawled out of caves and built all this. Don't sell humanity short.

Ok a fibre bundle is the collection of all possible right inverses to a function. And a section is one of those right inverses. Yes? I may be off the ...

Oh, it doesn't. I mentioned that the computable numbers have measure zero in the space of bitstrings, and @"Mephist" asked me how that's defined mathe...

I'm reading the data science paper you linked. They teach sheaf cohomology to data scientists. That is so fascinating. To me, with my math background,...

I have no idea what question is was a response to. But if you agree with me, you have excellent taste!

I think when I grok how fiber bundles can be likened to proofs, I'll be enlightened. Did you learn all this from the CS viewpoint? Just wondering.

Ok now I know this idea as ETCS: The extended theory of the category of sets, which is an implementation of set theory on top of category theory. Is t...

No this is totally fascinating, very clear writeup, worthy of study. I know what fiber bundles and sections are. I can't quite grok the application to...

No problem, you've gotten me interested in sheaf theory and then on to topos theory. But I'm still probably more oriented to the mathematical applicat...

I'm going to spend the next week working through this material. I'm encouraged that I can understand what a sheaf is and know a few examples; and I kn...

Now that is interesting, because fiber bundles are a big thing in differential geometry. It's interesting that they lead directly to type theory. Than...

That's what EVERYTHING is in category theory! So that didn't tell me anything about topoi! You wrote me two detailed technical posts that I'll try to ...

Yes thanks. I was trying to make this point to @"Mephist" the other day and this is a good example. The connections among topology, algebraic geometry...

Thanks. I know Goldblatt as the author of Lectures on the Hyperreals. I'll add this book to my growing list of books to read someday. So far the list ...

If they are points in an abstract mathematical metric space, yes. If they are physical points, no, for two reasons. One, the earth is constantly chang...

Great point. Everyone likes to make fun of philosophers!

Did you get that from God's lips to your ear? You have an opinion, nothing more. C is confused. The integers have no first element. But every element ...

i noted that many environmentalists are for population control of third worlders. Nobody ever asks the third worlders what they think. Some extreme en...

Surely this is true about the zero-set of any function whatsoever. The study of the zero sets of polynomials is algebraic geometry. That's where I'd l...

Be advised that any paragraph containing the name Martin-Löf instantly glazes my eyes. I've had all these conversations too many times. I totally beli...

I do not think this is so bad. I'm learning what a sheaf is and after that, topoi are the next step up. If I figure anything out I'll post it. What's ...

There are no points at infinity on the real line, so the function's not defined there. And just because a function has a limit at infinity, that does ...

OMG that sort of makes sense. Thank you for that example. I've been reading up on sheaf theory and every presentation that comes up on Google is heavi...

Uh ... yeah, is this a trick question? I don't see the relevance. But yes, I'd say so. Of course tiny fluctuations in the shape of the earth mean that...

On the contrary. We can exactly conclude that if f(a) = f(b) then a = b in this case. There are no endpoints or values at infinity. A function need no...

You mentioned topos theory in one of your posts. I read the Wiki page, or re-read it since I've looked at it before. It's abstract sheaf theory. What'...

What I'm saying is that the wager depends on a god who hands out eternal reward for believing, and eternal damnation otherwise. That's a vindictive go...

The first world environmentalists (are there any other kind?) always want the poor to stop making babies and not demand a modern standard of living. W...

Celebrity physicists bashing philosophy is as old as Feynman if not older.

(Eyes glaze). Name drops Voevodsky. Didn't we do this last week? Or was that someone else? Perfectly well known before Vovoedsky. Do you know topos th...

I was reading through the thread and this caught my eye. Why does mathematics need computations? Because before there were computers, the humans did t...

So what? The cosine function has infinitely many inputs that go to the same output. \cos \theta = \cos(\theta + 2 \pi n) for any integer n. And they a...

Did you find the picture helpful?

So the lambda formulation is more granular, able to support more nuanced theories? Something like that? Anyway I know about Coq and the proof assistan...

You're saying TMs don't exist but finite state machines do? Maybe so, but then you'll make your physics a lot harder if you can't even run an algorith...

If you allow infinite movement to the right, why not to the left? The situation is perfectly symmetrical except for your irrational attachments to fal...

As Bernie said to Liz last night, "I did not ever say that!" I said that the concept of the world as having had a distinct moment of beginning is a we...

I just happened to run across this article this very morning. In the quantum realm, cause doesn’t necessarily come before effect https://www.newscient...

I've never heard of this idea, that TM's don't exist. I see no problem expressing TMs in set theory. An unbounded tape of cells is modeled as the inte...

A TM with a program too long to write down in the age of the universe is still a TM. Practical resource limitations do not apply to the theory of comp...

https://en.wikipedia.org/wiki/Measure_(mathematics) Measure theory is an abstraction of the concept of length, area, volume, etc; and also of probabil...

Which has what to do with what we were talking about, the use of symbols to represent things we don't understand?

Name me a theory of science that hasn't been falsified or will not someday be falsified. You're a scientific nihilist. You deny the entire enterprise ...

I hope you'll forgive me but I prefer not to engage with your scientific nihilism, which itself is driven by scientific ignorance. If we threw out eve...

- \infty is not a point on the number line. For just a moment, forget that we're talking about time or causality. Just consider the number line of int...

Right. Constructive physics is physics based on constructive math. That's all it is. Instead of using the real numbers, you only use computable number...

Why are you trying to convince me that math isn't physics? I'm talking about the measure of computable bitstrings in the space of all bitstrings. The ...

My understanding is that the constructivists allow in nonconstructivity whenever they paint themselves into a corner. For example every type of constr...

“No man ever steps in the same river twice, for it’s not the same river and he’s not the same man”, said Heraclitus in 544bc. But you asked, "What if ...