boyobo

BTW, I am not using 'hottest buzzword of the decade' to denigrate the field of deep learning. I am using it to emphasize the op's shallow reference to the field.

It is certainly not a “new way of thinking”. First of all, there is hardly any thought here. Secondly, “understanding deep learning mathematically” is a well known problem to mathematicians.

It is a comment that could have been generated by an (old, 2000s era) AI.

"That’s right — the more you tip in-app on DoorDash, the less DoorDash pays the worker."

What you wrote is a different justification for why turing tapes are worse than lambda calculus. It has nothing to do with the number of people programming on turing tapes, which is the argument that I was responding to. I could easily have used 'lambda calculus' instead of 'turing tape' above. Most people do not code in the lambda calculus. They write haskell or javascript or whatever.

It doesn't mean that the lambda calculus is trash. Likewise, most mathematicians don't work directly with ZFC. Doesn't mean ZFC is trash.

> I'd be equally interested in a programme of doing metamathematics in some non-category-theoretic model that was still "normal" mathematics in the same way that category theory is (and ZFC isn't).

My point is that almost all pure math (e.g: linear algebra, topology, differential geometry, category theory, group theory) is already metamathematics. Of course, there is a spectrum of 'meta-ness' but I think this is a continuous spectrum. I do not think there is a well-defined division between 'mathematics' and 'metamathematics'.

For example, can you give an argument for why, say, the irrationality of sqrt(2) is not 'metamath', yet godel's incompleteness theorem is 'metamath'?

What percentage of coders do programming on a turing tape? Is this partial evidence that turing tapes are trash? Does that question even make sense?

> I don't expect this to be solved now (tooling, as per above), but mathematicians should learn more category theory now as that works just fine pencil paper and brain. When the type theoretic tooling is ready they will be ready.

The abstractions of category theory are useless in many areas of mathematics. Prime example: PDEs.

Laypeople think that category theory is the 'ultimate math' because they hear that it provides bridges or analogies between different areas of math. Perhaps programmers are especially prone to this because category theory does have some applications to programming.

The thing is, almost all of pure math is itself is a bridge between different areas of math. Some of these areas are bridged by category theory, some are bridged by other kinds of math, which have less catchy names.

E.g. https://mitpress.mit.edu/books/functional-differential-geome...

"Usain bolt won the olypmic gold medal many times (n=8).

If winning the gold medal was so rare, what are the odds that people like Usain Bolt exist?"

"a special right, advantage, or immunity granted or available only to a particular person or group."

In this case, the "advatange" would be 'able to find job without going through recruiter' and the 'particular person or group' would be 'the group of people who (through their hard work or otherwise) are sufficiently talented/and or secure enough in their career'

Anyway it's sad this this word has such a negative smell attached to it now, thanks to people using it to shame people on the opposing side of internet arguments.

Someone wins the lottery every week. What are the odds of winning the lottery? Is playing the lottery a good strategy to make money?

Consider the following graph. The nth fibonnaci number is the number of possible walks from n to 1.

(I made a mistake in the picture, there should be an edge from 2 to 1).

Of course it's probably too hard to make it compatible with all the different types of text boxes, so I'm envisioning a shortcut that you can press, which brings up a small editing window, where you can use vim commands, and then you can copy and paste into whatever text field you want.

Also, who determines what a 'macroscopic variable' is? Why do there only seem to be 3 for gassess (V, T, P?)

https://www.scottaaronson.com/incompleteness.pdf

See chapter 3.

The sentence did strike me a little wierd though.

Edit: it seems you are talking about 'The number of factors in the prime factorization of n'. This is not really relevant to the question posed in the submission.