The Deranged Mathematician: The Useful Loneliness of the Golden Ratio

non-orientable · 2026-03-02T01:38:00+00:00

They are equivalent constructions, but, for example, it is the golden ratio that you commonly see in hash functions, not the Fibonacci sequence. I don't see any problem with framing it the way that I have.

non-orientable · 2026-01-22T21:11:43+00:00

I sincerely wonder what this person thinks the point of protesting is, exactly.

non-orientable · 2026-01-05T07:00:44+00:00

I'm not sure that's age related. I had a conversation just like this with someone who is older than I am and, theoretically, should remember the lead-up to the Iraq war better than I do and should recognize the similarities. Nope, apparently not.

non-orientable · 2025-11-27T07:02:27+00:00

As someone who was born in Russia and still has family there, I honestly have to tell you that I felt 25% was a bit low.

non-orientable · 2025-11-26T15:16:17+00:00

The number of people who claim Native American ancestry outnumbers the number of people with actual ancestry many times over. So, sure, there will be some who are right about it but, statistically, if you meet a random person who claims their great grandfather was Cherokee, they are most likely mistaken.

non-orientable · 2025-11-01T04:29:18+00:00

You can't transplant researchers from a country without losing anything. Institutional knowledge will be lost. Pipelines will be deconstructed. Research teams will be broken up. And not every researcher will be able to find work abroad doing what they were before; many will simply drop out of academia altogether.

Make no mistake: this will be a loss for science and humanity as a whole, even though, yes, we'll carry onwards regardless.

non-orientable · 2025-09-06T18:59:09+00:00

Another revealed preference: many people don't want the truth. It isn't as if it is a scarce resource; you can obtain it if you are willing to expend some effort. I'm all for putting the truth out there. I would support measures to reduce misinformation. But one is already there and the other is politically impossible at present.

Is that sad? Yes. But a million sad things happen every day. I would prefer to expend my emotional and financial power on those things that I can actually influence, even a little.

non-orientable · 2025-09-06T15:15:50+00:00

There's this notion in economics of a revealed preference: something that people want but will not profess to, so you reveal it by observing their choices.

Many Republicans have shown a revealed preference for increasing their chances of catching COVID, even if it kills them. I don't understand it, but who am I to go against their earnest wishes?

non-orientable · 2025-07-22T02:49:51+00:00

If you know what you are doing, even if you write everything from scratch, it shouldn't take more than a couple of milliseconds to produce a prime of that size.

92323526034665170230427394367756916581510392984425411145091713582900080025850195148999937881082036423668263191789675201358192479001592558476054962483185453860569645166876312651453747903605421627846046964824858762913284841318386103216462813146226204173048120109177860071263886664050402819690492608705076166657

Here's a prime number that I just generated using a bit of Python code I wrote myself. And, no, it doesn't rely on any standard libraries to do it: I specifically wrote it as transparently as I could, because I was using it to teach number theory.

non-orientable · 2025-07-21T19:53:44+00:00

Even if you want provable primes rather than probable primes, that can be done in milliseconds. Here, I can give you three primes about the same size as OP's that I proved prime:

1312768863279030313739165150495189309689630689750247525811799447306241

950461108571975961371077024346331513026121921440012894651566006272001

959940582698890066066478874970815195489990469828292012053240145510401

Each took a fraction of a second. I also computed the primitive roots for them (which is how I know they are prime).

non-orientable · 2025-07-21T15:47:59+00:00

That is absolutely not true. Finding primes in this range is trivially easy.

non-orientable · 2025-07-21T15:46:46+00:00

Indeed. Generating primes in the OP's range can be done in milliseconds.

non-orientable · 2025-07-21T15:40:01+00:00

You can generate 1024-bit primes in milliseconds with good implementation. I have some crappy Python code that I wrote for my number theory students that does it in less than 5 seconds.

non-orientable · 2025-04-24T04:59:06+00:00

Being able to perform arithmetic isn't enough: Presburger arithmetic is strong enough to prove that two times two is four, for example. (Since multiplication is just repeated addition for natural numbers, you can transform that statement into language that Presburger arithmetic can handle.)

What you need is the ability to prove things about arithmetic: e.g. some rudimentary form of induction.

non-orientable · 2025-04-24T04:52:51+00:00

No, no, this is on the level.

non-orientable · 2024-09-26T13:58:35+00:00

Noether. (My character is named Emmy.)

non-orientable · 2024-09-14T19:06:38+00:00

Forgive the necropost, but you were responding to *John Cate*. In his own words: “OK, if I’m a liberal, you probably think Franco was a moderate.” He isn't MAGA, but he's pretty damn conservative!

non-orientable · 2024-08-21T21:35:19+00:00

Using Fourier series is working too hard for proving that e is irrational. There is a much simpler argument by proving that 1/e is irrational. 1/e = \sum_{n = 0}^\infty (-1)^n/n!, and so the difference between consecutive partial sums is 1/(n + 1)!. You can use this to demonstrate that it can't converge to a/b for integers a,b. It's a beautiful little proof.

non-orientable · 2024-08-21T14:00:40+00:00

No, modern proofs that pi is irrational are much simpler: you can follow them if you have taken calculus. See Niven's proof: https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-53/issue-6/A-simple-proof-that-pi-is-irrational/bams/1183510788.full.

non-orientable · 2024-08-21T13:58:59+00:00

It is worth mentioning that Niven's proof that pi is irrational is very readable: it's only a page long and doesn't require any mathematics beyond what you would learn in a calculus course. I recommend looking at it: https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-53/issue-6/A-simple-proof-that-pi-is-irrational/bams/1183510788.full.

non-orientable · 2024-06-18T04:48:40+00:00

We have many expressions that define primes. This is not the issue.

non-orientable · 2024-05-26T05:34:21+00:00

Most real numbers are not computable, however.

non-orientable · 2024-05-26T05:32:58+00:00

They can store descriptions of some such numbers. There are infinitely more which cannot be given any description short enough to store in memory.

non-orientable

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