Chinjut

53 ms·

601.
by Chinjut 10y ago
I presume you mean the idea of physical examples in general comes up in "Surely You're Joking"; I can't find any discussion of P vs. NP (or Fermat's Last Theorem, for that matter) within it. As for why Feynman didn&
602.
by Chinjut 10y ago
It's true I did not understand you were joking, but I didn't personally malign you either. If you are referring to the word "moron", I didn't call you a moron; I was shocked that you thought P vs. NP was so trivial,
603.
by Chinjut 10y ago
Or just in lines... a^n many lines of length 1 + b^n many lines of length 1 to cover the total length of c^n many lines of length 1. Or just in n-dimensional cubes from the start: 1 n-dimensional cube of side-length a + 1 n-dimensional cube
604.
by Chinjut 10y ago
Sorry, I'm having difficulty following you. What do you mean by an "n-3 cube"? Or are you actually talking about n - 3 many different cubes?
605.
by Chinjut 10y ago
Whoops, I had 10^4 above where I should've had 4^10. So, about 18 decimal digits rather than 16. The point remains.
606.
by Chinjut 10y ago
Fair enough on your first paragraph. (Though what distinguishes mathematical facts which are "coincidence" from mathematical facts forced true by mathematical structure?) Actually, I'd say it is odd to find this sort of analy
607.
by Chinjut 10y ago
This comment isn't meant to be dismissive. I think it's interesting to explore arguments like this. Math progresses by exploring thoughts. But... Couldn't we argue in the same way that there are unlikely to be any solutions t
608.
by Chinjut 10y ago
A little more detail, since I bothered to go learn it: Lemma: If x and y are coprime, then the gcd of x + y and (x^n + y^n)/(x + y) divides n. Proof: Expand out the polynomial division (note that x + y does indeed divide x^n + y^n), an
609.
by Chinjut 10y ago
NP is most certainly not "trivially definitionally not equivalent (equal) to P". (Do you think everyone puzzling over the question of whether P = NP is a moron? You are aware there is a million dollar prize for a proof one way or
610.
by Chinjut 10y ago
That description of what Sophie Germain did is slightly glib and inaccurate, I believe. I will give an abbreviated, but accurate, to the best of my knowledge, explanation of what happened: Note that, if you have proven Fermat's Little
611.
Artificial Intelligence's White Guy Problem(nytimes.com)
23 points by Chinjut 10y ago|44 comments
612.
by Chinjut 10y ago
But "no connection to" isn't synonymous with "not a descendant of"...
613.
by Chinjut 10y ago
"of recent centuries... in recent centuries" Whoops! Redundancy it's too late to edit. Oh well...
614.
by Chinjut 10y ago
Not explicitly, but it is implied by what was said, particularly in context. European civilization invented all these great things and non-Europeans on their own would be mired in dirt and ignorance, therefore European civilization is human
615.
by Chinjut 10y ago
Exactly how far would Europe have gotten with inventing those things if it hadn't built upon the numerous mathematical, scientific, and technological achievements of India, China, the Arab world, etc.? [Perhaps, counterfactually cut of
616.
by Chinjut 10y ago
Yes, I agree that a layperson is unlikely to feel Z[sqrt(-5)] is similar to Z. That's empirically just true. On this point, we are in no contention. But I disagree that laypeople are correct to consider unique prime factorization (or E
617.
by Chinjut 10y ago
Alright. I guess I misunderstood what you were getting at with your comment. And perhaps you misunderstood the nature of my conversation with PepeGomez? You appeared to be correcting me over some misunderstanding I never evinced. PepeGomez
618.
by Chinjut 10y ago
As for the remark at the end: you're right, it may be difficult to un-obfuscate phrased in that form, but had you phrased it "Make a table of two columns. Take the very top-most, left-most entry to be n, take every entry in the ri
619.
by Chinjut 10y ago
Oh, don't worry; the "you" in "I think you're..." was generic (for anyone who claims complete and utter obviousness of unique prime factorization without ability to explicate the reasoning behind it or even gra
620.
by Chinjut 10y ago
Sure, to a mathematician, these things become old hat, but note that Apostols spends several pages developing properties of the GCD that aren't generally considered "obvious"; in particular, he argues for Theorem 1.2 (that an
621.
by Chinjut 10y ago
Yes, but the only way in which that ordering compels the integers to be a unique factorization domain is through the fact that it allows us the Euclidean algorithm; put another way, through the fact that, for any bunch of integers, their sm
622.
by Chinjut 10y ago
Why? How do we know factorizations are unique? That is the claim under contention. That is precisely what Gowers in the original article is noting as non-obvious [but often mistakenly taken to be obvious]. If we don't already know (pri
623.
by Chinjut 10y ago
You're right that there's only so many possible nonzero remainders mod 3, and you can check for yourself that if you multiply any of them together, you end up with another non-multiple of 3. The same is true for 5: it takes a litt
624.
by Chinjut 10y ago
Who says "if it's divisible by a number, the number must appear in its factorization"? Why is that true? For example, 24 is divisible by 6, though 24 has the prime factorization 2 * 2 * 2 * 3, with no 6 to be found. "Rig
625.
by Chinjut 10y ago
Even in a restrictive sense of "Asian-American" as meaning those of Asian descent who grew up in America, there are a few presumably Asian-American minor characters on the show, perhaps most notably the Indian "brogrammer&quo
626.
by Chinjut 10y ago
Yes, Kumail Nanjiani (who plays Dinesh) grew up in Pakistan and moved to the U.S. for college. I believe Dinesh is also supposed to have grown up in Pakistan (albeit with a Hindu first name? Well, of course, even if rare, that can happen),
627.
by Chinjut 10y ago
Yes, I realize now my error: I was reasoning in the degree calculations for the relevant graph as if "local minimum" was synonymous with "valley", and similarly for "local maximum" and "peak", but of
628.
by Chinjut 10y ago
The author takes care to make the assumption that A and Z are _global_ minima and M is a _global_ maximum. But, in reading the proof, it seems not necessary to make such strong assumptions; would it not work just as well for A and Z to be m
629.
by Chinjut 10y ago
It's not exclusively some modern invention to be against slavery. There were people during the era of chattel slavery who thought of slavery as wrong too. Lots and lots of them. Almost 100% of the African-American population, for examp
630.
by Chinjut 10y ago
"According to the National Center for Education Statistics, humanities majors account for about 12 percent of recent graduates, and art history majors are so rare they’re lost in the noise. They account for less than 0.2 percent of wor

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