Surely You're Joking, Mr. Zeilberger?
in [Math]
|
Prev: solar power
Next: two most famous and important proofs in all of mathematics-- Pythagoras & AP-finite-selection #437 Correcting Math
From: wht on 15 Feb 2010 16:30 Try it on a 32-bit unsigned integer. You add 1 to the largest number in that domain and, voila, you get zero as a result. Is that the April Fool's?
From: Angus Rodgers on 15 Feb 2010 17:25 On Mon, 15 Feb 2010 13:30:52 -0800 (PST), wht <websterhubbletelescope(a)gmail.com> wrote: >Try it on a 32-bit unsigned integer. You add 1 to the largest number >in that domain and, voila, you get zero as a result. Is that the April >Fool's? Huh? Zeilberger does indeed refer to his integer arithmetic as taking place on some "giant computer in the sky" (or words to that effect), but obviously it can't be a binary computer, if the modulus is prime. I don't see your point (or joke, if that's what it is). I'm sorry if I'm being rude, but it looks as if you didn't understand what I wrote. I already mentioned Z_p. -- Angus Rodgers
From: David Bernier on 16 Feb 2010 02:19 Angus Rodgers wrote: > Health Warning: > > Not only have I not thought much about maths for the last year or > so, and not posted here since last June, but this is the sort of > topic which always seems to cause a thread in sci.math to converge > rapidly to a cycle of abuse containing much use of the c___k word. > > But it's been worrying me intermittently for a few days now, and I > don't know where would be a more appropriate forum to ask about it. > (Suggestions welcomed!) > > The Actual Point: > > In the UK, last Wednesday, BBC2 transmitted a television programme > in the scientific documentary series Horizon. Here is the episode > description in DigiGuide: > > ``To Infinity and Beyond. > > Series exploring topical scientific issues. By our third year, most > of us will have learned to count. Once we know how, it seems as if > there would be nothing to stop us counting forever. But, while > infinity might seem like an perfectly innocent idea, keep counting > and you enter a paradoxical world where nothing is as it seems. > Older than time, bigger than the universe and stranger than fiction. > This is the story of infinity. > > Copyright (c) GipsyMedia Limited.'' > > I was only half-watching the programme (Horizon is often annoyingly > dumbed-down - and I was doing something else at the same time), but > what grabbed my attention was an interview with Doron Zeilberger, > in which he claimed not only that there is a largest natural number > (I'd come across mention of Zeilberger's ultrafinitism before), but > that if you add 1 to this largest natural number, the result is 0. I can't understand the last part... A zillion marbles in a bag, we had one marble to the bag, and then there are no marbles (?) > (Pause for the reader to catch his or her breath, and re-read that > paragraph, to make sure that that was indeed what I said he said.) > > This forced me to wonder again, not whether this is true or false > (I hold unremarkably to the orthodox view that there is no largest > natural number), but how, and indeed whether, anyone could possibly > seriously believe in such a proposition. > > A visit to Zeilberger's website confirmed my vague memory that he > has a reputation for April Fool's Day mathematical pranks: > > http://www.math.rutgers.edu/~zeilberg/ > Homepage of Doron Zeilberger > > But it also seemed to suggest that this was not one of them. > For confirmation (or not), see, for example: > > http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/enquiry.html > An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding [...] In the first paragraph on page 20 of the essay, he says among other things that the mathematical universe is the same as the physical universe, that our unique universe is finite and that everything is computation. Also, near the beginning he gives the impression of being fond of (or admiring) skeptics, including Hume and others. I think he probably is a finistic Platonist (whatever that means), but it appears to me a bit of mysticism to say that the largest natural number, plus one, is equal to zero. David Bernier
From: Aatu Koskensilta on 16 Feb 2010 02:28 David Bernier <david250(a)videotron.ca> writes: > I think he probably is a finistic Platonist (whatever that means), but > it appears to me a bit of mysticism to say that the largest natural > number, plus one, is equal to zero. Taking the view that statements about naturals should be understood with reference to the physical (computational?) universe (in some idealised sense), and assuming we take it to follow on this view that there is a largest natural, what to make of the successor of the largest natural is a matter decided essentially by stipulation. We may decree it's zero, that it's undefined, that applying the successor function to the largest natural leaves it unperturbed, or pretty much anything that strikes our fancy, anything we find convenient; just as in ordinary mathematics whether zero is a natural or not is just a matter of stipulation. (Lest there be any confusion, lest any innocent mind be led astray, let us note here that it is not at all a necessary component of ultra-finitism or ultra-intuitionism that there be a largest natural. Coming clean, I must also admit that I didn't bother to consult Zeilberger's essays before composing this reply.) -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: James Dow Allen on 16 Feb 2010 02:49
On Feb 16, 3:28 am, Angus Rodgers <twirl...(a)yahoo.co.uk> wrote: > ... Doron Zeilberger, > in which he claimed not only that there is a largest natural number > (I'd come across mention of Zeilberger's ultrafinitism before), but > that if you add 1 to this largest natural number, the result is 0. I don't see the problem. Ramanujan once wrote 1+2+3+4+... = -1/12 I think you'll agree the left side is positive and large. Moreover if we multiply by 12, I think I can prove the result is larger than any natural number you can name: 12*(1+2+3+4+...) = -1 So this is the largest natural number; if you add 1 you get 0. Q.E.D. I don't think you want to argue with Ramanujan about large natural numbers. He knew about 1729, a number so large that many languages can't even express it. Sam (posting from jda's account) |