Comments on: The state of the spamosphere http://bit-player.org/2010/the-state-of-the-spamosphere An amateur's outlook on computation and mathematics. Thu, 17 May 2012 10:19:14 +0000 http://wordpress.org/?v=2.6.3 By: Bernhard W. Marx http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3264 Bernhard W. Marx Wed, 03 Nov 2010 11:25:33 +0000 http://bit-player.org/?p=742#comment-3264 There is no ONE right answer to such questions, although there may be one, which seems most plausible to most people. Any sequence of n numbers can be thought to be the values of polynome of degree below n with the independant variable x running from 0 (zero) to n-1. As such a next number can be developed as p(n) -- by the way without any multiplication, just additions and subtractions, unless one were interested in a closed form of the polynome. By the same token one could choose ANY next number and have these n+1 numbers be generated by a polynome q of degree not above n -- and upon being challenged for an algorithm by which this next number was got at, exhibit this polynome q. What is the next number in the sequence 0,1,0,1, ... ? Of course it must be 8. Or whatever you fancy. There is no ONE right answer to such questions, although there may be one, which seems most plausible to most people.
Any sequence of n numbers can be thought to be the values of polynome of degree below n with the independant variable x running from 0 (zero) to n-1. As such a next number can be developed as
p(n) — by the way without any multiplication, just additions and subtractions, unless one were interested in a closed form of the polynome.
By the same token one could choose ANY next number and have these n+1 numbers be generated by a polynome q of degree not above n — and upon being challenged for an algorithm by which this next number was got at, exhibit this polynome q.
What is the next number in the sequence 0,1,0,1, … ?
Of course it must be 8.
Or whatever you fancy.

]]> By: brian http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3228 brian Mon, 20 Sep 2010 13:43:05 +0000 http://bit-player.org/?p=742#comment-3228 Fred Merk writes: <blockquote>The typical vanity of mathematicians - never apologise, never explain.</blockquote> Obviously the correct response to this comment is enigmatic silence. But since I'm not actually a mathematician, I'm not required to observe all the usual vanities. By way of explanation, if not apology, I would note that when someone has taken the initiative to go to work on a problem and has run into difficulties, simply giving away the answer is not often the most helpful response. Isn't the process of finding the answer more important and more enjoyable than the answer itself? (In this case I happen to know through private back-channel communication that Amy Hayes did indeed solve the problem on her own shortly after posting her comment.) As for the alternative solution offered by Mr and Mrs. OEIS, those who simply want to know the answer can run off to <a href="http://www.research.att.com/~njas/sequences/A100016" rel="nofollow">consult the OEIS</a>. For those who would rather puzzle it out, I'll offer one more term of the sequence as a hint: 1, 2, 6, 42, 1806, 3270666, 10697259354222,... Fred Merk writes:

The typical vanity of mathematicians - never apologise, never explain.

Obviously the correct response to this comment is enigmatic silence. But since I’m not actually a mathematician, I’m not required to observe all the usual vanities.

By way of explanation, if not apology, I would note that when someone has taken the initiative to go to work on a problem and has run into difficulties, simply giving away the answer is not often the most helpful response. Isn’t the process of finding the answer more important and more enjoyable than the answer itself? (In this case I happen to know through private back-channel communication that Amy Hayes did indeed solve the problem on her own shortly after posting her comment.)

As for the alternative solution offered by Mr and Mrs. OEIS, those who simply want to know the answer can run off to consult the OEIS. For those who would rather puzzle it out, I’ll offer one more term of the sequence as a hint:

1, 2, 6, 42, 1806, 3270666, 10697259354222,…

]]> By: Fred Merk http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3227 Fred Merk Mon, 20 Sep 2010 04:36:38 +0000 http://bit-player.org/?p=742#comment-3227 The typical vanity of mathematicians - never apologise, never explain. I'm going to help out the lady by expanding on Dave of Tucson's answer: 1x2, 2x3, 6x7, 42x43, 1806x1807 = 3263442. Now if only Mr and Mrs OEIS will be so good as to explain theirs. Of course a pattern can be completed in more than one way - it's all a question of taste. Discrimination precedes measurement. And communication is a wonderful thing. The typical vanity of mathematicians - never apologise, never explain. I’m going to help out the lady by expanding on Dave of Tucson’s answer: 1×2, 2×3, 6×7, 42×43, 1806×1807 = 3263442. Now if only Mr and Mrs OEIS will be so good as to explain theirs. Of course a pattern can be completed in more than one way - it’s all a question of taste. Discrimination precedes measurement. And communication is a wonderful thing.

]]> By: Amy Hayes http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3223 Amy Hayes Tue, 14 Sep 2010 16:43:07 +0000 http://bit-player.org/?p=742#comment-3223 Okay, the math gene clearly skipped a generation. I have no idea what the answer to this problem is despite spending 15 minutes trying to figure it out. My only comfort is that two of the commenters came up with different responses. Okay, the math gene clearly skipped a generation. I have no idea what the answer to this problem is despite spending 15 minutes trying to figure it out. My only comfort is that two of the commenters came up with different responses.

]]> By: Jason http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3133 Jason Mon, 09 Aug 2010 21:00:28 +0000 http://bit-player.org/?p=742#comment-3133 Dave: same experience here, usually I have to try several things to get an answer but I spotted the pattern almost immediately. Pattern recognition is so mysterious to me, I think I've found what I'm going to read about for the rest of the afternoon. Dave: same experience here, usually I have to try several things to get an answer but I spotted the pattern almost immediately.

Pattern recognition is so mysterious to me, I think I’ve found what I’m going to read about for the rest of the afternoon.

]]> By: unekdoud http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3131 unekdoud Mon, 09 Aug 2010 02:01:38 +0000 http://bit-player.org/?p=742#comment-3131 It would take us an average of 25 seconds longer to post comments :) Time to try this on some Accounting Experts and Number Numbs, whoever those are. It would take us an average of 25 seconds longer to post comments :)
Time to try this on some Accounting Experts and Number Numbs, whoever those are.

]]> By: Mr and Mrs. OEIS http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3130 Mr and Mrs. OEIS Mon, 09 Aug 2010 01:58:55 +0000 http://bit-player.org/?p=742#comment-3130 3270666 The OEIS thinks different. 3270666

The OEIS thinks different.

]]> By: Dave in Tucson http://bit-player.org/2010/the-state-of-the-spamosphere#comment-3129 Dave in Tucson Mon, 09 Aug 2010 01:29:43 +0000 http://bit-player.org/?p=742#comment-3129 3263442 Normally, I get brain freeze on questions like this unless they're pretty easy. I got this one in just a few seconds, so...? 3263442

Normally, I get brain freeze on questions like this unless they’re pretty easy. I got this one in just a few seconds, so…?

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