Wikipedia:Reference desk/Archives/Mathematics/2020 May 23

= May 23 =

Sequence
147-2, 137-1, 340-7 what's the next two numbers in this sequence and what formula is being used? Thanks. — Preceding unsigned comment added by 41.212.16.230 (talk) 07:05, 23 May 2020 (UTC)
 * There exist an infinite amount of sequences, an infinite amount of sequences that contain your subsequence, and an infinite amount of possible continuations. The great Tibees recently joked about these kind of questions by fitting an excessively complex polynomial to the ordinary sequence 1,4,7,10 leading to the ridiculous but correct answer of 314 instead of the expected 13. https://www.youtube.com/watch?v=IXojoV9fngY&t=226s--TZubiri (talk) 08:00, 23 May 2020 (UTC)
 * It is meaningful to seek a formula with minimum description length. --Lambiam 14:39, 23 May 2020 (UTC)
 * While Lambiam is of course right, there is always Carl Linderholm's Mathematics Made Difficult to give a laugh too, discussing the sequence 1, 2, 4, 8, 16, ___:

It may be noted that by logarithms, as the example is often done, we got not 31, but 32. Does this worry us? Not a bit! First of all, there is not much difference between 31 and 32; the difference is only 32 − 31 = 1. Secondly, even if we are forced, in an unguarded moment, to admit that 31 and 32 are not quite the same, there remains the question: which answer is better anyhow,

1, 2, 4, 8, 16, 31, or

1, 2, 4, 8, 16, 32 ?

Which of these is really more logical, more true to a mathematical way of thinking? Which really shows the greater pattern-recognition facility? There can be no doubt that 31 is the better answer by a long-to-middling chalk; and this for the simplest of reasons. It must be admitted that if anyone should be so narrow-minded and curious as to put down 32 as the number that follows 1, 2, 4, 8, 16, then he had some reason for doing so. It is possible that he arrived at 32 in any of several ways. He may have noticed immediately that the numbers 1, 2, 4, 8, 16, if exchanged for the letters of the alphabet that correspond to them, are just the initial letters of the words 'Alien birds do have peculiar ...'; and that these are the words of an old Kentish proverb, the last word 'feathers' being omitted. Arranging the alphabet in a circle with z next to a, and counting on past z to a, which then becomes 27, we see that the letter f, with which the extra word 'feathers' begins, gets the value 32, which is the right answer. This is all well and good, and is a reasonable interpretation of the problem showing remarkable skill at pattern-recognition. But one can argue, of course, that the letter w, by its very name, is not really a letter at all; it is merely a way of writing the letter u, or just perhaps the letter v, when they are doubled. Hence this letter must be omitted in the counting, and while 32 is a good approximation to the correct answer, it is not as good as the true answer 31.

But it is also possible that the answer 32 was obtained in another way. It could even have been obtained by the graphical method explained earlier, in which by lucky chance someone thought of taking the logarithm. This leads to the formula

an = 2n,

where of course the first number of the sequence is considered as the zeroth or noughtth number of the sequence. On the other hand, our own work, which was based on a system, gives

an = 1 + $7/12$n + $11/24$n2 − $1/12$n3 + $1/24$n4.

Now both of these answers are backed up by perfectly good mathematical formulae, and so both are perfectly logical. Of the two answers, which is the better-both being correct? The answer is, of course, that the second answer is to be preferred, because it is much the simpler, and is easier to use, and is obtained by a more general method.
 * XD Double sharp (talk) 07:11, 25 May 2020 (UTC)


 * Is anything known about the context? Is this from an intelligence test of some kind? Numbers are usually not written with hyphens, so why are these three items called numbers? Or is it subtraction – but if so, then why not ask simply about 145, 136, 333? The only simple regularity I see is that (1+4+7) mod 10 = 2, (1+3+7) mod 10 = 1 and (3+4+0) mod 10 = 7. But this may well be a coincidence and, moreover, is not helpful for finding a next item. --Lambiam 14:39, 23 May 2020 (UTC)
 * I guess it's viewed as pairs of two numbers where "-" may or may not represent subtraction, and the goal is one more pair a-b (or a+b?). I haven't found a plausible answer. PrimeHunter (talk) 13:18, 24 May 2020 (UTC)

Relationship between manifolds and arrays.
A sequence is 1 dimensional, a matrix is 2 dimensional, what do we call 3 dimensional and n-dimensional objects? My best guess here is arrays, but these are terms from computer science, what were these called before computers? Also, aren't sequences better described as 2dimensional and matrices as 3 dimensional? A scalar would be 1d and a boolean would be 0d. A sequence would be roughly analogous to a line on a plane in this case. And by roughly analogous I mean that they contain a similar amount of information, and they can be accurately mapped in both directions (by mapping each element in a sequence to a point in a whose coordinates are determined by the ordinal and value of the element). And which of these should be considered a more accurate representation of a real world phenomenon? On one hand, a manifold contains more information, an infinite amount, on the other hand (if Democritus atomism hypothesis is to be believed), there is no infinite complexity in the real world and an array would be the most faithful representation of physical matter. --TZubiri (talk) 07:45, 23 May 2020 (UTC)
 * See Holor. (The holor! The holor!) --Lambiam 13:58, 23 May 2020 (UTC)
 * You are probably thinking of tensors. 2601:648:8202:96B0:3567:50D5:8BFF:4588 (talk) 04:16, 25 May 2020 (UTC)