Wikipedia:Reference desk/Archives/Mathematics/2015 October 29

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October 29

Bird in a Thornbush

One of the modules of XScreenSaver is Thornbird, which "Displays a view of the 'Bird in a Thornbush' fractal." I search for that phrase and all I find is *nix documentation. Has it another name? —Tamfang (talk) 06:52, 29 October 2015 (UTC)

For convenience, here [1] is a youtube clip (with some nice retro disk sounds), and here [2] seems to be C source code showing the update rule for the iterative process. The code has some author info so failing all else you could try to contact him. SemanticMantis (talk) 14:14, 29 October 2015 (UTC)

Galileo's paradox

In reference to Galileo's paradox, I don't quite understand the need to refer to squares vs. non-squares. Isn't it simpler to just compare, say, evens to all numbers? There are double the number of integers as there are even integers, and yet there are no more of the latter than there are of the former. I understand that this is simply a restatement of Galileo's paradox, but why the need to touch upon squares vs. non-squares, or anything else more complex, such as primes vs. non-primes. Thanks! DRosenbach ^{(Talk | Contribs)} 16:31, 29 October 2015 (UTC)

Barring someone finding some writing where Galileo explains specifically what led him to consider squares, I don't see how anyone can hope to answer you. My guess would be, it's just the example he happened to think of first, and who knows why. You're quite correct, of course, that "even numbers" versus "natural numbers" would work just as well. --Trovatore (talk) 17:14, 29 October 2015 (UTC)

In the translated dialogue in the article, Salviati makes the point that not only are there apparently fewer squares than natural numbers, but the density of squares decreases without limit as you consider larger prefixes of the natural numbers. So, at a guess, Galileo thought squares made for a stronger or more interesting argument than evens. -- BenRG (talk) 19:44, 29 October 2015 (UTC)

Ah, I thought of that point, more or less, but didn't realize Galileo had explicitly made it. I should have actually read the dialogue instead of just skimming it. --Trovatore (talk) 19:53, 29 October 2015 (UTC)

The argument also works for cubes, n^4, n^5, n^100, n^n, n^n^n, n^n^n^n^n^n^n^n 175.45.116.66 (talk) 04:19, 30 October 2015 (UTC)