Science Memes

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Science memes (mander.xyz)

submitted 4 months ago by [email protected] to c/[email protected]

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[–] [email protected] 10 points 4 months ago (3 children)

That depends on the decay factor of one centaur to the next. If the centaurs shrink by anything more than a factor of two, then no. The creature will converge onto a single length.

[–] [email protected] 13 points 4 months ago

What? If it's geometric it needs to be less than 1, that's all. 9/10 + 81/100 + 729/1000 + ... = 10

C•(1-r)^-1^ = C•x

Where r is the ratio between successive terms.

[–] [email protected] 5 points 4 months ago (1 children)

Should be anything less than a harmonic decrease (that is, the nth centaur is 1/n the size of the original).

The harmonic series is the slowest-diverging series.

[–] [email protected] 1 points 4 months ago (1 children)

The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can't just say "less than harmonic" though, I mean 1/(2n) is "slower".

[–] [email protected] 2 points 4 months ago (1 children)

Eh, that's just 1/2 of the harmonic sum, which diverges.

[–] [email protected] 2 points 4 months ago (1 children)

Yes, but it proves that termwise comparison with the harmonic series isn't sufficient to tell if a series diverges.

[–] [email protected] 3 points 4 months ago

Very well, today I accede to your superior pedantry.

But one day I shall return!

[–] [email protected] 3 points 4 months ago

Judging by the image the centaura shrink with about a factor of two so the entire creature should be either infinitely long or just very very long.