I have so many questions about that freaking creature. Can it partially unfold to reach anything arbitrarily far away? And how would it go about washing it’s infinite surface area?
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.
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”.
1- Yes, but the more it unfolds, the thinner and weaker the part of it that reaches the object will be. At one point it may be thinner than an atom, at which points further questions become too complicated for me to bother trying to answer. If Plank’s distance is mentioned I will run away.
2- If it goes into the bath water and you consider the water to be a continuous medium, then the surface of water touching it will also be infinite. If you consider a scale too small for the water to be considered a continuous medium, however, I will leap out the window.
The problem with washing it is more with trying to scrub it then just submerging it in water. But as you pointed out it probably gets very brittle further out so you might hurt it if you try to scrub it
I have so many questions about that freaking creature. Can it partially unfold to reach anything arbitrarily far away? And how would it go about washing it’s infinite surface area?
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.
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.
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.
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”.
Eh, that’s just 1/2 of the harmonic sum, which diverges.
Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
Very well, today I accede to your superior pedantry.
But one day I shall return!
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.
1- Yes, but the more it unfolds, the thinner and weaker the part of it that reaches the object will be. At one point it may be thinner than an atom, at which points further questions become too complicated for me to bother trying to answer. If Plank’s distance is mentioned I will run away.
2- If it goes into the bath water and you consider the water to be a continuous medium, then the surface of water touching it will also be infinite. If you consider a scale too small for the water to be considered a continuous medium, however, I will leap out the window.
The problem with washing it is more with trying to scrub it then just submerging it in water. But as you pointed out it probably gets very brittle further out so you might hurt it if you try to scrub it
A gentle sonic agitator.
Thanks, you solved the problem