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The cursed d65536

aleph.se

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Re: The cursed d65536

#11

Post by avmich »

sp332 wrote: post #5

From the broken first attempt: Each face has 3 vertices, shared between 6 faces, so the total number of vertices is 65536, and they become faces of my die. This should have tipped you off. If you have six triangular faces around every vertex, you have a flat Euclidean plane, not a sphere with positive curvature. For another example of this: https://m.youtube.com/watch?v=jfSTwqmrQDc

That's why "don't do math after midnight". But I don't get what's wrong with repeated throws of tetrahedron - 2 bits of result at a time - or even icosahedron, with re-throws if one of 4 "wrong" sides is up - 4 bits at a "good" throw...

Re: The cursed d65536

#12

Post by avmich »

mellavora wrote: post #6
anyfoo wrote: post #4

Earlier quoted context omitted.

Or do 16 throws of such a d(2) die, i.e. 16 coin flips, in succession. If you really want to do it in one throw, you don't really need to color them all differently, though. Just read them in a specified way, i.e. always from left to right and top to bottom. (You don't even have to always read them the same way as long as how you read them is completely independent from what their faces show.)

Kids these days. What ever happened to sacrificing a goat and reading the entrails?

Inflation of goats?

Re: The cursed d65536

#13

Post by recursive »

woliveirajr wrote: post #8

> XKCD joked about the problem of secure generation of random 32 bit numbers by rolling a 65536-sided die Well, 2^16 = 65536, so it's a 16-bit number. To get a random 32-bit number you'd need to roll more than once....

XKCD got it right. aleph.se got it wrong.

Re: The cursed d65536

#14

Post by jeramey »

jandrese wrote: post #7
aidenn0 wrote: post #2

I know it's not the point of TFA, but you can just roll a d8 6 times, generating 3 bits each time, for a total of 18 bits, and then discard two of them.

Why not just roll 4D16? https://www.amazon.com/Lanema-Polyhedral-Dungeons-Dragons-Si...

I'd be a little worried that I might be tempted to unconsciously order the values in some way which would bias the results. But you could build a box with four separate cells and a clear plexiglass top, shake them all up, and always read left-to-right or right-to-left! Sounds like a fun weekend project!

Re: The cursed d65536

#15

Post by tgb »

sp332 wrote: post #5

From the broken first attempt: Each face has 3 vertices, shared between 6 faces, so the total number of vertices is 65536, and they become faces of my die. This should have tipped you off. If you have six triangular faces around every vertex, you have a flat Euclidean plane, not a sphere with positive curvature. For another example of this: https://m.youtube.com/watch?v=jfSTwqmrQDc

Pedantry: it doesn’t have to be flat - for example a triangulated parabola could also have that configuration. You only get a topological result from just knowing edge and vertex counts. Now if the triangles are identical equilateral then you’re in business.

What if the triangles are all congruent but not equilateral? Can that even happen? That’s a fun one, so I won’t spoil it.

Re: The cursed d65536

#16

Post by kazinator »

> This is of course hilariously cursed. It will look almost perfect, but very rarely give numbers outside the expected range.

If the D65538 is fair, it is usable: you just discard the two unwanted values when they show up and roll again. Those faces could be labelled as "roll again".

If you have a uniform source of random numbers from 1 to N, you can get a uniform distribution from 1 to M < N simply by discarding values obtained above M. Those values are just "rain that fell elsewhere".

Re: The cursed d65536

#18

Post by sp332 »

tgb wrote: post #15
sp332 wrote: post #5

From the broken first attempt: Each face has 3 vertices, shared between 6 faces, so the total number of vertices is 65536, and they become faces of my die. This should have tipped you off. If you have six triangular faces around every vertex, you have a flat Euclidean plane, not a sphere with positive curvature. For another example of this: https://m.youtube.com/watch?v=jfSTwqmrQDc

Pedantry: it doesn’t have to be flat - for example a triangulated parabola could also have that configuration. You only get a topological result from just knowing edge and vertex counts. Now if the triangles are identical equilateral then you’re in business. What if the triangles are all congruent but not equilateral? Can that even happen? That’s a fun one, so I won’t spoil it.

Oh, do you think it could make a sphere then? If the angle at each triangle corner is a bit less than 60 degrees?

Re: The cursed d65536

#19

Post by tlb »

I'd like a physics analysis of how flat/hard a surface you need to roll a D65536, how long it would take to settle, and how good a microscope you'd need to read the top face.

Is there, like, 99designs for physics questions? I'd happily pay $99 for the answer, then post it here like I worked it out myself.

Re: The cursed d65536

#20

Post by samch »

Probably says something about me that my immediate reaction to the number 65536 wasn’t 2^16, but rather the frequency of the timer crystal you had to swap into a Radio Shack tone dialer to make a “red box”[1] that would let you make free phone calls on US pay phones by simulating the analog coin code sound of a quarter being deposited. Fun fact that the “red box” was the first hackaday article[2] posted way back in 2004. I learned about this back in the days of 2600 magazine. Fun stuff!

[1] http://www.techfreakz.org/2600faq.html#redbox

[2] https://hackaday.com/2004/09/05/radioshack-phone-dialer-red-...

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