[HN Gopher] The cursed d65536
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The cursed d65536
Author : EvgeniyZh
Score : 63 points
Date : 2022-06-09 09:25 UTC (13 hours ago)
(HTM) web link (aleph.se)
(TXT) w3m dump (aleph.se)
| sp332 wrote:
| 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
| tgb wrote:
| 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.
| sp332 wrote:
| Oh, do you think it could make a sphere then? If the angle at
| each triangle corner is a bit less than 60 degrees?
| avmich wrote:
| 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...
| samch wrote:
| 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-...
| scrame wrote:
| I just coded it in basic and the recorded it to a mini-casette
| lecture-recorder. Unfortunately, by that point the tones just
| triggered an operator call.
| reaperducer wrote:
| The DTMF chips that generated regular Touch Tones(tm) were
| capable of generating all kinds of fun sounds simply by
| extending the key matrix.
|
| You could build a red box, pink box, blue box, and others by
| modifying a standard tone dialer. The easiest thing to do was
| to add a fourth column of keys, which supposedly gave you the
| ability to use the ABCD digits required for military networks.
| I never tried that, though.
|
| For those of you who missed out on that era, a tone dialer was
| a little palm-sized box that had a small Touch Tone keypad on
| one side, and a speaker on the other. If you had a rotary
| phone, after dialing, you could hold it up to the mouthpiece
| and use many of the fancy features that came with the invention
| of Touch Tone, like using FON cards, or listening to your
| messages on your answering machine.
| aidenn0 wrote:
| 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.
| tialaramex wrote:
| You can buy hexadecimal dice ie D16 with the sides labelled 0
| through F, I have some, I use them to generate random numbers
| when it is important to me that I personally have confidence
| these are random numbers.
|
| With hex dice you can generate 16 bits with four rolls, four
| bits each time.
|
| Obviously you're more likely to already have a D6 somewhere,
| but then you're even more likely to own a coin, and 16 coin
| tosses is also an effective way to generate a 16-bit number.
| aetherson wrote:
| The article suggests flipping coins in the last sentence, which
| gets you exactly as many bits as you want.
| bombcar wrote:
| Yep, or use 16 dice that have only 0 and 1 on them. The order
| would be important, so you'd want to color them or otherwise
| indicate which was high order and which was low.
| anyfoo wrote:
| 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.)
| mellavora wrote:
| Kids these days. What ever happened to sacrificing a goat
| and reading the entrails?
| avmich wrote:
| Inflation of goats?
| bombcar wrote:
| Apparently some guy named Monty Hall is just giving away
| goats for free.
| jandrese wrote:
| Why not just roll 4D16?
|
| https://www.amazon.com/Lanema-Polyhedral-Dungeons-Dragons-Si...
| aidenn0 wrote:
| "... for Dungeons and Dragons" ah yes, I use a D16 _all the
| time_ when playing D &D /s
| jeramey wrote:
| 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!
| kazinator wrote:
| > _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".
| stkdump wrote:
| This process has an infinitely small (but non-zero) chance of
| never terminating.
| Dylan16807 wrote:
| Which doesn't matter on objects or programs because that
| chance already exists as a baseline. I'm not building a math
| here.
| davidgay wrote:
| But that probability rapidly drops below the probability that
| you will drop dead from some random cause while waiting for
| the roll's result :)
| mananaysiempre wrote:
| The process has an _exactly zero_ chance of never terminating
| in the usual probability space of infinite strings with iid
| characters, even though the set of strings (of RNG results)
| on which it does not terminate is nonempty (uncountably
| infinite, even, provided N >= M + 2); the term of art is that
| it terminates _almost surely_. (The usual definition of that
| space via "cylinder sets" may seem contrived, but it's
| usually introduced first because it's "elementary" in that it
| does not require developing the machinery of limits of [not
| _in_ ] probability spaces. That can be made to work, though,
| and then you can say that the space of infinite strings is
| the limit of the spaces of length-n strings for n - [?] and
| obtain the same thing. In fact, the cylinder-set definition
| is essentially the limit definition with the notion of limit
| inlined.)
| kazinator wrote:
| The die also has a very small chance of landing on an edge
| between two faces, which also requires a repeated roll.
| Smaug123 wrote:
| This is a rather sloppy way of saying "this process may fail
| to terminate, though the set of nonterminating outcomes has
| probability 0". No real number is infinitely small but
| nonzero.
| mananaysiempre wrote:
| _Rejection sampling_ , that is. Unexpectedly, but obviously in
| retrospect, the common (ancient) wisdom of using that in the
| continuous case instead of figuring out tricky combinations of
| special functions to get the result from a bounded number of
| uniform samples... fails miserably on LuaJIT. Of course atan2()
| is not the fastest thing in the world, but on a compiler that
| only really understands loops with linear bodies calling it
| even via FFI beats adding an unpredictable nested loop.
| pacaro wrote:
| I'm surprised that nobody has mentioned the d120 which AFAICT is
| the largest fair dice that you can just go out and buy. Sadly
| it's a smidge under 7 bits, but you can "reasonably" roll up 32
| bits of entropy with a mere 6 rolls (and still have 9 bits left
| over)
|
| https://www.wired.com/2016/05/mathematical-challenge-of-desi...
| woliveirajr wrote:
| > 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....
| recursive wrote:
| XKCD got it right. aleph.se got it wrong.
| tlb wrote:
| 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.
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(page generated 2022-06-09 23:00 UTC)