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52 Factorial

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Re: 52 Factorial

#51

Post by szvsw »

interroboink wrote: post #46
szvsw wrote: post #26

I would guess the author is a fan of Joyce: > What must it be, then, to bear the manifold tortures of hell forever? Forever! For all eternity! Not for a year or an age but forever. Try to imagine the awful meaning of this. You have often seen the sand on the seashore. How fine are its tiny grains! And how many of those tiny grains go to make up the small handful which a child grasps in its play. Now imagine a mountai…

And maybe Joyce was a fan of the Brothers Grimm! [1] "The third question is, how many seconds of time are there in eternity?" Then said the shepherd boy: "In Lower Pomerania is the Diamond Mountain, which is two miles and a half high, two miles and a half wide, and two miles and a half in depth; every hundred years a little bird comes and sharpens its beak on it, and when the whole mountain is worn away by this, then…

Love it!

I think it is a somewhat common analogy in catechistic texts but I’m not positive. I don’t think anyone could write it quite like Joyce though!

Re: 52 Factorial

#52

Post by wduquette »

IanCal wrote: post #50
Straw wrote: post #35

Earlier quoted context omitted.

If the RNG has < 226 bits of state, such as most non cryptographic PRNGs, you cannot reach all shuffles even if you use multiple numbers.

I'm not totally sure that's true. I get where you are coming from, an 8 bit rng can only output 256 distinct values at most. 256 would be the longest cycle. However if you combine the outputs of two, but don't step them at the same time, you can have more outputs. Imagine you had one that outputs just 0 and 1 and then loops. You could have two of these updating at a different frequency and have four distinct outputs.…

Oh, yeah, there are ways to finesse it. I’m just wondering whether anyone involved in those early poker machines had made the effort.

Re: 52 Factorial

#53

Post by hashtekar »

marvinborner wrote: post #40
kimbernator wrote: post #24

I sometimes wake up having an anxiety attack because my dream was attempting to play something like this out- always something to do with permutations of massive numbers. It was a little bit of a challenge to keep it together while reading this. No idea why that is, either. It's the only thing that has such an effect on me.

I have something similar but for lambda terms with huge normal forms, I always wake up exhausted when this happens

Wow. I read your comment a few hours ago. Disturbed sleep, the tight little loops of information retrieval, processing and repeat. That feeling of exhaustion. It’s real. It’s happening to me right now. What’s new is I knew I’d be here, writing this, all those hours ago. Mixed with the cards and the Maths.

Re: 52 Factorial

#54

Post by cardiffspaceman »

wduquette wrote: post #52
IanCal wrote: post #50

Earlier quoted context omitted.

I'm not totally sure that's true. I get where you are coming from, an 8 bit rng can only output 256 distinct values at most. 256 would be the longest cycle. However if you combine the outputs of two, but don't step them at the same time, you can have more outputs. Imagine you had one that outputs just 0 and 1 and then loops. You could have two of these updating at a different frequency and have four distinct outputs.…

Oh, yeah, there are ways to finesse it. I’m just wondering whether anyone involved in those early poker machines had made the effort.

In Nevada one was required to “prove the randomness” of random outcomes in video poker machines as well as other electronic gambling machines. So effort was made.

Re: 52 Factorial

#55

Post by petermcneeley »

lcnPylGDnU4H9OF wrote: post #28

The number has 12 zeroes at the end, which confused me for a bit, so I'm leaving this comment in case anyone else is similarly confused and would like to know why. There are 10 total numbers between 1 and 52 which include 5 as a factor (5 which also include 2 as a factor to make a factor of 10 and 5 more to be multiplied with a bunch of other 2-factor numbers) so intuitively I was thinking there should be 10 zeroes.…

2^49×3^23×5^12×7^8×11^4×13^4×17^3×19^2×23^2×29×31×37×41×43×47

There is a 5^12 and more than that for the 2s. So yes 12 zeros it will be as God intended.

https://www.wolframalpha.com/input?i=factors+of+806581751709...

Re: 52 Factorial

#56

Post by lkuty »

pixl97 wrote: post #12
nabla9 wrote: post #8

Earlier quoted context omitted.

mass of Earth is 6×10^27 kg mass of the Milky Way is 6x10^42 kg mass of the visible Universe is 1.5×10^53 kg Quality deck of cards weighs 0.3 kg. All deck combinations would weigh 2.4×10^67 kg. = 10^14 times the mass of the visible Universe. You need many multiverses to store all those cards.

Or just make each deck 10^14 times smaller

Reminds of "Could you fold a sheet of paper on itself 64 times?". "No problem! It's easy". Until you try or think about powers of 2 and calculate the height of the thickness of the sheet multiplied by 2^64. 64 might by replaced by 32 to make it seem more approcheable. That's funny how counter-intuitive it might be.

Re: 52 Factorial

#57

Post by ndsipa_pomu »

lkuty wrote: post #56
pixl97 wrote: post #12

Earlier quoted context omitted.

Or just make each deck 10^14 times smaller

Reminds of "Could you fold a sheet of paper on itself 64 times?". "No problem! It's easy". Until you try or think about powers of 2 and calculate the height of the thickness of the sheet multiplied by 2^64. 64 might by replaced by 32 to make it seem more approcheable. That's funny how counter-intuitive it might be.

32 is far too many as the World Record is currently 12 times: https://www.guinnessworldrecords.com/world-records/494571-mo...

I remember as a kid being told that it was impossible to fold a piece of paper in half 8 times and most of the time, that's true unless you use a very long and thin bit of paper.

Re: 52 Factorial

#58

Post by 49pctber »

lcnPylGDnU4H9OF wrote: post #28

The number has 12 zeroes at the end, which confused me for a bit, so I'm leaving this comment in case anyone else is similarly confused and would like to know why. There are 10 total numbers between 1 and 52 which include 5 as a factor (5 which also include 2 as a factor to make a factor of 10 and 5 more to be multiplied with a bunch of other 2-factor numbers) so intuitively I was thinking there should be 10 zeroes.…

25 and 50 contribute two 5 factors each. The multiplicity of 2 factors is even greater, as every other even factor contributes at least two, every fourth at least three, etc.

Re: 52 Factorial

#59

Post by carapace »

kimbernator wrote: post #24

I sometimes wake up having an anxiety attack because my dream was attempting to play something like this out- always something to do with permutations of massive numbers. It was a little bit of a challenge to keep it together while reading this. No idea why that is, either. It's the only thing that has such an effect on me.

Hit the pressure release valve. Next time this happens look around and find the button or lever or old fashioned knife switch labeled "pressure release valve" or something like that and push/pull/flip/throw it.

(I'm seriously. The brain works like that. Draw a door on the wall and open it and walk through.)

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