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Post by scottanderson on Oct 4, 2016 19:09:08 GMT -5
The odds of a die coming up with any particular face/number showing is given by 1/n where n = the number of sides.
If you have a d8, n = 8 and the oddds are 1/8 for instance.
What if you had an infinite-face die? A perfect sphere, for instance?
Then n = infinity, and 1/n would approach 0 as n approached infinity. At infinity, the chance of landing on any particular face would actually be 0.
It would roll forever.
I don't think there's a good way to harness such energy, but it's theoretically possible I think. Dice as perpetual motion machines!
Now, is a sphere really a die with infinite sides, or it is actually a die with zero sides? If it's zero, then there's a chance of landing on it equal to infinity (or in this case, 1).
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Post by Admin Pete on Oct 6, 2016 16:11:21 GMT -5
How are you thinking of making use of this?
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Post by scottanderson on Oct 6, 2016 22:04:14 GMT -5
I'm not smart enough to use it for anything, it was just a thought that wandered across my brain
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Post by Admin Pete on Oct 7, 2016 4:19:46 GMT -5
I'm not smart enough to use it for anything, it was just a thought that wandered across my brain Me either, but it looks like the first hurdle is making a perfect sphere. |
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Post by waysoftheearth on Oct 7, 2016 6:49:39 GMT -5
It's a fun idea to play around with, but I think you may want to iron out a couple of logical glitches before you start building your prototype  What if you had an infinite-face die? A perfect sphere, for instance? Is a perfect sphere really an infinite-face die? If the "face" of a die is the surface that can ultimately winds up "facing" us after a throw, then isn't a sphere more a one-sided die? I.e., no matter how many times we throw a sphere it always results in the same one face showing; that is the one, continuous, surface of the sphere. My (rudimentary) understanding of physics is that this could only be true in an (unlikely) environment with zero fiction. Where usual physics apply, I reckon that the "harvesting" of any of this perpetual motion (e.g., by "scraping" energy off the sphere as it perpetually rolled) would probably count as some kind of friction or resistance, and therefore would ultimately have to bring the sphere to a stop. Now, is a sphere really a die with infinite sides, or it is actually a die with zero sides? If it's zero, then there's a chance of landing on it equal to infinity (or in this case, 1). As per above, I'd suggest that it is absolutely probable (p=1) that a sphere-die will land with its one face facing, not because of any tricky mathematics around unreal numbers, but because it has exactly one side |
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Post by robkuntz on Oct 7, 2016 8:19:36 GMT -5
There is no way mathematics can interpolate infinity as there can be no returned value, so the matter of perpetuity is just that.
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Post by mormonyoyoman on Oct 7, 2016 10:07:05 GMT -5
I don't want to interpolate infinity. I want to waste it with my crossbow.
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Post by scottanderson on Oct 7, 2016 12:58:01 GMT -5
Yeah I knew there was some catch. Darn physics.
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Post by waysoftheearth on Oct 7, 2016 18:49:27 GMT -5
I believe scottanderson's original suggestion was an example of mathematical extrapolation rather than interpolation, see here. Then n = infinity, and 1/n would approach 0 as n approached infinity. At infinity, the chance of landing on any particular face would actually be 0. The second statement is untrue, because "at infinity" is undefined. There's a nice summary of how it works, mathematically, here. |
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Post by mormonyoyoman on Oct 7, 2016 20:29:49 GMT -5
I used to understand physics. Even was offered a scholarship for physics in 1971 or 1972. Instead, I majored in English with a minor in theater, which is another phrase for the word "unemployable."
Not that it would matter now. I barely can comprehend quantum physics and now astrophysics goes so far beyond science fiction, that it might as well be magic. ACC was right.
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Post by Admin Pete on Oct 7, 2016 21:10:11 GMT -5
I used to understand physics. Even was offered a scholarship for physics in 1971 or 1972. Instead, I majored in English with a minor in theater, which is another phrase for the word "unemployable." Not that it would matter now. I barely can comprehend quantum physics and now astrophysics goes so far beyond science fiction, that it might as well be magic. ACC was right. About many things! |
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Post by mormonyoyoman on Oct 7, 2016 22:00:02 GMT -5
Perhaps this is why Windows accessory files are named after - uh, no?
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Post by scottanderson on Oct 8, 2016 3:44:03 GMT -5
I majored in Political Science and I actually became a working political scientist. Apparently the odds against that are like 1 in a million. After my heart attack, I stopped.
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Post by robkuntz on Oct 8, 2016 5:07:30 GMT -5
I don't want to interpolate infinity. I want to waste it with my crossbow. Hopefully you miss your "to hit" roll, or else the collective "we" ceases to exist, which of course means that this and other posts like it never were, which might mean the cross bow was never invented, which might mean that you never fired it, so... carry on...  |
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Post by mormonyoyoman on Oct 8, 2016 10:54:17 GMT -5
I don't want to interpolate infinity. I want to waste it with my crossbow. Hopefully you miss your "to hit" roll, or else the collective "we" ceases to exist, which of course means that this and other posts like it never were, which might mean the cross bow was never invented, which might mean that you never fired it, so... carry on... Rats. I just failed my Sanity roll again. And Sanity, as my favorite Granny used to say, does not run in our family. |
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