Subject:
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Re: Is lego *truly* unlimited? (some thoughts)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Thu, 9 Dec 2004 03:32:02 GMT
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Viewed:
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4546 times
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In lugnet.general, David Eaton wrote:
> In lugnet.general, Samarth Moray wrote:
> > Some thoughts/comments from the Mathematicians out there?
>
> Well, 1st off, there's probably on the order of several hundred billion pieces
> on the planet.
Hi David,
Thats why I said something more finite, like our collections would be
easier/possible to calculate.
> 5x10^11 possible 1-piece MOC's
> Roughly 2.5x10^23 possible 2-piece MOC's
> Roughly 1.25x10^35 possible 3-piece MOC's
> Roughly 6.25x10^46 possible 4-piece MOC's
> Roughly 3.13x10^58 possible 5-piece MOC's
>
> That's not really accurate, of course, because colors combos are duplicated in
> spades. However, when you get to the 250-billion-piece-MOC's, that progression
> will get more accurate (dunno what 5x10^11 choose 2.5x10^11 is, but any computer
> asked to compute such a flagrantly ridiculous number would probably cry
> uncontrollably-- you might even want to use scientific notation to denote the
> 10's exponent for such a hilariously gigantic number[1]).
>
> Now, the shortest measure of time I can find that has a name is a "yocto"
> second. (10^-24 of a second-- a quadrillionth of a nanosecond). Assuming a
> 10-billion year age of the universe, there's about 3x10^41 yoctoseconds in the
> history of the universe. And we've already got WAY more possible MOC's than
> that.
>
> Hence, given the variety and quantity of Lego parts, I would argue that even
> knowing the exact number of ways to connect all types of pieces and precisely
> how many of each piece/color existed, you *still* couldn't even compute all the
> possible permutations, even with computers a billion times faster than what
> we've got today.
>
> In that regard, Lego really IS "unlimited". Instead of the Lego being limited,
> it's you as the builder who is limited, because there are far more possible Lego
> creations than are conceiveably buildable by all the humans that ever were and
> ever will be. For all intents and purposes, infinite.
>
> DaveE
>
> [1] Ok, at a very rough guess, 500 billion choose 250 billion is at least
> 1x10^(4x10^11) or 1x10^400000000000, which... is a lot. Guessed based on how
> quickly the "middle number" in Pascal's triangle increases. Every other row's
> middle number seems to grow logarithmically, at hits at LEAST 4 long before it
> gets even halfway to the billionth row. Hence, I used a factor of 4 to guess at
> the number of 0's that the center number goes up by after 500 billion rows (250
> iterations, since it's counting every other row). In actuality, there's probably
> a better factor to use to guess with.
All that fancy math........
>
> FUT .geek, fellow nerds!
I shouldve x-posted there in the beginning.
Thanks,
Samarth
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Message is in Reply To:
 | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) Well, 1st off, there's probably on the order of several hundred billion pieces on the planet. I remember reading in some FAQ the estimated number of pieces in the world, but I can't seem to find it at the moment. I know they make about 20 (...) (22 years ago, 8-Dec-04, to lugnet.general)
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