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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. 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
billion pieces per year nowadays, so probably somewhere between 100 billion and
1 trillion sounds like a good guess. Let's say 500 billion for argument's sake.
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.
FUT .geek, fellow nerds!
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Message has 3 Replies:
 | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) The 2004 LEGO Company Profile white-paper says "Over the years, enough LEGO bricks have been manufactured to give an average of 52 each to every single one of the world's 6 billion inhabitants." Another place indicates "Annual production is (...) (20 years ago, 8-Dec-04, to lugnet.off-topic.geek)
| | | Re: Is lego *truly* unlimited? (some thoughts)
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| (...) Ok, so it's asymptotic, not logarithmic, and it approaches 4, so 4 was a perfectly cromulent guess. However. Since the sum of any line N of Pascal's triangle is apparently 2^N (starting at row 0), and you'd theoretically count EVERYTHING (...) (20 years ago, 9-Dec-04, to lugnet.off-topic.geek)
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Message is in Reply To:
| | Is lego *truly* unlimited? (some thoughts)
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| I was just wondering today about how much lego is trumpeted as having an 'unlimited' number of possibilites. Now I'm no math whiz, but it seemed logically impossible to me. So here's some food for thought for the gurus out there to digest and make (...) (20 years ago, 8-Dec-04, to lugnet.general, lugnet.build)
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