Subject:
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Re: Mathematical proof that you can't build anything with LEGO bricks
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Newsgroups:
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lugnet.general
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Date:
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Mon, 27 Feb 2012 17:55:43 GMT
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Viewed:
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19345 times
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In lugnet.general, Larry Pieniazek wrote:
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He says “LEGOs” which makes his work suspect right there. :) Not very
rigorous. The paper is from 2001... the piece palette has improved somewhat
since then.
But generally I’m not sure he’s drawing valid inferences/conclusions. LEGO
elements are not neurons, or electronic components, and total network
connectivity is not their most important metric. Rather, at least in my view,
what is important is whether pieces interoperate well with each other
locally. And we know they do. There are more ways to interconnect LEGO
elements than any other building system I know.
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He would argue that the increase in the number of new types of pieces is
actually an indication that the LEGO system is getting less flexible.
But as you say, the system is designed so that every piece connects to at least
one other piece type, and most of them fit with most of the other types.
One problem with his method is that he used Peeron inventories to provide the
number of pieces and piece types in each set. He didn’t filter this data at all,
however. As we know, Peeron inventories have an entry for each element AND
color. He simply counted the number of entries in the inventory and called each
one a piece type - so he counts a red 1x2 brick as one type and a blue 1x2 brick
as a different type. Of course the color has nothing to do with the ability of
two pieces to connect, so his data is skewed.
There are also small errors introduced by the variation in inventory methods
within Peeron. Some inventories break every element into its atomic parts - I
have found some that even list the minifig hands as a separate element. The same
is true with elements whose function is always in conjunction with another
element (as sold in a LEGO set, that is) - both halves of a hinge piece, for
example. These are used as one element in the LEGO model, but Changizi counts
them as two types. (Of course builders often DO use the separate parts in
various ways, but he is only interested in the ways in which TLC uses the
elements in their sets) Also, discrepancies between the “official” piece count
and the number of elements in the inventory is pretty common - from errors and
from the practice of including extra pieces in the sets.
Minifigs are another thing. These are specialized pieces that are really
included as accessories to the main model and not as an integral part of its
construction, but Changizi counts each minifig element and accessory as a
different piece type.
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