Message #894

From: Melinda Green <>
Subject: Re: [MC4D] Sub-1000 for 4^4
Date: Mon, 07 Jun 2010 14:02:46 -0700

Yes, you are right that we are far from god’s algorithm and perhaps we
always will be. You are also right that this is because the solutions we
use are designed specifically for human use. I did not mean to suggest
that we are getting close to the limits of what is possible; just that
it feels as if we’re beginning to feel the limits of these particular
methods. Will we be able to find new, more powerful methods that humans
can still apply? This is a very interesting question though I doubt that
dimensionality has much to do with it.

The July 2008 issue of Scientific American contained an article with a
lovely sidebar titled "Puzzle Tactics" that teaches you how to find a
solution to any twisty puzzle.
It clarified the way that all these solutions are generated and helped
me master the Megaminx.

Assuming it is true that everyone uses the same high-level approach to
generate solution methods to any twisty puzzle, the real open question
in my mind is whether there are any *other* approaches that can result
in more efficient solution methods. I expect the best wisdom in this
area will be found in the speed-cubing community since they are all
about efficiency. Remi, I think of you as the representative of that
community. What do you think?


Andrey wrote:
> Melinda, Remi, thank you!
> I haven’t try 2^4 yet. But it seems to be much more 4D than large cubes - so it will be interesting to do something with it )))
> As for real difficulties of n^4, I think that we are very far from it. All human algorithms are based on some restricitions of possible actions - so we are closing short ways and select long but predictable. I tried to close as few ways as possible - but to have small enough set of resulting positions. I’m sure that there better ways (that use full power of 4D geometry)