Message #404

From: Melinda Green <>
Subject: Re: [MC4D] Further musings
Date: Sat, 11 Aug 2007 13:11:50 -0700


Do you have a feeling for how god’s algorithm works for even the 3D
cube? I’m not sure that is possible even for the 2^3. That’s because I
view god’s algorithm as a high dimensional problem where each cubie
represents a single dimension that is at some distance from where it
needs to be. I can visualize the shortest path between two points in 3
dimensions but that’s my limit. I don’t think that I can even "feel" my
way to a 3D cube solution. Maybe some of the best speed solvers can do
that. To me that would not mean that they approach god’s algorithm but
that they would abandon any step by step approach and place one or two
cubies at a time based on how quickly each one can be moved into place,
somewhat similar to how people solve jigsaw puzzles.

Computer solutions really are mostly just human solutions and are
usually much simpler than the sorts of things people do. Computers just
do them quickly and flawlessly. They are definitely not constrained by
our 3-dimensional visualization limitations however. Computers are only
limited by algorithmic complexity. Creating the algorithms is the real
creative part regardless of whether they’re performed by humans or
machines. In my mind Don’s N-dimensional computer solution proves that
he’s solved the N-dimensional cube even if he never solves a puzzle by
hand. An existence proof is still a proof. In other words, with enough
patience, he could follow his own instructions without a computer. In
principal you could do the same thing by creating a sufficiently large
pyramid of macros on top of macros until you could take a fully
scrambled cube, find and click on each cubie in order, and sit back and
let the computer do all the work. I would consider your master macro to
be a solution even though I probably wouldn’t hold a speed-solving
contest that includes macro and non-macro solvers.


Mark Oram wrote:
> I can readily believe that possible interfaces for 6
> (and upward) dimensional simulations would be
> workable, based on the 4-D paradigm along with the
> ability to selectively hide different layers/faces
> etc. Also, I think there is plenty of fun to be had
> with a step by step algorithm; with (in the case of
> the cubes at least) enough intermediate milestones
> such as one face complete, two faces complete etc etc,
> to provide sufficient motivation (and satisfaction!)
> to keep moving forward.
> My main fear would be that this step by step
> ‘orthogonal’ approach (I don’t know how else to
> describe it) misses a lot of the subtleties and
> ‘richness’ that the extra dimensions provide. Nor does
> it, I firmly believe, give any real insight into how
> God’s algorithm for each cube might look. Perhaps this
> is where software designed to solve the higher
> dimensional cubes will have a clear advantage over
> human visualisation and imagination, in that it is not
> constrained by the 3 dimensions we are familiar with.