Message #1294

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] 8Colors solved
Date: Fri, 24 Dec 2010 16:30:55 -0800

Very impressive, Andrey! Of course we have all come to expect greatness
from you, and with regularity, so I would like to suggest that we take a
step back for a moment and get a sense of what this accomplishment
means. In many ways the higher-dimensional puzzles we have been getting
used to can be understood well enough through dimensional analogy but
these hyperbolic puzzles require you to wrap your mind around warped
spaces which seems like a whole different story. In some ways there are
direct connections between hyperbolic and higher dimensional spaces as
we’ve seen with the Roice’s embedding of the 3D cube and Klien’s quartic
into hyperbolic 2D space, but hyperbolic 3D spaces are literally
mind-bending because we live in a 3D space and it seems impossible to
see these new spaces from the outside. It feels to me like the
difference between solving a 2D maze on paper versus solving a hedge
maze from the inside. I have no comfortable frame of reference from
which to solve it or even to fully grasp what I am seeing. Without
having seen Roice’s MagicTile in action I would have a lot more
difficulty understanding this display.

The one thing that is clear is that these are some amazingly beautiful
objects, and the mechanisms behind their function are even more
impressive. Don, Roice and Andrey are programming gods who have breathed
life into these clockwork universes. They give them to us and then dance
within them. Andrey’s new solution belongs in a shrine. It begs the
question of whether he is god enough to create a puzzle so difficult
that even he can not solve it. I think that the answer is no but
something tells me that he will continue trying to show me that I am wrong.

I love that he implemented twist animations. That really helps to show
its finite nature. I notice that in some cases only the clicked face
animates and other affected faces only change state at the end. I don’t
think that is a bug because it only seems to happen at the edges where
the tiling stops. Other than that the puzzle now seems very complete. I
particularly like the contiguous-cubies mode when setting the
face-shrink slider to its max. That mode never worked very well in MC4D
because it was never possible to see through the clutter, but the extra
room in hyperbolic space allows exactly that and in many ways seems like
it could be as useful as it is pretty. It makes the pieces look like so
much candy!

A couple of embellishments that I would like to put on the wish list
include

&#42; A cross-eyed stereo view. A stereo view is the most important<br>
  thing that I intend to add to MC4D. I had it sort of working but<br>
  not perfectly so I took it out for the moment. I think that it<br>
  will be very helpful when solving any of these puzzles when more<br>
  than a few hundred stickers are visible because the added depth<br>
  makes the view much easier to grok.<br>
&#42; A slider to control how much of the hyperbolic space to draw. The<br>
  animation is so fast on my machine that it can clearly handle a<br>
  lot more pieces.<br>
&#42; Highlighting by sticker or piece. This will look far more<br>
  impressive than it does in MC4D since stickers and pieces will<br>
  light up all over the puzzle. it will also help when demonstrating<br>
  the finite nature of the puzzle to others. Currently only the<br>
  twist animations make that clear but that also changes the puzzle<br>
  state.

Well it’s time to tear myself from this magical land and be social for a
few days. I wish that I had better ways to show all this beauty to
people without frightening them but I get an incredible amount of
pleasure just knowing that these things exist and that a few people can
grapple with them just fine. Thanks again Andrey and congratulations on
achieving the first ever solution of a 3D hyperbolic twisty puzzle, and
thank you for this wonderful holiday gift.

-Melinda

On 12/24/2010 1:29 PM, Andrey wrote:
> Yes, 3-cycle on 4C is not a bug, it’s really possible situation. But may way to resolve it was too long (more than 1500 twists?).
>
> Andrey