Message #72

From: Roice Nelson <>
Subject: RE: [MC4D] Intro from a new member
Date: Mon, 29 Mar 2004 10:21:39 -0600


Because of your volunteering at the space exhibit, I thought you might have
some interest in visiting a web site I’ve been running for about a year.
The site has a fun space related shareware program.

Sorry to mailbomb the group on this one, but here is a free registration
code you all can use if any are interested in playing with it. You can just
cut and paste this registration info into the program.

email address&#58; 4D&#95;<br>
registration key&#58; HZ6L-5NCB-R3JL-K0RB

So as to make at least a bit of a cube related response, I figured I’d
comment on the possibility of the 6x6x6 :)

This is probably obvious to all, but I drew up a little picture showing why
it gets much more difficult to physically create these puzzles as the number
of cubes increases. For 7 cubes on a side, twisting a face actually results
in floating cubies. They have nothing to attach to but the face they are
on. 6 cubes on a side provides a little bit of room, but not much! I’m
amazed someone was able to commercially produce the "Professor’s cube".

Anyway, I’ve never seen anything physical with more squares than the 5x5x5,
though I did once see someone (dubiously) claiming to have a way to create
these for as much as 10 cubes on a side. This was on the web, and I
unfortunately no longer have the link. I can say they didn’t provide any
details, saying they were protecting the idea until they could get a patent.
The use of magnets seems to be one potential design possibility I suppose.

I have seen a few online java applets that let you solve the puzzle with
more than 5 cubes on a side. Here’s one:

If you solve cubes from the centers outward like myself, this can quickly
become uninteresting however.

Another random idea I’ve had in the past is the idea of a cube where the
number of cubes on a side is infinite (and if you are into Cantor, you could
distinguish between countably and uncountably infinite here). Say for
example, you had one of these theoretical cubes 1 unit on a side where there
was a row of cubes at every rational number. As useless as such a thought
might be, one thing I did find interesting is that my normal algorithmic
solution method could not work in a finite amount of time on such a cube,
even if the thing was only a single interior twist from being solved. That
got me wondering about the possibility of a finite solution method for an
infinite cube that was scrambled with a finite number of twists. But I
didn’t think much on that as it seemed to quickly be heading into the
territory of the so called "God’s Algorithm" of the normal cube (this is the
actual shortest possible solution, where you just need to "know" the right
twists to make).

If you’ve ever thought about simply messing with the scale of a cube
instead, another bit of fun you guys might like is at:

Thanks for the nice intro and the book recommendation.


> —–Original Message—–
> From: Mark Oram []
> Sent: Saturday, March 27, 2004 5:29 PM
> To:
> Subject: [MC4D] Intro from a new member
> Greetings!
> Melinda kindly invited me to join this group and asked
> me to write a few lines of introduction, so here goes.
> My name is Mark Oram and I turned 37 in February of
> this year. I lived the first 35 years of my life in
> sunny(?) England (mainly in the London area) but moved
> to Denver USA just over two years ago to marry Diana
> and settle down on the other side of the Atlantic.
> (I’m pleased to say that Diana is still my wife,
> despite my many hours spent working on the 4D cube!)
> When we are working for our livings we both are
> research scientists, currently baseed at the
> University of Colorado Health Sciences Center;
> Micorbiology department. I am a molecular biologist by
> training and I’m finishing off some work related to
> how the particular sequence of DNA modulates the
> activity of the proteins designed to package it within
> a bacterial cell. I’m happy to expand on that if
> anyone is really interested. I also volunteeer at the
> Denver Nature and Science museum in thier new (10
> month old) Space Odyssey exhibit: an interactive
> setting where we present all ascpects of Space Science
> and exploration to the general public, and have
> immense fun in doing so.
> As far as the 4D cube goes, it seemed the next logical
> step for me. I have loved the cube (the ‘traditional’
> 3d version!) since it appeared (can you believe its
> been over 20 years ago??) and have the 2x2, 3x3(!),
> 4x4 and 5x5 versions displayed in our bedroom. (Has
> ayone ever come across a 6x6 btw?) This is part of a
> deeper love I have for recreational mathematics and
> mathematical games and puzzles. I grew up devouring
> Martin Gardner’s Scientific American columns and
> books, and also read ‘GEB’ (one of my all-time
> favourite books ever) and other works by Douglas
> Hoftstader just as avidly.
> Speaking of books, Ian Stewart has also written many
> excellent books on mathematics, and if any of you come
> across ‘Prime Obsession’ by John Derbyshire (it’s
> about the Riemann hypothesis) I cannot recommend it
> highly enough. It is superbly written: in my mind one
> of the best examples of this kind of ‘popularisation’
> book ever. Oh yes, and I also have a well-thumbed copy
> of Rudy Rucker’s The 4th Dimension, which helped me a
> great deal in dealing with the 4D cube.
> One of the biggest fustrations I have with the 4D
> version is that we are not 4-dimensional, and cannot
> see it in its ‘true’ undistorted form. (Wouldn’t it
> look incredibly beautiful?). Still, I think the web
> site is a wonderful simulation and a great
> achievement, so thank-you Don, Melinda and Jay :)
> Finally, I also love to see ‘patterns’ in numbers, and
> although this is akin to numerology I hasten to add
> that I am not a numerologist in any kind of
> ‘pseudo-science’ sense: I just find this kind of thing
> amusing. I was delighted to note, for example, that
> the Hall of Fame now contains as many members as there
> are hours in the day; as this links to clocks and
> other time-pieces: collecting them is another hobby of
> mine.
> OK, so that is more than a ‘few’ lines so I’ll stop
> here. If you are still reading this than (a) thank-you
> and (b) I look forward to joining in the discussions
> here for as many weeks/months/years as there are
> fascinating subjects - mathematical or otherwise - to
> talk about. Quite a long time in other words….
> ________________________________________________________________________
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