I came to them through an obsession with the mysterious boxes of Clive Barker's fiction and Peter Faberge's gentle ornamental eggs. For me, each formed one point of a triangle completed by Gray's work.

Lucas Gray was a mathematician, born in Hespeler, Ontario, in 1949 and dead in 1978, succumbing to Hodgkin's lymphoma while completing his doctorate at Waterloo. He constructed eight puzzles, seven of which were found among his effects. His mother did not wish to speak to me, but described them as "the unremarkable products of a hobby."

The first five puzzles are a pyramid, a cube, a diamond, a dodecahedron and an icosahedron. These represent the five platonic solids, which influenced the german astronomer Johannes Kepler, author of the laws of planetary motion. His scientific discoveries replaced the belief that our solar system traces a nest of perfect circles.

Gray's pyramid and cube are simple to put together, like Soma cubes. The diamond is a difficult interlinking disassembly puzzle. The dodecahedron is more complex, and the icosahedron will lose most: it took me hours to defeat it.

In his incomplete doctoral thesis, Gray argued that Kepler's brilliant work could not have been formulated without a systematic understanding of gravitation. Mainstream historians, however, credit that other achievement to Newton, working decades later.

Puzzle six is a complex sequential movement puzzle that moves between two configurations. One of them presents a smooth dome on the outside, with its interior a spiky collection of angles, like a geode. The seventh is a large and delicately curved puzzle box. Though reminiscent of Chinese boxes, the sides unfold to form a bowl instead of detaching.

His eighth puzzle was missing. I knew of it only because Gray mentioned it to a friend. I spent years looking for it, in fits and spurts.

The solution I found in a letter dating to the late 1970s. He wrote it to a professor, whose daughter contacted me after I gave Gray an oblique mention in a Wired item about unsolved technical mysteries.

"It really is just a hobby. Circling the square, if you will," Gray wrote, four weeks before he died. "I wanted to build a puzzle made from puzzles, the solids. But I found myself cheating in increments: first a frame in the middle, then the whole thing hollow. Kepler would not approve, but for me, it will have to do."

Puzzle eight, of course, was to combine the rest to form a single harmonious sphere.

Success eluded him. The result resembles a wooden model of the Death Star, skeletal and incomplete.

Given the allowances he permitted himself, and modern computer modeling, it would now be possible to create a set of puzzles that would fulfill his plan. So would end Gray's mystic science, a match for occult fiction and sublime art. Though it is not my place, or anyone else's.

"My son. He was remarkable," his mother said. "You'd never know, because all you care about are those things he made."

But Gray's shapes echo their creator. They solve themselves, one way or another.

— April 1, 2010

15 Comments Add a comment

Day Vexx #1 07:57 on Thu, Apr. 1 Reply

This is the most sedate April Fool's joke ever, Rob.

imag #2 08:20 on Thu, Apr. 1 Reply

Okay, I'm missing it. I tried rearranging letters, which I've never been very good at. 7 and 13 are primes... not sure what to do there. And what is up with Kepler?

I like the deadpan AF, but I feel like I'm somehow not even engaging the puzzle.

Ambiguity #3 08:36 on Thu, Apr. 1 Reply

Bah to the previous comments. I thought this was well-done!

Ito Kagehisa #4 10:31 on Thu, Apr. 1 Reply

Thank you, Rob. I enjoyed it.

"whenever the temper of the Women is thus exasperated by confinement at home or hampering regulations abroad, they are apt to vent their spleen upon their husbands and children"

imag replied to comment from Ambiguity #5 10:36 on Thu, Apr. 1 Reply

Bah yourself. I didn't say I didn't like it. If it was just a yarn, then I happily accept the yarn. I just can't escape the feeling that I am missing at least one puzzle in there.

Anon #6 11:17 on Thu, Apr. 1 Reply

Quick mention: if you like small works of speculative fiction, leaning towards the zany edge of the spectrum, remember to look at Brain Harvest Magazine. ( www.brainharvestmag.com )

Anon #7 11:20 on Thu, Apr. 1 Reply

I really enjoyed this as a piece of obscure math\puzzle history, the kind of legend geeks whisper to each other when huddled in packs - I hope this is a case where the book can be judged by the cover and not some AF joke.

Either that or this is a great big bit of bait to drive some 3D modeler or simulation programmer nuts with a feasibly mathematically impossible arrangement of shapes.

gmoke #8 11:34 on Thu, Apr. 1 Reply

Dancing the Cube in Jamaica:

This is a video of a cube made of 48 A Quanta and 24 B Quanta. Each Quanta is an irregular tetrahedron with a magnet at the center of each of the four faces.

I have built all 25 inter-relations of the Platonic Solids and also all the Quanta, the smallest symmetrical irregular tetrahedra, of the five Solids. There are four of these Platonic Quanta: A Quanta, B Quanta, Icosa Quanta, and Dodeca Quanta. In combination, the A and B Quanta produce both the cube and the octahedron which are duals of each other.

Day Vexx replied to comment from Ambiguity #9 11:42 on Thu, Apr. 1 Reply

Bah yourself, Ambiguity-- I liked this, it's like April Fool's crossed with Oblique Strategies or something. Certainly beats me rickrolling people today on MySpace by promising a video of Farmville animals "doing it" with each other. Sadly, I bet there's a lot of people clicking on that...

SamSam #10 11:44 on Thu, Apr. 1 Reply

Wonderful! I don't care whether the yarn is true or not.

bmcraec #11 21:29 on Thu, Apr. 1 Reply

Loved the presentation. No idea if it’s an AF joke, and I’m not that into the math to figure out the shapes, ’tho I appreciate people who really dig that stuff.

I’ve not seen a BoingBoing feature before, so congratulations on the design, very appealing! One minor quibble; I’m a typography geek, so I really noticed all the prime & double primes instead open and closing single and double quotes. It really brings the typography up to snuff if you can figure out how to use those. Of course, the site then has to use UTF-8 encoding, which I see that you do use… I know it’s a pain, especially if working in Windows. I don't know how you would key those characters in Linux, but I expect there’d be a hack to help out. Umm.

That is all.

Ambiguity replied to comment from Day Vexx #12 06:16 on Fri, Apr. 2 Reply
I liked this, it's like April Fool's crossed with Oblique Strategies or something.

That would be a cool thing. Maybe they need to get Eno on as a guest blogger.

Sorry if I misinterpreted your use of the word "sedate."

Anon replied to comment from gmoke #13 08:12 on Fri, Apr. 2 Reply

what the heck is this about?

Anon #14 08:23 on Fri, Apr. 2 Reply

I believe this is one of Prospero's Books! Thanks for fully explaining the contents.

Hypothete #15 08:35 on Fri, Apr. 2 Reply

An interesting read, and an even harder puzzle. I was playing around with 'folding' the site based on the dot and A and B points at the top, but couldn't find anything new; also changing the URL based on folding. Is Mr. Beschizza's story actually a puzzle, and if so has anyone solved this?

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