Happy 2001! Stanley Kubrick's movie 2001: A Space Odyssey made a thrilling impression on me when I first saw it in 1969 at the Cinerama dome in Los Angeles. I loved the music of Ligeti, the enigmatic story, the portrayal of an intelligent computer, the sense of wonder and the visionary light show ending. Thirty three years later the movie still resonates in my soul.
For the January 2001 issue of Discover Magazine I created puzzles that pay homage to the movie 2001. I'd like to take you behind the scenes and tell you how I came up with these puzzles.
Most of my ideas for the 2001 puzzles came from Jerome Agel's imaginative book The Making of 2001. Agel's book is out of print, but there is another book with the same title that is also worth a look.
One Man’s Monolith is Another Man’s Tetrahedron. Agel's book opens with Arthur C. Clarke's short story The Sentinel, which Clarke used as the basis for the 2001 script. In the original story, the famed monolith is not a rectangular slab, but a tetrahedron.
I enjoy polyhedra, so I thought immediately of a puzzle about cubes and tetrahedra. I started with the classic problem of drawing a tetrahedron on the surface of a cube, then asked myself whether I could do the reverse -- draw a cube on the surface of a tetrahedron. To my surprise I found that I could, but only if the cube is loosened into a hexahedron.
I compose each of my Discover puzzles as a sequence of questions that start easy and get harder, drawing readers gradually into deep waters. So I added an easier pair of questions about slicing off polygons, and a harder pair of questions about cutting up solid figures. The most time-consuming part for me was drawing the complex answer figures.
Here's a cube/tetrahedron puzzle that didn't make it into print. Pretend you are holding a cube between your two hands, using the thumb, index, middle and ring fingers to hold each of the eight vertices. Adjust your fingers until the cube is really cubical. Now retract every other finger -- the thumb and middle finger of one hand, and the index and ring finger of the other hand. The remaining four fingers now hold the vertices of a regular tetrahedron! Try rotating the tetrahedron so one of the triangles is parallel to the ground.
Here are more ways to make tetrahedra with your hands.
Screen Play. Agel's book explains how the fabulous journey through corridors of light at the end of 2001 was created using a special effects technique called slit scan. I have long been fascinated with slit scan, so I made a puzzle that explains how it works.
Slit scan was developed originally by pioneering independent animator John Whitney. A variant of slit scan was also used in 2001 to create the planet Jupiter. For years I had seen a picture of the "Jupiter machine" in Jerome Agel's book. But I didn't understand how it worked. Then Chris Yewell graciously sent me a copy of the July 1969 issue of American Cinematographer, which features an article by special effects supervisor Douglas Trumbull on slit scan. You can read more about slit scan here.
The problem with Jupiter was that it was hard for artists to paint Jupiter in realistic perspective. To solve this problem, the filmmakers used the principle of a lathe. First an artist painted the surface of Jupiter as a flat rectangular map. Then the filmmakers mounted a thin semicircular disk with a bright white edge on a rotating axis. As the disk turned slowly about its diameter, a projector moved across the painting to project a thin vertical stripe onto the edge of the disk. By keeping the camera shutter open while the disk turned, the filmmakers were able to transfer a flat painting onto a sphere. Why they didn't just paint just paint directly onto a sphere I have no idea...perhaps slit scan created a better effect.
Also Sprach Frank and Dave. In a key scene of 2001, HAL reads the lips of astronauts Frank and Dave as they plot to disconnect him. This was the only scene that Clarke did not feel was scientifically plausible; Kubrick inserted it for dramatic effect.
Years ago I wrote a puzzle for NewMedia magazine about lip reading. The original puzzle used the names of the twelve months as the spoken words, and mentioned software for automatically animating lips to match synthesized speech. For Discover I created a new version of the puzzle that used words from the lip-reading scene in 2001, and mentioned David Stork's book Hal's Legacy.
As it turns out there is indeed research into computerized lip reading. Although even the best program will probably never be able to read lips perfectly, Stork argues that it is plausible that HAL could have gleaned that a conspiracy was afoot.
WHAT’S NEW JANUARY 2001
Inversion of the Month: Happy New Year 2001. An animated greeting card featuring all the names of my extended family.
Discover Magazine Boggler. January: Three puzzles based on the movie 2001: Also Sprach Frank and Dave, Screen Play, and One Man's Monolith Is Another Man's Tetrahedron.
Discover Boggler, behind the scenes. The newly refurbished Discover area of my site now includes stories behind all the puzzles.
JuniorNet. Scott Kim's Puzzle Box now features twenty new puzzles created by kids every week. By subscription only. For kids 5-12.
FROM READERS
Student inversions. Mrs. Mendiola, who teaches at the all-girls St. Joseph High School in Lakewood, California has posted a page of inversions created by students in her Geometry classes. Click on each inversion to read the student's comments. You can also see a page of inversions by Mrs. Mendiola herself:
ASCII Inversions. Bernard Badger sent me these clever inversions, created entirely with typed letters. Can you make more like this?
HAWK: >-| /-\ \-/ |-<
UP/DOWN: [up] [dn]
OF/TO: o
f
-
t
o
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