Colossal Gardner, ch. 8


We close out the Plane Geometry section with the article The Wonders of a Planiverse, and the studies of 2D physics as developed by A. K. Dewdney. Dewdney was a computer scientist at the University of Ontario, and he wrote a report on his examinations of a flatworld in 1978 in response to Gardner’s article on the earlier Flatlands book by Edwin Abbott (1884). At the time Gardner wrote this article, Dewdney was still developing his physics and mechanics for a planiversal universe. His book, Planiverse wasn’t published until 1984. The article here discusses the operations of the some of the conceivable 2D machines, and the addendum adds comments by other physicists on how light, sound waves and gravity would, or wouldn’t work, in this environment. (One physicist claimed that sharp sound spikes wouldn’t decay properly, so no one would be able to complete full sentences.)


(Example of a simple 2D machine.)

Dewdney eventually took over the Mathematical Games department from Gardner in 1984. And, the concept of 2D physics has expanded to explore planar phenomena, including one-molecule-thick films and two-dimensional electrostatic and electronic Hall effects. There’s also a mention in the addendum of Arthur Clark’s Childhood’s End, in which intense gravity on a gigantic planet causes the evolution of creatures only 1cm thick.


(Example of the 2D planiverse creatures living at home.)

Some months back I was writing on topology, and I wanted to mention Planiverse, but I couldn’t remember the name of the book at that point, and instead got stuck with Flatland. There used to be a shopping center in St. Anthony Falls, Minneapolis, in Minnesota, that had been a repurposed factory building. They had a tex-mex restaurant that I loved, called Guadala-Harry’s. What was great about this place was that they’d give you wireless buzzers to let you know your table was ready, and you could spend up to an hour wandering the other shops. One of which was a very eclectic bookstore with a good selection of math and science books. I’d go to St Anthony Main every Friday for dinner, and I’d almost always find a book I wanted to buy. Naturally, one of those books was Planiverse.


(Planiveral steam engine.)

My main complaint about the planiverse world that Dewdney called Astria, and the Astrian lifeforms on it, revolved around what I considered to be a minor glitch with an illustration on one page. There was a small lip on a hatch door that was otherwise flush with the ground. If Astria had weather, it’d have an equivalent of rain. And any standing water on the ground would back up from any obstacles to find its own level. That is, flooding would be inevitable, and any Astrians outside in a deluge would be washed into a massive lake or ocean. Not to mention that humidity in the air would probably suffocate everyone. But, that’s a small complaint for something that was obviously written as fiction.


(How locks work.)

One of the readers of the article wrote in to say that this lock design is very similar to that of the 1895 Mauser military pistol. And, you can model these machines with cardboard cutouts, which is how John Browning used to work when designing his firearms.

Puzzles and games:
Examples of 2D games. (a) is the start of a checkers game. Pieces only move forward, 1 square at a time. Jumps are mandatory. On an 11-square board with pieces on the first 3 lines on each side, which player wins, the first one to move or the second?

(b) is a 2D variant on chess. Knights move two cells in either direction and can jump pieces of either color. Given rational play, which side will win? Or, can anyone win?

(c) is linear Go, called Pinch. The rules are available at the end of the following reprint of this chapter. (d) and (e) are further examples of the Pinch game.

 

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