The n-Category Café

Oh, and my father, the late Samuel Herbert Post, solicited, edited, and published “Ecstasy and Me,” the autobiography of Hedy Lamarr, whom the author promises to get to in Chapter 9.

I’m intrigued by the footnote 6 on page 41 of the PDF.

I think that one CAN learn 4-D geometry early in life. The proof was Alicia Boole Stott (yes, that Boole). She had specially made colored cubes of wood to play with, and rules imposed on color adjacency. She published 4-D and 5-D gemotry papers when adult. This also led to the classic science fiction story “Mimsy were the Borogoves.”

I have often discussed 4-D visualization both with those who can’t do, and with those who do it much better than I (who could do it well at age 12, and only in flashes since then).

I’ve insisted for many years (having beta-tested the first arcade computer games “Pong” and “Computer Space” – which became +Asteroids” – for their inventor Nolan Bushnell.

Really good “flight simulators” as the author says (I wrote a textbook on flight suimulators for the Air Force) or adventure computer games could almost surely raise a generation of children with great intuitive 4-D geometry. The USAF noticed a generation ago that students in flight school were much better, due to playing computer games beforee enlisting. My father was a flight instructor in World War II, when the Link Trainer was electromechanical, rather than digital.

Imagine a million or more people in a “Second Life” online, but in 4-D. What might they do? Invent the warp Drive? Solve Quantum Gravity? Or does our genetic programming limit this? I’ll assume that brain plasticity in youth is sufficient for 4-D, and more exotic spaces and manifolds.

Mimsy Were the Borogoves (1943)
Lewis Padgett (aka Henry Kuttner and Catherine L. Moore)

Far in the future, humans have not only improved their digestive tracts (eliminating the appendix and shortening their large intestine), they have not only invented a time machine, but they have also invented educational toys which guide their children to learn abstract mathematics (non-Euclidean geometries and algebras in which 2+2 is not four). Two boxes of such toys, in fact, are sent back in time and have a dramatic effect on the kids that find them.

The math here is certainly important to the story, though it is not discussed very convincingly. The psychologist who figures out what is going on confuses logic, arithmetic, and geometry – for instance – when he suggests a “non-Euclidean geometry” in which “two and two needn’t equal four”. But this story is fun to read and the idea that learning alternative mathematical structures (other than the arithmetic of the real numbers and Euclidean geometry) could expand one’s mind and abilities is probably true and a nice advertisement for mathematics.

This story originally appeared in Astounding Science-Fiction in 1943. It has been reprinted in The Ascent of Wonder and you can read the comments that accompany it in that volume here.

Spoiler: Stop reading now if you don’t want to know how it ends! The title of the story, of course, is taken from Lewis Carroll’s “Jabberwocky”. According to this story, it was actually written by Alice herself and is not just a poem but a mathematical formula with which one can travel to bizarre alternate realities. How does she know this? Well, of course, Alice discovered one of the boxes of toys from the future!

Thanks for corrections. But I do refer to Holland in the main text. Introduction cannot mention everything.