Reminder: Tonight (Wednesday, June 10), at 7:30 I’m reading from my novel Hylozoic at Books, Inc., in Mountain View.
I’ve decided that my character Weena Wesson in Jim and the Flims should be a very old living person from Earth, like 150 years old. And she should have some knowledge of the fourth dimension.
And thus I’m led to Alicia Boole Stott (1860-1940), an intuitive geometer of the fourth dimension, known for her cardboard models of the 3D cross-sections of the 4D polytopes, which are more sophisticated cousins of the “hypercube.” Above is a photo of Alicia with her mathematical collaborator Pieter Schoute.
[Paper models of 3D cross-sections of 4D hypersolids by Alicia Boole Stott.]
Alicia Boole learned about 4D from no less a man than Charles Howard Hinton, who was the suitor of Alicia’s older sister Marry Ellen Boole. Hinton used to bring his set of 4D-vizualization cubes over to the Boole’s house and show them off. Hinton, I should explain, had devised a system for imagining four-dimensional hypersolids by means of a set of blocks. Hinton was a true eccentric—a bigamist, inventor of a “baseball gun,” an early science fiction writer, and a mathematic professor. My kind of guy. It cracks me up to imagine Prof. Hinton teaching 4D geometry to his girlfriend’s sisters.
[A rare family photo of Hinton, scanned for me by Tom Banchoff, , a fellow investigator of the higher dimensions.]
About thirty years ago, I edited a selection of Hinton’s truly amazing writings, Speculations on the Fourth Dimension, which appeared from Dover Publications in 1980. This slim volume is now seemingly out of print, but a fellow Hintonite has, with my blessing, legally posted most of my Hinton selections online. In order to keep the legend of Hinton alive, I’ve decided it’s time to post the biographical essay on Hinton by me that introduced my anthology.
[Many European universities have these great old pre-computer collections of models of mathematical solids and surfaces—the models are made of paper, wire, plaster and so on. This picture shows a case of Alicia Boole Stott’s models at the University of Gronigen in the Netherlands.]
Alicia Boole Stott was able to visualize the cross-sections of various four-dimensional shapes—which she dubbed “polytopes”—and she made paper models of them. For more about this, see chapter 5 of Irene Polo-Blanco’s dissertation, “Models of Surfaces: A Dutch Perspective,” at the University of Groningen: “Alicia Boole Stott and four-dimensional polytopes. ”. (I copied the pictures of Alicia and her models for this blog post from the Polo-Blanco dissertation. )
I’ve scanned a 1993 letter from Tom Banchoff in which he reports some of the family stories he heard about Hinton and Alicia Boole.
One story is that Alicia Boole’s husband Walter refused to consider that his wife should have any career outside the home. But then there is a mention that it was he (or maybe their son Leonard?) who noticed an appeal by the Dutch mathematician Schoute for the solution to the other half of some four-dimensional geometry program he had partially resolved. Alice had the other half in the models she had made. Schoute came thereafter each summer, and they continued to work together. At the tercentenary of the University of Groningen, they made a big deal about the collaboration and the models, and they sent back to Alice a fancy scroll, in Latin, which she couldn’t read. Later her son read it and exclaimed, “Jesus Christ, they’re making you a Doctor.”
[When we think about 4D it’s like trying to imagine an orchid from its shadow.]
Re. my novel, I’m thinking that, at age 80, instead of actually dying, Alicia Boole Stott used a 4D twist to go over to the afterworld intact. Beyond the veil. And, in the year 2010, she reaches out to inveigle my hero Jim Oster into the greatest adventure of his life—a journey to Flimsy, the land of the flims.