My Martin Gardner testimonial

The Martin Gardner Centennial was in 2014 and I commemorated it on this blog. I also submitted my own testimonial to the official web site and linked to it in this post:

Martin Gardner Centennial & Testimonials

Now I'd like to reproduce my contribution here:

Martin Gardner Testimonials: Testimonial 55: Ralph Dumain

As a teenager I discovered Martin Gardner in the 'Mathematical Games' column of the June or July 1967 issue of Scientific American, having innocently bought it at the corner drugstore on account of my boyhood interest in science. That column featured John Horton Conway’s game Sprouts. From then on I was hooked on Gardner’s columns and related books.

In his June 1968 column Gardner proposed a problem concerning Baker’s Solitaire, and followed up with readers’ solutions in subsequent issues. My name appeared with several others in the September 1968 issue. These acknowledgments were not included when the column was anthologized in Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American in 1977.

Gardner’s columns radiated from the base of recreational mathematics to encompass quite a range of topics. Gardner stimulated my interest in the related hobby of abstract strategy board games, but that was only the beginning. Through Gardner I learned about the artist M.C. Escher, the 19th-century fad of four-dimensional space, anamorphic art, Raymond Llull (the godfather of the ars combinatoria), and numerous other fascinating topics reaching into obscure corners of intellectual history.

Gardner’s literary efforts were wide-ranging, but his other major claim to fame was his contribution to the 'skeptics' movement, decades before that movement was formally organized. I read Fads and Fallacies in the Name of Science not long after I discovered Gardner. I returned to this book several times over the decades. I was never fully convinced of Gardner’s criteria for the demarcation of science and pseudoscience. In addition to dealing with obvious crackpots, he delved into fringe areas where rationality bleeds into irrationality, such as Alfred Korzybski’s General Semantics, William Reich’s radical psychoanalysis and orgonomy, and Marshall McLuhan’s theory of the media. Still, the range of Gardner’s examples supplied a background I could draw upon throughout my adult life. This book can be said to have stuck with me, but I will forever be indebted to Gardner for all the wonders to which I was introduced via his work on recreational mathematics.

Like so many others I felt a serious loss when Gardner died. I paid tribute to him in my Reason & Society blog, in my podcast of July 19, 2010, and in my web guide to Board Games & Related Games & Recreations. Though my priorities have shifted over the decades, I can still say that Martin Gardner enhanced my life in a particular and unique way. He will always be remembered fondly."

         — Ralph Dumain, librarian and independent scholar, Washington, DC (22 May 2014)

Descartes' Secret Notebook (3)

Aczel, Amir D. Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe. New York: Broadway Books, 2005. xiv, 273 pp.

Now we come to Chapter 20: Leibniz's Quest for Descartes' Secret. Leibniz was attracted to aspects of Descartes' philosophy but was seriously repelled by it as well. Leibniz was critical of Descartes' principle of doubt, suggesting that degrees of doubt rather than absolute doubt be admitted in specific cases (209).

Some of Leibniz's major interests are outlined. I note a mutual interest with Descartes in Ramón Llull's ars combinatoria (210). After three years in Paris, facing the prospect of being recalled to Hanover, Leibniz urgently pursued his aim of inspecting everything that Descartes ever wrote. On June 1, 1676 he succeeded in gaining permission to view Descartes' hidden manuscripts. Scanning the Preambles, Leibniz, a Rosicrucian, recognized an oblique reference to the Rosicrucians (213). The secret notebook, De solidorum elementis, contained obscure formulas and figures. The geometrical figures were depictions of the five Platonic solids, and a connection to mysticism was evident. Leibniz began to copy the records, recognized what was going on, and added a marginal note (219).

Descartes' notebook disappeared, and Leibniz's papers on this subject remained undetected for two centuries. Several subsequent viewers of these documents failed to crack the code. Finally, in 1987, Peter Costabel published his analysis of Leibniz's copy of Descartes' manuscript (220). Leibniz had discovered that Descartes discovered a formula that generalizes the structural characteristics of the Platonic solids (221).

Chapter 21: Leibniz Breaks Descartes' Code and Solves the Mystery. Kepler had postulated a connection between the five Platonic solids and the spacing of the six known planets. Descartes found a formula for all polyhedra, but because others would connect this with Kepler and Copernicus, and so kept it to himself (225-229). Descartes' formula F + V - E = 2 inaugurates the field of topology. Euler discovered this formula, which was named after him.

Other misfortunes befell Descartes' legacy in the 17th century, when his works were proscribed by the Catholic Church and teaching of Cartesian philosophy banned in France. It wasn't until 1824 that his works were reprinted. Adrien Baillet came close to crediting Descartes' discoveries in his biography, but not being a mathematician, did not understand Leibniz's explanation and omitted publishing the information (230). Leibniz remained obsessed and ambivalent concerning Descartes, praising him while alleging limitations. Leibniz kept in contact with Cartesian scholars (231). Leibniz was at work developing the calculus. Concerned about the priority dispute with Newton, Leibniz would not have wanted to acknowledge an influence from Descartes (234-235).

Aczel adds an epilogue to this story. Descartes is seen as the great forerunner of contemporary astrophysics, heavily dependent on geometry linked to algebraic methods. The Platonic solids are n longer relevant, but . . . but satellite data obtained in 2001 supports the notion that the geometry of the universe as a whole fits the geometry of some of the Platonic solids (238-239). One new model posits the universe as an octahedron folded onto itself. The icosahedron and dodecahedron have also served as models.

It's a somewhat peculiar final tribute to Descartes, and Descartes' whole life story is a somewhat roundabout way of getting to discussing the mysterious notebook, but the story is nonetheless interesting, and, aside from the tribute to the mathematical and scientific geniuses of the early modern world, it reveals even more the peculiarities and complexities of the Enlightenment and the scientific revolution.

Martin Gardner Dead at 95

Martin Gardner is no more. Say it ain't so. I discovered Martin Gardner in the Mathematical Games column of Scientific American, having innocently bought it off the newsstand because of my boyhood interest in science. I think the issue I bought was June or July 1967: his column that month was about John Horton Conway's game "Sprouts". And then I was hooked. My name was published in one issue of Scientific American for my solution of some problem involving "Baker's Solitaire". Names were omitted though, when said article was reprinted in one of Gardner's anthologies. Gardner's columns radiated from the base of recreational mathematics to encompass quite a range of topics. Gardner stimulated my interest in the related hobby of abstract strategy board games, but that was only the beginning. Through Gardner I learned about the artist M.C. Escher, the 19th-century fad of 4-dimensional space, anamorphic art, the godfather of the ars combinatoria Raymond Llull, and numerous other fascinating topics reaching into obscure corners of intellectual history. I also read several of Gardner's books in addition to his collections of Mathematical Games columns, most memorably Fads and Fallacies in the Name of Science.

Gardner is also known for The Annotated Alice and other volumes, but his two biggest claims to fame are probably his contributions to recreational mathematics and to the "skeptical" movement. I returned to Fads and Fallacies several times over the decades. I was never fully convinced of Gardner's criteria for the demarcation of science and pseudoscience. In addition to dealing with obvious crackpots, he delved into fringe areas where rationality bleeds into irrationality, such as Alfred Korzybski's General Semantics, William Reich's radical psychoanalysis and orgonomy, and Marshall McLuhan's theory of the media. Still, the range of Gardner's examples supplied a background I could draw upon throughout my adult life. This book can be said to have stuck with me, but I will forever be indebted to Gardner for all the wonders to which I was introduced via his work on recreational mathematics.

Martin Gardner, 95, a journalist, provided in-depth analysis of Lewis Carroll's Cheshire Cat