*The Oxford Murders* is a 2008 British film directed by Álex de la Iglesia. This British thriller film is adapted from the novel of the same name by Argentine mathematician and writer Guillermo Martínez. [1]

The *Tractatus Logico-Philosophicus* is the only book-length philosophical work published by the German-Austrian philosopher Ludwig Wittgenstein in his lifetime. [2] Wittgenstein’s book is cited near the beginning of *The Oxford Murders*. In a public lecture, Arthur Seldom (John Hurt) quotes Wittgenstein’s *Tractatus* to deny the possibility of absolute truth. A young graduate student, “Martin” (Elijah Wood), disputes this, asserting his faith in the absolute truth of mathematics. [1]

Arthur Seldom ridicules the absolute truth of mathematics. In the movie it is claimed by Seldom that Wittgenstein’s *Tractatus* proceeds by the use of equations to disprove truth. This assertion in the movie caused Ersjdamoo to do some preliminary fact checking. It turns out that *The Oxford Murders* movie uses “artistic license” and that “Contrary to what Seldom states in his lecture at the beginning of the film, the argument of Wittgenstein’s *Tractatus* does not actually proceed by the use of equations (with the exception of a few simple equations in Wittgenstein’s introduction of the truth tables) and it is not expressed in the formal language of mathematical logic…” [1]

Where shall the weary traveller find rest? Readers of Ersjdamoo’s Blog may have noticed an hiatus between January 14, 2015 and February 6, 2015. For three weeks, there were no entries. Where was Ersjdamoo?

For those three weeks, sickened by all the lies, I sought refuge. I needed to find something true. So I dusted off the old mathematics books and got some new ones. “Ah, here at last is truth and no lies,” I sighed contentedly.

But then, even in this sanctuary, something disturbing crept in. There were problems with Euclid’s parallel lines axiom. There was something called Non-Euclidean Geometries. For me, it was the dark night of the soul. I began a crash course in Non-Euclidean Geometries.

The Non-Euclidean Geometries are divided into (1) spherical geometry, the geometry of the two-dimensional surface of a sphere; and (2) hyperbolic geometry, also called Lobachevskian geometry. In the spherical geometry, you have for example the longitudinal lines of earth, to the casual local observer seemingly parallel but actually meeting in “infinity” (the North and South Poles).

In the hyperbolic or Lobachevskian geometry, a “triangle” immersed in a saddle-shaped plane has interior angles which do not total 180 degrees as they do in the Euclidean geometry. (See image hopefully above. Notice also the strange “parallel lines.”)

Maybe they teach a little about the Non-Euclidean Geometries nowadays in high school and college. But over forty years ago, when I was in high school, only the Euclidean geometry was taught to me. I finished college in my late 30s (B.A. in 1991), and took various math courses then. However even in the late 1980s/early 1990s there was no mention of the Non-Euclidean Geometries in my courses. Have things changed since then? Do they now expose students to some slight sampling of the Non-Euclidean Geometries in high school and college? This I do not know.

But the Non-Euclidean Geometries have had a huge influence in our world and they have been around now for centuries. They first began during the Italian Renaissance with projective geometry. You can see its influence in the paintings: pre-Renaissance the paintings are flat and two-dimensional; post-Renaissance they have perspective and suggest three dimensions. [4] Centuries later, the theory of surfaces by Carl Friedrich Gauss was extended by Bernhard Riemann to continua of any arbitrary number of dimensions and thus paved the way for Albert Einstein’s general theory of relativity. [3]

So why is nothing much said about the Non-Euclidean Geometries? The basic idea of them has been around for hundreds of years, yet the newspapers cover the subject scarcely if at all. Don’t say it is “too complicated” because I, the merely Ersjdamoo, have managed to cover it somewhat in this and other blog entries.

——- Sources ——-

[1] “The Oxford Murders (film)”, Wikipedia, March 22, 2015.

[2] “Tractatus Logico-Philosophicus”, Wikipedia, March 21, 2015.

[3] “Albert Einstein on Space-Time”, Written by: Albert Einstein.

http://tinyurl.com/kwsdr4q

[4] *Mathematics for the Nonmathematician*, by Morris Kline. Mineola, NY: Dover Publications, 1985