This work of fiction purports to be Albert Einstein's last thoughts about non-Euclidean geometry, as written on his deathbed:
| (quoted from Albert's Cradle)
None of my work would have been possible without
Lobachevskian geometry.
...
The mathematics of Lobachevski says that two parallel
lines can somewhere-someday meet. This still comes as
a surprise to most people, who as schoolchildren were
raised on the tedious theorems of Euclid. That great
Greek wanted to prove that two parallel lines can never
meet, but he never did, and so had to settle for an axiomatic statement --
a postulate, not a proof. Euclid’s parallel postulate.
It was Lobachevski’s genius to speculate what happens
if we deny this postulate of Euclid’s, and construct a
whole consistent system of mathematics based on this
denial -- a system that allows us to describe a space
curved and warped by mass.
|
In my opinion, the claim that none of Einstein's work would have been possible without Lobachevsky is an unreasonable exaggeration in two different ways. - One, which the fictional "Albert" acknowledges later, is that there is a lot more to non-Euclidean geometry than the surface of constant negative curvature studied by Nikolai Ivanovich Lobachevsky and there were many other people who contributed to non-Euclidean geometry as well.
- Moreover, although it is true that Einstein's General Theory of Relativity involves curvature of spacetime and hence utilizes non-Euclidean geometry, quite a lot of his most famous work was not at all dependent on these ideas. For instance, neither his work on quantization of light (for which Einstein was awarded the Nobel Prize in Physics) nor his Special Theory of Relativity (which "lives" in flat 4-dimensional Minkowski space) involve non-Euclidean geometry at all.
In his popular writings, Albert Einstein did sometimes explain how simple everyday things (like elevators and trains) got him thinking about the ideas which eventually became his brilliant theories.
"Albert's Cradle" similarly goes on to suggest that playing the string game "Cat's Cradle" as a child is what got Einstein thinking about "parallel lines that meet". Apparently, we are meant to recognize the loop of string wrapped around a person's hands as being an example of that? I'm afraid that doesn't really make sense to me. In fact, I'm not even sure what the phrase "parallel lines that meet" means. (I think that there are no parallel lines in Lobachevskian geometry.)
Although I can't say I really liked this story, it certainly is mathematical fiction and so I'm happy to include it in this database. It was first published in the February 1993 issue of Amazing Stories. I learned about it from the website MathFiction.net. |
