Fantasia Mathematica edited by Clifton Fadiman
Part I: Odd Numbers

1 December 2002

 

Part II | Part III

A fairly brief section of essays (for want of a better word), none of which stir me to great excitement. Of course this is hardly a work of non-fiction, but perhaps I expected a little more solid intellectual grunt. I've even laid aside my beloved John Gribbin to finish Fantasia before it is due back to the library, so I hope it improves.

My favourite piece from this section is Arthur Koestler's Pythagoras and the Psychoanalyst, in which a young Pythagoras is shown that his puzzlement over triangles really stems from his deep subconscious concerns over his wife's relationship with his best friend. The last words, "and thus the Pythagorean Proposition was never found," brought a smile to my face. The whole story is a little "what if?" joke, and lends weight to my suspicion that it is unhealthy to be too mentally balanced.

There are several essays clamouring for the place of least favourite, but I think I must settle for Young Archimedes by Aldous Huxley. The editor sums it up rather well in his introduction to the book:

"...a writer trained, perhaps overtrained, in the humanities... our sympathy does not flow from a comprehension of the actual content of his [the protagonist's] mind, only from the waste and futility of his brief life."
Even considering Young Archimedes as purely an arts-side relationship story, not connected to the science-side at all, I continue to dislike it. The prose is too descriptive, the descriptions too long (I understand that they are fun to write, but descriptions are boring as hell). On top of that, the plot is improbable. The story's only saving grace is the narrator's musing on the nature and value of genius.

There are two other pieces from this section that I must comment on. Curiously enough they both deal with Classical Greeks. They are Socrates and the Slave, by Plato, and The Death of Archimedes, by Karel Capek.

Socrates and the Slave is, of course, an extract from Plato's Meno and shows Socrates demonstrating hsi principle of learning by question-and-answer which assists the pupil to "remember" the "pure knowledge" which, it was thought, every human carried from birth. I know from my own experience that the Socratic method is an effective and pleasurable way of exploring ideas or discovering a method of solving a problem; however, I remain suspicious about this "pure knowledge" thing. In fact, Plato's anecdote has left me downright sceptical. Socrates claims that he assists the slave boy to "remember" what he already knew about the law of a right-angled triangle, without telling the boy anything. However, Socrates' questions are phrased in such a way as to give the boy information. Take as an example the very first question he asks:

Socrates: Tell me, boy, do you know that a figure like this is a square?
Boy: I do.
The boy's answer here is immaterial. It is utterly immaterial whether he knew a few seconds ago that the figure is called a square. It is also immaterial whether he is telling the truth about his prior state of knowledge, for from the instant the question is asked he certainly does know that the figure is a square: Socrates just told him so. The interview proceeds in this manner, with Socrates supplying much of the information as "Do you agree?" questions and the boy readily agreeing.

I'm aware that the technique works, but it does not work the way Socrates thought it did. The knowledge is still being imparted, just in a different manner which sits more easily with most people.

I have little to say about The Death of Archimedes. I just want to state that I like it. It makes sense, it feels good somehow, and I understand (if I may presume so) and sympathise with Archimedes' disinterest in the spoils of war.

The next section is a selection of mathematical science-fiction shorts. I adore science-fiction shorts. Perhaps things are looking up.

 

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