Curves of Thought
It seems natural, and valid, to assume that there are twice as many whole numbers as even numbers. But, as the following table clearly shows, there is a unique one-to-one correspondence between the two sets of numbers. Ergo . . .
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 . . . |
| 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 . . . |
2, 4, 6 . . . → . . . ∞
For the aesthetic pleasure of some very elegant curves of thought by the mathematician Georg Cantor, and how he proved that the whole is no greater than some of its parts, I highly recommend a short section called A Grain of Sand, pages 155-68, in Roger Jones’ book, Physics as Metaphor.
If some of this doesn’t make you laugh out loud, check your funny bone! And have no fear, the math is easy . . . as easy as pi.
Let me throw you another curve:
This is my totem mathematical figure, the cardioid, the curve given by the polar equation r = a (1 – cos θ). One reason this is a natural for me is that the cardioid is a quartic curve, an algebraic curve of the fourth degree, and ties in beautifully with my fascination for what I call Meta-Fours, endless variations on a fourfold theme found throughout nature and in our conceptual schemes.
Here’s another elegant curve:
This is the Chinese character sui, meaning “to follow,” in the Grass Style of Wang Hsi-Chih.
As Chiang Yee observes, “The movement of the strokes suggests speed, but a dancing rather than a racing speed. The formation of the character is amazingly good, every stroke joined to the next in a continuous mobile line, like the contours of a dancing girl with her floating draperies.”1
Note
1. The quotation and the two images are on p. 122 of Chinese Calligraphy by Chiang Yee.
HyC