Every now and then, I read short sentences which contain so much insight that I feel the urge to write them down. I used to have a note pad full of them (quite a sizable one, more so, effectively, because my handwriting is tiny), but unfortunately I lost it when moving house. Fortunately, I found it again when moving a second time! Onwards and upwards! Here are some choice ones:
"[E]agles and lions can never be so plentiful as pigeons and antelopes"
- Alfred Russel Wallace
On a first glance, this looks vaguely mysticist if one is unacquainted with biology. However, it has to be true, because lions and eagles eat antelopes and pigeons. So if there were more predators than prey, the predators would starve and die, making the prey relatively more numerous.
"Diminishing marginal utility is increasing marginal cost".
- Frank Knight
Optimizing individuals who suddenly produce one fewer of something to make one more of something else are no longer optimizing. This is nothing huge to any economist, but it is a pithy formulation of the fact that increasing marginal cost implies diminishing marginal utility, and vice versa.
"And the angel of the Lord said unto her, I will multiply thy seed exceedingly, that it shall not be numbered for multitude"
Illustrating the concept of infinity as being beyond numbering, this is a very profound titbit of insight from the Holy Bible.- Genesis 16: 10 (quoted on p. 29 of Jan Gullberg's Mathematics: From the Birth of Numbers)
Here is another quotation to end this post:
"That's all, folks!"