"The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits." G.K. Chesterton

Saturday, October 25, 2014

There's no "hard way" of solving a problem --- an anecdote about John von Neumann as told by Eugine Wigner.

The following problem can be solved either the easy way or the hard way.

Two cyclists 40 miles apart are riding toward each other on a straight track; each one is going at a speed of 20 miles per hour. A swallow starting above one of one of them flies back and forth between them at a rate of 50 miles per hour. It does this until the cyclists meet. What is the total distance the swallow has flown?

The swallow actually flies back and forth an infinite number of times before the cyclists meet, and one could solve the problem the hard way with pencil and paper by summing an infinite series of distances. The easy way is as follows: Since the cyclists are 40 miles apart and each cyclist is going 20 miles an hour, it takes one hour for the cyclists to meet. Therefore the swallow was flying for one hour. Flying at a rate of 50 miles per hour, it must have flown 50 miles. That's all there is to it.

When this problem was posed to John von Neumann by Max Born, Neumann immediately replied, "50 miles!"
"It is very strange," said Born, "but nearly everyone tries to sum the infinite series."
"What do you mean, strange?" asked Von Neumann. "That's how I did it!"

Source: John von Neumann Documentary starting at approximately 18 minutes into the film.
Based on the version of the anecdote from "Math Jokes".

Wednesday, October 8, 2014

Best of imperfect worlds.

Lev somewhat dissatisfied with his previous cosmic project, decided to embark on a more careful enterprise of world creation, and turn down the perfection parameter from maximum. This time he decided to play with the parameters of fundamental values, and observe how they'd influence the hedonistic dynamics. The idea was to run a simulation where hugs are set as having principal value, and consequently become the sought after currency -- in other words, hugs in that world were to be the sole wealth determinant. But in what sense 'hugs'? -- one may ask. Receiving them of course! And naturally they'd have to be of genuine sincerity; neither bought nor forced in any way. That is, hugs have value only if they're sincere and welcomed. But then how does one accumulate such wealth, given that hugs are such ephemeral phenomena? Surely, one can't be in possession of a great number of hugs. The only way one can accumulate wealth of this kind, that is, become a prosperous hugee, is to guarantee and maintain the existence of those willing to give those hugs, i.e. huggers (aka ready-to-hug beings). In other words, one can attain a high flux of hugs, and wealth would be interpreted as maintaining a high hug-flux. This can be done in many ways of course, and Lev calibrated the simulation with no limit on the degrees of freedom concerning valid hug-acquisition. Naturally those who attain the ability to reach and maintain a high hug-flux steady state, aka hugagogues  are sought after as raw models for guidance, whose wisdom would guarantee the attainment of wealth in that world. Lev has hypothesized that such a world would be among those that are the closest to being perfect without giving rise to any absurd consequences, which inevitably accompany perfection.