Erlos

Hoffman, Paul. THE MAN WHO LOVED ONLY NUMBERS: the Story of Paul Erlos. Hyperion 1998. 302p. (ISBN 0-7868-6362-5. $22.95.

A brief biography of the Hungarian mathematician, Paul Erlos, with clear explanations of the various kinds of numbers (prime, perfect, friendly) and of various mathematical problems. There is an interesting parallel between the lives of Paul Erlos, Richard Feynman, Oscar Levant (and others) who were absorbed by their professions - their callings - and indifferent to creature comforts: with the same sense of humor, the same disregard for mere convention.
Mr. Hoffman refers to Erlos' disparagement of "technical" applications. He fails to realize (as Erlos did not) that technical applications are the bumping up of mathematics with the real world; or say rather the root attachment of mathematics to the real world: the surds from which math derives. Mathematics is the higher form of mere arithmetic: the overlap of geometry and arithmetic. Thus, the real but unending number Pi, which is our old friend, the squaring of the circle.
It can also be called the meeting of the two kinds of knowledge: that derived from calculation (cognoscere) and that derived from experience (sapere). This is what Erlos (and Feyman) meant when they said that "babies can ask questions that mathematicians cannot answer". These are the realm of logic and philosophy, of which mere scientific training is a branch.
Mr. Hoffman (like many others) gets suckered by the Monty Hall problem, failing to change both sides of the equation. It ends as 1/3 = 1/2. As this is done with a chart, I demonstrate it:
C G G Win Lose Lose
G C G Lose Win Lose
G G C Lose Lose Win
After a door has been opened the odds are said to be:
C G G Win Lose Lost
G C G Lose Win Lost
"C" "C" G "Win" "Win" Lost
The failure here is not to eliminate the column of the door which has been opened; this leaves
C G Win Lose
G C Lose Win
Choosing not to change is equal to choosing to change. This is Poppers' complaint about Heisenberg's "the viewer by looking changes the situation". Astrology.
Calculation bumps up against reality. Erlos comments on this as the "petering out" of the energies of the prodigy; as well they might be when faced by an absurd situation (the introduction of infinity). Feynman had the habit of devising a formula and then saying "let's see what the boys in the lab have to say".
The same situation arises with the statement that Pi to the 39th place gives the circumference of the universe (with a difference like a hole in a balloon) of the size of a hydrogen atom. The statement goes in both directions: "what we mean by the universe is that which is bounded by Pi to the 39th place plus the size of a hydrogen atom".
Apart this error, with some usual rhetorical nonsense about Dark Ages (as though people had forgotten how to reckon and could not build castles and ships and cathedrals), it is a fine read.

45: the square root of 2 is the diagonal of a square measuring 1 on each side
--: "A friend is the other I" (Pythagoras)
45: prime numbers are infinite. (This is the core of the Fermat theorem, as also of all other problems treating of infinity)
friendly numbers: the divisors of one add up to the other
22O: 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 +44 + 55 + 110 = 284
284: 1 + 2 + 4 + 71 + 142 = 220
perfect numbers: sum of those (not itself) which divide into it
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7
53: Ramsey problem: to devise formulas which eliminate brute counting
166: a computer cannot stop in a calculation; adding more computers slows the process down. (i.e., analogical computers do not exist).
228: transcendental numbers, such as Pi. (He fails to see the connection between the Fibonacci series and the spiral (which give us fractals). The spiral is the circle squared.