I thought about you before I knew you!

Having a somewhat romantic disposition, I used to indulge in the following fantasy, in my former, bachelor years, when my passion for philosophy and science left little room for a long term relationship: 

"Suppose I fall in love sometime in the future, and meet the girl of my dreams. If that indeed happens, then she is alive today somewhere, going about her everyday life, oblivious to the fact that we're going to be together, and the fact that I'm thinking about her at this very moment." I indulged in the fact that I could think of her before we even met. 

But was I really thinking of her, or merely about a set of people who merely satisfied the predicate 'my next girlfriend'? This is analogous to thinking about the winner of a race before it has started. But it was difficult for me to accept that I'm merely thinking about a potential person, given that she already existed. Surely it wasn't determined who she is (going to be), before we actually met, and therefore at the time of my romantic deliberations. But such speculations aside, surely the predicate picks out a single person, although it can be said to apply to a number of potential candidates, as it were. At least the romantic mind tends to folly in this manner (I am thinking about her) where cold reason suggests otherwise (I am thinking about a set of potential the ones).

However, presently when I say to her "I thought about you before we met" it seems to be true, because now we know that it would actually be her. This is truly romantic! If so, then we have logically validated, or at least salvaged some of the reality underlying my spells of romantic imagination! And at the same time, it is also true that in some sense I was thinking about her before I met her.

ALOSZA I DRZWI

Mój szczur po prostu nie radzi sobie z pojęciem drzwi. Jak są zamknięte to je obwąchuje z ewidentną ciekawością. Gdy drzwi są otwarte to jego zdziwienie wcale nie ustaje---obwąchuje próg i framugę z zaciekawieniem; rozgląda się z widocznym osłupieniem: jak to może być, że perspektywa wcześniej nie widoczna, nagle się ujawnia? Nagła zmiana w topologii podłogi musi robić wrażenie. Ale, mimo trudności z ogarnięciem swoim szczurzym umysłem pojęcia drzwi, trzeba temu ciekawskiemu gryzoniowi przyznać godną pochwały wytrwałość.

A valuable lesson.

Mother to child---'If you learn how to tell the time from an analogue clock by the end of the week, you shall be rewarded'. Within a week the child returns, demonstrating mastery in the ability of telling the time from a clock, and reminds the mother about the reward that was promised. 'You have already received your reward'---answeres the mother.

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".

A lesson from Bach

This anecdote has been attributed to the biography of young Johann Sebastian Bach.
One evening, Johann was playing his latest sonata to a German baroness at her estate. When he had finished, the baroness exclaimed with a bewildered delight: “Ah! Maestro! It was wonderful!… But what did you mean by it?" Bach promptly approached the keyboard again, and replayed the sonata. When he had finished, he turned to the baroness and explained: “That, dear madam, is what I meant.”