The Artist's Signature

encontrei a felicidade

em PI






(vide isto, isto e isto)

" It is somewhat questionable as to how an intelligence can encode a message inside a number like π. Some numbers which define essential properties of our universe, like the fine structure constant or Newton's gravitational constant, could conceivably vary among universes. (The physical conditions in these universes would be radically different, and it is possible that intelligent life could not exist in all of them. This recalls Stephen Hawking's conundrum, the question "Did God have any choice in creating the Universe?") However, π falls into a different category. It is defined by the nature of the circle, which in turn has a specific definition as a set of points in a metric space. Any intelligence, working in any universe--no matter what the characteristics of its particular "space-time fabric"--must deduce the same value of π given the same definition of a circle. (One presumes that a circle would be a useful abstraction to make in any reasonable universe which could sustain intelligent life.)

This type of argument goes back to philosophers like Averroes, who proposed that not even God could create a triangle whose internal angles did not add up to 180 degrees. The degrees within a triangle is a fixed consequence of Euclidean geometry; God may choose to build a universe that follows different geometrical axioms, but once the axioms are chosen, the results are essentially determined.

It is also worth recalling a question Richard Feynman raised while exploring the capabilities of mechanical calculators at Los Alamos, during the Manhattan Project. In a letter to his wife, Arline Feynman, he pointed out that the decimal expansion of the fraction 1/243 repeats in a rather amusing way:

This letter irritated the censor reading mail between Los Alamos and the outside world, who feared that strings of numbers may communicate technical secrets. Gleefully, Feynman pointed out that if you actually do divide 1 by 243, you do get that string of digits, so there cannot be more "information" in the long string of numbers than there is in the single number 243. This illustrates how "information" can be a subtle concept; is there more information in π, for example, than in the definition of a circle? "