All the Ways of Intuiting 1729

Stanislas Dehaene brings up the Ramanujan-G.H.Hardy anecdote concerning the number 1729. The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two integral cubes is inappropriate and obscures the workings of the naive mathematical mind. To be sure, a computer-mind could come up with that list at a wink. But what would induce it ...

 Encyclopedia Galactica

A. I do not say now that we can prevent the fall. But it is not yet too late to shorten the interregnum which will follow. It is possible, gentlemen, to reduce the duration of anarchy to a single millennium, if my group is allowed to act now. We are at a delicate moment in history. The huge, onrushing mass of events must be deflected just a little, – just a little – It cannot be much, but it may be enough to remove twenty-nine thousand years of misery from human h...

 The Parameters of "Spaceship Earth"

Our little Spaceship Earth is only eight thousand miles in diameter, which is almost a negligible dimension in the great vastness of space. Our nearest star — our energy-supplying mother-ship, the Sun — is ninety-two million miles away, and the nearest star is one hundred thousand times further away. It takes approximately four and one third years for light to get to us from the next nearest energy supply ship star. That is the kind of space-distanced pattern we are flying. Our little Spa...

 The Past and Future of the Mississippi

In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the old Oolitic Silurian Period, must a million years ago next November, the Lower Mississippi River was upward of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the ...

 Life Can Go On for Billions of Years

I believe that life can go on forever. It takes a million years to evolve a new species, ten million for a new genus, one hundred million for a class, a billion for a phylum—and that's usually as far as your imagination goes. In a billion years, it seems, intelligent life might be as different from humans as humans are from insects. But what would happen in another ten billion years? It's utterly impossible to conceive of ourselves changing as drastically as that, over and over again. All y...

 Can a Machine Die?

"Die? Can a machine die?" "I can cease to exist, sir. Call it by whatever word you wish. I am old. Not one sentient being in the Galaxy that was alive when I was first given consciousness is still alive today; nothing organic; nothing robotic. Even I myself lack continuity." "In what way?" "There is no physical part of my body, sir, that has escaped replacement, not only once but many times. Even my positronic brain has been replaced on five different occasions. Each time the contents of m...