The best paradoxes raise questions about what kinds of contradictions can occur-what species of impossibilities are possible.

Expectation is a statistical fiction, like having 2.5 children.

Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.

Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is.

The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its improbability.

The best strategy is one that offers the highest compound return consistent with no risk of going broke.

The ultimate compound return rate is acutely sensitive to fat tails.

In real conversations, we are always trying to outguess each other.

The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.

A bit is worth 10,000 basis points.

The assumption that anything true is knowable is the grandfather of paradoxes.

There are certain moments in the history of a nation when the choices made define the decades to come.

I think that by the middle of this century people will still be eating meat (though less), and their meat will mostly be produced in factories through synthetic processes, cell cultures, and so on.

Major flaw in government arise from a fear of making radical internal changes even though a need is clearly seen.

He is always a slave who cannot live on little.

You better not mess with chimps. They are much stronger than humans.

I have loved and been in love. There's a big difference.

The city of Pittsburgh gleaming suddenly before her . . . so startling in its vastness and its beauty that she had gasped and slowed, afraid of losing control of the car

You're the last Olympian,' I said. 'And the most important.' And why is that, Percy Jackson?' Because Hope survives best at the hearth,' I said.

There's no such thing as boundaries only limits that get pushed further and further.

We are not wounded so deeply when betrayed by the things we hope for as when betrayed by things we try our best to despise. In such betrayal comes the dagger in the back.