John Horton Conway Quotes

Let me phrase the free will theorem that Simon and I proved. ...[I]f we... have free will... then so do elementary particles have their... very small quantity of free will... to mean, our behavior is not a function of the past. ...[I]f some experimenters have free will ...then so do elementary particles... even the ones outside us...

There is... strong evidence that these three axioms... are true.

Why do we care about finding dense packing in n-dimensional space? ...This is an interesting problem in pure geometry. Hilbert mentioned it in 1900 in his list open problems... [T[he best packings... have connections... with other branches of mathematics. ...

FIN [from finite speed] is the axiom... from relativity theory that information... can't travel faster than the speed of light.

... I have said for twenty-five or thirty years that the one thing I would really like to know before I die is why the monster group exists."

[T]he strangest contribution of quantum mechanics to this discussion is the EPR paradox. ...That's an essential contribution to our theorem too. ...Despite the fact that information can't be transmitted faster than the speed of light, ...remotely separated events can be correlated ...and this is the content of our TWIN axiom, you can put two particles into a... singleton state... the angular momentum of the pair of particles is zero... [B]y the conservation of angular momentum... if you measure the angular momentum of this in any direction, then for the angular momentum of the other you get the negative answer, but... we're going to square it, that means... the squared component of spin is the same... [T]hese particles have been sort of hypnotized. If you ask... they will give the same answer... like I and my twin brother... [T]he funny thing is, even though the proves that the answers do not exist ahead of time, the equality of the answers can exist...

[T]he arguments that suggest that we have free will can't be turned into logical deductive proofs. There's nothing wrong with that. If you argue in a court of law... we ...conclude, although we haven't got a proof, that probably the culprit was Mr. X.

[Leibniz] has this ... "that nothing happens without a reason why it should be so..."

Neither of us could have done it without the other.

<nowiki>[</nowiki>Robert Nozick]: Philosophical Explanations "...it would be foolhardy ...to place ...significant weight upon the necessity or even truth of SR. ...Moreover theorems show that any theory that retains certain features of Quantum Mechanics also will not satisfye SR." SR is Leibniz's . ...[T]here's a reference to the Kochen-Specker paper ...in which Kochen, my co-author, and Specker ...both logicians, not physicists ...prove this ...From our point of view this is not enough. The is not as strong as the new theorem.

There are many varieties of . ...It says that there's nothing incompatible about determinism... and free will. ...This is from a dispute between Hobbes and.... Archbishop Bramhall... "A man was free, in those things... were in his power, to follow his will, but... he was not free to will..." The will was determinate, but that he was free. ...It's not contradictory, although it looks it at first sight...

[I]n two dimensions the... [19 point] hexagonal lattice solves the packing, kissing, covering and quantizing problems. ...[T]his ...book is ...a search for similar nice patterns in higher dimensions.

If I ask this question of this particle, and... my colleague on Mars asks the same question of the other particle, then even though those questions aren't determined, ...they don't exist ahead of time, ...they'll give the same answer. ...It's meaningless to compare the times at which we do it, because time is not an invariant concept. ...[I]f my colleague on Mars has asked the same question, or ...will ask the same question... or if he's now asking the same question... he'll get the same answer. That is the EPR paradox, the fantastic thing that Einstein thought would disprove quantum mechanics. It is... perfectly consistent, but ever since it was discovered people have been trying to explain it away... because it's hard to believe.

SPIN and TWIN are operationally definable... Do the operation that's called, measuring... as many times as you like, and see that they always give the same answers. That's what is meant by saying that those things are operationally definable...

It's one of the things I most admire about Simon Kochen, my co-author, that... in August 2006, we'd been talking about this... for years... Suddenly the scales fell away, that had been obscuring the thing, and I said... "We've proved if we have free will, so do the particles" and he... said "Yes... this means that my stuff with Ax is all nonsense, doesn't it?"