14 November 2007

time-traveling mathematicians

Take a look at today's Brown Sharpie.

So what if someone with a time machine went back in time and gave Fermat a book about elliptic curves, therefore enabling him to prove his famous "theorem"? Then he probably wouldn't have written his famous marginal note. But large parts of number theory came into being precisely because people were looking to prove Fermat's last theorem -- it's such an innocuous-looking assertion that it feels like it "should" have a simple proof. But that means that the book that our time traveler brought back in time never would have been written. And so on.

If you remember one thing today, it's that time travelers shouldn't give people proofs.

There's a similar example in Brian Greene's book The Fabric of the Cosmos. Greene imagines that he travels into the future, checks online to see what the latest advances in string theory are, and finds out that his mother proposed some grand unified theory of everything. He reads her paper, and in the acknowledgements he finds that she thanked him for teaching her physics. But his mother, as far as he knows, doesn't know any physics! So he travels back in time and goes to teach her physics. But she just doesn't get it. Knowing that she writes the paper, he eventually just tells her what to write, which he can do because he read it in the paper. Who gets the credit for the paper? Brian Greene shouldn't, since he just learned what was in the paper from reading it; but his mother shouldn't get the credit, either, because her son told her what to write! So if backward time travel is possible, then knowledge can appear out of thin air. The resolution is that in backwards time travel one must also travel between parallel universes.


John Armstrong said...

Alternately, the resolution is that "entia non sunt multiplicanda præter necessitatem" and to stop all this time-travelling solipcism.

And Greene should be ashamed of himself saying that just because something seems counterintuitive on its face it must be a paradox to be avoided. What's he doing in modern physics at all if that's the case?

Mike Cassidy said...

Greene shouldn't worry; string theory will end being a dead end.

John Armstrong said...

That's certainly a difficult statement to parse, Mike. Do you mean to say that string theory will turn out to be a dead end, or that it will cease to be the dead end it is now?

Aaron said...

Perhaps he means that string theory will put an end to the very state of being a dead end! A dead end to end all dead ends, if you will. :)