Topos Theory in the New Scientist
Posted by John Baez
Our favorite science magazine has decided to take on Chris Isham and Andreas Döring’s work on topos theory and physics:
- Robert Matthews, Impossible things for breakfast, at the Logic Café, New Scientist, April 14, 2007.
At the n-Category Café we serve only possible things for breakfast. But, many things are possible…
Over on the category theory mailing list, the renowned topos theorist Peter Johnstone writes:
Category theorists in general, and topos theorists in particular, may want to check out this week’s cover story in the New Scientist (www.newscientist.com). The author (Robert Matthews of Aston University in Birmingham) is clearly a fan of Chris Isham: it’s not clear to me whether he actually knows what a topos is, but he has committed himself to statements such as
“Topos theory could lead to a view of reality more astonishing and successful than quantum theory”
which is splashed all over page 32 of the magazine. Even if you don’t believe this (and I don’t think I do) it’s pleasant to see topos theory getting this sort of publicity.
The “impossible things for breakfast” line is, of course, borrowed from the logician Charles Lutwidge Dodgson:
“Alice laughed: “There’s no use trying,” she said; “one can’t believe impossible things.”
“I daresay you haven’t had much practice,” said the Queen. “When I was younger, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”
To someone steeped in classical logic, it may at first seem impossible to believe that the law of excluded middle:
could fail, as it can in the intuitionistic logic described by topos theory. It may also seem impossible that the distributive law
could fail, as it can in quantum logic! But after serious thought, it seems eminently possible — especially upon examining the results of experiments in quantum mechanics.
Could the laws of logic have an empirical aspect to them? Could they be subject to revision and refinement as we carefully study the world around us?
Why not? Who ever promised us instant direct access to immutable truth? Even if logic is a matter of convention, some conventions are better than others — so we may want to change them.
SUBSCRIPTION REQUIRED; Re: Topos Theory in the New Scientist
I have a New Scientist subscription. I got it for my son, and recently renewed for another 3 years, even if the magazine is sometimes weirdly fact-checked (as Greg Egan and John Baez have pointed out). I cannot get their online edition to believe that I have a subscription, hence all that I (and some other of your readers) can see is:
Article Preview
Impossible things for breakfast, at the Logic Café
* 14 April 2007
* Robert Matthews
* Magazine issue 2599
Our rigid notions of true and false just don’t work for a quantum world. It’s time to dish up a new logic
CHRIS ISHAM has a problem with truth. And he suspects his fellow physicists do too. It is not their honesty he doubts, but their approach to understanding the nature of the universe, the laws that govern it and reality itself. Together with a small band of allies, Isham is wrestling with questions that lie at the very core of physics. Indeed they run even deeper, to such basic concepts as logic, existence and truth. What do they mean? Are they immutable? What lies beyond them?
After years of effort, Isham and his colleagues at Imperial College London and elsewhere believe they can glimpse the answers to these profound questions. They didn’t set out to rethink such weighty issues. When they started nearly a decade ago, the researchers hoped to arrive at a quantum theory of the universe, an ambitious enough task in itself. Yet in the process they might have …
The complete article is 2421 words long.
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