Archive for August, 2012

New Old Ideas

Tuesday, August 28th, 2012

There is something both appealing and repellent in the idea that our “modern” attitudes are prefigured in the work of ancient philosophers. It is exciting to find a voice from the past that feels like “one of us” but at the same time a bit discouraging to think that there is nothing new in our ideas after all. Stephen Greenblatt’s ‘The Swerve’ delights in telling the story of how a modern voice was discovered through the work of the Roman poet Lucretius but Morgan Meis prefers the earlier analysis by Hans Blumberg whose ‘The Legitimacy of the Modern Age (1966)’ emphasizes the difference between classical epicureans and the modern outlook. The world view may be very similar in physical terms but the attitude is perhaps quite different with the classical emphasis on an accepting and arguably incurious “ataraxia” being replaced by a more curious engagement and eagerness to manipulate the world around us. But I am not convinced. Those of us actually engaged in the sciences do not need to claim a philosophical difference in order to see that we have “gone further”, and the idea that any age can be characterized by a universal attitude denies our individuality. Some ancients were deeply engaged in enquiry and engineering, and a goal of emotional equilibrium is not in fact incompatible with deep curiosity and passionate engagement in the modern world. In fact one can fight a desperate battle perhaps even more effectively by keeping a corner of one’s mind detached from the consequences and accepting of whatever comes to pass.

On Wavefunction Collapse in QM

Tuesday, August 28th, 2012

This, and especially this, reminds me of something I did long ago which, it turned out, had already been done by Hepp expanding on von Neumann’s treatment of the measurement problem.

The idea was to explain “collapse” of the superposition into a mixed state on the basis of having the measurement process consist of interaction with a macroscopic apparatus which would typically of course always be prepared in a mixed state itself.

I haven’t really thought how the “many worlds” approach relates to the “mixed state of apparatus” idea, but the latter seems to me more natural and does not seem to require the extra philosophical overhead.

The Camera Often Lies

Tuesday, August 28th, 2012

This article by Melanie Fahlman Reid came out while my brother Tony and I were up in Haida Gwaii and by coincidence the guesthouse where we were staying had a book about the various kinds of (mis)representation by photographers “documenting” native culture.

Progress in mathematics

Tuesday, August 28th, 2012

Among the many fond recollections that followed the recent death of William Thurston, I came across a reference to this article on proof and progress in mathematics.

Thurston, a geometer of great insight and also I think a great contributor to the popularization of mathematics, argues for a view of mathematical progress which does not restrict itself to just the production of completed proofs.

Thurston’s view of mathematics and how mathematicians think is in contrast to that expressed by Feynman in his lecture on the relationship between Physics and Mathematics where he repeatedly identifies the mathematical approach as starting with fixed axioms as opposed to looking at the overall network of logical relationships. To some extent that is true but only as one of the exercises of mathematical thinking and the question of alternative axiomatizations is always in the air – with a view of the whole network being not just essential to this but also always being at the heart of truly “complete” understanding.

One point of interest to me is that Thurston’s article was written in response to a suggestion by Arthur Jaffe and Frank Quinn that credit for the kind of work Thurston describes be more explicitly separated from that for actually completing rigorous proofs. I certainly share Thurston’s discomfort with their use of the word “theoretical mathematics” for the more speculative and less fully locked-down types of discussion. (The fact that theoretical physicists do a lot of speculative math seems to be a very poor justification for that choice of wording.) But I find it ironic that there is a tone of conflict when both papers seem to be arguing for the same thing in one sense – namely more attention to the role of intuitive and speculative thinking in mathematics. I suspect that Jaffe and Quinn were being a bit tongue-in-cheek with their suggestion of a separate discipline, but of course Thurston had some reason to take it personally as he was cited as an example of someone whose incompletely documented speculative advances may have discouraged others from pursuing the same goals. Thurston, who was working hard to bring others up to speed with his ideas, seems to feel unfairly criticized, but it may well be that those outside his circle had good reason to suspect that whatever progress they made would gain little recognition because it would always appear that their ideas were already known in Thurston’s group.

A further irony, especially considering Jaffe’s frustration with the premature announcement of Dobrushin and Minlos, is that his own close colleague Thaddeus Balaban announced an impending proof of existence of the YM4 Quantum Field Theory which undoubtedly deterred a number of others from proceeding to investigate that topic in the late ’80s.

Of course the issue of credit has always been fraught. And ever since well before Newton and Leibnitz, or even Cardano, Ferraro and Tartaglia, the question of fair attribution when one party appears to be ahead but holds cards close to the chest has been problematic. In one sense it would be much better if priority counted for less, but perhaps the overall rate of progress would be slower if it was dependent on dullards like me and those who take us ahead would fail to do so without the thrill of victory as a potential reward.

Perhaps (in fact almost certainly).
But I think I could live with that!

Are there any applications of complex numbers which can be explained to High-School students? | LinkedIn

Monday, August 27th, 2012

This recent discussion on LinkedIn asks for applications of complex numbers which can be explained to High-School students.

The case of AC electric circuits is one familiar application which was mentioned by several respondents and one of them pointed to http://www.picomonster.com/ where an attempt is made to motivate their use for describing relationships between other cyclical phenomena.

Another commenter mentioned the use of complex numbers in Quantum Mechanics but I find this hard to explain in elementary terms. (more…)

What’s Wrong With Religion?

Wednesday, August 22nd, 2012

This is just a prompt for me to consider the issue. It’s very far from “right” for me but does contain some points I agree with.

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Free Speech vs. Hate Speech

Monday, August 20th, 2012

Stephen Downes has commented on a discussion of free speech issues at the University of California but I think his focus on intended harm as the only excuse for restricting freedom of speech is too limited.

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