Quote of the Week
Thanks to David Corfield for this survey paper (on foundational categorical topology) from the mathematician Paul Taylor. Breaking my personal rule of mostly ignoring criticism of physicists from mathematicians, I put here the following gem of a quote.
Physics very probably relies on compactness of the interval, but I would be very sceptical if you told me that some property of black holes depends on excluded middle. Have you actually developed the analogous constructive theory, and found observational evidence to distinguish it from the classical one? This is, after all, what the experimental method says that you should do.
posted by Kea | 1:53 PM
4 Comments:
One reason that the good guys will win is that some theories are constructive, and make testable predictions.
Still hoping that the visa thing works out. I hope my blog post doesn't sound too angry.
I should explain that my paper, called Foundations for Computable Topology uses physics to criticise mathematicians, not vice versa.
The philosophical section 3, from which this quotation is taken, argues for the reaxiomatisation of General Topology, regarding it as a module in the system of Science.
The requirements of physics contribute to the specification of this module, so I would be very keen to hear from any physicists who may be able to clarify what I have written.
Great to hear from you, Paul! Interesting comment. My point of view as a physicist is that the physics clearly indicates the need for several new axiomatic systems, and I really think your work is very progressive. But, it may take some time to shift our focus from inventing simple computational tools to hammering out sophisticated descriptions of your kind.
Personally, I am always thinking in terms of what might be called higher dimensional arithmetic topos theory, which certainly does not exist yet, and must in some sense contain General Topology in your sense. If I ever get to the UK, I would like to meet you sometime.
Please would you email me directly, Kea, as I couldn't find out your address, so that we can clarify some things privately. This tiny box on your public blog site is not a good place for mathematical communication.
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