Tim Hodgetts – The interplay between simplicity and complexity in mathematical physics

Date/Time
Date(s) - 12/06/2022
12:30 pm - 2:00 pm

Location
The Duke of Battersea




Scientists and philosophers of science have been fascinated since at least the time of classical Greece by the idea that our descriptions of the universe should in some sense be simple, even if the details are complicated. The Greeks, for instance, were so impressed by the simplicity and symmetry of circles that they expected to find them everywhere in the heavens, and began constructing models of the planetary motions with circles nested in or on other circles. The mediaeval philosophers formulated a simplicity principle, often associated with William of Ockham or Occam, which for our purposes can be stated as “the simplest explanation is the one most likely to be correct”.

However, the judgment of simplicity is itself far from simple; aesthetics, mathematical probabilities and symmetries all play a part. The role of symmetry, or mathematical pattern, is particularly intriguing, because it is cyclic; it has happened again and again in mathematical physics that several phenomena which have individual simple patterns can be unified using a single but more complicated pattern. It has also happened many times that the new complicated pattern is not accepted by older scientists because it is “psychologically” invisible or incomprehensible to them (the quantum physicist Max Planck was fond of saying that “science advances one funeral at a time”, as inflexibly-minded seniors die off and are succeeded in their positions by younger people who have been familiar with the new ideas all their scientific lives).

Kepler’s laws of planetary motion were rejected by some of his contemporaries, not because they could find any fault with his astronomical observations, but because he had abandoned the divine simplicity of the circle – but he had also replaced a complicated nest of circles with a single ellipse. Maxwell’s equations of electromagnetism can be written as a single equation – but it involves a mathematical entity with an internal structure so subtle that it impressed Einstein (never an easy thing to do). And Einstein’s own ideas were rejected by many of the German philosopher-scientists of his day, not because they could find any fault with his working out, but because he had abandoned the Kantian (and Newtonian) ideas of absolute space and time.

Tim Hodgetts will attempt to flesh out some of these concepts and their consequences. For the mathematically-curious, see:

https://en.wikipedia.org/wiki/Occam’s_razor
https://en.wikipedia.org/wiki/Kepler’s_laws_of_planetary_motion
https://en.wikipedia.org/wiki/Maxwell’s_equations
https://en.wikipedia.org/wiki/Einstein_field_equations

We meet in The Duke of Battersea, but this meeting will also be on Zoom see SLPC Zoom Meeting

 

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