Chaos, Chaos Everywhere

In 1996 (or thereabouts) the new Meteorology building was opened at the University of Reading....

Figs, Solar Storms, and Celebrity Endorsements

Here are a few of the things I have been watching , while living a somewhat less active life due...

Travelling by YouTube during the Lockdown

Travelling by YouTube during the Lockdown During the lockdown, and not even able to take a...

The Pharaoh, The Suburb, And Mathematics.

Not long ago, I was watching a documentary The Pharaoh in the Suburb on Channel 5 (UK terrestrial...

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Robert H OlleyRSS Feed of this column.

Until recently, I worked in the Polymer Physics Group of the Physics Department at the University of Reading.

I would describe myself as a Polymer Morphologist. I am not an astronaut,

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A bizarre title, but nothing to do with the fact that I am constitutionally lazy. Rather, it is related to the war I and a colleague are attempting to wage against the way physics is (in the UK at least) treated as a form of applied mathematics. It also has direct application to astrophysics – I know one student who went to study physics at university in 2002, in large part attracted by astronomy, but after a second year including astrophysics was saying "I hate stars." He was quite reasonable at maths, but it is the way that the subject was presented that put him off.
I first came across the word synchrotron in connection with the Crab Nebula, as well explained here at Hyperphysics. However, the phenomenon is these days very much down-to-earth: last weekend I returned from our last ever session at the Daresbury Synchrotron, which is soon to be shut down (final public use Saturday 1st August 2008). It first came on-line for experiments in 1981: prior to that, intense X-ray and hard UV synchrotron radiation was obtained as a by-product through “parasitic” operation on particle storage rings. Among others, Reading’s own Keith Codling had shown that much more useful science was being obtained from the synchrotron radiation than from the particle experiments. As a result of their concerted effort, the first Second-Generation light source was built at Daresbury.
Have you ever been puzzled by a statement like this: “Rotating a spin-1/2 particle by 360° does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720° rotation.” (Wikipedia). Last week I zoomed back to 1820 and introduced Ørsted and his famous experiment, and left you with a promise of going mathematical tomb raiding. Tomb Raider was first released in 1996 for the Sega Saturn, and other platforms followed. The lore has it that this was the first mass market video game to be programmed using quaternions. Prior to that, rotations had been represented by Euler Angles or similar. Imagine you are flying an aeroplane. You are going in direction A, heading up or down at angle B, and your wings are tilted at angle C. Euler’s achievement in introducing these to the worlds of mechanics, astronomy, etc., in the mid-18th century was a landmark in itself. But they do come with mathematical problems when you are flying and tumbling at the speed of Lara Croft, one of which is that in certain orientations you can get a bad case of gimbal lock. Step in quaternions: the mathematical tomb raider who brought these to the worlds of video gaming and flight simulation appears to be Ken Shoemake, of the University of Pennsylvania, with a seminal paper in the journal Computer Graphics, 1985. But whom exactly did he, so to speak, “excavate”?

It’s Physics World time again, folks!

This month’s (July 2008) issue has a cover headline “On reflection: Symmetry and the Standard Model”, and a diagram of the 8-dimensional E8 group squashed flat like a beached jellyfish on the 2-dimensional page. The article itself (by Stephen Maxfield of Liverpool University) is as good a summary of the development the Standard Model as I’ve come across, and does serve to persuade me that those guys, by and large, really do know what they’re talking about. But what are they talking about?

In February this year there appeared in Physics World an article entitled Constant Failure by Robert P Crease of Stony Brook University, in which he showed in how many formulae of physics and mathematics 2π turns up, rather than π. This article struck a chord with me, since even after many years I remember the feeling of “cognitive dissonance” when being taught that the formula was 2πR rather than πD.

I felt it a bit much, though, suggesting that Archimedes might have been mistaken in choosing to calculate the ratio of circumference to diameter rather than to radius. In those days, the fundamental dichotomy seems to have been between the geometers who thought of circumference, diameter and their ratio, and the astronomers who used the radius in their calculation of chord tables.

Hipparchus used a radius of 3438 which is the nearest integer to the number of minutes in 1 radian, but Ptolemy preferred 3600 as this is easier to calculate within the sexagesimal system. The work of these astronomers, further developed by Hindu and Arabic mathematicians, gives us our trigonometry of today.