Our friend, WD (Bill), in his early nineties and a widower, lives alone in his own house and continues to be 'shielding' from the Coronavirus. He doesn't complain; he has his books, books and books plus Countdown on television.
I visit him from time to time. If we cannot sit, socially distanced, in his back garden (directly under the Glasgow Airport flight path - quiet these days!) I stand at his front door while he stands in the porch and we catch up on our news.
This week it was the front porch where I proffered a chocolate cupcake from Marks. He misses 'treats' and finds my baking a bit too crunchy or crusty for his liking.
For reasons I cannot remember I have been searching for geometric patterns, not so much from the natural world, e.g. sunflower whirls, (with which I am familiar) but rather something along the line of of molecular structures (i.e. a different part of the natural world). It occurred to me that the DNA helix would be an example. I mentioned this to our friend Ken M., whose subject is crystallography, and he told me to google 'Penrose tiling'. Oh my goodness! What an intriguing topic! It is all about a geometric pattern with five-fold symmetry and furthermore the pattern can be expanded infinitely without ever repeating itself. "Weird", I say to myself. There is a whole area of science related to this. What I find fascinating are the aesthetic aspects.
Once I started looking at the shapes and colours and how it can be incorporated in decorative use, it just got interesting-er and interesting-er.
Basically it is about "aperiodic tilings of the plane, made from 2 sort of tiles : kites and darts". [1]
Photo: Herbert Kociemba
As it happens on October 6th the 2020 Nobel Prize in Physics was awarded to Roger Penrose, Reinhard Genzel and Andrea Ghez for their work on black holes.
Two Anecdotes:
An article from Prospect Magazine: [2]
Before I get to Bill's story, here is an item relating to the significance of his geometric contribution to science.
The author states: "These tilings – there are other shapes that have an equivalent result – are strikingly beautiful, with a mixture of regularity and disorder that is somehow pleasing to the eye. This is doubtless why, as Penrose explained, many architects have made use of them. But they also have a deeper significance. After Penrose described the tiling [in 1974], the crystallographer Alan Mackay – one of the unsung polymathic savants of British science – showed in 1981 that if you imagine putting atoms at the corners of the tiles and bouncing X-rays off them, you can get a pattern of reflections that looks like that of a perfect crystal with the forbidden five- and tenfold symmetries. Four years later, such a material was found.
You can use these tiles, he [Penrose] said, to represent the rules of how things interact in a hypothetical universe in which everything is non-computable: the rules are well defined, but you can never use them to predict what is going to happen until it actually happens."
In the article the author included an anecdote about Penrose "inspecting a new tiling being laid out on the concourse [...]. Looking it over, he felt uneasy. Eventually he saw why: the builders, seeing an empty space at the edge of the tiling, had stuck another tile there that didn’t respect the proper rules for their assembly. No one else would have noticed, but Penrose saw that what it meant was that “the tiling would go wrong somewhere in the middle of the lawn.” "
Penrose in the foyer of the Mitchell Institute for Fundamental Physics and Astronomy, Texas A University, standing on a floor with a Penrose tiling.
[Photo: Wikipedia]
Bill's recollection of Penrose:
Bill, a mathematician, did not know about this tiling business but told me that he knew Penrose and was friendly with him when they were both at Cambridge in the early 1950s.
Standing on the doorstep he told me "He was by far the smartest man I ever knew... and the closest I will ever come to knowing a Nobel Prize winner! I played squash with him and one year we travelled to Amsterdam to a conference." *
Bill mentioned that Penrose was supervisor to Steven Hawking and noted: Hawking would make claims and then later retract them; "Penrose never did that."
* * * * * * * * * * * * * *
*
[Update: February 2021: Bill had his 94th birthday on Jan 20th. A note from a previous conversation says that trip to Amsterdam was 1963. It was with Douglas Munn where they attended a Mathematical Congress.
_ _______________________________________________
[1] http://www.neverendingbooks.org/penrose-tilings-and-noncommutative-geometry
[2] Prospect magazine 2013 article by P Ball :
https://www.prospectmagazine.co.uk/blog/science-blog/fearful-symmetry-roger-penroses-tiling/
No comments:
Post a Comment