I don’t know whether you caught this already, but if not, do consider listening to the 2nd November edition of BBC Radio 4’s “In Our Time”. It is about Poincaré, his work, and the famous conjecture. From their website’s page on the programme:
The great French mathematician Henri Poincaré declared: “The scientist does not study mathematics because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living. And it is because simplicity, because grandeur, is beautiful that we preferably seek simple facts, sublime facts, and that we delight now to follow the majestic course of the stars.â€
Poincaré’s ground-breaking work in the 19th and early 20th century has indeed led us to the stars and the consideration of the shape of the universe itself. He is known as the father of topology – the study of the properties of shapes and how they can be deformed. His famous Conjecture in this field has been causing mathematicians sleepless nights ever since. He is also credited as the Father of Chaos Theory.So how did this great polymath change the way we understand the world and indeed the universe? Why did his conjecture remain unproved for almost a century? And has it finally been cracked?
It is a particulalry good programme this time. This is a programme that focuses mostly on philosophy, and is often accused of being only rather superficial when it comes to covering the more hardcore and up-to-date science, but not this time. The guests are June Barrow-Green (History of Mathematics, Open University), Ian Stewart, (Mathematics, University of Warwick), and Marcus du Sautoy, (Mathematics, University of Oxford), and they do a pretty good job. The presenter is Melvyn Bragg, as usual.
This piece also makes a nice complement to the posts I’ve done here on other aspects of the conjecture (see here and here, for example).
Let us know what you think. Link here. Enjoy.
Oh, this reminds me – I was particularly interested and amused to read the listener comments, which range from delighted to annoyed about the programme’s coverage of the subject. You can find the comments on the site here.
Four of my favourites:
Dumbing up? well done! We get too much of the opposite elsewhere. I must admit I struggled with the topic, but it spurred me into reading more about this fascinating subject, and now at least I can get a grasp. I downloaded the podcast and went through the difficult bits a couple of times, which was very useful and help to clarify the points. More like this, please!
Never written a feedback to a programme before but am moved to by this excellent programme. The speakers presented v. complex ideas in a way that was understandable. The use of analogies very helpful. Melvyn’s struggle to understand, brings me along too. A good example was his “but a teapot has three holes?” question. This brought about an almost throw away clarification from one speaker that really drove the points home about what a) hole was and b) that it is the number of holes that is fundamental. […]
[…] I think today’s experts did jolly well, though all that talk about pretzels might be hard for some people to take seriously. […]
[…] One point I did not understand: what is a pretzel?
-cvj
ack ! Steward should read Stewart. Could you correct and delete this request.
Thanks Clifford
I just wanted to agree with the writng abilities of Ian Steward as well. To take mathematics and make it interesting is quite a feat of artistic expression? That one may compare the rabbit to the Alice’s world, is no small thing in comparison to how “points in space” can be applied to a geometrical perspective?
Poincaré Conjecture
If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is “simply connected,” but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.
I seen this the first time and I let it go because I could not keep up, with the posts materializing at different speeds in different locations. Yet a comment on what one may of thought of and what is demonstrated from blog to blog is very important to the whole picture? From “my position of learning” how could this apply to the universe?
Tegmark did answer it?
Clifford, thanks so much for bringing this outstanding talk on Poincare to my attention! After all, Ian Stewart and Marcus du Sautoy are two of my most favorite writers of pop-math!
Ian Stewart’s “Does God Play Dice?” is perhaps one of the best summaries on chaos theory for the armchair reader of math to sit down and mull over. Even though John Derbyshire’s “Prime Obession” is indeed a fine technical account (geared towards the technically challenged layperson, that is, of course;)) of the Riemann Hypothesis, Marcus du Sautoy’s perspective on the hypothesis, as conveyed in his work “The Music of the Primes,” is decisively greater in breadth of thought, hence, has a more cosmopolitan flavor to it.
Poincare was not only a brilliant mathematician who just so happened to have remarkable literary skills, but was a man who was very comfortable in the public arena. Riemann – on the other hand – was highly introverted, in fact, has been described as being painfully shy. While Poincare led an open sort of life, Riemann’s life still remains – to this day – shrouded in mystery. Without a doubt, an incredibly mysterious mathematician, like Riemann, will always make a great subject for writers of math, consequently, will capture the hearts or readers, such as myself. On the flipside, there’s much to be said for a charismatic mathematician, like Poincare.
Nevertheless, both mathematicians were regarded as exceptional polymaths. While Riemann had fluid dynamics and prime numbers – simutaneously – on his brain, Poincare had orbiting bodies and topos/chaos – simultaneously – on his brain. Therefore, I’ll predict, similar to Riemann, Poincare will be the next great object for writers of math to behold, in turn, to tackle.
Needless to say, Ian and Marcus are both not only extraordinary public communicators of math, but are both beautiful writers, in the artistic sense, as well. However, after unwisely releasing her tasteless article to “The New Yorker”, which primarily focused upon the human drama (a mighty conjecture in itself;)) behind the Poincare Conjecture, Sylvia Nasar, I believe, blew her chances of ever having a pop-math work published on Poincare. Truth be told, I’ve developed a bias against works composed by science journalist in favor of works created by legit (keyword, here) physicists/mathematicians.
Much to my dread, though, book publishers still continue to offer contracts to science/math journalists, despite the fact these authors tend to write without the required know-how of either math or science. Thus, in my humble opinion, Ian and Marcus ought be two viable candidates in the running to have books published on Poincare and his conjecture, not a garden-variety sort of science writer, such as Sylvia Nasar.
I think they podcast it now. You can grab a file that way….
-cvj
They use Real Audio, instead of mp3 files. So, i can’t just download it and play it on my commute. They want me to be glued to my computer. I can justify spending a minute to download it at work, but the RAM audio just isn’t going to work over my phone line at home. Not enough bandwidth.
The BBC has offered symphonies for mp3 download in the past. For example, all of the Beethoven symphonies. So, i can’t say they don’t know how, or what the issues are.
I’m amused to see anyone asking “what is a pretzel?” That may be the best piece of bait Clifford put out here, because the Poincaré Conjecture and Poincaré himself are not strange to me, whereas that question is. Um, does it have something to do with manifolds? And/or knots?