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THE POINCARE CONJECTURE
Judy, Poincare conjecture
I'm sorry but i must disagree with the majority of you. In fact i did so last Thursday but the computer crashed and the comment failed to be accepted and now i feel a bit dismayed that you are all so positive about the programme. this makes me feel inadequate. Personally , and i say this as a lover of the programme- this has got to be the worse programme yet. i didn't understand a word - riveted because I was desperate to glean just one fact that made sense. Please i beg of you Melvyn do not cover topics that are beyond the comprehension of us non- mathematicians./scientists. All i can say is bring on the sociologists! It did reinforce one point however; the differences we experience of learning . I longed for a picture of the lassoo and the football but my ability to visulaise the concept was just about zero!
Joan Jacobsen - a modest thank you
I would like to extent a modest 'thank you' to Melvyn Bragg and the many various panelists who take part, and have in the past taken part, in this series of shows. In Denmark this kind of academic debate-program would stand no chance of getting aired, and I lament that. In six months, I will have my masters in history, majoring in the history of the Catholic Church in early modern ages. My theses will be dealing with the Gunpowder Plot and the long and short term ramification on the lives of English Catholics, and quite a number of your shows have been very interesting. Both historical and religious shows, dealing with reformation, angelology, the catholic church and the likes have all been extremely interesting and I shall continue to visit this web site often, and listen to new shows as they are put up on the net. Once more thank you for interesting radio broadcasting on an academic level worth listening to.
Chris Isbell
More maths at this level, please! Imagine a football match where the commentator was constantly trying to explain the basic rules of the game. This would be thought very silly because it is assumed, quite reasonably, that the audience knows enough not to need such explanations. Why should maths and science be any different? One point I did not understand: what is a pretzel?
Poincare conjecture
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!
James Baring - Poincaré
From your newsletter:- "It is, of course, possible that our space is in the shape of a hyperbagel or hypertorus, but if this is the case, the space would be folded round in such a way that a lasso would not pull tight." You may not be quite correct in this assumption. Or you may have stumbled on the truth - a hypertorus where the lasso is pulled tight, at the singularity. All these dimensional models are being considered as if they can exist in the absence of the others, and that is also probably an error. A dynamic universe implies higher dimensions and you will have noticed your Green Room has disappeared. It was just a question of time...and it might come back in another form at another time.
Paddy Hackett -Maths
You must present a programme on Bertrand Russell. He was both a mathematician and philosopher. His contribution to modern symbolic logic is of interest for a variety of reasons.Logic is viewed as a branch of maths by some and by others perhaps the foundation of maths. He was influenced by Frege and Peano among others.
Robert LIMB on Poincaré
The subject was almost incomprehensible but totally fascinating. Please, Melvin, don't shy away from complex subjects - this is what your programme is about
Alan Barak: Poincare
Don't know where I read this little puzzle, maybe a sci fi anthology in the 1960's. I think it's about that sphere of M. Poincare, and its representation in 4 dimensions. And the clues in the original were without question better. Here is what I imperfectly remember: Mr. Smith tells his story to you in a bar at a mathematicians' convention. He has, he says, lived a life of extraordinarily good fortune. Then, sure enough, at an appointed hour he found himself in a windowless, spherical room with the Devil. He describes the scene: The Devil is polite, erudite, and confident of his victory. We chat. He is there to claim my soul, as the completion to a bargain. I try all manner of persuasion to keep my soul -- without success. The Devil reminds me of the deal, and how I had sought it, and boasts that I had gotten nothing more in life than I would have if I had simply worked hard. But, also as part of the deal, the Devil offers to allow me to save myself if a puzzle can be solved: "Follow me out of this room built around you according to the laws of nature, and you keep your soul and return to your life. Fail, you suffocate, and I take your soul." The Devil vanishes. Smith, at the bar, continues his narrative: Back in that room, he panics. He sees no way out, and an eternity in hell coming nearer with every breath. But he calms himself, thinks very carefully about the Devil's parting words, takes one more look around the room... and vanishes. Now at the bar, he asks you "So, I bet you are wondering just how did I make it out of the room, and beat the old monster, right?" You nod. "The answer [which appears just a few lines below, so stop here and think it over] was simple, when I considered that description of my situation................................. The "laws of the universe" meant that my room had been built in a four-dimensional universe, consisting of three physical dimensions and time. The room had been built in three dimensions around me; I had NOT been put in it after it was built. So the Devil had simply exited the room through time -- he went back to the moment before the room had been built and was, therefore, free of it. As soon as I knew that, I knew I could follow him, and I did." Now, I don't pretend that the topologist's n-dimensional space is merely this 3 physical-plus-time construct, but the story helps me think of spheres as something like tubes in a 4-space. Didn't one of the program's speakers mention balloons? So a sphere in 4-space is like a long balloon you twist with others into an animal shape?
M Freiberger: Poincare conjecture
This was a brilliant epsiode! It clearly shows that this level of maths can be made fascinating and accessible. We rarely ever get the chance to learn about maths from the mainstream media, yet it's such a goldmine when it comes to interesting ideas. It just takes the right people to explain them!
Jon Rasbash Poincarre
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 download stuff from the archive lots and listen in bed before I go to sleep. I would happily pay the license fee just for access to the archive. It is great to have an intro to all these big ideas, often accessibly presented and available at the click of a mouse. Thanks for the great service. jon rasbash
naqash siddique,13: poincare
Henri poincare's suggestion that a scientist does not study maths because it is useful but because he finds it delightful is incorect. I want to be a scientist when I am older and even though studying scientific maths is fascinating i am not very interested in pure and applied maths. For example;the maths of how christian huygens developed his motion theories is fascinating but algebra is very dull.However,poincare is right in suggesting that a scientist should take delight when he/she is studying nature.This is an interesting idea to discuss.I thought it this was a philosophy programme not a maths history radio show!great show!!
Steve R, Tottenham: The Poincare Conjecture
The topology speaker did not describe the "Bridges of Konigsberg" problem very well. He failed to point out that there were two islands in the river, and seven bridges. The latter each connected one island to one bank of the river, except for one bridge that connected the big island to the small one. The aim was to design a walking route that crossed all the bridges once only, without omissions or repetition.
Mark: Nash Equilibrium
I would greatly appreciate a programme on this subject. "A Beautiful Mind" was an Oscar winning movie and maybe people wonder what all the fuss was about.
Christian H: The Poincare Conjecture
Another high-quality episode -- thank you! I was esp. interested in the mentioned current work on low-energy trajectories to the moon , and I would appreciate if sb. could provide e.g. links to relevant papers or similar.
Jenny; Poincare
An excellent episode; enough to understand what the fuss is about and a hint of how mathematicians might begin to solve the problems. Just two things- (1) Melvyn Bragg's pronunciation of 'science' has become rather squewed so that I now think he is saying 'signs'(2) I wish there wasn't such a fuss about how complicated these concepts are when they, to some, seem rather neat and capurable, compared to e.g. poetry. Perhaps this just reflects what a good job they did this week.
Rita Kingham: The Poincare Conjecture
Though no mathematician, I was fascinated by this programme. I recalled that the episode where Poincare has a flash of inspiration when boarding an omnibus is recounted in Roger Penrose's book 'The Emperor's New Mind'. There are several references to Poincare (and space-time motion) in the same book, if anyone is interested in further reading.
Gilbert Hall; The Poincare Conjecture
Mathematics is always extremely hard to talk about to a general audience. Since really understanding anything would take far too long and be far too hard, somehow the expert has to slice off a thin enough layer of the subject for it to be digestible but thick enough for it not to just collapse into complete nonsense. I think today's experts did jolly well, though all that talk about pretzels might be hard for some people to take seriously. Small asides, such as the one about using minimum energy trajectories to send rockets to other parts of the solar system (an astonishing technique), could easily be expanded into programmes in themselves. I'm afraid the layman comes away with only the slightest flavour of the richness and power of this mathematics and no real understanding. But that's better than nothing.
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