Comments for en-gb 30 Thu 21 Aug 2014 12:24:48 GMT+1 A feed of user comments from the page found at Rodolfo I have recently found this very good program and have now subscribed to receive future programs as podcasts. My question is, can you not distribute programs in your archive as podcasts as well? Since I live in Mexico, it is sometimes difficult to stream a program because of the very low bandwidth with which I connect. Wed 17 Feb 2010 17:52:38 GMT+1 Jane I've listened to the half hour 'consciousness' programme (amongst others) and whilst Roger Penrose made great sense, I felt that the other guest possibly misunderstood the format and adhered rather defensively to one philosophical perspective. (My own consciousness 'listened' with admiration as Melvyn's consciousness procured an impressive professionalism.) It was listed in the philosophy archive and I'm wondering if it's possible (I realize you plan well in advance) to do a 'consciousness updated', 'revisited', 'objectified' or such in the science category...maybe incorporating any relevant philosophy, as it increasingly intertwines with science. I personally think it's the biggest subject of all...'the final frontier' is not 'space'....surely. Best wishes Tue 16 Feb 2010 18:28:40 GMT+1 anonymity For myself I make a clear distinction between academic and scholarly work; Academics try to organize and categorize data, the Scholar turns that data into a resource. That resource can be identified or defined as information. Each Natural Philosopher as distinct from any other type of Philosophy, has in their own style, expressed the thought:If you can not explain it simply enough; You do not understand it well enough. *- - - - - - - - - - - - - -The Delve; Consistent in seeking to nail a relationship between Art & Science.Philosophy is a battle against the bewitchment of our intelligence by means of language. ~ WittgensteinWhat we cannot speak about we must pass over in silence. ~ Wittgenstein *The limits of my language are the limits of my mind. All I know is what I have words for. ~ Wittgenstein*A little bit of knowledge is a dangerous thing?- - - - - - - - - - - - - - . . . You can keep counting forever. The answer is infinity. But, quite frankly, I don’t think I ever liked it. I always found something repulsive about it.I prefer finite mathematics much more than infinite mathematics. I think that it is much more natural, much more appealing and the theory is much more beautiful. It is very concrete. It is something you can touch and something you can feel and something to relate to.Infinity mathematics, to me, is something that is meaningless, because, it’s abstract nonsense. ~ Professor Doron Zeilberger. To Infinity and Beyond. BBC Horizon - 12. 10.02.10Said it can; All is abstract; That is until: A self defining definitive (Axiom) be discovered? Thinking occupies itself by dealing with no more or less than; Concept: As such a topics; Mere aspects of the subjects. Biology is the search for the chemistry that works. ~ R. J. P. WilliamsA camel is a horse designed my a committee. ~ Alex Issigonis- - - - - - - - - - - - - - Leonardo Da Vinci; Polymath? Scientist? Engineer? Artist?Whoever in discussion adduces authority uses not intellect but rather memory. ~ Leonardo Da VinciFar, far better to understand the wheel. Than to try, to reinvent it. Be aware lest you lose the substance by grasping the shadow. ~ Aesop * Tue 16 Feb 2010 15:47:34 GMT+1 Jane I'd expected more academic responses this week....the different perspectives really add to the programme. Best wishes Mon 15 Feb 2010 13:12:26 GMT+1 Gerald The programme "The Unintended Consequences of Mathematics" took me back to my half unit on the "History of Mathematics". I went to the British Museum and read the Rhind Papyrus" (one of the objects in "A History of the World in 100 objects"), I went to the Science Museum to look at Napier's Rods and Leibniz's calculator I and read Hardy's "A Mathematicians Apology". The lecturer, Brian Wilson, Chelsea College, UofL, put into historical content the rest of our courses and made the discoveries of theories as exciting as any battle field of war. Mathematics is not only the Queen of the sciences but has a beauty as great as any work or art, symphony or poem. Sun 14 Feb 2010 21:31:03 GMT+1 John Archer Moderator,Superscripts work in the preview pane but apparently not when a comment is finally posted. That screws up my prior post somewhat.I'd be grateful if you could fix the facility. Sun 14 Feb 2010 18:14:50 GMT+1 John Archer The solution of the cubic was mentioned in the latest programme but anyone with basic school algebra—at least algebra sufficient enough to cover the derivation of (rather than just being given 'the formula for') the solution to the quadratric, i.e. 'by completing the square'—can understand, in outline, pretty quickly how the cubic was solved. Moreover, recourse to complex numbers isn't even necessary for those unacquainted them. Sure, their existence, at least, should have been mentioned in coverage of the quadratic, but whether is was or not doesn't really matter.So I see no reason not to give that outline here. Indeed this forum seems to be an ideal place for such a quickie. To quote GH Hardy, "...what the public wants is a little intellectual 'kick', and nothing else has quite the kick of mathemitcs." So roll up your sleeves and 'pump this one up your veins'.STAGE 1 — Convert cubic to a convenient formAlthough the general cubic in, say, y can be written asy3 + ay2 + by + c = 0 ——— (1)it so happens that it is more convenient to deal with it in a form that omits the quadratic term, namelyx3 + px + q = 0 ——— (2)This form can be obtained directly from equation (1) by making the substitutiony = x - a/3 ——— (3)to be followed by some simple jiggering around with the resulting expression to tidy things up.This results in p = b - a2/3 ——— (4), and q = c + (2a3 - 9ab)/27 ——— (5)Any solution then found to equation (2) can then be converted directly to a corresponding solution of the original cubic (equation (1)) by using the substitution (3).So, to recap, the task now is reduced to solvingx3 + px + q = 0 ——— (2)STAGE 2 — The key: a useful identityThe expression (u + v)3 can be expanded to give the following identity (u + v)3 = u3 + 3u2v + 3uv2 + v3. ——— (6)Again, after some jiggering around, this gives(u + v)3 - 3uv(u + v) - (u3 + v3) = 0. ——— (7)Now here's the clever part. Looking carefully at equation (7) one can see that it can be regarded as a cubic in (u + v) if one regards the terms 3uv and (u3 + v3) as simple coefficients.Pushing this a little further, one can see that equations (2) and (7) are similar in form, and exactly the same if one hasx = (u + v), ——— (8) p = 3uv and ——— (9) q = (u3 + v3) ——— (10)Well, one can — by deeming it so. Simple.Since p and q are known, equations (9) and (10) are just two simultaneous equations in two unknowns, u and v. If these can be solved for u and v then we have x by equation (8) and, finally y by equation (3). And they can be solved, and easily. It turns out their solution involves solving a simple quadratic, which we already know how to do. So Bingo! It's done. This reduction to a quadratic is the essence of the trick.The rest is merely following all this through. I shan't do this for three reasons: firstly it is tedious; secondly it involves using complex numbers; and thirdly it doesn't add anything to main purpose here, namely to outline how the thing can be done in such a way that many will be able to 'see' it and, with luck, get a nice freebie mathematical 'kick'. However, I shall show the previously mentioned 'reduced' quadratic for a fuller pictureSTAGE 3 — The 'reduced quadratic'From equation (9)v = p/3u ——— (11)Using equation (11) in (10) gives q = u3 + p/(27u3) ——— (12)Multiplying both sides of (12) by u3 and rearranging the terms gives (u3)2 - qu3 +p/27 = 0 ——— (13)Equation (13) is the required 'reduced quadratic', in u3. Solve this for u3 then take the cube root to get u. v then follows from equation (11).I hope that gave you a kick. If it did, you might want a few more. You could sign up for a course. The more mathematicians we have the more mathematics there will be. And the more mathematics there is the more fun we can all have. Anyway, It beats working for a living.P.S. I hope I haven't cocked up with typos here. Still I'm sure any will be corrected rapidly by others. Please. Sun 14 Feb 2010 18:01:55 GMT+1 Jane Newsletter, unintended consequences...and interconnectedness. I enjoy (somewhat nostalgically) hearing about Melvyn's walk's possible to find a lot of green walks in London. There's a sense of freedom to be had in the city...and a different sense of freedom in the country...and they can both be magnificent. How selectively we each listen to the subjects... history bringing the maths to life hadn't even registered on me... maths seems more alive in its own right than either 'we' or history can fathom. The 'unintended consequences of mathematics' really showed the role of broader boffins having to 'bruise their heads' to push against limited concepts. Forgive me if this next bit is on a somewhat personal note, but when I prattled on about the interconnectedness of things after last week's newsletter (I often wonder how much I think the thoughts and how much they 'think me'), I couldn't have imagined my own interconnectedness with this week's. Okay...Ian Mckellen is my grandfather's cousin's son 'though we later generations haven't kept in touch. My last ever afternoon in London (I didn't know that the daemon had other plans) was unwittingly spent with Andrew Lloyd Webber (and co.) at his flat. (I'd performed his 'Requiem' here there and everywhere). Andrew's father, William Lloyd Webber, was my first one to one theory teacher at the RCM. The guy I lived with for several years in London was a long term cello soloist for Webber's 'Song and Dance' ie the 'Variations' which are the 'South Bank Show' title music - so I'm intimate with every note of that piece. No big deal, but a fair bit of interconnectedness for one newsletter and one recipient. Why can't the 'South Bank Show' or its format move BBCwards? Best wishes...Jane (I hope this isn't too's just that the timing was so good!) Sun 14 Feb 2010 14:31:41 GMT+1 Paul This was an exceptionally good broadcast on a mathematical topic and I agree with Solarium's comment. These were three panellists who really could communicate enthusiasm and context in equal measure. I do hope IOT leverages this chemisty of speakers and Melvyn, perhaps a broadcast on Groups and Évariste Galois?Jane mentioned Martin Gardner, a fantastic writer, I would recommend his Annotated Alice for a deeper enjoyment of Lewis Carol and his characters. Sun 14 Feb 2010 12:05:28 GMT+1 John Archer Cubic Hair Shirt IntendedUnintended consequences in mathematics — another superb IOT from the ever excellent Baron Bragg. Thank you kindly.However, there is an inconsistency between your mathematical offerings."The Babylonians, a thousand years before Pythagoras, knew quite a lot. ... The Babylonians really knew a lot of mathematics in various ways. They could solve cubic equations for example. ... Their method for cubics was rather rudimentary but nonetheless they had one." — Prof Ian Stewart, Pythagoras, IOT 10 Dec 2009, 1:27 to 1:54 into the podcast (1:30 to 1:56 into the archive version)"Now, this had been a long-standing problem for thousands of years. People had known how to solve quadratic equations ... but [in] 16th century Italy they finally discovered a formula for solving cubic equations." — Dr Colva Roney-Dougal, Unintended consequences in mathematics, IOT 11 Feb 2010, 2:07 to 2:19 into the podcast (2:21 to 2:33 into the archive version)So which is it? Who was first to 'solve to the cubic', that is give the full solution(s) to the general cubic with real coefficients? The Babylonians or the Italians? Well, my money is on Dr Roney Dougal being the person with the right answer—the 16th century Italians were the first, such knowledge being that which any undergraduate mathematician would pick up in his first year if he hadn't known it already. Of course Prof Stewart knows this full well too.So it was something of a surprise to learn from Prof Stewart that the Babylonians beat the Italians to it by 3,000 years. I don't think so.The Babylonians may have been able solve particular forms (e.g. n^3+n^2 = q) of the cubic, but not all. And given that they used tables (of the values of n^3+n^2 for instance) most of those solutions would not be exact expressions but rather mere numerical interpolations at best, i.e. not pure mathematics at all, but an engineer's solution (no disrespect at all intended to engineers—different strokes for different folks). Now, Prof Stewart, being a professional mathematician, is also necessarily thereby an ace precision. Yet he chose to express himself as: "[The Babylonian] method for cubics was rather rudimentary but nonetheless they had one." To anyone listening, including any mathematician who didn't know the history of his subject, that unqualified statement would be taken to mean that the Babylonians could solve the general cubic. Tut tut. How misleading.But why do it? I don't know the answer to that, but I do know there has been something of fashion, let's call it, in certain circles, and one absolutely rife in academe where it all started, for at least the last four decades or so, to talk up 'the other' and to talk down the West. But that is just one example among the many similarly self-destructive Darwin's-loser fashions currently and, lamentably, still in vogue.One thing though in this particular case: for anyone acquainted with Prof Stewart's (otherwise) excellent popular writing, there is, for some of us at least, the delicious irony that a woman, Dr Roney-Dougal, gives the actual history here and not Prof Stewart. I really like that one in view of his well-known promotion of the 'politically correct' standard-model 'gender' agenda. Tee hee. Sat 13 Feb 2010 21:14:49 GMT+1 muswellnel What is it that makes those who deal in numbers so often so much more lucid and eloquent than those those trade is in words, like philosophers and historians? Never a stumble or hesitation, never an um or er, simply a wonderful programme, probably the best since you last had 3 mathematicians to enlighten and enliven us with the sheer poetry of ure and applied maths. Thank you Sat 13 Feb 2010 17:37:22 GMT+1 anonymity Unintended consequences in mathematics.History in the making.It was only a short while after starting the starting the program, that I was compelled to stop listening: Kettle on, spoon in hand and POP. The word CLASSIC sprung to mind. Sat 13 Feb 2010 10:46:48 GMT+1 bjs1 I like the new web site which is much clearer now. However I have a small problem with the archive. I have tried to listen again to the programme on marriage but can only get the first 12 minutes before it cuts off. Is there a problem with the older recordings or is it my software? Could the site use the BBC iPlayer which I always find satisfactory? Sat 13 Feb 2010 10:38:41 GMT+1 Mark Aldridge The newsletter, and the programme itself, was very enjoyable and it was reassuring to discover that Melvyn too had to struggle with decontextualised Mathematics at school. I even began to feel I understood the Bell curve. Would a treatment of statistics make a good Mathematics programme for the future? Fri 12 Feb 2010 21:24:54 GMT+1 lastlistener Great programme, great series.How about expanding on something I came across when following up another great programme A History of the World in 100 Objects The Beginning of Science and Literature (1500 - 700 BC), Mold Gold Cape Looking up Mold on wiki and elsewhere I came across the following. “About a mile west of the town is Maes Garmon, (The Field of Germanus), which is the traditional site of the Alleluia Victory by British forces led by Germanus of Auxerre over invading Picts and Scots, fought shortly after Easter 430.”“. A commemorative obelisk was erected at Maes Garmon in 1736.” (A monument is still shown on the map.)If you look Germanus up on Wiki You find he was here to do battle on behalf of the Pope against the Pelaginists (see Pelagianism). “….Pelagius taught that moral perfection was attainable in this life without the assistance of divine grace through human free will,…”Seems a bit like stamping out opposition to corporate interests.A discussion of this theological standard and its occurrence or not in other religions would be interesting. Fri 12 Feb 2010 19:31:00 GMT+1 Cobblestone Re the newsletter: why is country walking better than town walking? Forty-five minutes on the tradition of the flaneur, please. Fri 12 Feb 2010 18:18:14 GMT+1 Dominic I haven't yet had a chance to listen to the most recent programme and I have a question that is of a technical nature: does anyone know a way around the persistent errors that arise when trying to access the past broadcasts in real player format? I already have the latest version of real player. Fri 12 Feb 2010 16:27:37 GMT+1 chill-lizard I agree with Pythagorasofsam. There are numerous examples of solutions looking for problems - the glue used in post-it notes is one of the best known. Isn't it intriguing that the highly intangible square root of minus 1 crops up in some very tangible physics - for example refractive index. I particularly enjoyed Dr Roney-Dougal's explanations - clear, concise and incredibly vivid. Please can we have more from her in future? The joy of IOT is that it gives non-experts a crash course in subjects they might not have known existed, and entertains experts with new angles on subjects, by taking a really broad viewpoint. Thu 11 Feb 2010 23:04:55 GMT+1 Kelly Fantastic! Give me more math please! I could listen to five more shows just like this one... you can do it, there are so many math stories still unturned... same guests too, they were great! Thu 11 Feb 2010 20:58:06 GMT+1 Risto Nordman Melvyn may have never thought that his program series could be first class material to foreigners for studying English language. However, that is the case. Programs are very intersting, indeed, and since they are available as podcasts they can be listened over and over again. Discoursing of the professors provides, besides knowledge, also a lot models for high level English speech. I've been listening to In Our Time podcasts for more than three years, and I'm very delighted to notice that the innate clumsiness in my spoken English has in part been replaced by the elegant expressions of Melvyn's quests. That's something, isn't it. Thu 11 Feb 2010 20:22:33 GMT+1 Jane I 'phoned my daughter's dad to find out which book he lent me that transformed my understanding of the nature of mathematics. He turned out to have three books...all by the same writer, Martin Gardner. I think the book I read was 'Mathematical Circus' but I'm not certain - it's at least fifteen years ago. The other two titles were: 'Ambidextrous Universe' and 'Further Mathematical Diversions'. Best wishes...Jane Thu 11 Feb 2010 18:12:01 GMT+1 ardcarp Why is this morning's programme not available on i-player? Thu 11 Feb 2010 17:10:36 GMT+1 Kam I may be displaying terrible ignorance here, but is there any capacity to suggest / request future subjects? I would be very interested in a show on Derrida, having found deconstructionism, grammatology etc inexplicable at uni, i've always wanted a coherent explanation. Thu 11 Feb 2010 16:19:40 GMT+1 pythagorusofsamos Mention of G. H. Hardy and his acknowledgment of the uselessness of pure mathematics in a programme about the unintended consequences of mathematics was a stroke of genius. It brought to mind an item that had been included towards the end of the Today Programme yesterday (10th February) about the threat to close Britain’s only chair of palaeography at King’s College, London. For the prosecution, Miles Templeman of the Institute of Directors made the case that universities should cater for present demands of students and the future demands of students and what the outside world needs; otherwise we can’t afford it. For the defence, Dr Irving Finkel from the department of the Middle East at the British Museum said that universities should not look to the demands of students, but to the demands of scholarship and learning. While I would not express the case in quite such absolute terms as Dr Finkel, we must maintain a balance between the commercial and industrial demands and scholarship for its own sake: much better that a student studies a language for the love of the language itself and an interest in the people that speak it than that there will be a commercial demand for speakers of Mandarin, Russian, Arabic, Japanese... I listened to In Our Time because I am passionate about mathematics as an academic discipline and recognise how much poorer we would be without the experimentation of the Hardys, Euclids, Leibnizs and Pythagori through the ages – mathematicians who, frequently unwittingly, improved the lot of humanity because of their academic curiosity. Thu 11 Feb 2010 12:46:06 GMT+1 Peter Bolt I really do not know how to say this without sounding a little sycophantic.But todays programme yet again confirms what I have thought for a long time.IOT is playing no small part in maintaining the UK reputation of intellectual excellence Thu 11 Feb 2010 12:45:39 GMT+1 neil andrew fletcher How can your guests refer to Alan truing & a machine to help in calculations & not mentions Charles Babbage inventor of the mechanical computer or a difference engine as he called it. You can see a reconstruction in the British Science Museum. They went on to suggest that Alan truing invented the electronic computer. What rubbish, I wish you get your fact right, the invented was in fact Tommy Flowers an telephone engineer who had to fund it himself. Thu 11 Feb 2010 11:19:00 GMT+1 Sidney Whitaker I heartily agree with Solarium and Jane, above. A sparkling and stimulating program! Perhaps more concession for the struggling listener could restrain the natural fervour and dazzling velocity of these experts, without gagging them. (e.g. certain less familiar names may need to be clarified by the lay "editor"-chairman.) But..., we can LISTEN AGAIN! Thu 11 Feb 2010 11:04:53 GMT+1 climateguardian Unintended consequences in mathematics.The most Unintended consequences in mathematics is the down fall of civilizations over the millennium and it is this that also could prove to be the answer to the currant problems long and short term.The long term problems of the interrelationships of culture, economics, and population are of the uttermost of importance to the very survival of civilizations and ours is no different to any that have gone before.It is the way civilizations are controlled through the fiscal and legal means imposed from the canter that determines the outcome, and the role of mathematicians to model and demonstrate scenarios of the future horizons is of the uttermost importance in a context of openness and discussion.The article yesterday about inviting the Queen to oversee the economic situation in the UK is one that I feel is important, as it identifies the need of more analysis and scenario discussion so as provide the legislatures the information needed to empower them to arrive at a consenting decision.The mathematicians, philosophers, academics in all areas of study and debate, are required by any civilized society to provide inspiration, ideas, scenarios, discussion, and debate, in not just their small circle but in society as a whole To enable a more reasoned outcome to be achieved. Thu 11 Feb 2010 10:47:32 GMT+1 climateguardian Unintended consequences in mathematics. is a great way to say it is the problem sover or problem maker of all time.Your program is ideal to discuss this in a lot more detail in the effects of mathematics on the climate , economics , philosophy.welfare and indeed the very existence and survival civilization.The way everyone slots all these issues into indervidual compartments, is the main reason why civilizations fail , it is this very misunderstanding of the inter-relationships of which often is the root cause of many problems in society locally and especially internationally due to language, culture and the lack of interdisciplinary skills to bring a common concenious together Thu 11 Feb 2010 10:19:12 GMT+1 Solarium After Horizon last night, I despaired of the BBC ever being able to deal with mathematics sensibly without being showy and banal. But Melvyn Bragg comes along and singly handedly saves the BBC's reputation. A seriously wonderful program, with connections and insights that even a trained mathematician can appreciate. Please letMelvyn take over Horizon. Thu 11 Feb 2010 10:18:05 GMT+1 Jane In great haste...congratulations...the time flew faster than in any other programme I've was superb and so enjoyable. Interestingly, whilst I was lying in bed this morning, the story of 'Jonah and the Whale' came into my mind and so when I heard it mentioned on the programme I had to once again question the nature of time because this happens to me a lot and I wonder if we are much 'looser' than we realize in relation to the 'stuff of time'. Also, as the programme started, an Albert Schweitzer quote came to mind: 'As soon as man does not take his existence for granted, but beholds it as something unfathomably mysterious, thought begins.' Can't thank the guests and Melvyn enough for the down to earth presentation which made this subject so accessible for we non-mathematicians. Look forward to some responses from listeners. If I can find the title of the book which first gave me a fascination with numbers, I'll post it took my brain to a place of wonder and away from the narrow, utilitarian stuff that school tried to cram into us. Best wishes and many thanks as always Jane Thu 11 Feb 2010 10:10:29 GMT+1 Stephenonrock3 What a refreshing change to hear past events talked about in the past tense!And your aside comment, Melvin " what Noel Coward said about art" expands my observations on common attitudes to maths. Maths doesn't always have to be useful to be justified. Thu 11 Feb 2010 10:04:18 GMT+1 memeandme I find it unusual that the mathermaticians are not awair that St Thomas Aquinas and the Catholic church and his belief in Aristotles ideas held back science Thu 11 Feb 2010 10:00:00 GMT+1 theinnocent42 A most enjoyable 45 mins, everything came to a stop as I concentrated, was entralled, laughed and learned. Top radio ! Thu 11 Feb 2010 09:54:18 GMT+1