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AUDIENCE COMMENTS |
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An opportunity for the audience to have their say on In Our Time. |
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RENAISSANCE MATHEMATICS
Robert Carnegie (again), Renaissance maths
I seem not to be able to find the comment on the "unsung" researchers who brief the noble Lord - perhaps the remark was elsewhere? - but from time to time he has mentioned notes provided by the guests, implying that the clever researchers are, in fact, the three other people speaking on air. Of course, someone still has to book them, make their travel arrangements, and get their stuff from the library for Lord Bragg to bone up on. Anyway, to the point: I am rather surprised, even before Galileo and Newton, that no one could think of an application for solution of quadratic equations. Surely there are problems in interior decoration that call for the tethnique? And the Muslims were very much into geometric decoration. I suppose that technically it isn't practical, though. Very well, then, but surely exercises in ploughing... after all, this was commercial mathematics... I don't know if an insight not mentioned is something that I read in a book or thought of independently, with a book as cue, regarding Euclidean geometry and Descartes' coordinate geometry. The insight is that Euclidean geometry consists of axioms about hypothetical objects and the logical consequences of those axioms - you're with me so far, I hope - and therefore the numerical formulae of Descartes (x and y coordinates of a point, etc) do not merely represent Euclid's points, lines, and figures, they actually ARE Euclidean points and lines and figures. Descartes himself either didn't get this, or he did, but he recommended constructing geomerical proofs for numerical insights in order to keep the older generation happy. I bet Bertrand Russell got it, but I haven't read his awful big book. An ordered pair of coordinates behaves like a point, and a set of such points behaves like a line or a curve, and therefore they fit the axioms - and you can build the coordinate system from scratch inside Euclidean space - so Euclid's geometry is nothing but Descartes' with fewer sums. And Descartes is Euclid's with no strict necessity for diagrams. A pair of numbers IS an actual geometric point.
Mark Williams, The Renaissance Mathematician
Hia - a huge fan of the programme and the quality it represents. So please don't let yourselves down by perpetuating the impression that it's funny and acceptable, if not expected, for those with an arts education to become coy and foolishly proud of their mathematical or scientific ignorance. This disposition certainly wouldn't be adopted when confronted by a short fall in understanding classic literature, neither by mathematician nor classicist. Whine over & keep up the wonderful work!
David McCarthy
Could they produce a set of cassette tapes of past editions of the program so that I can listen to them in my car? It's so hard to find interesting stuff to listen to on the radio.... Thanks
Wendy Turner - Renaissance Maths - 2
Thank you Mr Carnegie. So it is true that Europeans invented algebraic notation and not the Arabs. That IS a surprise. I found algebra very unpleasant at school but even so, or rather because of that, I can still remember how to solve a quadratic equation! They called it "completing the square". It was all very painful. But how can one possibly do anything without the notation? I couldn't even do what little I know without it. What did the Arabs do with their wordy algebra? Did they make any discoveries?
Kevan Martin - Renaissannace Mathetmatics
The difficulty of introducing the concept of zero ('the devil's work')to western Europe was briefly referred to by Robert Kaplan. It would have been nice to hear more of how the concepts of algebra changed the way in which we think now. The ambiguity of zero was exploited in Shakespeare's King Lear and in Ben Jonson Volpone, both plays being written in London around 1605. Both Shakespeare (1564-1616) and Jonson (1573-1637) were in the first generation of English schoolchildren who would have been taught the concept of zero from Robert Record's Arithmetic, which itself mixed the old roman-style abacus and the new decimal system. (remember the Fool in King Lear: 'Thou art an 0 without a figure. I am better than thou art now; I am a fool, thou art nothing.') Leibniz - Newton's famous adversary, believed in the construction of a language that would perfectly reflect the structure of reality. We hear this same view echoing in the writings of our own contemporary, Roger Penrose, who was on the recent program Dark Energy. In England the Royal Society, founded in 1662, disallowed metaphor and rhetoric in favour of plain literal and precise language. It also encouraged publication of experiments by establishing the modern practice of using the date of publication as the means of deciding precedent for a particular discovery. This practice stimulated Darwin, 200 years later, to publish after a very long gestation, because of the submission of a MS by Wallace to the RS.
Robert Carnegie, The Renaissance Mathematician
Ms Turner - the Arab mathematicians apparently - despite better ancient precedents - did algebra with a lot of words. Only decimal numbers had symbols. An example was given; instead of a letter as variable, a personal pronoun was used - a similar concept, really; the effect was a little like an acrostic riddle; "My first is in apex, but is not in pole; my two last in both chord and circle both fall; my whole is of your circle less than the all." Although not quite as like as that!
Patrick Walter
1947 Advanced Maths School Certificate passed, so am Maths literate? Now as then, even after your normallly superb prog, unable to understand What Differential Calculusn is, nor Why we want it! Your dissertation is graded ' Could do better '.
Tim - Renaissance Maths
In my impression Geometry was discussed with just a little too much certainty. Of course it is that branch of knowledge that appears to be the most consistent and justifiable. But any branch of knowledge is a human creation, whether it accurately reflects the objective world or not. We didn't evolve to develop geometry. Its realisation has arisen through an interaction of our general ability to reason with our technological culture. Our thought processes are infused with our social psychology, which evolved not to discover absolute truths but strategies that are useful to us as animals. There are a large number of instances where what is useful is not necessarily true, and what is true is not necessarily useful. As I said the subject was treated with a little too much certainty. Absolutist convictions will not in the long term allow for the deepening of our understanding in any subject matter.
Wendy Turner - Renaissance Maths
So, algebraic notation was first developed in the West? How did the Arabs do algebra without a notation? Or have I completely misunderstood what was said?
Renaissance Mathematics
Here we go again!!!!More Anti Arab sentiment. In your introduction to Renaissance mathematics, you mention that algebra was invented by the Indians and Arabs. Algebra originated from the Arabs and not Indians. Next you will be saying because of our British Empire with our barbaric violent past raping and pillaging other countries that we had an influence in orchestrating algebra and take the glory. I think not. Do you?
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