Tag: mathematics

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War on the humanities, again

The THE reports that leading historian Professor Peter Mandler has delivered a paper on the “crisis in the humanities”, concluding that there isn’t one. In particular, he says:

It is hard to take too seriously talk of a crisis in Britain when even by the narrowest definition of the humanities the absolute number of humanities students has increased fivefold since 1967, and by the broader definition almost 10-fold.

In the US, over a period of much slower expansion, their numbers have still doubled…Talk of a crisis triggered by a decline in a percentage point or two does seem like an over-reaction that is likely to contribute to rather than ameliorate the alleged problem.

As well as looking at student numbers, we can look at the UK data for academic staff numbers, as a proxy for resource allocation.

hesa-1

The figure shows the percentage of academic staff in STE (Science, Technology, and Engineering), Humanities (shown dashed), and Medicine from 1994 to 2008, using the freely available HESA data sets. The break in the curves corresponds to a change in the reporting of data. The details of how staff numbers were assigned to the three categories are given in a separate PDF.

The first part of the plot shows a drop in the percentage of STE staff, which might correspond to the closure of Chemistry departments over that time (the data for these years are not broken down to subject level), while Medicine rises, and Humanities are fairly steady.

After the change in reporting methodology in 2003, Medicine has about the same proportion of staff as before the change, while Humanities increases markedly and STE reduces. Clearly, this is an artifact of the breakdown of data and does not indicate real changes in the proportion of academic staff in STE or Humanities. The trends from 2003 onwards are validly indicated, however, and show STE and Humanities holding more or less steady.

In summary, the data from 1994 onwards show a sharp drop in STE, a rise in Medicine, and a small drop in Humanities.

Crisis in the humanities? What crisis?

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Turbulence and Noise

I have produced some notes for a final year aerospace engineering unit on Turbulence and Noise (PDF). The introduction reads:

This is not a textbook and should not be read as one. It is a set of notes written for a final year unit at the University of Bath, with the aim of introducing aerospace engineering students to the extra concepts, mainly mathematical, which they will need in order to be able to read research papers in turbulence and noise. These papers are a mixture of classic work, such as Lighthill’s analysis of aerodynamically-generated noise, and more recent studies which apply state-of-the-art techniques to hard problems, and either extend our understanding of the physics, or give us completely new insights, in a way not previously possible.

The notes are written fairly informally, to give some intuitive sense of the concepts, as an aid to getting started on the real thing. Having read about correlation functions, for example, you will be in a position to read a paper which makes use of them, but that does not mean you will find it easy. You will find it possible, and the more papers you read, the deeper the understanding you will develop as you see how different people have made use of the same techniques. In practice, any writing of substance will require multiple readings, and will reveal more of itself under each reading.

Turbulence and acoustics are difficult, and you will not master them on this unit. You will have to work hard on ideas which will not be obvious, and were not obvious to the smart people who developed them. You will often feel stupid and confused, and you will wonder why you are doing this. You are doing this because it is worth it: you are taking on a difficult topic which some of the brightest people in history have found hard, but have nonetheless been able to contribute to.

Feeling stupid means you are working on something worth the trouble: if you want to feel clever, watch Sesame Street or read the Daily Mail.

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A mathematician writes …

From the preface to Introduction to the Theory of Fourier Integrals, Titchmarsh:

A great variety of applications of Fourier integrals are to be found in the literature, often in the form of `operators’, and often in the works of authors who are evidently not specially interested in analysis. As exercises in the theory I have written out a few of these applications as it seemed to me that an analyst should. I have retained, as having a certain picturesqueness, some references to `heat’, `radiation’, and so forth; but the interest is purely analytical, and the reader need not know whether such things exist.

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Mayan Mystic Mathematics, no thanks

Ed Vulliamy has some reasonable things to say about the Mayan `prophecy’ of the end of the world  but he gets it wrong here:

The Maya were no fools. Likely inventors of the figure zero, their mastery of astronomy – bequeathed to history through various codices and stoneworks – was breathtaking not only for its time, but for all time. Their systems for measuring time were more sophisticated than ours, with pivotal numbers of 13, 18 and 20, based upon lunar, Venusian, astronomical and mathematical measurements, and expressed in glyphs.

Vulliamy seems to confuse obscurity and sophistication. Our Arabic-numeral, place-system, method for arithmetic is much more sophisticated than one based on different `pivotal numbers’, because it makes things simpler for the person using it. By having one, and only one, set of rules, all calculations are the same, no matter what size of problem you deal with, a point which will be appreciated by those who had to learn the pounds, shillings, pence system of currency, or by those in benighted countries which continue to use imperial measures. Try doing mental arithmetic switching from base 13 to 18 to 20, without mechanical aids.

Vulliamy then talks of `lunar, Venusian, astronomical and mathematical measurements’, without saying what a `mathematical’ measurement is, and how it might differ from the other three he mentions.

Finally, he is impressed by the Mayans’ use of glyphs: `glyph’ is a fancy word for `character’ or `letter’.

We seem to have here a journalist falling for the idea that any ideas which survive long enough are `ancient wisdom’ and therefore better than our own. Actually, mathematics, and arithmetic, are areas where we can be fairly sure that the modern state of knowledge is definitely better than what people had X centuries ago.