Under the auspices of the Edinburgh Mathematical Society, a Mathematical Colloquium was held in the Mathematical Department of Edinburgh University during the week beginning Monday, 4th August, 1913, lasting five days. The following courses were arranged for:
No preliminary knowledge was required for this Course beyond an acquaintance with trigonometry. The methods were applied to analyse data derived from physical, meteorological, and astronomical observations.
The first Mathematical Colloquium held in Edinburgh met during the first week of August, and proved a great success. It was organised by the office-bearers of the Edinburgh Mathematical Society, A G Burgess, M.A., F.R.S.E., and Peter Comrie, M.A., B.Sc., F.R.S.E., respectively the President and Secretary of that Society, being also President and Secretary of the Colloquium. The idea of holding such a colloquium was an outcome of Professor Whittaker's announcement that he purposed organising, as part of the Mathematical Honours curriculum in the University of Edinburgh, a mathematical laboratory for systematic numerical discussion of functions and methods of calculation. Several correspondents had expressed the hope that vacation courses in this line of study might be established; and it was decided to make a first experiment. It was resolved, however, not to limit the colloquium to a discussion of one branch of mathematics, but to enlarge its scope by the inclusion of two other domains of mathematical thought. The broad features of the programme we owe to Professor Whittaker; and its variety was such as to appeal to all types of mathematical mind.
By a curious chance the three courses of lectures provided were given respectively by an Englishman, an Irishman, and a Scotchman. Each day at ten o'clock Professor Conway of University College, Dublin, discoursed on the Theory of Relativity and the new Physical Ideas of Space and Time. At 11.30 Professor Whittaker explained practical Harmonic Analysis and Periodogram Analysis; and at two o'clock Dr Sommerville of St Andrews expounded the mysteries of non-Euclidean Geometry and the Foundations of Geometry.
Professor Conway and Dr Sommerville lectured in the Mathematics Classroom of the University; but Professor Whittaker held his séances in the large basement hall, which has recently been fitted up as a mathematical laboratory. This, indeed, was the first occasion on which it had been used. Each student was provided with a specially designed desk, with a convenient book-rest fixed to the back, and with drawers and shelves for storing note-books, scribbling paper, graph paper, and books to aid calculation, such as Barlow's Tables and Crelle's Rechentafeln. At these desks learned professors, lecturers, teachers, and a few students, nearly eighty in all, totted up their columns of figures and drew their periodographs, and were quite elated when their totals came out right. Professor Whittaker chose for his working data the light periods of two variable stars, the one to illustrate the periodogram method of discovering unknown periods, the other to illustrate the analysis into harmonic components of a given periodic variation. The theory of the Fourier analysis was incidentally given and the last lecture finished with an account of Mäder's Harmonic Analyser.
This hour of practical work, combined with demonstrations involving only the familiar circular functions, gave the necessary balance to the weird imaginings of the other two courses. Without it to bring us back to the obvious world of apparent realities we should have been floundering hopelessly in the Absolute or in Minkowski's Welt. After we had been taught that velocities did not compound according to the parallelogram law, it was a positive delight to find that the Fourier series remained ordinarily additive; and with this in possession we had no great difficulty in apprehending the possibility of a space devoid of parallel lines.
One of our number, who hailed from Dundee, had been renewing his acquaintance the preceding evening with Gilbert and Sullivan's "Patience." When an exceptionally imaginary theorem was enunciated and proved, he turned round to his friend in the bench behind and whispered, "Yes, it is nonsense but oh! such precious nonsense!"
Newtonian dynamics, we found, was only a first approximation to the dynamics of our visible universe; while the Euclidean space in which this universe was vulgarly believed to move and have its being was a crude assumption from an axiom of ignorance. Again our Dundee professor hit off the situation with the quatrain,
The classic phoenix, sprung from fire,
Fable no longer dare we scorn;
Euclid and Newton both expire -
Conway and Sommerville are born!
Sandwiched in between these physical and mathematical heresies came the hour of comparative mental rest and the hour of physical recuperation in the luncheon room, and we were saved from unbelief in the realities of life. We learned many things. We were told that even if the theory of relativity were not true it had taught us truths.
The tendency of modern Physical Theory was in the direction of still further atomising the atom; yet it was necessary in geometry to have an assumption of continuity, so that all possible numbers might be brought into correspondence with an infinitude of points on a finite line. The dictum of the logician that we cannot define by means of a negation seemed to have no terror to the modern geometer with his glib talk of non-Euclidean, non-Pascalian, non-Desarguesian, and even non-Archimedean.
It was indeed a grand week. Each lecturer surpassed himself; and every one of the audience enjoyed himself or herself to the full. Professors and lecturers of world-wide reputation renewed their student days, and sat and took notes with humble zest. Professor Steggall, in moving a vote of thanks to the lecturers and to the organisers of the colloquium, hoped that this experience of taking notes for one brief week would make us feel more sympathetic with the unfortunate students who had to do the same for weeks and months. Under the leadership of the three lecturers we had been seeing visions and dreaming dreams; and he was sure we would all look back upon this colloquium with the keenest delight.
The three hours' hard mathematical thinking was followed every afternoon by suitable recreation. Mr Burgess and Mr Comrie arranged for golfing parties to the principal golf courses in the neighbourhood - Mortonhall, Barnton, and Baberton. On the Wednesday afternoon it was my privilege to lead a party through the beautiful grounds of the new Scottish Zoological Park at Corstorphine. The lions, bears, jackals, monkeys, parrots, antelopes, and the antique-looking gnu were all duly admired or wondered at. A discussion arose as to whether a certain four-footed creature was a camel or a dromedary. The problem was finally solved by the formula, ln = constant, where l is the name-length and n the hump-frequency. A charming hour was spent taking tea on the lawn in front of Corstorphine House, from which was a splendid view of the Pentland Hills. Reminiscences of college days in Cambridge, Dublin, and Edinburgh formed the nucleus of a varied gossip, which had usually a certain mathematical flavour.
On the Thursday afternoon a large party were shown over the statistical department of the Register House by Dr Dunlop, who demonstrated the striking mechanical methods by which groups of statistics could be sifted and arranged in any required combination.
On the Friday, after Dr Sommerville's last lecture, the whole company were entertained to tea in the Reception Room (the Mathematical Library) by the President and Secretary; and thereafter visitations were made to the University Physical Laboratory under the leadership of Dr Carse, and to the Heriot Hospital School, where Mr Gentle and others of the staff showed what is probably the most complete school laboratory for science teaching to be found in Scotland.
In formally closing the colloquium, Mr Burgess attributed the success of the gathering to the untiring labours of the Secretary, Mr Comrie, to the splendid efficiency of the lecturers, and to the good fellowship which had existed. This was the first colloquium; but he hoped it would not be the last. Possibly next year it might be combined with the Napier Tercentenary Celebration.
C G KNOTT.
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