From the January 9, 1937, issue


Offhand you might not expect a great mathematician to be interested in why it is that men throughout countless ages have taken joy in looking on the moon, a shapely tree, a pearl, or the rhythmical curves of a woman’s form.

Yet Dr, George D. Birkhoff, Harvard mathematician, who was elected president of the American Association for the Advancement of Science for the coming year, has made the mathematical measure of art one of his main branches of research.

He has devised formulae that enable you to analyze the source of delight in the creations of painters and poets. The esthetic value of a shape or form as determined by the Birkhoff formula conforms to the emotional judgment of those who look upon it. Not that you need to be a mathematician to delight in art. Esthetic pleasure is due to an unconscious appreciation of the mathematical proportions of the object.

In a detailed treatment of esthetic measure which he published not long ago, Dr. Birkhoff has told how painters, architects, and others can use consciously some rules that he has discovered. Take forms made with straight lines. The square is rated as the straight line form having the highest esthetic appeal, being rated as 1.50 compared with the diamond at 1.00 and the triangle at 0.63. Take a famous painting. Dr. Birkhoff finds that its composition involves geometric forms which are pleasing to the eye.

The pretty girl is pretty because all her measurements are in correct relation to each other—if her arms were longer or her nose shorter or her height just a little different in relation to her weight, the effect would not be at all the same.

Dr. Birkhoff’s formulae for esthetic values can also be applied to music and poetry. The scale used for poetry, for example, is not the same as the one applied to pictures, but it involves such artistic qualities as rhyme, rhythm, and alliteration. Dr. Birkhoff has even tried building experimental poems and musical compositions by deliberately placing in them the elements indicated by the formula.

Just a short time ago Dr. Birkhoff, who is only 52, was made dean of Harvard’s Graduate School of Arts and Sciences, where he has been professor of mathematics since 1919.


Fatal blood clots in the veins or arteries, the tragic consequence in many an operation and blood transfusion, may be prevented in future by the use of heparin, it appears from a report of a University of Toronto research team to the Canadian Medical Association (Journal, December).

Members of the research team are Drs. D.W.G. Murray, L.B. Jacques, T.S. Perrett, and C.H. Best, the latter a co-discoverer of insulin.

Heparin, these scientists found, acts in two ways: 1. By making the blood clot more slowly, which would make it a valuable aid in blood transfusions where there is always danger of clotting; 2. By preventing dangerous narrowing or closing of the veins following injury to them.


Three new chemical elements—osmium, iridium, and thulium—have been added to the positively identified elements found in the sun during 1936, declared Dr. Charlotte E. Moore of Princeton Observatory before the meeting of the American Astronomical Society.

Out of the 92 chemical elements of the Earth, 61 are surely present in the sun; three are doubtfully present, on two there are insufficient solar data, on seven insufficient laboratory data, and 19 are absent.

Method of identifying the solar elements, explained Dr. Moore, is to obtain spectrographic plates from the sun’s light and then try to duplicate those characteristic spectral lines by experiments in the laboratory.

During the last year, she said, Dr. Walter Albertson of the Massachusetts Institute of Technology thus identified osmium and iridium. Dr. W.F. Meggers, noted scientist of the National Bureau of Standards in Washington, obtained the spectrum of the rare-earth thulium in his laboratory and thus aided in its solar identification.

Strangely absent, so far, are identifications of the gas neon and the rare-earth caesium in the solar spectrum. Both have long been identified in the laboratory.

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