December 15, 1916] 



SCIENCE 



843 



from which nothing could emerge, for which no 

 future was possible but extinction. It represents 

 an utterly dead school of art which closed its eyes 

 to natural facts (for however ignorant a person 

 may be he need only look at a human being to see 

 that it has a mouth as well as eyes) and made the 

 attempt to adorn or idealize natural facts accord- 

 ing to its own notions (for it put red spots in the 

 middle of the hands and sharpened the thumbs, 

 thinking to improve them). Here you have an ex- 

 ample of the worst that is possible in idealism. 

 Whenever people don't look at nature they always 

 think they can improve her. 



From this dead barbarism let us turn to a living 

 barbarism, to work done by hands as rude and by 

 minds as uninformed, let us turn to a picture of 

 the Serpent Beguiling Eve, from the Church of St. 

 Ambrogio of Milan. Its date is not known, but it 

 is barbarous enough for any date: but rude and 

 ludicrous as the sketch is, it does certainly have 

 the elements of life in it. The workman's whole 

 aim was straight at the facts, and not merely at 

 the facts but at the very heart of the facts, for he 

 did indeed show Eve's state of mind, that she is 

 pleased at being flattered and yet in an uncom- 

 fortable mood of hesitation; some look of listen- 

 ing, of complacency and embarrassment he did 

 verily get into the picture; note the eyes slightly 



Fig. 2. The Serpent Beguiling Eve. The be- 

 ginnings of art in Italy. 



askance, the lips compressed and the right hand 

 nervously grasping the left arm. Nothing was im- 

 possible to the people who began their art thus. 

 The world was open to them and all that is in it; 

 whereas nothing was possible to the man who did 

 the symmetrical angel, the world was keyless to 

 him. He built a cell for himself in which he was 

 barred up forever. 



Our conventionalized courses in mathe- 

 matics do not, however, take strong enough 

 hold on young men to shut them up, as in a 

 cell, forever ! No, they certainly do not ! But 



these courses do tend to separate ordinary 

 mathematical ideas from sense material: 

 whereas the very essence of physics and chem- 

 istry is to develop mathematical ideas in con- 

 nection with sense material. 



Let no one imagine that we, in our unfriend- 

 liness towards conventional mathematics 

 teaching fail to appreciate the necessity of the 

 kind of precise thinking which is peculiar to 

 the mathematical sciences, although much that 

 has been said on this subject by mathemati- 

 cians seems to us to be only a near-vision of 

 that abstract heaven which, according to 

 William James, is the one refuge of tender- 

 minded philosophers, but which to the tough- 

 minded is merely an empty dream. 



Nothing in this world is necessary which 

 can be avoided, and it is much better to at- 

 tempt to show that we can not get along with- 

 out precise thinking than it is to pronounce 

 eulogy thereon ; and if one speaks of the neces- 

 sity of precise ideas as a distressing thing, 

 which it certainly is to many young men who 

 aspire to be engineers and scientists, one may 

 as it were by stealth gain entrance to their 

 primitive minds and convince them that men 

 do not now live by hunting and fishing. This 

 is what we have tried to do in our "Intro- 

 duction to Mechanics." 1 



Imagine a never-to-be-escaped human need 

 of a twenty-foot arm. What age-long develop- 

 ment, and what unthinkable pains! It is 

 easier to build a steam shovel! All of which 

 means that homo sapiens is now bent towards 

 social inheritance; but social inheritance has 

 its own pains, as many know who burn the 

 midnight oil. 



Weh dem die Enkeln sind.2 



How shocking to reduce the tender-minded 

 philosopher's love for perfect precision to a 

 materialistic preference for steam shovels as 



i See our ' ' Mechanics and Heat, ' ' The Mac- 

 millan Co., 1910. This essay is reprinted under 

 the title The Study of Science in "Bill's School 

 and Mine," published by Franklin, MacNutt and 

 Charles, South Bethlehem, Pennsylvania, 1913. 



2 This was addressed by Goethe directly to a 

 young student "Weh dir das du ein Enkel bist. " 



