December 5, 1913] 



SCIENCE 



799 



forces : discord and concord. By the one it 

 is driven; by the other, drawn. Intellect 

 is a perpetual suitor. The object of the 

 suit is not the conquest of matter, it is a 

 thing of mind, it is the music of the spirit, 

 it is Harmonia, the beautiful daughter of 

 the muses. The aim, the ideal, the beati- 

 tude of intellect is harmony. That is the 

 meaning of its endless talk about compati- 

 bilities, consistencies and concords, and 

 that is the meaning of its endless battling 

 and circumvention and transcendence of 

 contradiction. But what of the applica- 

 tions of science and public service? These 

 ■are by-products of the intellect's aim and 

 of the pursuit of its ideal. Many things it 

 regards as worthy, high and holy — appli- 

 cations of science, public service, the 

 "wonder" of Aristotle, Jacobi's "honor of 

 the human spirit," Diotima's "glorious 

 fame of immortal virtue ' ' — but that which, 

 by the law of its being, intellect seeks 

 above all and perpetually pursues and 

 loves, is harmony. It is for a home and a 

 dwelling with her that intellect creates a 

 world ; and its admonition is : Seek ye first 

 the Kingdom of Harmony, and all these 

 things shall be added unto you. 



And the ideal and admonition, thus re- 

 vealed in the light of analysis, are justified 

 of history. Inverting the order of time, we 

 have only to contemplate the great periods 

 in the intellectual life of Paris, Florence 

 :and Athens. If, among these mightiest 

 contributors to the spiritual wealth of man, 

 Athens is supreme, she is also supreme in 

 her devotion to the intellect's ideal. It is 

 ■of Athens that Euripides sings : 



The sons of Ereetheus, the olden, 



Whom high gods planted of yore 

 In an old land of heaven upholden, 



A proud land untrodden of war; 

 They are hungered, and lo, their desire 



With wisdom is fed as with meat; 

 In their skies is a shining of fire, 



A joy in the fall of their feet; 



And thither with manifold dowers, 



From the north, from the hills, from the morn, 

 The Muses did gather their powers. 



That a child of the Nine should be born; 

 And Harmony, sown as the flowers. 



Grew gold in the acres of com.2 



And thus, ladies and gentlemen, our lec- 

 turer will say, what I wish you to see here 

 is, that Science, and especially Mathemat- 

 ics, the ideal form of science, are creations 

 of Intellect in its quest for Harmony. It is 

 as such creations that they are to be judged 

 and their human worth appraised. Of the 

 applications of mathematics to engineering 

 and of its service in natural science, I have 

 spoken at length, he will say, in the course 

 of previous lectures. Other great themes 

 of our subject remain for consideration. 

 To appraise the worth of mathematics as a 

 discipline in the art of rigorous thinking 

 and as a means of giving wing to the subt- 

 ler imagination ; to estimate and explain its 

 value as a norm for criticism and for guid- 

 ance of speculation and pioneering in fields 

 not yet brought under the dominion of 

 logic ; to estimate its esthetic worth as show- 

 ing forth in psychic light the law and order 

 of the psychic world ; to evaluate its ethical 

 significance in rebuking by its certitude 

 and eternality the facile skepticism that 

 doubts all knowledge, and especially in 

 serving as a retreat for the spirit when as 

 at times the world of sense seems madly 

 bent on heaping strange misfortunes up and 

 "to and fro the chances of the years dance 

 like an idiot in the wind"; to give a sense 

 of its religious value in ' ' the contemplation 

 of ideas under the form of eternity," in 

 disclosing a cosmos of perfect beauty and 

 everlasting order and in presenting there, 

 for meditation, endless consequences tra- 

 versing the rational world and seeming to 

 point to a mystical region above and be- 

 yond : these and similar themes, our speaker 

 2Translation by Professor Gilbert Murray. 



