APRIL 26, 1912] 
and precious sense, it is ‘‘the eternal type 
of the wondrous whole.’’ For poetry and 
painting, sculpture and music—art in all 
its forms—philosophy, theology, religion 
and science, too, however passional their 
life and however tinged or deeply stained 
by local or temporal cireumstance, yet have 
this in common: they all of them aim at 
values which transcend the accidents and 
limitations of every time and place; and 
so it is that the passionlessness of the mer- 
man’s thought, the infiniteness of the kind 
of being he contemplates and the everlast- 
ingness of his achievements enter as essen- 
tial qualities into the ideals that make the 
glory of the seraph’s world. I do not for- 
get, in saying this, that, of all theory, 
mathematical theory is the most abstract. 
I do not forget that mathematics therefore 
lends especial sharpness to the contrast in 
the Mephistophelian warning: 
Gray, my dear friend, is all theory, 
Green the golden tree of life. 
Yet I know that one who loves not the 
eray of a naked woodland has much to 
learn of the esthetic resources of our north- 
ern clime. A mathematical doctrine, taken 
in its purity, is indeed gray. Yet such a 
doctrine, a world-filling theory woven of 
gray relationships finer than gossamer but 
stronger than cables of steel, leaves upon 
an intersecting plane a tracery surpassing 
in fineness and beauty the exquisite art- 
istry of frost-work upon a windowpane. 
Architecture, it has been said, is frozen 
music. Be it so. Geometry is frozen 
architecture. 
No, the belief that mathematics, because 
it is abstract, because it is static and cold 
and gray, is detached from life, is a mis- 
taken belief. Mathematics, even in its 
purest and most abstract estate, is not de- 
tached from life. It is just the ideal hand- 
ling of the problems of life, as sculpture 
SCIENCE 
645 
may idealize a human figure or as poetry 
or painting may idealize a figure or a 
scene. Mathematics is precisely the ideal 
handling of the problems of life, and the 
central ideas of the science, the great con- 
cepts about which its stately doctrines 
have been built up, are precisely the chief 
ideas with which life must always deal 
and which, as it tumbles and rolls about 
them through time and space, give it its 
interests and problems, and its order and 
rationality. That such is the case a few 
indications will suffice to show. The 
mathematical concepts of constant and 
variable are represented familiarly in life 
by the notions of fixedness and change. 
The concept of equation or that of an 
equational system, imposing restriction 
upon variability, is matched in life by the 
concept of natural and spiritual law, giv- 
ing order to what were else chaotic change 
and providing partial freedom in lieu of 
none at all. What is known in mathe- 
matics under the name of limit is every- 
where present in life in the guise of some 
ideal, some excellence high-dwelling among 
the rocks, an ‘‘ever flying perfect’’ as 
Emerson ealls it, unto which we may ap- 
proximate nearer and nearer, but which 
we can never quite attain, save in aspira- 
tion. The supreme concept of functional- 
ity finds its correlate in life in the 
all-pervasive sense of interdependence 
and mutual determination among the ele- 
ments of the world. What is known in 
mathematics as transformation—that is, 
lawful transfer of attention, serving to 
match in orderly fashion the things of one 
system with those of another—is conceived 
in life as a process of transmutation by 
which, in the flux of the world, the con- 
tent of the present has come out of the 
past and in its turn, in ceasing to be, gives 
birth to its successor, as the boy is father 
to the man and as things, in general, be- 
