An introduction to mathematics, by A. N. Whitehead.

198 INTRODUCTION TO MATHEMATICS
beyond the regions of mathematics. Our
limited intellects cannot deal with complicated material all at once, and our method of
arrangement is that of approximation. The
statesman in framing his speech puts the
dominating issues first and lets the details
fall naturally into their subordinate places.
There is, of course, the converse artistic
method of preparing the imagination by the
presentation of subordinate or special details,
and then gradually rising to a crisis. In
either way the process is one of gradual
summation of effects; and this is exactly
what is done by the successive summation
of the terms of a series. Our ordinary
method of stating numbers is such a process
of gradual summation, at least, in the case
of large numbers. Thus 568,213 presents
itself to the mind as500,000 +60,000 +8,000 +200 +10 +3
In the case of decimal fractions this is so
more avowedly. Thus 3.14159 is3 +o +f 1 + -1î +T +TOoo
Also, 3 and 3 + -l, and 3 + 0 +1 o, and 3 + l
+1]4 +To0o, and 3+-1 40 +I + —
are successive approximations to the complete
result 3-14159. If we read 568,213 backwards
from right to left, starting with the 3 units,