ve the amount
of progress made by the next generation; then the amount of progress made
by the second generation will be _PR__2_; that made by the third
generation will be _PR__3_; and so on; now denote by _T_ the number of
generations, counting the first one and all that follow in endless
succession. Then the following series will show the law of human progress
in the chosen field:

_PR, PR__2__, PR__3__, PR__4__, PR__5__, ..., PR__T__, PR__T+1__, ..._;

notice how it goes; the first generation ends with PR; the second
generation starts with _PR_, adds _PR__2_, and ends with _PR + PR__2_; the
third generation starts with _PR + PR__2_, adds _PR__3_ and ends with _PR
+ PR__2__ + PR__3_; and so on and on; the _gain_ made in the _T__th_
generation is _PR__T_; _the total gain_ made in _T_ generations is

_PR + PR__2__ + PR__3__ + ... + PR__T_;

this total gain is given by the formula,

Total gain in T generations = (R / R-1) (PRT-P).

If we take _R_ to be 2 (which is a very small ratio, requiring the
progress of each generation to be merely double that of the preceding one)
and if we take _T_ to be (say) 10, then we see that the progress made by
the single 10th generation is _P_ x 210, which is 1024 times the progress
made in the "first" generation; and we readily compute that the total gain
in 10 generations is 2046 times the progress made in the "first"
generation. Moreover, to gain a just sense of the impressiveness of this
law, the reader must reflect upon the fact that it operates, not merely on
one field, but in all fields of human interest. "Operates in all fields" I
have just now said; as a matter of fact, as before pointed out, it does
not so operate _now_ in _all_ fields nor has it ever done so. My point is
that it _will_ so operate when we once acquire sense enough to let it do
so. That sense we shall have when and only when we discover that by nature
we are time-binders and that the _effectiveness_ of our time-binding
capacity is not only a function of time but is, as I have explained, a
logarithmic or exponential function of time--a function in which time (_T_)
enters as an _exponent_, as in the expression _PR__T_, so that we humans
are, unlike animals, naturally qualified not only to progress, but to
progress more and more rapidly, with an always _accelerating
acceleration_, as the generations pass.

This great fact is to be at once the basis, the regulator and guide in the
science and art of Human Engi