act of observation, that in some of the great
matters progress proceeds in accordance with one law and one rate of
advancement and in others in accordance with a very different law and
rate; it is a fact, a fact of observation and sad experience, a fact
attested by all history and made evident by reason, that owing to the
widely differing laws and rates of progress in the great essential
concerns of humanity, the balance and equilibrium among the parts is
disturbed, the strain gradually increases until a violent break ensues in
the form of social conflicts, insurrections, revolutions and war; it is a
fact that the readjustment that follows, as after an earthquake, does
indeed establish a kind of new equilibrium, but it is an equilibrium born
of violence, and it is destined to be again disturbed periodically without
end, unless by some science and art of Human Engineering progress in all
the great matters essential to human weal can be made to proceed in
accordance with one and the same law having its validity in the nature of
man.

Taken in combination, the facts just stated are so extremely important
that they deserve to be stated with the utmost emphasis and clarity. To
this end I beg the reader to consider very carefully and side by side the
two following series of numbers. The first one is a simple geometrical
progression--denoted by (_GP_); the second one is a simple arithmetical
progression--denoted by (_AP_):

_GP_: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc.;
_AP_: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc.

For convenience of comparison I let them begin with the same number and
for simplicity I have taken 2 for this initial term; observe that in the
(_GP_) each term is got from the preceding term by _multiplying_ by 2 and
that in the (_AP_) each term is got from its predecessor by adding 2; in
the first series the multiplier 2 is called the common _ratio_ and in the
second series the repeatedly added 2 is called the common _difference_; it
is again for the convenience of comparison that I have chosen the same
number for both common ratio and common difference and for the sake of
simplicity that I have taken for this number the easy number 2. Other
choices would be logically just as good.

Why have I introduced these two series? Because they serve to illustrate
perfectly two widely different _laws of progress_--two laws representing
vastly different _rates_ of growth, increase, or _advancement_.

Do not fa