A'2, 2A, AB, CD, EF, represent the lagging arithmetical law of progression in the so-called social sciences (peaceful evolution).
Both of these during the same periods of time.
BC, DE, FG, represent revolutions or wars, with the aftermath of revolution of ideas—the “jump”—violent readjustment of ideas to facts—forced by events.
ab, bc, cd, and AB, CD, EF, take the same amount of time, but the second progression being much slower than the first one, the “jumps” or revolutions occur at shorter intervals as time goes on and thus more frequently force us to coordinate our ideas to facts. Periods of peace or seeming peace alternate more and more frequently with periods of violence; the mentioned disparity of progress in peaceful times is the hatching seed of future violence.[1]
As a matter of fact these few mathematical considerations can hardly be called mathematics or mathematical philosophy; nevertheless, without bringing attention to these very simple mathematical ideas we should not be able to proceed any further than in the past. Our life problems have always been “solved” by verbalists and rhetorical metaphysicians who cleverly played with vague words and who always ignored the supremely important matter of dimensions because they were ignorant of it. There was no possible way to arrive at an agreement on the significance of words, or even the understanding of them. Let us take, for instance, such words as “good” or “bad” or “truth;” volumes upon volumes have been written about them; no one has reached any result universally acceptable; the effect has been to multiply warring schools of philosophy—sectarians and partisans. In the meantime something corresponding to each of the terms “good,” “bad,” “truth” exists as matter of fact; but what that something is still awaits scientific determination. If only these three words could be scientifically defined, philosophy, law, ethics and psychology would cease to be “private theories” or verbalism and they would advance to the rank and dignity of sciences.
Here I may quote a characteristic of life as expressed by one of the “heroes” of my esteemed friend Harvey O'Higgins, in his book, From the [pg 026] Life, Imaginary Portraits of Some Distinguished Americans (Harper, N. Y.).
“Warren never philosophized; he handled facts as an artisan handles his tools; but if he had philosophized, his theory of life would probably have been something like this: ‘There is no justice, there is no morality, in nature or in natural laws; justice and morality are laws only of human society. But society, natural life, and all civilization are subject in their larger aspects to natural laws—which contradict morality and outrage justice—and the statesman has to move with those laws and direct his people in accordance with them, despite the lesser by-laws of morality and justice.’ ”
If such are the creeds of “distinguished people” anywhere, what better can we expect than that which we see in the history of humanity?
But the fact that the old philosophy, law, ethics, psychology, politics and sociology could not solve the practical problems of humanity, is not any reason whatsoever why we should despair. The problems can be solved.
To follow the reasoning of this book, it is not necessary to be a highly trained specialist; the only qualifications required are candor, an open mind, freedom from blinding prejudice, thoughtfulness, a real desire for truth, and enough common sense to understand that to talk of adding three quarts of milk to three-quarters of a mile is to talk nonsense.