_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 __ 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.’ ”