Nothing can be more disastrous. For what are the consequences of that kind of error? Let the reader reflect. He knows that, if our ancestors had committed that kind of error regarding lines and surfaces and solids, there would to-day be no science of geometry; and he knows that, if there were no geometry, there would be no architecture in the world, no surveying, no railroads, no astronomy, no charting of the seas, no steamships, no engineering, nothing whatever of the now familiar world-wide affairs made possible by the scientific conquest of space. I say again, let the reader reflect; for if he does not, he will here miss the gravity of a most momentous truth. He readily sees, in the case supposed, how very appalling the consequences would have been if, throughout the period of humanity’s childhood, there had occurred a certain confusion of types, a certain mixing of dimensions, and he is _enabled_ to see it just because, happily, the blunder was _not_ made or, if made, was not persisted in, for, if it had been made and persisted in, then the great and now familiar things of which it would have deprived the world would not be here; we should not now be able even to imagine them, and so we could not now compute even roughly the tremendous magnitude of the blunder’s disastrous consequences. Let the reader not deviate nor falter nor stagger here; let him shoulder the burden of the mighty argument and bear it to the goal. He easily perceives the truly appalling consequences that _would_ have inevitably followed from the error of confusing types—the error of mixing dimensions—in the matter of lines and surfaces and solids, _if_ that error had been committed and persisted in throughout the centuries; he _can_ perceive those consequences just because the error was _not_ made and hence the great things of which (had the blunder been made) it would have deprived the world are here, so that he can say: “Behold those splendid things—the science of geometry and its manifold applications everywhere shining in human affairs—imagine all of them gone, imagine the world if they had never been, and you will have a measure of the consequences that would have followed violation of the law of types, the law of dimensions, in the matter of lines, surfaces and solids.” But, now, in regard to the exactly similar error respecting the nature of man, the situation is reversed; for this blunder, unlike the other one, is not merely hypothetical; we have seen that it was actually committed and has been actually persisted in from time immemorial; not merely for years or for decades or for centuries but for _centuries_ of _centuries_ including our own day, it has lain athwart the course of human progress; age after age it has hampered and baulked the natural activity of the time-binding energies—the civilization-producing energies—of humanity. How are we to estimate its consequences? Let the reader keep in mind that the error is fundamental—a type-confusing blunder (like that supposed regarding geometric entities); let him reflect, moreover, that it affects, not merely one of our human concerns, but _all_ of them, since it is an error regarding the _center_ of them all—regarding the very _nature_ of man himself; and he will know, as well as anything can be known, that the consequences of the ages-old blunder have been and are very momentous and very terrible. Their measure is indeed beyond our power; we cannot describe them adequately, we cannot delineate their proportions, for we cannot truly imagine them; and the reason is plain: it is that those advancements of civilization, those augmentations of material and spiritual wealth, all of the glorious achievements of which the tragic blunder has deprived the world, are none of them here; they have not been produced; and so we cannot say, as in the other case: “Look upon these splendid treasures of bound-up time, imagine them taken away, and your sense of the appalling loss will give you the measure required.” It is evident that the glories of which the misconceptions of human nature have deprived manhood must long remain, perhaps forever, in the sad realm of dreams regarding great and noble things that might have been.