The imperfections here proved to be _essential_ to the intellect are constantly increased, however, in particular cases, by _non-essential_ imperfections. The intellect is never in _every_ respect what it possibly might be. The perfections possible to it are so opposed that they exclude each other. Therefore no man can be at once Plato and Aristotle, or Shakspeare and Newton, or Kant and Goethe. The imperfections of the intellect, on the contrary, consort very well together; therefore in reality it for the most part remains far below what it might be. Its functions depend upon so very many conditions, which we can only comprehend as anatomical and physiological, in the _phenomenon_ in which alone they are given us, that a decidedly excelling intellect, even in _one_ respect alone, is among the rarest of natural phenomena. Therefore the productions of such an intellect are preserved through thousands of years, indeed every relic of such a highly favoured individual becomes a most valuable treasure. From such an intellect down to that which approaches imbecility the gradations are innumerable. And primarily, in conformity with these gradations, the _mental horizon_ of each of us varies very much from the mere comprehension of the present, which even the brute has, to that which also embraces the next hour, the day, even the morrow, the week, the year, the life, the century, the thousand years, up to that of the consciousness which has almost always present, even though obscurely dawning, the horizon of the infinite, and whose thoughts therefore assume a character in keeping with this. Further, that difference among intelligences shows itself in the rapidity of their thinking, which is very important, and which may be as different and as finely graduated as that of the points in the radius of a revolving disc. The remoteness of the consequents and reasons to which any one’s thought can extend seems to stand in a certain relation to the rapidity of his thinking, for the greatest exertion of thought-power in general can only last quite a short time, and yet only while it lasts can a thought be thought out in its complete unity. It therefore amounts to this, how far the intellect can pursue it in so short a time, thus what length of path it can travel in it. On the other hand, in the case of some, rapidity may be made up for by the greater duration of that time of perfectly concentrated thought. Probably the slow and lasting thought makes the mathematical mind, while rapidity of thought makes the genius. The latter is a flight, the former a sure advance upon firm ground, step by step. Yet even in the sciences, whenever it is no longer a question of mere quantities, but of understanding the nature of phenomena, this last kind of thinking is inadequate. This is shown, for example, by Newton’s theory of colour, and later by Biot’s nonsense about colour rings, which yet agrees with the whole atomistic method of treating light among the French,