Translated by Stephen MacKenna and B. S. Page.
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Well, in hearing magnitude is known incidentally; but how? Touch conveys a direct impression of a visible object; what gives us the same direct impression of an object of hearing?
The magnitude of a sound is known not by actual quantity but by degree of impact, by intensity — and this in no indirect knowledge; the ear appreciates a certain degree of force, exactly as the palate perceives by no indirect knowledge, a certain degree of sweetness. But the true magnitude of a sound is its extension; this the hearing may define to itself incidentally by deduction from the degree of intensity but not to the point of precision. The intensity is merely the definite effect at a particular spot; the magnitude is a matter of totality, the sum of space occupied.
Still the colours seen from a distance are faint; but they are not small as the masses are.
True; but there is the common fact of diminution. There is colour with its diminution, faintness; there is magnitude with its diminution, smallness; and magnitude follows colour diminishing stage by stage with it.
But, the phenomenon is more easily explained by the example of things of wide variety. Take mountains dotted with houses, woods and other land-marks; the observation of each detail gives us the means of calculating, by the single objects noted, the total extent covered: but, where no such detail of form reaches us, our vision, which deals with detail, has not the means towards the knowledge of the whole by measurement of any one clearly discerned magnitude. This applies even to objects of vision close at hand: where there is variety and the eye sweeps over all at one glance so that the forms are not all caught, the total appears the less in proportion to the detail which has escaped the eye; observe each single point and then you can estimate the volume precisely. Again, magnitudes of one colour and unbroken form trick the sense of quantity: the vision can no longer estimate by the particular; it slips away, not finding the stand-by of the difference between part and part.
It was the detail that prevented a near object deceiving our sense of magnitude: in the case of the distant object, because the eye does not pass stage by stage through the stretch of intervening space so as to note its forms, therefore it cannot report the magnitude of that space.
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