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By measuring their courses we find the different seasons, their durations and vicissitudes, which, if they are known to men alone, we must believe were made only for their sake. Does the earth bring forth fruit and grain in such excessive abundance and variety for men or for brutes? The plentiful and exhilarating fruit of the vine and the olive-tree are entirely useless to beasts.
The situations of a physical object are conditioned by uniqueness and continuity. The uniqueness is an ideal limit to which we approximate as we proceed in thought along an abstractive set of durations, considering smaller and smaller durations in the approach to the ideal limit of the moment of time.
We may accept it as impossible for any one to deal with such vast durations save with figures which are never really comprehended. It is well, however, to enlarge our view as to the age of the earth by such efforts as have just been indicated.
This recognition does not merely concern the comparison of a factor of nature posited by memory with a factor posited by immediate sense-awareness. Recognition takes place within the present without any intervention of pure memory. For the present fact is a duration with its antecedent and consequent durations which are parts of itself.
Time hath spared the epitaph of Adrian's horse, confounded that of himself. In vain we compute our felicities by the advantage of our good names, since bad have equal durations and Thersites is like to live as long as Agamemnon. Who knows whether the best of men be known, or whether there be not more remarkable persons forgot than any that stand remembered in the known account of time?
I neither am going nor coming; nor is my dwelling in any one place; nor art thou, thou; nor are others, others; nor am I, I." As if he had said, "All is for the soul, and the soul is Vishnu; and animals and stars are transient painting; and light is whitewash; and durations are deceptive; and form is imprisonment; and heaven itself a decoy."
A temporal series, as we have defined it, represents merely certain properties of a family of durations properties indeed which durations only possess because of their partaking of the character of passage, but on the other hand properties which only durations do possess.
But sounds are also measurable in their own category: they have comparable pitches and durations, and definite and recognizable combinations of those sensuous elements are as truly objects as chairs and tables.
Consider a set of durations all taken from the same family. Now the relation of whole and part is asymmetrical; and by this I mean that if A is part of B, then B is not part of A. Also we have already noted that the relation is transitive.
Since these were, in 1874, separated by about three and a half hours, and the interval may be much longer, the choice of posts for the successful use of the "method of durations" is a matter of some difficulty. Its chief attendant difficulty is the necessity for accurately fixing the longitudes of the points of observation.
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