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Updated: May 3, 2025
Of the many obligations which Political Economy owes to him, one only can be noticed consistent with the scope of the present article: the care which he has taken he alone, or at least, he more explicitly and formally than any other expositor to set forth the general position of that science in the aggregate field of scientific research; its relation to sociology as a whole, or to other fractions thereof, how far derivative or co-ordinate; what are its fundamental postulates or hypotheses, with what limits the logical methods of induction and deduction are applicable to it, and how far its conclusions may be relied on as approximations to truth.
The list of slaves at the beginning of 1794 is the only one giving full data as to ages, colors and health as well as occupations. The ages were of course in many cases mere approximations. The "great house negroes" head the list, fourteen in number.
Always avoid vague approximations where exact estimates are possible; about so many, about so much, instead of the precise number and quantity. Now, if there is anything on which the biological sciences have prided themselves in these latter years it is the substitution of quantitative for qualitative formulae.
It would be interesting to know just how commonly this device is used in the singing of the Tinguian and also in the music of other tribes of these Islands. From it we might learn something of the contact of other tribes with the Igorot. Japanese Scales. For structure of these scales, see analysis of those songs using one or another of the Japanese "tunings" or approximations to them. Tonality.
Above all, here, for the snatched instants, they could breathe so near to each other that the interval was almost engulfed in it, and the intensity both of the union and the caution became a workable substitute for contact. They had prolongations of instants that counted as visions of bliss; they had slow approximations that counted as long caresses.
He thought the archetypes of all things, and devised their variations; and when we rediscover any one of these his wondrous institutions, we seize his mind in its very literal intention. But as the sciences have developed farther, the notion has gained ground that most, perhaps all, of our laws are only approximations.
Formulæ designed to assign numerical values to fighting ships have been laboriously worked out, notably by Constructor Otto Kretschmer of the German navy; but the results cannot be accepted as anything except very able approximations. Furthermore, if ship A could whip ship B under some conditions, B could whip A under other conditions.
Vain would be the attempt to tell all the figures of them circling as in dance, and their juxtapositions, and the return of them in their revolutions upon themselves, and their approximations, and to say which of these deities in their conjunctions meet, and which of them are in opposition, and in what order they get behind and before one another, and when they are severally eclipsed to our sight and again reappear, sending terrors and intimations of the future to those who cannot calculate their movements to attempt to tell of all this without a visible representation of the heavenly system would be labour in vain.
Parts of the country not having been at the time correctly mapped, these distances are in some instances approximations only. The Religions of Cashmere and Thibet.
But we now know that pure mathematics can never pronounce upon questions of actual existence: the world of reason, in a sense, controls the world of fact, but it is not at any point creative of fact, and in the application of its results to the world in time and space, its certainty and precision are lost among approximations and working hypotheses.
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