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Updated: May 3, 2025


Somehow I think that I could lead you on to this; perhaps even make you say that you had actually ordered it from your library, before I told you the horrid truth that Ommany's Approximations was an invention of my own. Let us, therefore, be frank.

In like manner, there is throughout nature something mocking, something that leads us on and on, but arrives nowhere; keeps no faith with us. All promise outruns the performance. We live in a system of approximations. Every end is prospective of some other end, which is also temporary; a round and final success nowhere. We are encamped in nature, not domesticated.

If there is one thing which advancing knowledge makes clearer than another, it is that death is swallowed up in life, and life in death; so that if the last enemy that shall be subdued is death, then indeed is our salvation nearer than what we thought, for in strictness there is neither life nor death, nor thought nor thing, except as figures of speech, and as the approximations which strike us for the time as most convenient.

Such averages, therefore, are commonly of little use for the practical guidance of any affairs but those which concern large numbers. Such averages can only be considered as supplying the first term in a series of approximations; the subsequent terms proceeding on an appreciation of the circumstances belonging to the particular case.

With or without her witness, at any rate, she was led by comparison to a sense of the quantity of earnest intention operating, and operating so harmoniously, between her companions; and it was in the mitigated midnight of these approximations that she had made out the promise of her dawn.

It might be pure energy a form ethereal and outside the realm of substance or it might be partly material; some unknown and equivocal mass of plasticity, capable of changing at will to nebulous approximations of the solid, liquid, gaseous, or tenuously unparticled states.

"Then, too, the uneducated assume the unvarying exactness of mathematical results; while, in reality, mathematical results are often only approximations.

There are incipient stages; there are gradual approximations; there are twilight states between sanity and insanity which are clearly recognised not only by experts but by all sagacious men of the world.

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.

There are various approximations in actual experience to the ideal community, each more or less perfect according to the degree in which the good of the individual is also made the good of all, and the interests of governors and governed are alike.

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