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Updated: June 18, 2025
Each moment is a group of abstractive sets, and the events which are members of these sets are all members of one family of durations. The moments of one family form a temporal series; and, allowing the existence of different families of moments, there will be alternative temporal series in nature.
In other words, when the duration is small enough, the situation of the physical object within that duration is practically unique. The identification of the same physical object as being situated in distinct events in distinct durations is effected by the condition of continuity.
That is to say, though we cannot imagine the absolute duration of any such cycle of experience, we can, by the simple device of conceiving certain durations as multiples of others, perfectly well compare different periods of times, and so appreciate their relative magnitudes.
There are within it antecedents and consequents which are also durations which may be the complete specious presents of quicker consciousnesses. In other words a duration retains temporal thickness.
When lines have the same number of syllables, the time required to read them is approximately the same, and we tend to make the duration of the thought-divisions equal. Our time-sense is so fallible, we do not notice the departures from exactness; and when the durations of processes are nearly equal and the values which we attach to them are equal, then we are conscious of them as equal.
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 paintings; and light is whitewash; and durations are deceptive; and form is imprisonment; and heaven itself a decoy." All of which we see reproduced in Emerson's poem "Brahma."
These are a peculiarity of the character of passage as it is found in nature. This character has the reality of nature, but we must not necessarily transfer natural time to extra-natural entities. For each mind, in its awareness of nature is aware of a certain complex of related natural entities in their relations to the living body as a focus. But the associated durations may be identical.
Last month, in the Paris congress, Douglas Breeden, dean of Duke University's Fuqua School of Business, warned that to quote from the same issue of Risk Magazine: " 'Estimation risk' plagues even the best-designed risk management system. Firms must estimate risk and return parameters such as means, betas, durations, volatilities and convexities, and the estimates are subject to error.
Age, date and place of birth, ancestry on both sides three generations back, with complete and illuminating biographical details of ancestry and individual; education, financial standing, manner of living, illnesses in the family, including dates and durations of said illnesses, accidents, if any, medical attendance, marriages, births, deaths, opinions, reverses, present locations and various careers of descendants, list of misfortunes, festivities, entertainments, church affiliation past and present, political leanings, and a vast amount of other personal data had been immediately forthcoming.
Let us first consider what help the notion of antiprimes could give us in the definition of moments which we gave in the last lecture. Let the condition σ be the property of being a class whose members are all durations. An abstractive set which satisfies this condition is thus an abstractive set composed wholly of durations.
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