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Whatever motion really may be, it surely is not static; but the definition we have gained is of the absolutely static. It gives a set of one-to-one relations between space-points and time-points, which relations themselves are as fixed as the points are. It gives positions assignable ad infinitum, but how the body gets from one position to another it omits to mention.
When each is referred to some possible place in the conceptual system, it is thereby 'understood. This notion of parallel 'manifolds' with their elements standing reciprocally in 'one-to-one relations, is proving so convenient nowadays in mathematics and logic as to supersede more and more the older classificatory conceptions.
There are many conceptual systems of this sort; and the sense manifold is also such a system. Find a one-to-one relation for your sense-impressions ANYWHERE among the concepts, and in so far forth you rationalize the impressions. But obviously you can rationalize them by using various conceptual systems.
Because of the quality of our inheritance the response to a situation is not a one-to-one affair, like a key in a lock, but all sorts of minor causes in the individual are operative in determining his response; and, on the other side, situations are so complex in themselves that they contain that which may call out several different instincts.
And none of the Svants ever reacted the same way twice to anything we said to them. There's just no one-to-one relationship anywhere." "I'm beginning to doubt they have a language," the Navy intelligence officer said. "Sure, they make a lot of vocal noise. So do chipmunks." "They have to have a language," Anna de Jong declared. "No sapient thought is possible without verbalization."
"I believe they look on the C.R.F. people as some species of simpleton, sir. They hate all offworlders; memory of their desertion has been passed on verbally for generations. So by their one-to-one logic we should either hate back or go away. We stay instead. And give them food, water, medicine and artifacts. Because of this they let us remain on sufferance.
Pitts. It was in the icebox." Then he took another tube. "This," he remarked, "is a one-to-one- thousand solution of sodium nitrite." He held it up carefully and poured three or four cubic centimetres of it into the first tube so that it ran carefully down the side in a manner such as to form a sharp line of contact between the heavier culture with the acid and the lighter nitrite solution.
Furthermore the set of straight lines in space β which are thus associated with points in space α form a complete family of parallel straight lines in space β. Thus there is a one-to-one correlation of points in space α with the straight lines of a certain definite family of parallel straight lines in space β.
Conversely there is an analogous one-to-one correlation of the points in space β with the straight lines of a certain family of parallel straight lines in space α. These families will be called respectively the family of parallels in β associated with α, and the family of parallels in α associated with β.
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