over 6 years ago

More generally, all our concepts and explanations (whether of universal and necessary character or not) have at their core the perception of a totality of ratios or proportions. [...] Thus, to perceive such a simple thing as the straightness of a line is to see that each segment of it is related to the next segment, as the next is in turn related to the one that follows it. Or, in more concise terms, if S1, S2, S3, denote any three successive segments, then S1 : S2 :: S2 : S3. If, however, the line should suddenly change its direction, at a certain point, then we would see that the segment that precedes this point is not related to the one that follows in the same way as prevails among the rest of the segments. If we could introduce the symbol X to mean "is not to" then, for this case, we could write S2 X S2 :: S2 : S3 (i.e., S1 is not to S2, as S2 is to S3). ΒΆ When we are perceiving one line meeting another, we are immediately aware of a totality of such similarities and differences of ratio. And, of course, as our attention goes to more complex structures of lines and surfaces forming a geometrical figure, we begin to be aware of a whole hierarchy of such ratios and their relationships. This hierarchy can develop indefinitely in its complexity and subtlety, as our perception extends into every phase of life. No matter what we perceive, however the essential meaning or content of this perception involves a totality of ratio, in the most general sense of this word.

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