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A Note on Magnitude


Magnitude and Size are essentially synonyms, belong in the Euclidean Domain, and are calibrated intervals.

For example, let there be two points (i.e., places), A and B.

Euclidean geometry assumes that A and B have an absolute, objective and constant distance between them, which is also assumed to be independent of the orientation of the line joining them. It is further assumed that this distance can be exactly spanned (calibrated) by an arbitrarily-large count of serially-abutting, absolute, objective, and equal sub-intervals (“units”).

It is assumed that the distance between fixed places, A and B, will always be measured by absolutely and immutably the same count of a pre-defined sub-interval, such as a metre, because the sub-interval is also a distance between two fixed places, and hence immutable.

One may perhaps detect a hint of circularity in these Euclidean assumptions!  They are not made in projective geometry, which fact fundamentally distinguishes the two geometries.

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