
Re: Euclid's Elements Book 1 Proposition 1  something Euclid missed?
Posted:
Feb 17, 2014 8:44 PM


KQ: What is a reifiable point?
http://www.spacetimeandtheuniverse.com/math/45070999equalone353.html#post22093
A reifiable point is a point that corresponds to the measure of a given line segment. For example, a straightedge calibrated with natural numbers. The natural numbers marked on the ruler reify those points. For example,
0_________1
0 and 1 are reifiable points. 1 is the measure of the magnitude of the line segment between 0 and 1.
0_____________sqrt(2)
0 is reifiable but sqrt(2) is not, because sqrt(2) is not a number. It is incommensurable.
I can take two line segments and physically place an invisible marker between them to describe 0, 1 or sqrt(2). In the case of 0 and 1, both my line segments are measurable. In the case of sqrt(2), the line segment is not measurable. The point between the line segment sqrt(2) and the line segment following it does not correspond to any number.
Points are reified not by only marking off distances with an invisible marker(point), but by associating a number with each invisible marker.
The above link explains this.

