On May 13, 6:32 pm, mike3 <mike4...@yahoo.com> wrote: > > How can one intuitively grasp the geometry of a non- > Archimedean valued field
All triangles are isosceles and the unequal side is the shortest one. Two discs cannot partially intersect. Every point of a disc may be regarded as its center.
Think of different orders of magnitudes: from across the room, two different molecules in a glass are pretty much the same distance from you. But you and the glass are pretty much the same distance from the stop sign down the street.
Two different people in new york are pretty much the same distance from a person in Chicago but all three are pretty much the same distance from a rock on the moon. Them moon, the three people, the stop sign and the glass are all pretty much the same distance from the rings of Saturn...
From Alain Robert "A Course in p-adic Analysis" p. vi "Intuitively, this absolute value plays the role of an order of magnitude. If x has a magnitude greater than 1, one cannot reach from 0 it by taking a finite number of unit steps (one cannot walk or drive to a neighboring galaxy!)"