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Thought I should jot down this idea, which I have been thinking about for a bit.

Who knows of will lead anywhere.

The basic idea is that the geometry is based on distances between points, and that all distances are multiple of a basic quantum distance.

A quantum line is a line l between two points a and b  of length one.  A line is an ordered set of quantum lines between an ordered set of points. Its length is the number of quantum lines included.

A quantum line has no direction, or maybe it is better to at that it has both directions

We can then define a number of things such as ...

A straight line between two points a and b is any line from a to b with the minimal length.

The lines from a point a to the points of a straight line are perpendiculars if they have the minimal length.

The space of points is connected, in that there is always at least one line joining up any two points.

So there must always be perpendiculars, from s point to a straight line, and these perpendiculars must be straight lines themselves.

A plane will be defined by three points, being the set of all points on straight lines that intersect at least one straight line through each of the pairs of points.

Clearly these spaces have strange features.

. there can be more than on straight line between two points

. two straight lines may intersect at a number of points

Not sure how far this can be taken, but clearly it is the basis for real space.

Martin

# posted by martinW @ 11:41 pm 0 comments