The Summer Hill Journal Of New Physics

Points in a Line

One of the differences in views of zero is with simple matters such as:

Q: If a point is an imaginary, dimensionless object, how many points are there in a line 1cm long?

A: If viewed as { 0 } then 1 / 0 = Type 2 infinity

A: If viewed as { } then 1 / 0 = 0

On the other hand, if we re-define a point to be any arbitrarily small value greater than zero, then both views give the answer as a Type 1 infinity. The key difference is when a point has exactly zero size.

At first this may seem a counter-intuitive result when using { }, but it is easily proved: If we can divide a line into an infinite number of zero-sized points, then we should also be able to construct a line from zero-sized points.

Try building a line using only zero-sized points and you soon realise it cannot be done. Starting at 0, simply stack up zero-sized points until you get to 1. No matter how many points you add, even an infinite number, you never move from 0.

We can derive from this another principle for the null view of zero in physics:

Null Principle #2: Dimensionless points are purely imaginary and can play no part as quantities in the mathematics of physics.

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