the 0th dimension

We exist in the third dimension. You have infinitely thin paper in the second dimension. In the first dimension all you have is an infinitely thin, infinitely short, infintiely wide line.

In the 0 dimension, there can only be 1 point, that is infinitely thin, short, and cramped. However, because there is only 1 single point, and no other, than everything must exist at that point, whether a 1 dimensional, 2 dimensional, or 3 dimensional being. Because of that, we all share at least 1 point in the universe, with everything.

Update: I have since realized that we would not share one point in common -- we are comprised of many different points, thus of many different 0th dimensions. If we were all forced to fit inside a 0th dimensional space; then we would all share a point in common.

When we drop one of arbitrary variables for representing a point (or vector) in R³ (x, y, and z) we obtain the variables we use to specify points in R² -- and we continue to use x and y. Further dropping a dimension/variable, we end up with the number line, and a single variable, x. Now, let's take a cross section of that number line: a single point. This point reprents the entire R⁰ space. We cannot specify a position, as there is only one "location"; nor can we specify a "value" -- the only "value" for our "point" is whether the point exists -- or doesn't.

So, let's assign a variable to represent position in R⁰ and just for familiarity's sake, we'll use x. Function f(x) represents whether our zeroth-dimensional "space" is "on" or "off." (Notice that a basis set for this space is a null vector, sort of counterintuitively.)

Jumping back to R¹, let's graph this f(x) over time: we have a timing diagram. This might be useful if we had a large number of R⁰ spaces or could implement them using, say, electronic devices......