Space Structures

Defining a new geometry

Things and the relationships between them

Here is a picture in a frame. You can see the frame and you can see the background on which the picture is drawn, but what is this a picture of?

nothing

That's right, nothing. This is a picture of nothing, which is why there is nothing drawn inside the frame. Human beings tend to want to explain a picture of nothing. A classic explanation of this picture is that it is "really" a picture of a polar bear in a snowstorm, and the bear has just walked away. Even if there was a bear, it is gone now; and in the blinding snow you can't see anything. So this is still a picture of nothing.

The second picture is infinitely different. The frame is the same, but the representation is different.

something

The second picture shows something instead of nothing. It still is not a very interesting picture, just a picture of a rather non-descript dot, but it is a picture and not just a blank canvas. The fact that something exists is crucial; it is essential. This is fundamentally different from having nothing at all.

Now we come to a third picture. In this frame you see 2 of those vague dots. You still can't tell what those vague dots are, and the dots seem to be identical to each other. Yes, there are more dots — twice as many, in fact — but doubling the number of dots is hardly as big a change as the infinite change from nothing to something. And yet, there is a stupendous change.

everything

Again there is something completely new. There is a relationship between the 2 points. This can only be true where there are 2 or more things.


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