Reply To: Time: tree or circular?

Forums Forums Physics and Philosophy Time: tree or circular? Reply To: Time: tree or circular?

#6716
Ashish Dalela
Keymaster

There are three descriptions of space–(1) a tree, (2) lotus petals, and (3) spherical. These appear to be confusing normally but you can think in terms of the circle limit diagrams. http://mathworld.wolfram.com/PoincareHyperbolicDisk.html

The center of the circle is the root and the triangles are the branches. You can also think in terms of a lotus flower. Also, because the triangles toward the circumference become smaller, you can never reach the circumference, and this is an analog of Zeno’s paradox.
In terms of numbers, if the center is visualized as 1, and the successive emanating leaves as fractions of 1, then the fractions get smaller and smaller, and they are all parts of the center, and yet different from the center, and there is potentially no limit to dividing, and yet no matter how many times you divide, you never actually finish dividing. So, there is a “circle limit”, which means that space is infinite, and yet there is a boundary to this infinity that cannot be crossed.

Then again you can view this picture as the flattened projection of a sphere, in which the center is the north pole and the circumference is the south pole. The exception is that if you begin from the north pole, you can never reach the south pole, but you can get closer and closer to it.

If you draw this kind of geometry with colors, then the north pole will be white, and the south pole will be black. That type of drawing is called a “color sphere”. White is the full color and black is lacks color, but you can never get pure black because it could never be seen.

So this kind of picture is useful in visualizing the tree with closed spaces which then spawn more closed spaces. And even though you can imagine infinite divisibility you can never reach that infinite division. This applies both to space and time. This kind of space is hyperbolic but if you insist that equal distance is traveled in equal time, then the same thing becomes a sphere. In other words, if you presume that the world is uniform the tree becomes a sphere.

This is the approximate sketch, but it needs formal mathematics (for semantics) in which we are able to represent the branches as parts of the whole and yet separate from the whole. I still don’t understand it well enough but if I do someday I may be able to write that geometry.