The mystery of length?

An incredibly deep zoom of the  Mandelbrot set. If you have a 15.6" screen then after 1 minute the set is the size of the known universe.

This is a key feature of reality that it has scale and we can zoom in and zoom out. As a result we need to chose our measurement standard, that is our scale. For distance we chose the French Metre. How big is the Metre?

The largest known distance is the universe estimated at 10^27m and the smallest theoretical distance is the plank length at 10^-35m so we're quite big when you look at the whole picture. But we don't see the whole logarithmic picture we see it linearly which is where scale comes in.

Once you chose your scale then you step around at this scale and miss all the details. At the start of the set above very nearly all that will be revealed is within a single pixel. Without a lot of computing power you will only ever see this high level. I have tried before and once it gets below machine size 64bit parameters you must virtualise arithmetic which gets very time consuming. Few people every develop a very short scale for stepping around the Mandelbrot set and so most of it is hidden. Exactly as the world was before the invention of the microscope and the telescope.

For some unfathomable reason while the world is just a single entity, we experience it at a scale. We experience it like a fractal into which we can zoom in and out. This is the deep mystery of length. More thought to do...

We might think that the best scale is the middle. But the Manelbrot zooms out infinitely in both directions. This means that any scale you chose for the Mandelbrot has an infinite zoom in both directions. There is no middle. Just as Zero is not actually the middle of the number line so 10^0 = 1 is not a special level of zoom for the Mandelbrot (zoom scales are exponential). Yet the "interesting stuff" does start at this scale with imaginary numbers of the order of 2 and below. Likewise what is special about the scale of humans? 0.1mm is the middle scale of the known universe. Is there something special about this level? Or if the universe scales infinitely in all directions (which would break current theories) perhaps there is no middle size and however large you are things can ge infinitely larger of smaller.