You're catching on! I thought I was clever thinking up "Mandelbrot relativity" but I put that phrase in a "google" search and found not everything I've been coming up with lately is entirely new. But there seems to be enough that could be new so I look forward to writing it up.
"How long is the coast of Britain?" asks Benoit Mandelbrot. Depends what length yardstick you use.
Measure with a giant measure; and you might miss out some smaller headlands and bays. Use a shorter yardstick, and you go in and out the terrain in more detail, getting a longer total length! (Has a great deal to do with explaining Dick's discovery about the relativity of how we "measure" (know) reality.)
Walk it and use your stride as measure, and you wander in and out a lot of little curved sections.
Hire a mouse to walk it, and you end out with even longer length from the measuring of his walking in and out each moderate-size boulder.
Hire a microbe, and you get a very long coast length from including all the ins-and-outs of every pebble.
So the length of the coast of Britain is called, by Mandelbrot: a fractal curve; its length increases as you use smaller yardsticks! But the measured length of the coastline increases in fractions of dimension, actually called fractal dimensions. (I would suggest the so-called expansion of the universe and associated symmetry-breaking works similarly).
Dick's paper is about yardstick relativity. The physics equations approximate his partial differential equation probably for the same reason that Richardson and Hausdorf and Mandelbrot give us an equation that gives an approximate measure in whatever yardstick you use for the originating-dimension you use it, where you can compare different coastlines because the formula that I haven't got with me here (this is off the top of my head impromptu without my notes)
gives an approximate measure independent of the measure-reference frame.
Mathematics itself is like a mandelbrot set; you can view all numbers as fractal dimensions of any one number. Probability wave functions, gravity, collisions of particles, etc. etc. all seem to fall out when you analyse this.
What I call "Three-way-jump theory" relates to the basic: 1 + 1 in new 1 dimension. A wave-particle is a particle in one dimension but a wave spread among two (or more) dimensions (can be fractal dimensions).
No problem explaining double slit experiment, Schrodinger's cat, quantum mechanics, Einstein Relativity, superstrings, M-theory, etc. etc. it would seem. We are effectively "Mandelbrot holograms" of our past-future pattern-matches; thus your past does change constantly in so far as it gets new fractal dimensions of pattern-matches of past-future added to it.
Like we are a wave moving through our holistic self; where everything looks fractal from any point we regard as the present. (Hence "mandelbrot relativity" bit like Penrose's 'phase space').
You advance via quantum agreements in past-future cells. Lots to explain , just a brief survey there. |