The Froth Line – Walking the Planck
There comes a point where clear, logical and pure scientific exploration for fundamental truth arrives at a Venn intersection with metaphysics and produces insight that simply surpasses all mathematical understanding.
The law of unintended consequences
In the 1970’s, when computers were getting cheaper and more powerful (Compared to my Curta), along came Benoit Mandelbrot who said that things typically considered to be a mess or chaotic, like clouds or shorelines, actually had a degree of order. My interest was purely selfish at the time, and that was to figure out how to develop a stock trading application centered on his and other concepts around Fractals and Chaos to make money.
While I was writing the trading application, the meme I used for development was to look at the boundary of the Fractal set as a Froth line – the chaotic place where land and sand mix, where all bets are off for any given element in transition. Questions like “will a chip in the froth end up on shore, or back in the sea after ‘n’ cycles”, “will it hang around in the froth line forever or not”, and “is there a ‘why’ that we can quantify and count on”. You get the idea.
So here we are, Forty years later, with more time and less self; the graphics and logic that Benoit used to create and display his Fractal Mandelbrot set are old friends, but no longer attached to money. We are now free to explore without agenda or purpose – a holiday from education, the science is settled, and must haves. Unintended consequences. Who knew?
The Fractal Froth Line
Metaphorically, the froth line separates the sand from the sea as the interface where the waves lap or crash along the shoreline intersection. Up on the beach, there is no doubt that it’s sand. Out in the water, it’s clear that’s the sea.
The Lawyer in you will hate this next part related to scale: At the intersection, where does the sea end and the sand start? To test your definition, how long is the shoreline? You may well answer that it depends on your legal definition of scale and the elemental unit of dimension.
For the Fractal Froth line, you’ll have a problem. Scale is meaningless. Every piece of shoreline is infinite at every scale. No matter how far you zoom in, it’s still shoreline in full detail, and its DNA still looks familiar and recognizable. You have no idea if you are at Mile 0 or Mile 10 million, and the shoreline is just as complex to infinity. An Ant and an elephant walking the same shoreline on their own relative scale will tell similar stories to their offspring about the scenery and mapping of the bays and inlets along the way.
Walking the Planck
No, that’s not a typo. Read on.
To recap, driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. There are things about the universe we inherently know that seem a bit strange. It is essentially chaotic, full of surprises, of the nonlinear and the unpredictable. Without the Chaos and (strange and otherwise) attractors, it can’t evolve. At the same time, Fractal patterns are extremely familiar, since nature is full of fractals. For instance: coastlines, mountains, rivers, clouds, trees, plants, Climate, and so on. Geometrically and mathematically they co-exist in between our familiar dimensions.
The Fractal Recursion loop logically sets up the concept of time. You need to wait for the output from the underlying algorithm (or DNA) to feed into the next iteration at the lowest quantum level in order to build the next step. So, is there a limit in our universe as to how fast any Fractal system can propagate to the next iteration in time?
To think on that, take a moment to look at Planck’s constant on this side of the quantum limit of our understanding at the frontier of the known universe, where quantum uncertainty begins.
In physics, the Planck time is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length. Within that Planck timeframe and distance, we as observers can’t be sure what’s happened in the gap, or what the Master Magician is pulling off behind the scene.
Werner Heisenberg figured that out in 1927 and published the Heisenberg uncertainty principle. Thus, our Fractal Natural Universe is essentially in a quantum stop-frame space-time movie, one Planck frame behind the unfolding now which gets pre-set in the Planck-width bow wave gap running in front of the universe, engaging and collapsing the endless quantum possibilities that unfold as the realized next recursive block of our particular fractal universe.
If you think this is nuts, (which well you might) know that the current search for the laws of physics, valid at the Planck length is a part of the search for The Theory of Everything. It seems possible that that the Planck gap has enough room for it all, recursively setting the hard limits of our physical space-time universe to this side of the gap, one step behind the now. So close logically, yet eternally out of touch to the mind’s eye. The Science is never settled
-the old man
There is a crack, a crack in everything / That’s how the light gets in – Leonard (Planck) Cohen 🙂