How did we get here? The power to be unpredictable; “there is a strange and unexpected relationship between order and chaos…” a direct quote from a BBC series “The Secret Life of Chaos” begs the question is it mathematically plausible? Patterns that remain hidden from most of us are obvious to a select few is the premise of today’s blog.
I now have to add a new book to review and internalize: Alan Turing: The Enigma by Andrew Hodges. Turing spent a great deal of time immersed in the enigma of Bletchley Park during WWII. Other scientists that followed had discoveries that complemented theories of Turing a genius who saw patterns when others saw none.
Morphogenesis – from the same to different; a self organization: how and why? It happens in life as it forms from a single cell and it is happening constantly all around us. A definition of morphogenesis gives us clues: n. Formation of the structure of an organism or part; differentiation and growth of tissues and organs during development. Is there really a simple mathematical basis for this living process? Is there some morphogenic rule that dominates and governs the formation of all organisms and systems? From the few, many.
Further investigation is required:
The Secret Life of Chaos (Part 2/6) –
Alan Turing seems in many ways like Nikola Tesla; neither man completely understood all of what they proposed or investigated but each seemed to have an innate understanding that escapes detection or in fact is not understood. Great thinkers have the talent for discovery that goes beyond simple insight. They see the patterns or deeper relationships that govern things. These relationships are the why and the what of the way things are. To these savants what appears complicated is quite simple; they are hypersensitive to the complex interconnectivity of things.
Turing and Tesla experienced tragedy and disasters that ended their contributions to science. If circumstances had been different for both it is possible that our understanding might be closer to what we still seek. Structures, shapes and systems out of a morphogenic self organization of the seemingly unrelated are the basis of a predictability of science and creation we search for but still not have fully discovered. Although man has stumbled and been slowed down by setbacks like these and an over reliance on other specific theories as universal it will not stop the progress toward answers and resolutions.
With mathematics we expect and demand predictability. From 3 of 6 “The Secret Life of Chaos”: “a system that is completely described by mathematical equations is more than capable of being unpredictable without any outside interference whatsoever.” Although this might be thought to throw a monkey wrench into the works, if the theory is correct, it helps explain rogue waves and other anomalies that have no apparent rhyme or reason. It is possibly due to the fact that what we think was completely described by mathematical formulas had a few things missing from the calculations. Possibly “The Butterfly Effect” is a concrete fact that affects systems to give such ‘random’ unexpected results.
“The butterfly effect is a metaphor that encapsulates the concept of sensitive dependence on initial conditions in chaos theory; namely that small differences in the initial condition of a dynamical system may produce large variations in the long term behavior of the system. Although this may appear to be an esoteric and unusual behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position. The butterfly effect is a common trope in fiction when presenting scenarios involving time travel and with "what if" cases where one storyline diverges at the moment of a seemingly minor event resulting in two significantly different outcomes.” (http://en.wikipedia.org/wiki/Butterfly_effect)
There is a hitch in the giddy up of the progression of this BBC presentation and to go further along it is necessary to switch over to the “3 of 7” progression (instead of the “3 of 6”) of the links at http://www.youtube.com/watch?v=QyTs0yYKXZI&NR=1 (ad infinitum).
Order and chaos are so deeply intertwined that it is almost beyond our comprehension; to the point that chaos is the true natural relationship of things instead of ordered patterns. We need to stop trying to concentrate on the few patterns that we see reflected in our interpretation and measurement of things as the “be all end all”. Life is one huge feedback loop, a picture within a picture within a picture as small changes are radically amplified to demonstrate the ‘Butterfly Effect’ so the seeming chaos that emerges is not really chaos at all. It is the natural order of things. Because of morphology and self organization the chaos that emerges transmutes into the patterns we eventually observe. The patterns and the chaos are really the same thing differentiated only by where they lay on the continuum of the spectrum where they are. It is our understanding of the process of how this happens and why that it limited. Is it possible to give up the idea that opposites attract because they are different and instead adopt the possibility that opposites attract because they are on in the same?
We still try to oversimplify things into a two dimensional world or continuum when our existence and the world are multidimensional and far more complicated than only two, three or even four or more. Life is not a compilation of straight lines, circles or regular known shapes. There is a mathematical principle that underpins this (as much as we can identify it) - the simplicity of things: the Principle of Self Similarity. We have moved beyond the ancient Greeks and no longer believe the entire universe is composed of earth, air, fire or water. It took Aristotle, a philosopher to add a fifth element Aether. It took science to dispel these theories dating to the Babylonians only about 38 centuries to narrow it down to only one; we now believe that all things are composed of energy.
I am certain this is only a part of the puzzle as Newtonian Physics is only a small part of the whole. Like Newtonian Physics which was adequate as a part of the solution but not the complete one, what we know is only fractal. As a child I spent hours wondering if we (humans and our systems) were but electrons in some larger system, a small parasite on a larger animal. Infinity and our known world are all elements in a “Mandlebrot set”. http://en.wikipedia.org/wiki/Mandelbrot_set - “When computed and graphed on the complex plane the Mandelbrot set is seen to have an elaborate boundary which, being a fractal, does not simplify at any given magnification.”
From the simple to the complicated without any conscious thought; morphogenic self organization of the seemingly unrelated pieces parts smaller than atoms to conscious thought - this is quite an achievement. It is an evolution just because that it is what happens regardless, at least in our universe as we know it.
It amazes me how much a Mendlebrot Set fractal graphic representation looks like anything from a DNA molecule to a black hole.
Mandlebrot Set Zoom
© 09.27.2010 stevendphilbrick SR+ DakotaDawg
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