The Analytic Aspect of Patterns In Nature

A recent post from Brad Dutton on my web page raised a question which I chose to answer and I’m repeating here. He asked: “…I am starting to wonder if there is a standard way to analyze nature. Something that might even be like a software algorithm. So your analytic aspect is what interests me. Do you have a section strictly to do with the analytic aspect ?”

I answered, in part, as follows:

Until recently, Western science has taken the worldview that any knowledge can be gained by breaking something down to its lowest common denominators and examining same by predictions using mathematics. The process is called “reductionism”. It has resulted in many “mathematical laws” that attempt to predict the actions of components (Newton’s law, etc.etc.). In fact, most Patterns in Nature books that I’ve read (typically written by mathematicians or their advocates) insist that patterns can be described through mathematical laws.That is a very incomplete point of view.

For centuries, a different view of nature has been held by the Confucian “Li”. A very good explanation can be viewed at:
http://liology.wordpress.com/category/chinese-thought/the-li-series/.

The Li says that nature is described by organizing principles rather than mathematical laws. The Li emphasizes a profound truth in nature – that everything is connected. Everything is a complex system. It goes on to explain that nature needs to be described as a set of organizing principles. (not as a set of mathematical laws as proposed by the reductionist paradigm)

We’ve known for some time that the behavior of complex systems cannot be predicted by mathematical laws. They can only be described algorithmically where the final outcome is never predictable or known. This gradual shift to a systematic paradigm by Western science has taken place only in the last 20-30 years. But, if you are looking for a way to analyze nature, I believe you’ll need to start by thinking “simulation” rather than “computation”.

What makes all of this very interesting, Brad, is that a guy named Geoffrey West has been recently suggesting that there is a “unity” in nature (he never dares to couch it using that term) that can be described using a mathematical law that we know as a power law. He suggests that many interrelating natural phenomena, at a systems level, are interrelated by their scaling power law exponent which is some multiple of “1/4”. He goes on to explain that the proposed reason is that natural systems are all connected and require some form of network architecture to be connected. He suggests that these networks are scale-free and have a dimension of “1/4” or a multiple of that. Much of this can be described with the Pareto Distribution which is a power law distribution. None of this is “exact”!! None is predictable. But it may now be explainable.

To quote West: “… biological systems obey a host of remarkably simple and systematic empirical scaling laws which relate how organismal features change with size over many orders of magnitude. These include fundamental quantities like metabolic rate (the rate at which energy must be supplied to sustain an organism) , time scales (like lifespan and heart rate) and sizes (such as the length of the aorta or the height of a tree trunk). It is remarkable that all of these can be expressed as power law relationships with exponents that are simple multiples of ¼ (e.g. ¼, ¾, 3/8) . They appear to be valid for all forms of life whether it be mammalian, avian, reptilian, unicellular or plant-like. These “laws” are clearly telling us something important about the way life is organized and the constraints under which life has evolved. ”

To me, in your search of a way to analyze nature or to organize nature’s “information”, you are dwelling in a very important field. Unlike Western science’s reductionism, however, with West’s ideas you are on a path where your “analysis” would be by examining nature’s organizing principles instead of trying to predict nature through impossible mathematical laws.

In the course of your work, I would be looking strongly at self-organizing systems (emergence), self-similarity (fractals), network theory (particularly scale-free and small-world networks), and scaling (power law growth and change).

Below are some references (to name only a few) that I’ve found useful:

http://complexityblog.com/papers/aaron/Amaral-Complex%20Networks.pdf

http://research.yahoo.com/files/w_ARS.pdf

http://www-personal.umich.edu/~mejn/courses/2004/cscs535/review.pdf

http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html

http://www.npr.org/templates/story/story.php?storyId=12877984

Google “Geoffrey West” where there are at least two of his lectures on YouTube where he talks about the idea of a universal scaling (power law) exponent. West is the “man” on this subject.

http://www.alliancemagazine.org/en/content/interview-geoffrey-west

http://video.google.com/videoplay?docid=7108406426776765294#

http://people.ccmr.cornell.edu/~ginsparg/Phys446-546/gbwscl99.pdf

Google “Strogatz”, “Duncan Watts”, or “Albert-Laszlo Barabasi” for all sorts of material on netwoks.

http://www.ted.com/talks/lang/eng/steven_strogatz_on_sync.html

http://en.wikipedia.org/wiki/Self-organization

Many more. But, this should give you a start.

My name is Bill Graham. As a Marine Biologist who has worked in the US and Mexico for 30 years, I am a student of Nature, a teacher, a researcher, and a nature photographer. Through my work, I have acquired an ever growing passion for how everything in Nature is connected. Today, I travel extensively contemplating about, writing about, and photographing Nature’s connections. I also work with conservation projects in the USA and Mexico and mentor talented youth.

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