Sunday, 1 September 2013

A fascination with fractals

In July 2010, I posted If you knew SUSY in response to an article in Physics World, the magazine of the UK Institute of Physics. At the end of that post, I cautiously suggested:
But the suggestion that information is in some way embedded in the heart of reality is thought provoking to say the least, and seems amenable to an analogical theological expression. However, some care needs to be taken to make sure that that analogical expression does not say something that isn't what the physics itself says - the pioneer to whom James Gates makes reference towards the end of his article , John Archibald Wheeler, for example, links the information-theoretic aspect to the problem of measurement, the measurement (subjectively) determining the reality that has been measured. James Gates own work, being theoretical, seems to me to present an information-theoretic basis that is independent of this question of measurement.
In June this year - that is, pretty much three years on from my original post - a comment on If you knew Susy alerted me to the very real possibility that my post had caught the attention of the author of the original Physics World article. A blog post that does sound very much like mine is referred to in a radio interview broadcast in the United States: Uncovering the Codes for Reality with S. James Gates. You need to scroll quite a way down the transcript to find the reference to (my) blog post. The commentor who made the link writes on it here: Superstring Theoretical Physicist on the Codes of Reality.

What is interesting, in the light of my own post on the subject, is that James Gates acknowledges in the interview just how stunning it was to the team of physicists and mathematicians working on string theory that error correction codes had such a role in the equations of string theory:
... the kinds of codes we found, which was the most shocking thing for us, is that there's a class of codes that allow your browsers to work in an accurate way. They're called error-correcting codes. We found a role for error correcting codes in the equations of supersymmetry, and this was just stunning for us.
I do appreciate - assuming that it is indeed my blog post to which he is referring - both the way in which James Gates accurately captures the caution of my own suggestion of an analogical theological expression of  the idea that information is embedded in reality and the way in which he responds to that suggestion:

...if the equations of fundamental physics are based on information theory and essentially information theory is at the very center of string theory, how did it get there? And his implication is that indeed this is something for theologians to contemplate. You know, that was, again, for me a stunning assertion and it still has yet to be fully studied. But it probably will not be studied by physicists ..
The reason for posting on this now is that the September 2013 issue of Physics World carries an article by Richard Taylor entitled "A fascination with fractals". One aspect of the article is an overview of the history of chaos theory and the fractal patterns that occur in graphical representations of chaotic behaviour. This aspect is not novel, but indicates three components of this area of physics:
(1) The evolution over time of complex physical systems that obey deterministic laws is surprisingly sensitive to the original conditions of those systems - the smallest of changes in initial conditions can lead over time to radically different outcomes, rendering unpredictable behaviours that, in principle, are entirely predictable. Systems showing this type of "chaotic" behaviour range from weather systems to chemical reactions and electronic circuits.
(2) A mathematical formulation based on taking a basic pattern or expression (a "seed") and then using another rule (the "generator") to repeatedly apply the basic pattern towards an overall outcome. Mathematicians were doing this type of thing as long ago as 1861. It parallels the iterative application of deterministic laws typical of the chaotic behaviour described at (1).
(3) A geometric representation in which a shape on one scale was repeated and repeated at smaller and smaller scales to produce patterns that were visually surprising. This was about geometric structures that turn out to be "self-similar" - that is, they look the same when viewed as a whole, and when magnified repeatedly to different scales. When computing power enabled the types of mathematical formulations at (2) to be iterated very many times, the patterns emerging were precisely the visually surprising patterns that we now know as fractal patterns. It was also noticed that many phenomena in nature also displayed these fractal patterns - leaf shapes being one such example. The significance of the coming together of the mathematical formulations (that, in principle, reached back about 100 years) and real examples in the physical world was prompted by the employment of computing power not previously available.
None of this is new to physicists. It does represent another situation where the significance of a mathematical formulation for understanding a range of physical phenomena might well be open to an analogical theological expression, as I suggested in my earlier post with regard to superstring theory.
However, what is novel about Richard Taylor's article is that he discusses all of the above in the context of an encounter between art and physics. This is what is, apparently, termed "action art". The kind of action involved is that of taking a freshly painted canvas, attaching it to a car and then driving from Paris to Nice with the canvas exposed to the (chaotic) behaviour of the weather during the journey. The canvas records the patterns of the evolution of a dynamic system, and has something of the nature of a "traditional" fractal. Another example cited in the article is that of holding a tin of paint with a small hole in both hands, over a flat canvas. As the artist moves their arms and body over the canvas an abstract piece of art is produced. Comparing the difference between the outcomes when this was undertaken by a 5-year old and an adult - the latter having a much more developed sense of balance to adjust as they moved the paint can over the canvas - indicated that the resulting fractal patterns reflected the differences in development in the physiology of balance of the respective artists. The author has also explored which types of fractal patterns are most aesthetically pleasing, characterising this by a quantity called the fractal dimension, that is, by a measure of the balance of coarse and fine structures in the fractal patterns. Mid-range fractal dimension fractals appear to be most aesthetically pleasing - and most stress relieving - leading to them being termed biophilic fractals.
It is the final paragraph of Richard Taylor's article that sparked my interest. The author has both a long standing personal interest in the cultural implications of chaos and fractal patterns, and a more recent professional interest (the article is describing his work across physics, psychology and art). Though he is clearly writing of his own experience in this final paragraph, I do think that he nevertheless indicates another level at which the philosopher or theologian might undertake an analogical reflection as to why a style of mathematical formulation and its geometric manifestation might belong both in nature and in the human person's intuition of culture.
In 1959 physicist-turned-novelist CP Snow warned of the growing rift between the arts and science in influential lecture "The two cultures". In my experience, most people misinterpret Snow's treatise as a declaration that this rift is natural and therefore inevitable. In reality, he was highlighting the need for common language across the arts and sciences to defeat the rift. In my own career, the common language of fractals has allowed me to weave chaotically in and out of art school and physics departments. There really does seem to be a pattern in this unintentional process. I cannot help but thinkg that an underlying model describes how we seek out and explore our creative interests, and that - as in nature - this behaviour is fractal.

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