Building Blocks of Reality ~ Part 3

Turing began to look into why plants and animals develop their unique shape and structure; how is it that a spherical embryo becomes a non-spherical organism such as a human being? He had been inspired by the biologist D’Arcy Thompson’s work, which had showed how a series of qualitative geometrical transformations was capable of mapping the shape of one species onto that of another. Thompson’s work may have allowed for vitalism, defined as “a belief that living organisms are fundamentally different from non-living entities because they contain some non-physical element or are governed by different principles than are inanimate things”; further, that “where vitalism explicitly invokes a vital principle, that element is often referred to as the ‘vital spark’ or ‘energy’ or ‘élan vital’, which some equate with the soul. In the 18^th and 19^th century vitalism was an alternative to Darwin’s explanation of adaption or natural selection and was discussed by biologists who held that life could not be reduced to a mechanistic process".

Turing came up with a mathematical basis for the process of cell, tissue and organ differentiation as an example of self-organisation. He published his findings in a paper called ‘The Chemical Basis of Morphogenesis’ in 1952. It was an era in which scientists remained loyal to natural selection as being the cause of all things and the majority of the general public believed in the presence of a creator God. Through the use of his mathematical models, Turing was able to demonstrate how random chemical fluctuations which are diffusing and reacting in a dynamical system, give rise not to disorderly chaos but to an emergence of structure, pattern and complexity.

Unfortunately, Turing’s paper did not get the recognition that it warranted, in part as a consequence of Crick and Watson’s subsequent discovery of how genetic information may be encoded in DNA and of this seeming to invite a more substantial or credible platform from which to explore the roots of growth and form. It is only in recent years that this gene-centred view of biology has begun to reconnect with Turing’s mathematical and chemical one.

In my previous blog, I wrote that “Cartwright and Littlewood’s contributions were valuable, but it was to be another 20 years or so later before chaotic behaviour would be recognised as vital and integral to all manner of physical systems in the world. The physicist Freeman Dyson has pointed out that true mathematical originality and innovation can be missed until later in time when the initial groundwork for the work has been done. He has said that he remembers being impressed with one of Cartwright’s lectures in 1942 and although could appreciate the beauty and elegance of her discoveries, was unable to pick up on its potential beyond an immediate context in which the work was being applied”.

Perhaps there is an element of ‘seeding’ or preparatory work within the sciences that is a necessary component of being able to recognise an emergent nature or complexity of pattern or relationship. This may in part explain why Turing’s appreciation of pattern and form took somewhat of a backseat to Crick and Watson’s discovery of the double helix. It is interesting to note that some recent studies have been done to show that a focus on building specialist knowledge early on in a person’s career can be valuable, but that as time goes on can become increasingly inflexible and hinder creativity and innovation. This suggests that it would be wise to encourage for more polymath (a person with a wide range of knowledge or learning). In an educational environment which seeks to preserve an historic track record and advocates for demonstrable routes of excellence, as well as a tendency to ‘follow where the money is’, such encouragement might not be forthcoming. It is beneficial then, for a person to be receptive towards and to engage with their own calling, no matter where it might lead them.

Turing had put forward in his paper that “… the system to be considered consists of a number of chemical substances (morphogens) diffusing through a mass of tissue of given geometrical form and reacting together within it.” And, “Such a system, although it may originally be quite homogenous, may later develop a pattern or structure due to an instability of the homogenous equilibrium, which is triggered off by random disturbances.”

Also, “… a mathematical model of the growing embryo will be described … the model takes two slightly different forms. In one of them the cell theory is recognised but the cells are idealized into geometrical points. In the other the matter of the organism is imagined as continuously distributed … with either of the models one proceeds as with a physical theory and defines an entity called ‘the state of the system’. One then describes how that state is to be determined from the state at a moment very shortly before. With either model the description of the state consists of two parts, the mechanical and the chemical.”

Wired magazine has written “At the heart of any Turing pattern is a so-called reaction-diffusion system. It consists of an ‘activator’, a chemical that can make more of itself; an ‘inhibitor’, that slows production of the activator; and a mechanism for diffusing the chemicals. Many combinations of chemicals can fit this system: What matters isn't their individual identity, but how they interact, with concentrations oscillating between high and low and spreading across an area. These simple units then suffice to produce very complex patterns.”

Science magazine has written of Turing’s model: “… this model has yet to gain wide acceptance among experimental biologists. One reason is the gap between the mathematical simplicity of the model and the complexity of the real world … concerted efforts to align theoretical models to real-world systems, however, have begun to bear fruit, pointing to a much broader range of situations in which the general principles underlying the Turing model might apply. Gierer and Meinhardt showed that a system needs only to include a network that combines “a short-range positive feedback with a long-range negative feedback” to generate a Turing pattern. This is now accepted as the basic requirement for Turing pattern formation.”

“… The ability of Turing patterns to regenerate autonomously, even after experimentally induced disturbances, is also important and of great utility in explaining the autonomy shown by pattern-forming developmental processes. In addition, through the tuning of parameters and boundary conditions, the system underlying Turing pattern formation can generate a nearly limitless variety of spatial patterns.”

“The interacting elements need not be limited to molecules, or even to discrete entities; a circuit of cellular signals will do just as well. There is also no need for the stimulus to be provided via diffusion; other modes of transmission can achieve the same end result. Theoretical modelling has shown that a relayed series of direct cell-to-cell signals can form a wave having properties similar to one formed by diffusible factors … we are hopeful that with an increased acceptance among experimental biologists of the principles he first elucidated, we will see Turing’s mechanism take its place as a model for the understanding of spatial pattern formation in living systems.”

Darwin had informed us that pattern is coded for in genes and according to circumstance, may or may not be passed on. There is something about this theory which appears to regard a person as a bystander or passive recipient of genetic coding which nature is using for its own purpose. Turing’s model has at the very least encouraged us to connect with and to explore pattern and complexity and to appreciate that what at first appears as random or chaotic is not something to be feared or disregarded but is an essential component in an emergence of life; a unified field that humanity is very much part of.

At the time that Turing was working on his paper on morphogenesis, a Russian chemist called Boris Belousov was investigating the way that our bodies extract energy from sugars.  He formulated a mixture of chemicals to mimic part of the process of glucose absorption in the body. The solution started out as clear and colourless but as he mixed in the final chemical, the whole solution changed colour before returning to a state of being clear and colourless. Ordinarily, chemicals can react together but don’t return to a prior state without intervention. Even more extraordinary was that the solution began to switch back and forth between being coloured to clear. Belousov repeated his experiment several times and got the same result. He then submitted a paper of his findings to a leading Russian scientific journal. The editor of the journal informed Belousov that his findings were impossible and could not be published as they had contravened the fundamental laws of physics. Belousov was discouraged that his work was not going to be taken seriously and gave up on science altogether, never having encountered Turing’s work.

It is evident now that instead of contravening the laws of physics, Belousov’s oscillating chemicals were a real world example of the type of behaviour that Turing’s equations had predicted. Subsequent experiments have been done by other scientists to show that if a variation of Belousov’s chemicals are left unstirred in a Petri dish, instead of simply oscillating, they self-organise into beautiful structures and patterns. This has been called the Belousov-Zhabotinsky reaction and is recognised as an example of non-equilibrium thermodynamics.

Further, the way that Belousov’s chemicals move as co-ordinated waves is exactly the way that our heart cells are co-ordinated as they beat. Not only are we able to see beyond mathematical models and the abstract, but can now see the formation of patterns of animal skins as well as the very rhythm of cells. Self-organisation has moved beyond the theoretical and into the functionality of the natural world.

Since the days of Newton, the universe has been viewed as a complex and mechanical device which obeys orderly mathematical rules. This gave it a certain level of predictability, particularly if you were able to observe and understand the rules or mathematics of how it was configured to begin with. Physics was viewed as the new ‘crystal-ball’ but with far more credibility of success (as long as the initial measurements were accurate). However, the Newtonian worldview was to have an unexpected consequence, in that the level of confidence and hubris being placed in it was to generate an extreme reluctance to revisit its underlying theory. This meant that if something unpredictable arose in results, it was immediately attributed to an outside force having interfered with an experiment, rather than being internally generated.

One of the principal reasons as to why Turing and Belousov had both encountered inertia in the mainstream scientific community was that for self-organisation to be accepted, the dominant Newtonian worldview had to collapse; this was going to be a struggle in the midst of the 1960s, given all the wonders that science and technology had so convincingly brought to the world.

In my previous blog I had written about Edward Lorenz, who in the 1960s had run a weather simulation and found that subsequent testing of the configuration produced differing outcomes. His contribution greatly influenced the scientific community to look into what was going on. There was a recognition of the phenomenon known as chaos, the meaning of which in science is that a system that is completely described by mathematical equations is more than capable of being unpredictable without any outside interference, which meant that scientists had to take self-organisation seriously.

It is particularly important to distinguish this attribute of there being an underlying geometric form or order in chaos and which can yield unpredictable results, from a widespread misapprehension of chaos as referring to a maelstrom or complexity of phenomenon into which order has to be imposed. Again, this means that even the most basic of rules or equations, completely determined, can have outcomes which are completely unpredictable; even the tiniest difference to a point within a configuration can make a world of difference and generate something unexpected. ‘The butterfly effect’ as it came to be known started to show up across different fields. For instance, mathematical models have been done to show how immeasurably small changes to the rates at which animals reproduced have had huge consequences on their overall population over time, but that the numbers could fluctuate wildly and for no obvious reason.

The Newtonian worldview of assuming that a mathematical equation could predict how a system was going to behave was no longer relevant. One ripple effect of this is that an assumption of simply increasing an amount of computing power and it being able to solve ever more complicated sets of equations is false; just as trusting in an academic institution to fill a mind with knowledge and specialisation in any one subject and assuming that it will yield intelligence and wisdom within the real world is likely to prove just as misleading. Observation makes it impossible to know about everything that is present within a system and with sufficient accuracy so as to remove any behaviour which gives rise to chaotic solutions. The whole notion of a clockwork universe has turned out to be an illusion which was based on nothing but logic and faith.

 
Where does this leave us in being able to determine reality? If chaos is hardwired into every aspect of the world we live in and we can’t with certainty assume that any given input will yield a particular result, does it require for us to live only in the moment, without preparation or planning for the future? The indications are that we can no longer hold certainty of any records of the past, as the trail of data will not prove to be an accurate determination of events as they occurred. If the past is not a precursor of the present or the future, what does it inform us? Are we sure that we know what intelligence is, if it cannot be measured with accuracy? Has the phenomenon of chaos been misunderstood and undervalued and could it turn out to be our greatest teacher?