COMPLEXITY EXPLAINED: 17. Epilogue
In this concluding part of the series on complexity I recapitulate the basic ideas about complexity, and then revisit the questions about the origin of the universe we live in, the origin of life, and the origin of consciousness. The bottom line is that the word ‘origin’ should be replaced by ‘evolution.’ And what evolves with time is complexity, resulting in the emergence of new properties or phenomena which could not have been anticipated.
17.1 Recapitulation of the Main Ideas in Complexity Science
With reductionism comes the conviction that a court proceeding to try a man for murder is “really” nothing but the movement of atoms, electrons, and other particles in space, quantum and classical events, and ultimately to be explained by, say, string theory.
Stuart Kauffman (2006)
- Classical microscopic laws of physics are characterized by determinism and time-reversal symmetry. Determinism means that if the position and the momentum of a particle are known at any instant of time, then the laws of classical mechanics determine the position and momentum at all instants of time, both future and past. The success of space missions is an example of the applicability of the deterministic equations of motion to simple (or simplifiable) systems (in contrast to complex systems). Simple systems have the linearity feature: The inevitable imprecision in our knowledge of the physical parameters of such a system does not lead to disastrous or runaway consequences in our predictions about the mechanics of the system.
- By contrast, chaotic systems, though deterministic, are governed by nonlinear equations of motion, and consequently we cannot predict their behaviour far into the future. Chaos is an example of the fact that determinism does not necessarily imply predictability.
- The familiar second law of thermodynamics is a striking example of emergence in complex systems. The laws of mechanics (classical or quantum) applicable to any microscopic particle comprising a macroscopic system are time-symmetric; but the macroscopic system has the emergent property of time-asymmetry, embodied in the fact that the entropy of the system cannot decease with the passage of time.
- In the macroscopic world, we associate the direction of increasing entropy with the direction of increasing time. Entropy is a measure of disorder, and negative entropy or negentropy is a measure of information.
- The emergence feature of complex systems makes the reductionistic approach to understanding complex natural phenomena quite inapplicable. But that does not mean that we should swing to the other extreme and adopt only a holistic approach. It is important to understand the distinction between chaotic, random, and complex systems. In a chaotic system there is determinism without predictability. Order and disorder coexist in a complex system. And randomness means a complete lack of structure or order (‘algorithmic irreducibility’). I shall be addressing these issues in a forthcoming book.
- Complex systems have a hierarchical structure of complexity. The structure at one level leads to the next level of complexity, and each level of complexity often results in the emergence of new laws.
- The new laws do not violate any of the laws operating at the lower levels of complexity. There is no question of ‘downward causality’ because, deep down under, everything interacts with everything else and we only have interactions, rather than actions and reactions (or causes and effects).
- Physical laws, though always valid, are not always convenient or relevant for explaining, say, the chemical behaviour of a system. Similarly, biology is not always conveniently understood in terms of the laws of chemistry or physics alone. Nevertheless, if we consider only neighbouring or contiguous levels of hierarchical complexity, a reductionistic or constructionistic approach can often be useful.
- Flow of energy through an open thermodynamic system can take the system so far away from equilibrium that there is a bifurcation in phase space, resulting in self-organization. Such bifurcations can occur repeatedly in a complex system, and there is no way to predict as to which branch of a bifurcation will be chosen, because the choice depends on random fluctuations at the moment of the bifurcation. This fact lies at the heart of (unpredictable) emergence of novel features during the time-evolution of a complex system.
- Simple local rules can lead to the emergence of complex overall patterns, behaviour, or properties. This is how swarm intelligence emerges.
- The flow of energy through a complex system results in a build up of the information content of the system. A state of complete order, as also a state of complete randomness, has low information content and a low degree of complexity. The more interesting complex systems usually fall in-between these two extremes.
- Complexity thrives best at the ‘edge’ between order and disorder. Complex adaptive systems tend to self-organize so as to inch towards this so-called ‘edge of chaos.’
- Per Bak’s notion of self-organized criticality provided important insights into how and why complex systems move to a state at or near the edge of chaos.
- Positive feedback is an important mechanism of how self-organization can occur. However, it is not the only possible mechanism for this. Often, chain reactions achieve something similar. And negative feedback provides the necessary antidote for maintaining a state of optimal balance and perpetual novelty.
17.2 How did the Universe Emerge out of ‘Nothing’?
Everything existing in the universe is the fruit of chance and necessity.
Diogenes Laertius IX
This is the toughest of the three questions I revisit in this article. I wrote about cosmic evolution in Part 7 of this series, but want to make up here for some important omissions.
What happened immediately before the Big Bang? The answer to this question is important for understanding some observations in astronomy. How can energy be created out of nothing, and how is it continuing to increase as the universe expands? I quoted Seth Lloyd (2006) in Part 7: ‘Quantum mechanics describes energy in terms of quantum fields, a kind of underlying fabric of the universe, whose weave makes up the elementary particles – photons, electrons, quarks. The energy we see around us, then – in the form of Earth, stars, light, heat – was drawn out of the underlying quantum fields by the expansion of our universe. Gravity is an attractive force that pulls things together. . . As the universe expands (which it continues to do), gravity sucks energy out of the quantum fields. The energy in the quantum fields is almost always positive, and this positive energy is exactly balanced by the negative energy of gravitational attraction. As the expansion proceeds, more and more positive energy becomes available, in the form of matter and light – compensated for by the negative energy in the attractive force of the gravitational field.’
Apart from quantum-mechanical effects and the gravitational interaction, other dominant factors in the early stages were the immensely high temperatures and pressures. In the beginning it was all radiation, and no matter. And the energy content and the information content were very small. The energy content and the information content built up as the universe expanded and extracted more and more energy out of the underlying quantum fabric of space and time.
According to the current theories, the energy grew very rapidly in the beginning (by a process called inflation), and the amount of information grew less rapidly. Immediately after the Big Bang there was a hot plasma of elementary particles, which expanded and cooled very quickly. In fact, the first structures got formed within a fraction of a second after the explosion. Protons and neutrons were formed from quarks.
One minute after the Big Bang, helium nuclei were formed. Soon, a full 24% of all matter was in the form of helium nuclei. Radiation interacts primarily with ions (rather than atoms).A few tens of thousand of years after the Big Bang, the first electrically neutral matter was formed, when protons and electrons combined to form atoms of hydrogen. This marked the separation of electrically neutral matter from radiation. On further cooling, gravitational effects became more and more important, as electrically neutral atoms could now clump together because of gravitational attraction. This clumping went on to produce galaxies ultimately.
There are gaps in our understanding of how structure arose out of what was a structureless field of radiation in the beginning. In particular, we do not yet know whether there are forms of matter other than what we already know. Even as early as in the 1930s, it was known that gravitational effects in large galactic clusters are much higher than what can be expected from the known amount of matter there. Apparently, there is another, unknown, form of matter that is a full 90% of all matter, as indicated indirectly by the gravitational effects. It is called dark matter because we are unable to observe it; we infer its existence only through its gravitational effects.
Perhaps neutrinos have something to do with this dark matter. Or perhaps some still undiscovered elementary particles, including some very heavy (but unobserved) ones, may be involved. These particles might have got formed in the very hot conditions soon after the Big Bang.
The reasons for the occurrence of the Big Bang are still a puzzle. Another puzzle in modern cosmology is the fact that matter and the cosmic background radiation are distributed quite homogeneously throughout the observable universe. Consider a galaxy that is 5000 million light years away today from our galaxy, namely the Milky Way. When the universe was, say, just one million years old, it (the universe) was only a thousandth of its present size. Therefore at that time the two galaxies must have been 5 million years apart. But since the age of the universe at that time was only one million years, not enough time was available for the two galaxies to have exchanged signals of any kind (assuming that nothing travels faster than the speed of light). There could not have been any kind of communication between the contents of one galaxy and the other. So how did the homogenization of the shock waves associated with the Big Bang occur?
There is general agreement that the emergence of matter from the early radiation field was a kind of symmetry-breaking phase transition. This can be likened to the phase transition from liquid water (which is homogeneous, or translation-invariant) to ice (which is not translation-invariant). The radiation field was translation-invariant, and the appearance of matter broke this translational symmetry. A hypothetical field called the Higgs field has been introduced in cosmology to understand these phenomena. This field breaks the symmetries of the interactions among the elementary particles, and gives the particles their mass.
The Higgs-field theory predicts the existence of a cosmological constant. Such a constant was indeed introduced much earlier by Einstein, and then withdrawn because it amounted to introducing into his theory of gravitation a parameter ‘by hand,’ with no theoretical justification. Einstein’s cosmological constant was intended to provide the repulsive force needed to compensate for the attractive force of long-distance gravity. In other words, if gravity could be switched off, Einstein’s cosmological constant would result in a rapid inflation of the universe. But once it was known that the universe is expanding, it became unnecessary to try to counterbalance the attractive gravitational force.
The Higgs field results in the existence of a new cosmological constant, which turns ‘empty’ space into a space that has an energy content. The problem at present is that the predicted cosmological constant has too large a value for a correct understanding of the observed cosmic evolution. It is believed that perhaps the Higgs cosmological constant had a large value right after the Big Bang, resulting in a violent and very rapid expansion (or inflation) of the universe. At a certain stage of this inflation, a cosmic phase transition occurred, which freed enormous amounts of energy (rather like the release of latent heat when steam condenses to liquid water). In a way, this energy flash or Big Bang marked the actual birth of our cosmos. After this prelude of inflation and cosmic phase transition, the normal (much slower) expansion of the universe set in, and has continued ever since.
During the inflation prelude, the universe grew extremely rapidly from a volume smaller than that of the nucleus of an atom to the size of a tennis ball. If we associate the Big Bang with the moment at the end of the (very quick) inflation episode, certain cosmological mysteries get resolved. When the universe was just the size of a tennis ball, regions that are far apart today could have been in contact then, thus resulting in the observed homogenization of the universe.
This new model of the Big Bang (i.e. a phase transition after the inflation prelude) answers a few additional perplexing questions as well. The model implies that the observable cosmos is a part of a much bigger system. Our Big Bang occurred in a certain region of the cosmos, leaving other regions untouched. More Big Bangs can keep occurring in other regions of the cosmos, opening up the possibility of parallel universes. There is thus a multiverse, rather than a universe.
In a multiverse, Big Bangs occur repeatedly, and each resulting universe has values of fundamental constants that just happen to be what they are. The universe we live in happens to have values of fundamental constants that make our emergence and existence possible. Otherwise we would not have emerged and evolved. This brings us to the much-maligned anthropic principle. The principle states that: The parameters and the laws of physics in our universe can be taken as fixed; it is simply that we humans have appeared in the universe to ask such questions at a time when the conditions were just right for our life. I have not included a discussion of this principle in the present series because it is covered in another article (on biocentrism) on this website, which I coauthored with Ajita Kamal.
Although there is no law saying that the degree of complexity of the universe must always increase, an empirical observation is that it is increasing, and increasing at an exponential rate. There can be some local decreases in complexity (there is even an anthropocentric angle to this issue), but the overall complexity of our universe is increasing. This has been explained in terms of the fact that our universe is expanding, and thus getting a continuous supply of free energy or negentropy (cf. Part 7).
But how long will the universe continue to expand? Did time begin? Will time end? Here are three likely answers given by the noted cosmologist Paul Frampton in a recent (2010) book:
Most likely: The present expansion will end after a finite amount of time, the universe will contract, bounce and repeat the cycle. In this cyclic universe, time had no beginning, and will have no end.
Next most likely: The present expansion will end after a finite time in a Big Rip. Time began in the Big Bang some 13.7 billion years ago, and will end some trillion years in the future.
Least likely: The present expansion will continue for an infinite time. Time began 13.7 billion years ago, and will never end. In his book Prof. Frampton challenges this prevailing ‘conventional wisdom.’
17.3 How did Life Emerge out of No-Life?
It was discovered that RNA molecules can not only carry genetic information, but act as enzymes, speeding chemical reactions. Work is underway to create an RNA enzyme, or ribozyme, that can copy any RNA molecule including itself. The probability that an RNA molecule can catalyze a given reaction is roughly 10 divided by 10 raised to the 15th power. It is conceivable that such a molecule can arise by chance, but it faces the difficulty that were it to copy itself and make errors, those error copies would be more error prone than the initial copy, and a run away error catastrophe might ensue.
Stuart Kauffman (2006)
As discussed in Part 10, it is not easy to define life. One consequence of this situation is that life must have emerged very very gradually. Thus it is meaningless to try to identify a point of time which marked the ‘origin’ of life on Earth. As discussed in Parts 8, 9, and 12, a whole lot of chemical evolution of complexity preceded the emergence of what we intuitively understand as life.
I discussed only two models of the likely origins of life in Part 12. For a more comprehensive description, please see the 2006 online article by Stuart Kauffman.
I described Kauffman’s work on autocatalytic sets of molecules in Part 9, and his RBNs (random Boolean networks) in Part 12. He has been emphasizing the importance of the self-organization feature of complex systems in the evolution of biological complexity. He uses the phrase ‘order for free‘ for this non-Darwinian evolution of complexity:
“While it may sound as if ‘order for free’ is a serious challenge to Darwinian evolution, it’s not so much that I want to challenge Darwinism and say that Darwin was wrong. I don’t think he was wrong at all. I have no doubt that natural selection is an overriding, brilliant idea and a major force in evolution, but there are parts of it that Darwin couldn’t have gotten right. One is that if there is order for free – if you have complex systems with powerfully ordered properties – you have to ask a question that evolutionary theories have never asked: Granting that selection is operating all the time, how do we build a theory that combines self-organization of complex systems – that is, this order for free – and natural selection? There’s no body of theory in science that does this. There’s nothing in physics that does this, because there’s no natural selection in physics – there’s self organization. Biology hasn’t done it, because although we have a theory of selection, we’ve never married it to ideas of self-organization. One thing we have to do is broaden evolutionary theory to describe what happens when selection acts on systems that already have robust self-organizing properties. This body of theory simply does not exist.” (Chapter 20, “Order for Free”, The Third Culture, 1995).
Kauffman’s work brings out the inevitability of the emergence of life. The prevailing conditions were such that life just had to appear because of the relentless evolution of complexity. A knowledgeable alien would be very surprised if life had not emerged here. Thus, the ‘origin’ of life is the easiest of the three questions I am revisiting in this article. There is nothing miraculous or supernatural about the origin of life.
17.4 How does Consciousness Arise?
Meanwhile, my approximate theory is that mind is acausal, quantum mechanics is acausal on the familiar Born interpretation of the Schrödinger equation, (to the grief of Einstein), that consciousness is due to a special state where a system is persistently poised between quantum and classical behaviour, that the emergence of classical behaviour in the mind-brain system, perhaps by decoherence, is the “mind making something actual” happen in the physical world, and – big jump – that consciousness itself consists in this quantum coherent state as lived by the organism. This is a long jump, but not impossible. I don’t even think it is stupider than other theories of consciousness, and may be true. Whatever the case, consciousness is ontologically emergent in this universe.
Stuart Kauffman (2006)
The problem with the word ‘consciousness’ is that it is what Marvin Minsky calls a ‘suitcase word.’ It stands for a whole set of processes. Naturally, it is difficult to discuss it in a scientific manner. From the complexity perspective, consciousness arises from swarm intelligence, the swarm here being that of neurons. In a large swarm, local rules can lead to astonishingly complex behaviour and novel phenomena and sensations.
The self-referential nature of consciousness is what makes it look so puzzling. But the fact is that, long ago (in 1931), Kurt Gödel shook the foundations of mathematics by proving that even such an innocuous thing as the formal system of positive integers can have self-referential properties. Self-reference and formal rules can make systems acquire meaning, despite the fact that each constituent of the system in without meaning.
Nevertheless, there are difficulties galore:
‘All the limitative theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally. Gödel’s Incompleteness Theorem, Church’s Undecidability Theorem, Turing’s Halting Theorem, Tarski’s Truth Theorem — all have the flavour of some ancient fairy tale which warns you that “To seek self-knowledge is to embark on a journey which … will always be incomplete, cannot be charted on any map, will never halt, cannot be described.”‘ (Douglas Hofstadter 1979)
The debate on consciousness is not likely to end anytime soon.
The idea of writing this series of articles was suggested by Mr. Ajita Kamal, Editor of Nirmukta. Ajita has been of great help throughout, and made several useful suggestions.
My Ph. D. student Indranil Bhaumik was immensely helpful by sending me several important books in pdf format.
Ms. Malgorzata Koraszewska took the trouble of translating these articles into Polish and publishing them at www.racjonalista.pl. She has done a thorough job indeed, consulting experts when in doubt about the exact Polish equivalent of a technical word in English. The Polish versions of these articles were discussed in a much more lively way than the originals in English. Unfortunately I could not take part there because of the language barrier, but was happy to answer some questions forwarded to me by Malgorzata.
I not only enjoyed writing these articles, it was also a great learning experience for me because of the comments and questions posted on nirmukta.com, as also on richarddawkins.net and some other websites which picked up some of these articles. I also received a lot of feedback from scientists-friends through private emails.
I shall feel amply rewarded for the time and effort I have put into the writing of these articles if I have succeeded in inducing even a few of the readers to shun all kinds of irrational belief systems.
Science is rational. Science is fun. Science has both a humbling and a liberating influence on those who have imbibed the spirit of the scientific method. The skepticism inherent in the scientific method, and its emphasis on making only falsifiable statements, are essential tools for acquiring knowledge we can trust with a high degree of confidence.
Nature is highly creative, and this creativity comes from the relentless evolution of complexity. A flower is a piece of art, and complexity science tells us how this ‘natural art’ can arise (emerge) without the need for the existence of the artist or the creator.
Dr. Vinod Kumar Wadhawan is a Raja Ramanna Fellow at the Bhabha Atomic Research Centre, Mumbai and an Associate Editor of the journal PHASE TRANSITIONS. All parts of Dr. Wadhawan’s series on Complexity Explained can be found here.