Most people don't need to be persuaded that the physical world is bewilderingly complex. Everywhere we look, from molecules to clusters of galaxies, we see layer upon layer of complex structures and complex processes. The success of the scientific enterprise over the last 300 years largely stems from the assumption that beneath the surface complexity of the universe lies an elegant mathematical simplicity. The spectacular progress in particle and atomic physics, for example, comes from neglecting the complexity of materials and focusing on their relatively simple components. Similarly, the amazing advances in cosmology mostly ignore the complications of galactic structure and treat the universe in a simplified, averaged-out, approximation. Such simplified treatments, though they have carried us far, sooner or later confront the stark reality that many everyday phenomena are formidably complex and cannot be captured by traditional reductionist approaches. The most obvious and important example is biology. The techniques of particle physics or cosmology fail utterly to describe the nature and origin of biological complexity. Darwinian evolution gives us an understanding of how biological complexity arose, but is less capable of providing a general principle of why it arises. “Survival of the fittest” is not necessarily “survival of the most complex”.

THE BIG PICTURE

One of the gloomiest scientific predictions of all time was made in 1852 by the physicist William Thompson (later Lord Kelvin) (Thompson, 1852). From a consideration of the laws of thermodynamics, and the nature of entropy, Thompson declared that the universe is dying. The second law of thermodynamics, which had been formulated a few years earlier by Clausius, Maxwell, Boltzmann and others (see, for example, Atkins, 2010), states that in a closed physical system, the total entropy – roughly a measure of disorder – can never decrease. All physical processes, while they may produce a fall of entropy in a local region, always entail a rise of entropy somewhere else to pay for it, so that when the account is tallied, the total entropy will be seen to have risen. Applied to the universe as a whole, the second law predicts an inexorable rise of the overall entropy with time, and a concomitant growth in disorder. The one-way slide of the universe towards total disorder – popularly known as the heat death of the universe – imprints upon it an irreversible arrow of time. One need look no further than the Sun, slowly burning through its stock of nuclear fuel, radiating heat and light irreversibly into the cold depths of space, to see an infinitesimal contribution to the approaching heat death. Eventually its fuel will be exhausted, and the Sun will die, along with all other stars when their time has come. The sense of futility and pointlessness that the dying universe scenario engenders in some commentators was eloquently captured by Bertrand Russell in his book Why I Am Not a Christian (1957) and has been echoed in recent years in the writings of Peter Atkins (1986).

It might seem obvious that the universe becomes more complex over time. After all, isn't a gas cloud consisting only of hydrogen and helium a few seconds after the big bang simpler than a cloud of hydrogen, helium, carbon, silicon, and oxygen two billion years later? Aren't the dynamics of a system at the level of particle physics simpler than the dynamics of a group of interacting cells?

As intuitive as these proposals are, we don't currently possess an adequate quantitative measure of the increase or decrease in complexity either across cosmic evolution or across scientific disciplines. In the past, many theorists presupposed that the gap between actual entropy and maximum entropy is not permanent, that heat death will win in the end. These theorists were eager to link complexity in a quantitative way to this “entropy gap”, so that the two would rise and fall together. Others now argue that, in an expanding universe, the maximum possible entropy will increase more quickly than actual entropy, casting the “heat death” hypothesis into question.

I have long been rather dubious about the notion of complexity. Certainly, it is not something that is always desirable. For instance, in theology, as is well known, a central Christian claim is that God is the ultimate simple. In mathematics, simplicity and elegance are highly valued. One thinks for example of the Euler identity: eiπ + 1 = 0. And in science too, there is much to be said for simplicity. Charles Darwin's supporter Thomas Henry Huxley, on being informed about natural selection, is supposed to have exclaimed: “How simple, how stupid not to have thought of that!” More generally in science, the ultimate in scientific achievement is bringing disparate parts of enquiry together under the same hypothesis. This process, known as a “consilience of inductions”, is the paradigmatic exercise in producing simplicity (Whewell, 1840).

However, there is no doubt that the notion of complexity (and related notions of progress) continue to fascinate and absorb our attention. In this discussion, I would like to offer a few remarks about complexity (and progress) as they play out in evolutionary biology. To anticipate, it has long been recognized by historians of evolutionary biology that in the middle of the nineteenth century in Britain there were two competing views of the evolutionary process (Richards, 1987; Ruse, 2013a). One was expressed by Charles Darwin in his Origin of Species (1859), the other by Herbert Spencer in a series of writings, culminating in the 1860s with his First Principles (1862) and his Principles of Biology (1864).

My large aim in this chapter is to take us from our deeply received scientific world view and, derived from it, our view of the “real world” in which we live, that is, from the understanding of the world that was spawned by Newton and modern physics to an entirely different, newly vibrant, surprising, partially unknowable world of becoming in which the living, evolving world, biological, economic, and cultural co-creates, in an often unprestatable mystery, its own possibilities of becoming. If the latter perspective is right, we are beyond Newton, and even beyond Darwin, who, in all his brilliance, did not see that without natural selection “acting” at all to achieve it, the evolving biosphere creates its own future possibilities. And we will see, at the foundations of all this, that no laws entail the evolution of the biosphere, economy, or culture. But the biosphere is the most complex system we know in the universe. If it arose beyond entailing law, we must ask how this can be possible? More, is that “how” a hint to how complexity emerges at least in the living world, and perhaps in the abiotic universe?

We will begin to see ourselves in the living, evolving world in a world of inexplicable and unforeseeable opportunities that emerge with neither the “action” of natural selection in the evolving biosphere, or often without intent in the human world, that we partially co-create. It will follow that we live in not only a world of webs of cause and effect, but webs of opportunities that enable, but do not cause, often in unforeseeable ways, the possibilities of becoming of the biosphere, let alone human life. But, most importantly, I seek in this new world view a re-enchantment of humanity, of which this chapter may be a part. Our disenchantment following from Newton led to modernity.

A glance out the window confirms that the universe is complex. By day, intricate weather patterns chase the Sun along its path. At night, galaxies, stars, and planets wheel across the sky. Rabbits hop across the lawn, pursued by coyotes. Trucks rumble along the highway. Turning one's gaze inside the room confirms the diagnosis. People chat and argue. Children grow. Food cooks on the stove. Spam accumulates in the computer inbox.

How and why did all this complexity come about? The answers that we currently possess are largely qualitative and historical. The big bang happened, gravitational instability made matter clump together, stars started to shine, planets formed, life began, humans showed up, societies formed, all hell broke loose. We know that the universe is complex, and we know something of the sequence in which more and more complex systems developed. It would be good, however, to know WHY the universe is complex. Is there some intrinsic drive to the creation of complexity in matter and energy? Are there other universes, and if so, are they more or less complex than ours? Will this generation of complexity go on for ever?

RISING COMPLEXITY, NATURAL SELECTION, AND THERMODYNAMICS

It seems that many systems both increase their complexity if initialized in a low complexity state, and then reliably and robustly maintain high (but finite) complexity once it is attained. Some of the most prominent examples are the many biological systems undergoing natural selection that seem to start with low complexity and then increase their complexity (Krakauer, 2011; Carroll, 2001; McShea, 1991; Smith, 1970). Such systems are typically modeled as localized individuals that reproduce in an error-prone process, with their offspring weeded out in competitions with other individuals that select for higher complexity. In this natural selection process the individuals in a line of biological descent increase their complexity in time.

Some have argued from these examples that natural selection is a necessary condition for complexity to increase. The idea is that for a particular lineage to have a large fitness advantage over its competitors, it must become increasingly “complex”. However, we should not confuse the properties of an example of a phenomenon with the phenomenon itself: complexity increase is not synonymous with adaptionist natural selection. Indeed, one can engineer by hand models of systems undergoing natural selection where the competition selects for low complexity of the individuals in a line of descent, not high complexity. One can even engineer models where the competition ends up weeding out all the individuals, so that the natural selection causes all the lines of descent to die – in which case the complexity of the system has been driven to its minimal value. So natural selection, by itself, need not cause complexity to increase.

THE COMPLEXITY OF COMPLEXITY

1. Proud Biologist: “Life forms are more complex than stars”

2. Humble Astronomer: “You'd look simple too from a trillion miles away”

One of the central questions of evolutionary biology and cosmology is: is there a general trend towards increasing complexity? In order to answer that question, it would help to have a definition of complexity that can be quantified. Various definitions of complexity have been proposed (Gell-Mann, 1994, 1995; Kauffman, 1995; Adami, 2002; Gell-Mann & Lloyd, 2003; Fullsack, 2011). With useful oversight, Lloyd (2001) groups various conceptions of complexity into three groups based on (1) difficulty of description (measured in bits) (2) difficulty of creation (measured in time, energy or price) and (3) degree of organization (measured in…?…, we're not sure). For more details see: Weaver, 1948; Traub et al., 1983; Chaitin, 1987; Weber et al., 1988; Wicken, 1988; Bennett, 1988; Lloyd & Pagels, 1988; Zurek, 1989; Crutchfield & Young, 1989; McShea, 2000; Adami et al., 2000; Adami, 2002; Hazen et al., 2008; Li & Vitanyi, 2008; McShea & Brandon, 2010.

Nature writ large is a mess. Yet, underlying unities pervade the long and storied, albeit meandering, path from the early universe to civilization on Earth. Evolution is one of those unifiers, incorporating physical, biological, and cultural changes within a broad and inclusive cosmic-evolutionary scenario. Complexity is another such unifier, delineating the growth of structure, function, and diversity within and among galaxies, stars, planets, life, and society throughout natural history. This chapter summarizes a research agenda now underway not only to search for unity in Nature but also, potentially and more fundamentally, to quantify both unceasing evolution and increasing complexity by modeling energy, whose flows through non-equilibrium systems arguably grant opportunities for evolution to create even more complexity.

COSMIC EVOLUTION

Truth be told, I am a phenomenologist – neither a theorist studying Nature from first principles (I’m not smart enough) nor an experimentalist actually measuring things (although I used to). My current philosophy of approach aims to observe and characterize Nature thermodynamically, seeking to explicate a scientific worldview that chronicles systematically and sequentially the many varied changes that have occurred from the big bang to humankind on Earth. I call that epic worldview cosmic evolution.

MONDRIAN AND DIRAC ON MINIMALISM

The Dutch painter Piet Mondrian is best known for strikingly simple canvases populated by vertical and horizontal planes rendered in primary colors. Mondrian's paintings from the 1930s: Composition with Yellow Patch, Composition No. 8, and Vertical Composition with Blue and White, are a far cry from his earliest canvases, Landscape with Ditch, Mill in Sunlight, and Red Tree. The early canvases feature colorful and vigorous representations of scenes, and are indebted to the post expressionists, Suerat and Van Gogh. These in time give way to the later compositions influenced by the analytical abstractions of the cubists, Picasso and Braque. The names of the later paintings reveal a parallel trend towards descriptive simplicity. In his correspondence, Mondrian provides a clue to his thought leading to this change of style: “The principle of this art…is not a negation of matter, but a great love of matter, whereby it is seen in the highest, most intense manner possible, and depicted in the artistic creation.” (1912) and “We arrive at a portrayal of other things, such as the laws governing matter. These are the great generalities which do not change.” (1913) (Faerna, 1997). Over the course of the cultural evolution of Mondrian's creative life, we observe a systematic trend away from detail and realism and towards minimalism and abstraction. Painterly subjects easily recognized in his early canvases become a kind of affine symbolism in the later paintings.

The concept of complexity reminds one of the tasting notes of a rare vintage: everybody knows what you are talking about, but the realities continuously slip through our fingers. Moreover, in the scale of complexities most would agree that life is intrinsically more complex than, say, a galaxy. So too we suppose that some sort of metric stretches through the history of life: be it in terms of ecologies, bodyplans or nervous systems. In other words what we see today is manifestly more complex than what was found in the Precambrian. Yet an evolutionary perspective on complexity reveals some unexpected angles. To start with, although the history of life might fall into the cliché of “Once there were bacteria, now there is New York”, in fact when one investigates what are evidently the most primitive representatives of a given group repeatedly they turn out to be “unexpectedly” complex. Many such examples are now available, but amongst the most telling are the eukaryotes. Second, there is the phenomenon of evolutionary inherency, the observation that much that will be required for the emergence of a complex form has already evolved at a substantially earlier stage. A good example involves the protein collagen, essential as a structural molecule in metazoans, but whose origins not only lie deeper in eukaryotic history but whose functions were evidently quite different. Inherency indicates, therefore, that much of complexity is nascent, almost homunculus-like, lying far deeper in the Tree of Life than generally appreciated. Third, whilst the arrow of time seems to lead to ever greater levels of organic complexity, it is as well to remember that these may well include examples that are often dismissed as “simplification” or “regression”.

A large part of the structure that is recognized and understood in the vacuum (Weinberg, 1995; Weinberg, 1996) and in condensed matter (Ma, 1976; Mahan, 1990; Goldenfeld, 1992) is the result of a hierarchy of phase transitions in either quantum-mechanical or thermodynamic systems. Each phase transition creates a form of long-range order among components of the system that in the absence of the phase transition could fluctuate independently. To the extent that the phase transitions are nested or sequential in order of decreasing energy or increasing spatial scale, both of which correlate with increasing age of the universe, the progression through the sequence and the accretion of additional forms of long-range order constitute a progression of complexity.

In this chapter I argue that phase transition continues to be the appropriate paradigm in which to understand the emergence of the biosphere on Earth, and that at least some universal patterns in life should be understood as what are called the order parameters (Goldenfeld, 1992) of one or more such transitions. The phase transitions that formed the biosphere, however, are dynamical transitions rather than equilibrium transitions, and this distinction requires a different class of thermodynamic descriptions and leads to some striking differences in gross phenomenology from what has become familiar from equilibrium systems.