Monday, April 1, 2013

Is the Universe "Rational"?

It is a curious, surely not insignificant observation that the universe appears (or appears to appear) to us in a comprehensible way. Children, for example, prior to any specific instruction, are capable of discerning emotions on faces, finding patterns in numbers and predicting with admirable precision the path that a ball makes through the air. As an adult living in the 21st century, we can be similarly amazed by the extent to which our universe seems to make itself understandable enough to us for its behaviour to be expressed in the language of mathematics. It is difficult not to be taken in by the elegant efficiency of Newtonian laws, for example, which compress the behaviour of physical phenomena into a few simple formulae, each containing just a handful of variables. With such examples in mind, it is difficult to avoid the conclusion that the universe is ordered according to a rational plan, designed to obey laws amenable to human understanding. 

It is this conclusion, certainly, that many theologians would like us to reach. With all other avenues of "natural theology" blocked off by the march of scientific progress, the role of God in nature has since been resigned to the above observation: that the universe is, and could only ever be, the way it is due to the premeditated design of some rational creator. Superficially, the argument doesn't appear to be without merit: even some non-theistic scientists have marvelled at the fact that the universe is comprehensible to us to the extent that it is. There is no inherent reason for the universe to have made itself comprehensible to us, so we are right to find something remarkable in the fact that we can explain certain facets of the universe with such extreme precision and, what is more, that these explanations appear to be true for all places at all times. Is this necessarily a sign that the universe is inherently rational, though?

One trouble with using the word "laws" to explain the behaviour of the universe is that we've inadvertently introduced an anthropic concept to explain otherwise inert, purposeless objects and events. A "law", of course, is something that is designed with forethought to control or modify the behaviour of people in a society. When we use "law" to describe physical phenomena, then, we inadvertently smuggle in a package of unintended theological implications. If there are "laws", afterall, and physical phenomena obey these "laws", then that immediately implies the existence of a law-maker who intended to control or modify the physical phenomena to facilitate the development of some teleological end. This a consequence of the poverty of the current terminology, and in lieu of replacing such terms with more teleologically neutral language, we must instead endeavour to explore why the "laws" of the universe are not the kind of "laws" that necessitate a law-maker.

The first observation to make is that all physical laws have necessarily been designed by human beings. The universe did not appear to us with any kind of comprehensible blueprint, so whatever regularities we observe in the universe have had to be mined from nature through years of dedicated observation and number-crunching. That is, if the "laws" of nature are presently clear, comprehensible and rational to us, they certainly weren't to the ancients, who were no less intelligent or perceptive than we are. So let us be clear on this: it is we who superimpose our "laws" onto the phenomena we observe in the universe, not the universe which imposes its inherently rational nature onto our consciousness. An example used by Stephen Hawking is to imagine the kind of laws a goldfish might create to explain his world from the confines of its bowl. It could (were it sufficiently clever) certainly invent some rules that were true from its vantage point (which would include the refraction of light as it hit the fishbowl, hence why the universe would appear to be inherently curved to the fish) but that these rules plainly wouldn't be universal for the simple reason that they probably would not be applicable to those who live beyond the confines of a fishbowl. Hawking uses this example to posit the idea that "there is no theory-independent concept of reality".1 This is not to say that all attempts at an objective explanation of universal phenomena are futile, or that we should all collapse into solipsistic despair as prisoners of our own mind with no possibility of ever accessing "true" reality, but simply that all the physical "laws" we create are necessarily mere "approximations" of reality that constitute our attempts at imposing rationality upon nature, rather than the discernment of rationality in nature itself. This is why scientific theories can be supplanted despite never really being shown to be wrong (or definitively right): the latter theory simply constitutes a better approximation of reality than the one which preceded it.

Allow me to illustrate with an example, shamelessly cribbed from Isaac Asimov's Essay, The Relativity of Wrong. For most people in the ancient world, it was accepted wisdom that the world was flat. For the first several thousand years of human existence, people had no way of knowing that they actually lived upon the surface of a three dimensional sphere. We may smirk now at their naivete, but in truth they weren't far wrong. At the human scale, the curvature of the earth is extremely slight, almost exactly zero. When building a house or undertaking a car journey we can safely disregard the curvature of the Earth entirely: that is to say, to treat it as though it were flat and two-dimensional. We know now that the Earth is not flat, of course, but for most human endeavours, if we proceed under the assumption that it is, then we will not be penalised for it. In a purely pragmatic sense, the flat Earth theory is correct enough to correctly guide us upon the undertaking of most everyday activities.

Next it was realised that the Earth was actually three-dimensional in shape, and that if one started walking in one direction that one would eventually return to the point at which one started, rather than falling of the edge of the Earth. It was therefore presumed that the Earth was spherical in shape, a misapprehension shared by most people down to this very day. For although it is true that the Earth closely resembles a sphere, due to the influence of centrifugal forces it is actually wider around the equator than it is from pole to pole. Thus, although the spherical Earth theory is more correct than the flat Earth which preceded it (more correct in the sense that it is able to make accurate predictions for a wider variety of phenomena) it still fails to accurately depict the state of nature so as to conform to our best, most precise observations. Though the story doesn't even end here: according to Asimov at least, there is actually slightly more mass in the Earth's southern hemisphere than in its northern hemisphere, thus making it ever so slightly pear-shaped. So note the progress here: each theory along the way has been correct on its own terms, in the sense that it can be used accurately as the basis for some action or prediction, though there is also a definite progression towards being more "correct. It is clear, for example, that spherical Earth theory is more correct than the flat Earth theory, the distended sphere theory is more correct than the sphere theory and so on. As our body of evidence grows and changes, earlier theories come to be displaced by theories that better fit the evidence.

Another example - perhaps more pertinent to the topic at hand - is the progression in our understanding of the movement of the planets. It is the elegant, almost metronomic order of planetary orbits that epitomise the theologians insistence that this rationally comprehensible universe could only be the product of some divine watchmaker. Indeed, the regularity of the planetary movements through the sky have long been used by religious authorities as evidence of divinity in the universe. For the ancients - including the Babylonians, the Egyptians, the Mayans and so on - the planets themselves were gods, their daily wandering across the sky associated with the personalities of the divine. Venus, for example, was commonly linked to gods of love and fertility in the ancient world. Again, it may be tempting to snigger at such naivete, but when we consider that the appearance cycle of Venus (the period during which it is visible in the night sky) occurs in periods of around 260 days - almost exactly the same period a human pregnancy takes - we can begin to see that the connection makes sense. In fact, doubtless the ancient Mayan theologians would have tried to tell us that the universe must be rationally ordered to some divine plan, because the simultaneity of the human reproduction cycle and the cycle of the fertility God in the sky is simply too perfect to be the result of mere chance or coincidence. Furthermore, the astrological tables drawn up by these ancient cultures could still be used today to predict the future positions of planets in the sky. Within the social context that they lived, the astrological "theories" the ancients proffered concerning the movement of the planets in the sky were perfectly rational and perfectly consistent with the data that they had so assiduously collated.

Next came the Greeks, who believed - for theological reasons as much as for scientific ones - that the universe must be ordered to according to perfect geometric principles, expressible in simple mathematical formulae. Ptolemy, rejecting the crass arbitrariness of astrological tables, took it upon himself to find some universal order in the movement of the planets during the sky, some pattern expressible in the perfect language of geometry. His solution was a geocentric model comprised of nested spheres and epicycles, based, he claimed, on over 800 years of observations. The model he proposed was in some sense an improvement on what came before it, and like the astrological tables of the ancients, we could still use Ptolemy's model today to predict the movement of planets relatively accurately for a period of at least some months or years (the accuracy of the more distant, slower moving planets would hold for longer than those of the inner planets, particularly Mercury, whose orbit wasn't well understood until the 20th century).

The next major development came with Nicolaus Copernicus who was the first to develop a heliocentric model of the solar system, and while again we can view it is an improvement over what came before it due to its correct placement of the sun at the centre of the solar system, it still contained a fatal inaccuracy that limited the long-term scope of its predictive powers. Like the Greeks before him, Copernicus believed that the universe must be order according to some perfect schema, namely one based on perfect circles. As the planets actually revolve along elliptic orbits, it wasn't until Isaac Newton elucidated his laws for the movement of the planets in his masterful Principia Mathematica that we had a relatively accurate depiction of our solar system that could be used to predict and explain the movement of the planets over a long period of time. In fact, Newton's theories proved to be so accurate that they are still used today to navigate spacecraft over a distance of millions of kilometres to within an astronomical hair's width of their intended target. In time, however, it was recognised that even Newton's theories fail under particularly extreme circumstances - e.g. in situations involving very high speeds or masses. Newtonian physics therefore came to be replaced by Einsteinian Relativity at the beginning of the 20th century, and even that may not mark the end of our story: the fundamental incompatibility of quantum mechanics and relativity (despite each proving to be powerfully accurate in their own fields of application) hints strongly at the need for the development of some newer theory, of which string theory is just one of the potential candidates.

So again note the development here: at each stage in the understanding of the shape of our planet or the behaviour of bodies in our solar system, human beings have been able to devise seemingly "rational" theories to explain the available observations, and all of the aforementioned were capable of making accurate predictions concerning future events. We must, however, be careful not to presume that our ability to express the patterns of physical behaviour in "rational" terms says anything about the inherent rationality of the universe. The ancient Babylonians could say, with some justification, that the universe must be inherently rational because the fertility god represented by the planet Venus was born and killed with such regularity (one which parallels the human reproductive cycle) that it could only be the work of a divine presence in the world. However, we moderns would be similarly justified in baulking at the suggestion that the explanation proffered by the Mayans could give us any genuine insight into the rational order (or lack thereof) of our universe, as we now know that any correlation between the heavenly cycles of Venus and the human reproductive cycle are entirely coincidental and share no causal relationship. Perhaps, then, our descendants will look back on our curious proclivity to try to explain such complex phenomena in the form of simple, rarefied mathematical language in the same disdainful way that we look back on the proclivity of the ancients to explain such complex phenomena in the form of dying and rising gods. That we are capable of making the universe rationally comprehensible to ourselves is indeed a remarkable achievement, without which our modern world would have proved unrealisable, but we must make sure that our wonder is directed at just that fact - that is, that we can make the universe rationally comprehensible, not that the universe is rational in and of itself.

On this latter point, again we might do well to return to Newton. The simple, elegant laws he devised were - after an initial period of resistance - eventually employed by theologians as evidence for the fact that the universe must be run like clockwork; so ordered and intricate in its construction that it would be literally impossible for it to have come into being without pre-ordained instruction from some all-powerful watchmaker. The argument continues to be used with great regularity among modern theologians, though the sense of awe has been expanded beyond the periodic movement of the planets to deeper cosmological facts (such as the value of the cosmological constant and other physical values) that, frankly, they are not qualified to ruminate upon quite so casually. In any case, the wonderment they express is entirely backwards: these "values" and their relationship to one another were not rationally programmed into the universe, just waiting for some perceptive scientist to reverse engineer them, but rather had to be created and elucidated by these same preceptive minds. Newton didn't simply discern some obvious mathematical relationship governing the movement of bodies in the solar system, he actually had to invent some new method by which he could create some laws. When the existing body of mathematical logic failed to help him in his quest to "uncover" the rational basis of the movement of heavenly bodies, he was actually forced to create an entirely new form of mathematics (calculus) in order to make this movement rationally expressible. In other words, there is nothing about the universe (at least in this case) that makes it inherently amenable to human logic. Where the universe doesn't make itself amenable to human reason in an immediately obvious way, we just happen to have been clever enough on occasion (or, rather, certain pre-eminent members of our species have been clever enough) to devise a new form of logic in which the observed relationships and regularities can be expressed.

And this is something that we are coming to appreciate ever more deeply: the universe does seem to be, in a very fundamental sense, operating on principles that are at best counter-intuitive to human beings, or - perhaps more accurately - deeply and inexorably irrational in nature. In one way, we should expect that world around us - that is, the everyday world, divorced from the loftier concerns of theology - be, in some sense, rationally comprehensible. Our "folk-physics" - our innate ability to predict the flight of a ball in the air, for example - and our ability to express these predictions logically, do seem to be in such a state of consonance with nature which must surely must transcend mere coincidence. Our ability to track a ball through the air, predict its path and then to catch it in our outstretched hands is a feat beyond even the most advanced robots we have been able to develop, and it would be tempting to discern a divine teleology at work in this regard: Earthly physics are so rational - and our minds so rationally attuned to them - that it could again only be the result of divine forethought. While it would be correct to note that there is nothing "coincidental" about the consonance of  human rationality and the rationally discernible laws of Earthly physics, the explanation has nothing to do with the divine. We are the product of 4 billion years of evolution that has ruthlessly culled those whose understanding of their immediate environment was subpar: only those with a functional understanding of the physical world (e.g. that falling from a tall cliff would kill you) stood any chance of surviving to produce offspring. Our folk-physics have been slowly refined by this evolutionary process to help us navigate the world in which we live, each minor improvement in our innate understanding of the world being preserved down future generations. So yes there does seem to be a compatibility between our "logic" and the "logic" of physical events on Earth, but we needn't look for divine explanations: given our existence as physical beings and the relentless drive of evolutionary pressures, it simply could not have been any other way.

When we leave our immediate human world and begin to explore the nature of the universe on the smallest and largest scales, however, we find that our intuitive preconceptions about the nature of physical events very quickly cease to conform to reality. We expect the universe to adhere to certain "rules" concerning cause and effect (as Hume noted some three centuries ago) and for objects to adhere universally to rationally discernible principles. We now know, however, that the universe often fails to conform to our expectations in this regard. The most blatant examples can be drawn from the science of quantum physics, where the universe at the most fundamental level has shown itself to be irrational, indeterministic and completely irreconcilable with the expectations of our folk-physics. The completely random (and seemingly uncaused) appearance and disappearance of sub-atomic particles is not possible to square with the idea of a rationally apprehensible universe, as even a suitably well-informed observer (i.e. a god) would have no way of predicting exactly where or when a particle and it's anti-particle might come into existence. As a consequence, even the most mundane predictions concerning the behaviour of objects in the universe turn out to be mere probabilistic statements rather than inviolable natural laws. For example, we can take it for granted that I will not be able to walk through my wall were I to try, yet it turns out that this is merely a statement of probability: it actually isn't impossible for me to walk through my wall (i.e. it's not an inviolable "law" of the universe) it's just overwhelmingly unlikely.2

Such randomness and indeterminacy on the quantum scales may still credibly be dismissed as irrelevant by the believer in the rational universe, however. They may, for example, argue that even if the universe is predicated upon random and indeterminate factors, that on bigger scales determinate laws can still be discerned. That is to say, even if the location of an electron is entirely indeterminate, the location of large groups of electrons (for example, those in my body) appear to behave collectively in ways that are roughly deterministic. In other words, I could try to walk through my wall every day until the end of the universe and could reasonably expect to get the same result every time, which if not strictly an "inviolable law" of the universe surely constitutes the next best thing. Such an argument is problematic, though, because it fails to address the reality that the universe was formed at least in part by completely random factors that even a hypothetical being blessed with omniscience could not have predicted. While it may be true that it is not necessary to take quantum factors into account when presently addressing the orbital path of a planet, say, the argument breaks down when we examine the early history of the universe: at the very beginning, a fraction of a second after the big bang, the universe was still small enough for quantum effects to have a massive influence on the path that the evolution of the universe would take. We now know from our mapping of the early universe that these very early quantum jitters came to have a lasting influence on the shape of the universe, including (most likely) the distribution of matter that may have permitted the formation of galaxies. This prohibits the possibility of the current universe being created with genuine teleological foresight: there is no way that any being - omniscient or otherwise - could have predicted that the universe would emerge with the exact structure it presently has. If we rewound the clock to zero and started the universe again, we would end up with a universe very different from our present one, and this is due entirely to the influence of quantum randomness in the earliest fraction of a second of the universe's being. God may have rationally chosen to create a universe with quantum jitters, but he couldn't have rationally chosen to create a universe with human beings.

Even on bigger scales we find that probability plays a much higher role in the behaviour of matter than could have ever been envisaged by the classical, deterministic physics that the theologians seem to remain beholden to. The distribution of gas in a room, for example, can only really be probabilistically determined. We can take it is as something akin to a "law" that gas in an enclosed space (the air in a room, for example) will tend to distribute itself fairly evenly given enough time. That is, we should expect the air pressure and the distribution of molecules within such a space to be distributed relatively evenly from one cubic centimetre to the next. In actuality, though, there is no physical reason why the molecules of air couldn't find themselves confined only to one side of the room, for example, leaving the other half a complete vacuum. Such a bizarre eventuality wouldn't violate any physical principles, it would just be exceedingly unlikely (in the sense that there are far more ways for the air in a room to be evenly distributed than for the air in a room to be confined entirely to one half). So, even when we're talking about the behaviour of physical processes on scales far greater than that of the quantum level, we find that these process are often not governed by rationally discernible "laws" so much as they are governed by probabilities. Even on distinctly human scales, it seems that God enjoys playing dice.

But we can take such indeterminacy to even greater scales. When it comes to the belief of rationally discernible laws governing physical objects in the universe, there is surely no more elegant example than the aforementioned metronomic movement of planets around the sun. If nothing else in the universe could be said to obey rationally apprehensible laws, expressible in the elegant, efficient language of mathematics, then surely it could still at least be said about the "music of the spheres". In practice, however, when physicists attempt to quantify the gravitational relationship (and therefore the movement and periodicity of planetary orbits) between anything more than three bodies, the mathematics because ungainly and completely unworkable. This is known as the n-Body problem, which remains unsolved. So even here, with something as simple as the orbit of a spacecraft around the Earth, we lack the ability to rationally express or predict with any sort of exactitude the path the spacecraft will take. We could of course get a good approximation by taking into account only the effect of the gravity of the Earth on the spacecraft (and if such approximations weren't pretty close to reality then satellite technology would be entirely impossible) but such a method would only be an approximation of reality, because we have failed to take into account the gravitational influence of the sun and the moon into the equation. And the gist of the n-Body problem is that calculating the orbital path of a spacecraft around the Earth is fundamentally impossible with such precision, because we don't have the mathematical tools to calculate fully the gravitational relationship between all 4 bodies simultaneously.
And so we return to the point I wished to make at the beginning of this post: even where the universe appears to be obeying rational laws, we find that these "laws" are little more than approximations of reality (albeit very good ones) that cannot be treated as reflections of some deeper logic governing the behaviour of physical events in our universe. We will continue to find patterns and regularity in the universe - to do so is part of our nature as a species - and we will continue to create physical "laws" that approximate reality with ever greater precision, but we shouldn't suffer under the conceit that we are therefore "discovering" the laws the were programmed into the universe into the universe from its very beginning. On almost any scale we probe, the universe frequently shows us that it is under no obligation to conform to the expectations of human rationality. Perhaps we should just accept that - certainly at the most fundamental levels - the universe is an impenetrably irrational place.


 1) The Grand Design, Chapter 3.

 2) This is a consequence of a phenomenon known as Quantum Tunnelling. Essentially, the precise location of an electron around an atomic nucleus can never be determined with exact precision - this is Heisenberg's Uncertainty Principle at work. As such the location of an electron can only be specified fuzzily - as a kind of "cloud" - governed by laws of probability. In principle, there is nothing preventing all of the electrons in your body to "jump", simultaneously, to a location on the other side of the wall, it would just take an unfathomable amount of time for such an event to occur.