Cosmic Fantasies by Numbers

Posted by Beast Rabban

Max Tegmark is in the British science magazine New Scientist this week (the week of the 15^th of September), once again arguing for a multiverse. In the article ‘Reality by Numbers’ he argues that the universe is a mathematical object, like the dodecahedron of the Pythagoreans. An exploration of this possibility will not only give us an ultimate Theory of Everything, but also include parallel worlds and allow us to know this one in far greater depth than was previously conceivable. Basically, it’s another attempt at supporting atheist pantheism, arguing that the universe must also be eternal, impersonal, and, although he doesn’t mention this, without a creator.

The argument runs thus: Scientists and philosophers from Pythagoras to Eugene Wigner have noticed the uncanny ability of mathematics to describe and predict the universe. If reality is independent of humans, then it must also be defined by entities that lack human concepts. However, mathematics describes the universe abstractly without human conceptual notions like ‘stars’, ‘protons’ and so on. So, he concludes, ‘if you believe in an external reality independent of humans, then you must also believe in what I call the mathematical universe hypothesis: that our physical reality is a mathematical structure’. 1

The article then proceeds to investigate what this would mean, using the analogy of the world perceived by a frog fixed on the ground and bird flying above it. The physicist is the bird studying the universe’s mathematical structure from above, while the frog is the observer within the structure. A mathematical structure is abstract, outside of space and time, and immutable, so the bird would see a tangled spaghetti of world-lines according to relativistic perceptions of the world, while the frog sees the uncomplicated view of Newtonian physics. However, the observer would also be a tangled sphaghetti itself: ‘the frog must consist of a thick bundle of pasta whose structure corresponds to particles that store and process information in a way that gives rise to the familiar sensation of the universe’. 2

It then goes on to state that this view of reality is validated by the progress of science in discovering mathematical regularities in nature, such as the Standard Model of particle physics. The amount of information required to describe our particular frog’s eye view of the universe would is extremely large 10 to the power of 100 bits. 3 Most physicists hope for a Theory of Everything that will be far simpler. If so, the argument runs, then it would describe a multiverse, as if it lacks enough information to describe our reality, then it must be a general description of all possible realities. These universes are compulsory: they aren’t created, they just exist, as ‘the point is not that a mathematical structure describes the universe, but that it is a universe’. 4 Tegmark feels that this would answer John Wheeler’s question of why the particular equations that describe the universe do so, and not others. The answer is that there are other equations governing other universes.

Recognising that for this to be a scientific theory, rather than metaphysical speculation, it has to make predictions, the article argues that it could be falsified if it is found that the mathematical distribution predicted of parallel universes means we don’t exist in a typical universe.

It then goes on to argue that we should believe in the universe as a mathematical construct as it is counterintuitive. According to Darwin, human minds did not evolve to discover the truth, only to give the cognitive advantages necessary for survival. Quantum physics is true, but is counterintuitive and disturbing, therefore there is a warrant for believing that the universe is a mathematical structure, as this is similarly counterintuitive and disturbing.

However disturbing it might be for humans, Tegmark is confident that ‘if the mathematical universe hypothesis is true, then it is great news for science, allowing the possibility that an elegant unification of physics and mathematics will one day allow us to understand reality more deeply than most dreamed possible’. 5 Moreover, we could abandon the attempt to ask which particular equations describe all of reality, and devote our time instead to trying to work out how the frog’s point of view is derived from the bird’s view. ‘That would determine whether we have uncovered the true structure of our universe, and help us figure out which corner of the mathematical cosmos is our home.’ 6

The article is based on a paper by Tegmark, “The Mathematical Universe”, which is online at www.arxiv.org/abs/0704.0646. I haven’t seen this version of the argument, but as outlined above in New Scientist it seems profoundly flawed and needs to be seriously critiqued.

Firstly, it seems to be an attempt to keep the old multiverse idea alive. Despite widespread publicity, very few scientists actually take it seriously and there is widespread scepticism. Sceptics have argued that as the extra universes proposed are invisible and their existence is the result only of the predictions of certain equations, they are unverifiable and hence a metaphysical, rather than a scientific concept. As for the statement that the equations for a multiverse must be simpler than that for a universe, and that such multiverses simply are, rather than are created, this appears to be an attempt to get round the awkward fact that it appears that if universes did exist which spawned other, baby universes, through a process of budding, as suggested by Stephen Hawking and Martin Rees, the parent universes would have to be more complicated mathematically than the daughter universes, as they would have to contain not only the equations to describe themselves, but also to describe the conditions in their daughters. Also, such universes would stop producing baby universes before reaching the numbers demanded by those versions of String Theory that require their existence. 7 This version of multiverse theory simply tries to get round that by stating that such universes don’t have to come into being, they just are.

However, the theory’s very incompleteness, its radical inability to predict how these extra universes have come into existence, casts doubt on its validity. It doesn’t explain how they come into existence, only asks you to believe that they’re there largely through a process of philosophical induction.

As such, it’s an attempt to get round the fine-tuning problem and the kalam cosmological argument. This states that whatever begins to exist, has a cause. The universe obviously began to exist, therefore it is caused, and this cause is God. Tegmark is trying to argue that as a mathematical entity, the universe hasn’t begun to exist. However, it plainly has: there has been a start to time, and the contents of the universe clearly begin to exist, so the argument that the universe has no beginning simply isn’t true, whatever the perspective one adopts to look at it. One can also argue that this in itself demonstrates that the universe is not an abstract mathematical entity.

The article also seems to me to be a bit of Physicalist morale-boosting. Last week or so there was an article in the New York Times reporting the problems physicists were having trying to untangle the problem of dark matter and dark energy, with various celebrity scientists glumly speculating that the universe might, after all, be incomprehensible. Tegmark’s article with its promise of an ultimately comprehensible cosmos strikes me powerfully as a rhetorical effort to dispel this gloom. Unfortunately, there are powerful arguments against any Theory of Everything being possible, or making the universe at all comprehensible. Way back in the 1980s when String Theory was much less challenged, it was remarked that it would be 300 years before anybody could work out what the equations behind the theory actually meant, if anything. For critics of String Theory, like Lee Smolin, these problems of comprehensibility actually haven’t gone away, but just got worse. John Barrow in his 1990 book, Theories of Everything, suggested that there was absolutely no reason to believe that such a theory was possible. It was perfectly possible for the universe to contain any number of surds – mathematically absurd elements – that would make its reduction to a single theory impossible. His example of one such unpredictable event was the symmetry breaking in the primordial universe that produced far more normal matter than antimatter. And even if such a theory could be produced, it would most likely be so general as not to explain anything, except on very large or very small scales. As for the Standard Model of particle physics being an example of maths accurately predicting reality, well, yes, it does. However, very many physicists are unhappy with the Standard Model, because of its ad hoc quality. It’s been described as having been tacked together, with scientists finding it radically incomplete. Hence the desire to find a Theory of Everything. Yes, the Standard Model of particle physics does describe reality, as far as it goes, but its incompleteness is not a good indication of the ultimately intelligibility of the cosmos.

The argument for the mathematical nature of the cosmos is also undermined by its reductionist assumptions about the nature of consciousness. Consciousness is merely the product of particle interactions within the various creatures in the universe, according to the theory. This is extremely problematic. Despite arguments to the contrary, there are severe problems with materialist interpretations of the basis of consciousness, and for many philosophers Cartesian dualism – that the mind is independent of, but linked to the brain – far better describes the origin of consciousness.

The appeal to Darwin to support a belief in the theory is also problematic. It can be argued that regardless of whether the theory is counterintuitive or not, the fact that we can conceive of it at all argues against Darwin’s view of the mind. If Darwin is correct, and the human mind did not evolve to discover the truth, but only for survival, then it may be argued that quite simply there is no way that such a counterintuitive idea could be conceived at all, as Alvin Plantinga has argued against Naturalism. Besides, God in the classical traditions of Judaism, Christianity and Islam, is also a spirit and beyond description, as the Mathematical Universe model supposes the universe is, and commonsense atheists find His existence irrational and counterintuitive. Tegmark’s argument tacitly demands God to be excluded as irrational for the same reason as belief in the mathematical nature of the universe is recommended. Clearly, there is a deep contradiction here.

And then there are the more fundamental problems faced by the theory and its conception of reality. Firstly, there is absolutely no reason to believe that the existence of an objective reality independent of human minds should require that a true, basic interpretation of reality be completely mathematical and impersonal. The Critical Realist philosopher, Roy Bhaskar, has pointed out that although there is an objective, external reality out there in the cosmos, this reality is always apprehended through human ideas. It is possible to describe a crystal in terms of the lattice formed by the individual molecules, themselves defined and formed according to the laws of chemistry and physics, but this does not rule out the human experience of such a crystal as an object of aesthetic appreciation, or that the purely mathematical interpretation of the object is to be preferred in all circumstances.

This points to a more fundamental problem with the theory: its underlying philosophy of mathematics. It is unashamedly Platonic and Pythagorean, viewing numbers as real, existing, though abstract entities. Yet this is itself a problematic assumption. A contrasting view is that numbers are entirely abstract, and the product of human brains extracting a common element – the quality of number or quantity-from concretely existing, entirely non-abstract entities, like rocks, trees and gazelles, or any other set of objects in the universe. Even those philosophers, who did accept the Platonic account of number, like Leibniz, saw it more as a set of archetypes held in the mind of the Creator by which he fashioned the universe. It’s a conception of the universe that still finds support amongst contemporary scientists. Eugene Wigner, one of the architects of Quantum theory, noted that consciousness appears to be a basic element of the universe through observation collapsing the quantum wave functions into perceptible events. This has opened the way to a revival of the kind of Idealism associated with Berkeley and Kant: that the universe is the product of the ideas of the human mind. The Mathematical Universe hypothesis is an attempt to argue against this hypothesis through its appeal to an objective reality outside of human consciousness. However, merely because something is outside human consciousness, does not mean that it is outside of consciousness and observation. Raymond Chiao, Professor of Physics at the University of California at Berkeley, has argued that it is far less fantastic to suggest that it’s God’s consciousness and observations that actualise the quantum nonlocalities of the universe into a real, concrete existence. 8

Here part of Tegmark’s argument seems to be a confusion between object and conceptualisation. While he argues that two plus two equals four, regardless of whether one writes ‘2 + 2 =4’ or ‘dos mas dos igual a cuatro’, nevertheless when it comes to mathematical descriptions of reality, there is a difference between the description and the object. 9 For example, in the example of the mathematical description of a crystal above, there is a difference between the description of a crystal, and a real existing crystal, in the same way that Magritte’s painting This Is Not A Pipe was not a pipe, just the painting of a pipe. However written or described in words or numbers, mathematics would describe such an object, rather than be it.

Perhaps a dose of Structuralism would be healthy here. Saussure and others insisted that there was a binary opposition between the words used to describe an object ‘tree’, for example, and the object itself – a tree. It’s a philosophical statement that contradicted earlier mystical accounts of the cosmos, such as those of the Qabbalists, which see the cosmos as structured around the sounds and numerical values of the Hebrew alphabet, which are intimately and transcendentally tied to the nature of reality itself. The Mathematical Universe hypothesis is atheist, rather than theist, but nevertheless it appears to partake of the same number mysticism. 10 The conception of the numbers structuring the universe as existing in the mind of God gets around this problem of the objective existence of numbers by acknowledging that they are not invented, but are also the products of mental activity. 11

Thus, there is no reason to identify the universe as number, rather than an object describable by number. And rather than pointing towards atheism, the comprehensible, mathematically structured nature of the cosmos pointed instead to the existence of God. The great British astronomer and science populariser, Sir Arthur Eddington, considered that the mathematically intelligibility of the universe showed it was the product of a conscious, purposeful intelligence which thought in terms of mathematics like humans. And indeed, the Bible shows this, with the description of God in the Old Testament measuring the depths of the sea and laying out the boundaries of earth and the heavens like a surveyor. The leaders of the scientific revolution in the 16^th and 17^th centuries used passages like these to support their argument that the universe was intelligible and able to be mathematically modelled and predicted. This, in my opinion, offers a far richer view of the universe, one where the cosmos is indeed truly intelligible, but not by accident of evolution, but as the deliberate construction of a transcendent, purposive deity, who wishes to reveal Himself and the wonders of His world to intelligent creatures, made in His image. Transcendent, purposive, intelligible, and with intelligent creatures at the heart of it. It’s a far better view of the world than as the bleak operation of impersonal mathematical laws, in which the multiple universes envisioned as making every eventuality possible may be infinitely hellish. 12

Ten years ago Tegmark’s article on parallel worlds in Scientific American sparked a flurry of interest in the possibility of a multiverse. In the decade since the concept has been critiqued and largely rejected. This article in New Scientist seems to be an attempt to revive it. Critically examined, it does not seem to do this, and the problems with multiverse theory will very probably continue.

Notes

1. New Scientist, 15^th September 2007, p. 40.
2. Ibid, p. 40.
3. Ibid, p. 40.
4. Ibid, p. 41.
5. Ibid, p. 41.
6. Ibid, p. 41.
7. For a brief but clear statement of these problems with multiple universe theory, see the interviews with William Lane Craig and Robin Collins in Lee Strobel’s The Case for a Creator (Grand Rapids, Zondervan 2004), pp. 113-152 and 153-188.
8. See Keith Ward, Pascal’s Fire: Scientific Faith and Religious Understand (Oxford, Oneworld 2006), p. 84.
9. Tegmark, op. cit., p. 40.
10. A strong postmodernist attack from an atheist perspective on such number mysticism can be found in Brian Rotman’s Ad Infinitum: The Ghost in Turing’s Machine – Taking God out of Mathematics and Putting the Body Back In (Stanford, Stanford University Press 1993).
11. Ward, op. cit., p. 88.
12. Ward, op. cit., p. 138.