Max Tegmark's Our Mathematical Universe - a quest for nature of reality

There are two ways in which a book can affect you. Either you read it, or you read reviews of it. I suspect many of us encounter more books through the second route than the first. This can be a problem if the reviewer's prejudices unduly bias the presentation of the material.

A recent case in point is Thomas Piketty's tome, Capital in the Twenty-First Century, on the evils of inequality and capitalism. Much early reaction was ecstatic with delight. Left-of- centre liberals seized on "scientific" proof that capitalism was ruinous for society if left unchecked. Later, less publicised commentators remarked on the limitations of Piketty's analysis. Whether or not you agree with Piketty, the nature of these reactions and the heat with which they were expressed is revealing. Highly emotional responses often result from how the ideas mesh with deeply held personal views, in this case in relation to what sort of society we should live in.

Now what has this to do with Max Tegmark's Our Mathematical Universe? Well, have a look at an online "review" by Peter Woit (another physicist), dismissively entitled "Not even wrong". The tone reveals much about how far Woit feels challenged at some fundamental level. My schoolboy mathematics is not up to assessing Tegmark versus Woit but his aggressive and highly personal tone is striking. Woit asserts that Tegmark's propositions are "empty" or "nonsensical" and concludes by wondering "why the scientific community tolerates … all this?" Shades of medieval book burning!

Why the hysteria? Tegmark's book falls into two parts. It begins by uncontroversially reviewing the history of human understanding of the cosmos. Then Tegmark develops his proposition; that the universe is inherently mathematical.

"Our reality isn't just described by mathematics, it IS mathematics," he says. "You and I are self-aware parts of a giant mathematical object."

Tegmark is addressing what reality "really" is, in a way that makes many feel uncomfortable because it undermines their most basic professional assumptions. This leads to efforts to reject the distasteful ideas with personal attacks. Historically, almost every major step forward in scientific understanding has proceeded in this way: hysterical rejection and marginalisation or worse. Giordano Bruno was burned at the stake for claiming the universe was infinitely large.

If you simply read Woit's review, you would conclude that Tegmark sets out a series of untested - and indeed untestable - speculations. In practice, he argues directly from basic assumptions which most people - other than Berkeleyan solipsists - accept; that there is an external reality, which exists even when you and I are not looking at it. From this seed and the emerging evidence of the structure of the cosmic background radiation from the time of the big bang, Tegmark develops the idea of not just one but a tier of multiverses as the inevitable consequence, one of which we inhabit but as a vanishingly small element of the vast whole. So far this is controversial but not new. By framing his proposition about reality as a mathematical structure, however, he presents it in a different way. Everything is mathematical (Pythagoras would be happy). This is neither accidental nor just a convenient way of describing reality; it is inherent in the nature of reality.

Tegmark's approach has the significant merit of addressing some key puzzles that the so-called standard model of physics has yet to explain. Although the discovery of the Higgs boson seems to have saved its status for the time being, there remain a number of fundamental conundrums which have been troubling physicists for decades. Here are some examples:

Initial conditions: the laws of physics can explain what happens to "stuff" but only if the initial conditions are specified, where did they come from?

Randomness: quantum fluctuations are said be completely random, but why?

Uncertainty: Heisenberg's uncertainly principle describes our inability to determine the position and speed of a particle at the same time but cannot account for why.

Fine-tuning: how is that a series of special numbers - the density of dark energy, the mass of the electron etc - are at the very precise levels they need to be to give rise to our universe?

Complexity: the universe appears to contain so much information that no model could possibly describe it.

In Tegmark's mathematical universe, all of these difficulties become functions of our perception of reality and not fundamental principles that we cannot explain. Human-centric perspectives of the cosmos have inhibited progress in understanding it since it was presumed the earth was at its centre. Tegmark's position is that even now our view of what are irreducible "fundamentals" of physics is still too anthropocentric. What may look like universal laws might simply be a function of our "address" in the universe.

Don't draw the conclusion that Tegmark's book is off-puttingly mathematical. His thinking leads to many insightful passages reflecting on the illusion of time, the experience of consciousness, the subjectivity of time flow, whether we are alone in the universe, what are the risks to our civilisation and more.

Whether you are willing to go the distance with Tegmark's arguments depends on how prepared you are to contemplate what appears to be absurd. We are inside a mathematical object. There are four levels of multiverse, in each of which an endless proliferation of universes are developing. There may be an infinitive number of "you" in many of these and you don't know which one you are? When Hugh Everett first developed the "many-worlds" proposition in 1957 his career bombed and his ideas faded from discussion. This could happen to Tegmark too. But one very telling table in the book compares the reaction of an audience of leading physicists to the many-worlds approach, first in 1997 and again in 2010. In 1997, only 16 per cent polled thought Everett's many-worlds ideas worth a light but by 2010 the number was 46 per cent. And of course we all know from the Hitchhiker's Guide to the Galaxy that the answer to "Life, the Universe and Everything" is simply a number, 42.

Nick Sallnow-Smith is a graduate of Cambridge University with a lifelong interest in philosophy