The Science of Can and Can't - Chiara Marletto *****

Without doubt, Chiara Marletto has achieved something remarkable here, though the nature of the topic does not make for an easy read. The book is an attempt to popularise constructor theory - a very different approach to physics, which Oxford quantum physicist David Deutsch has developed with Marletto. Somewhat oddly, the book doesn't use the term constructor theory, but rather the distinctly clumsier 'science of can and can't'.

The idea is that physics is formulated in a way that is inherently limited because it depends on using mechanisms that follows the progress of dynamic systems using the laws of physics. This method isn't applicable in circumstances where either something may happen, but won't necessarily, nor where something isn't allowed to happen (hence the science of can and can't, which probably should be the science of could and can't if we are going to be picky).

Deutsch and Marletto have proposed a way of using 'counterfactuals' - describing systems where such limitations apply and getting to understand their characteristics in a way that makes it possible to at least consider formulating physics anew, overcoming these limitations and, they hope, even making it possible to consider overcoming the divide between quantum physics and general relativity.

The only way really to get your head around counterfactuals is through examples - for example, Marletto considers a book. We can't use conventional physics to project its future influence on the world around it because it's a case that it could be read and that could change someone's behaviour. One of the significant changes that the counterfactual view delivers is to bring information to the heart of the description of physical processes.

All this is genuinely fascinating - it really isn't at all clear if it will ever deliver anything useful, but it is a totally different way of looking at physical systems and makes a kind of mind-boggling sideways sense. Marletto's writing is approachable and, though I initially suspected her idea of ending each chapter with a short story would prove rather irritating - fiction with a message rarely work well - most of the stories work well. I wish the book got going sooner - Marletto spends an inordinate time skirting around defining what counterfactuals are, and the book doesn't really get beyond the groundwork until about 50 pages in. Oh, and it appears the proofreaders at Allen Lane don't know what the plural of 'aircraft' is.

Probably because the book is an attempt to present in a hand-waving fashion what is no doubt a mathematical concept, it does seem sometimes as if the description of what's happening could be tightened up, as it can veer from the ambiguous to the downright confusing. So, for example, in developing one of the required elements of this theory, we are given the example of an aircraft factory, where we are asked to identify the one thing that will stop the factory working properly if it is eliminated. This, we are supposed to deduce, is the sequence of instructions for constructing the plane. But it would seem equally possible to stop it working by preventing raw materials arriving or removing all the machinery or the workers.

Elsewhere, Marletto uses common terms in ways that don't really match the way they are normally used. Both knowledge and information medium, for example, are given new definitions. Here, for example, a book would not be an information medium, because in the definition used you can't have a read-only information medium. A couple of times in the book, Marletto gives a rather fan-like mention of Philip Pullman's fantasy concept of 'dust' (using it as a parallel for dark matter) - but the real fictional parallel for the whole thing is with the work of another Oxford author, Lewis Carroll.

It was Carroll who had Humpty Dumpty using words to mean what Humpty wanted them to mean - and there's a distinct sense of that going on here. In fact, because counterfactuals feel strange and intangible as a concept, I was constantly reminded of Carroll's poem, The Hunting of the Snark. In the poem the characters are in pursuit of something really important - requiring huge effort - yet they don't really know what it is, until we get to the dark final lines: 'In the midst of a word he was trying to say, In the midst of his laughter and glee, He had softly and suddenly vanished away - For the Snark was a Boojum, you see.' 

I very much hope that counterfactuals are not a Boojum. We don't know yet - but there is no doubt that the hunt is a fascinating one, just as was that for the Snark - and despite the difficulties of getting constructor theory clear in the reader's head, this book is a remarkable attempt to bring this particular Snark to life.

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Review by Brian Clegg