Stuart Kauffman argues that physics cannot explain biology, and he is right. However, I am willing to grant him this not because his book Reinventing the Sacred makes a clear case, but because I already agreed with its central premise, which is that the reductionist approach to science — the idea that physics explains chemistry, chemistry explains biology, and so forth — has its limits. The book nevertheless provides much food for thought; indeed, its chief merit is that it makes the reader ask fruitful questions. However, it falls short of making an argument that might overturn an entrenched position.

In addition to his central theme of reductionism and what might replace it, Kauffman — a complexity theorist and professor of both biology and physics at Calgary University in Canada — has two further aims for his book. One is to present to the non-expert some fascinating areas of science such as chemical-reaction networks, evolution and graph theory. The other is more ambitious: it aims to reassess in a positive way those areas of human life normally called sacred or spiritual, but from a point of view that does not accept supernatural theism.

Kauffman is at his best when writing about what he knows: complexity theory applied to theoretical biology, and some philosophy. Complexity theory deals with systems that typically involve feedback, non-linearity and structure at many scales; such systems turn out to share patterns of behaviour. Physics has made great strides in describing deterministic behaviour on the one hand and randomness on the other, but “critical behaviour” lies right on a fascinating borderline between these two regimes, and it deserves the widespread attention that Kauffman invites.

His introduction to Boolean networks is clear and stimulating, and their application to the cell’s genetic control machinery is both beautiful and striking. While reading this chapter, it suddenly became obvious to me why a mere gene count is a completely inadequate measure of the complexity of the associated organism. The fact that the human genome is shorter than some, such as the lungfish, should not have surprised anyone.

Kauffman’s treatment of the philosophy of mind is not as careful as a technical treatise would need to be. Still, it is sound and avoids the woefully inadequate statements that have sometimes appeared in connection with neuroscience in otherwise serious scientific journals — particularly claims that demonstrating a correlation between physical brain activity and particular thoughts resolves the mind–body problem or proves the absence or presence of God.

Another strength of the book is that Kauffman maintains reasonably clear lines of demarcation between speculation and knowledge. Within that proper constraint, the text makes some bold and useful speculations, such as the idea that quantum coherence could extend far enough from the surface of protein molecules in the cell to link one protein to another via aligned water molecules. Such speculations are useful because they are both testable and (just) feasible.

Because of these strengths, I would recommend Reinventing the Sacred as a healthy read for anyone who thinks that reductionism is the whole story of science. Reductionism is a good slave but a poor master; in other words, it is the right model for almost all the science we have discovered so far, but it is not necessarily the whole story. Cracks in the reductionist edifice include quantum entanglement, emergent phenomena, criticality and the oldest one of all: human free will, without which it is debatable whether any reasoning, and therefore any science, is possible.

On balance, this is a useful book. However, it also contains some glaring errors and omissions. The chapter on the quantum brain, for example, overinterprets the concept of decoherence, misapplies the word “acausal” and misses out entanglement altogether. The book is also repetitive, and sometimes unpersuasive or overblown. Take, for example, Gödel’s incompleteness theorem, which states that any large enough, finite system of axioms and rules of deduction must give rise to propositions the truth of which cannot be decided within the system. This theorem is relevant to Kauffman’s argument because it shows that not even formal logic can be reduced to a finite number of ideas; mathematics is a rich tapestry of concepts, not a pyramid. Kauffman briefly sketches Gödel’s theorem no less than four times, but he never describes it sufficiently well for a reader unfamiliar with it to follow the argument. On the other hand, if readers are already familiar with Gödel, they do not need repeated incomplete sketches.

Moreover, the central argument is unconvincing when the book implies that a case has been proven when it has not. Concerning the animal heart, for example, an early chapter promises “the organization of the heart arose largely by natural selection, which, as we will see, cannot be reduced to physics”, and in due course some relevant evidence is given. However, when later the text says things like “…as we have seen, this cannot be reduced to physics”, it leaves the reader feeling that something was missing in the middle. The evidence offered is that the emergent complexity of the biosphere may exceed the capacity of any compact description available beforehand to capture it. This and other arguments provide telling evidence for the case against reductionism, but it is, I think, premature to claim that we can prove the case sufficiently well to make reductionism clearly untenable.

The single greatest problem with this book is not in the science, however, but in the reasoning about the sacred. I am encouraged that Kauffman is willing to address questions of meaning and purpose, and his approach is surely preferable to pseudo-scientific statements along the lines of “the purpose of human life is to replicate genes”. His aim is valid and worthy: to draw people together around shared values. With a view to this, the book argues for a kind of pan-theism in which the word “god” is applied to the emergent creativity that exists in the universe.

Kauffman is welcome to promote this idea, but he should recognize that this type of thinking has a very long history and its shortcomings have been carefully thought through. For example, it does not adequately address our most basic hunches, such as the value of individual people above grand impersonal systems, and the need for justice or forgiveness. I would encourage him to explore instead those threads of religious thinking that are willing to seek answers beyond physicality, but that take physical evidence seriously.