John D. Barrow: Impossibility: The Limits of Science and the Science of Limits (1998)

Edition: Oxford University Press, 1998
Review number: 483

In what is almost a response to John Horgan's The End of Science, Barrow examines the limitations of scientific thought from several different points of view with the aim of working out what science can say about what it cannot say. He skims quickly over some of the problems Horgan talks about, such as the increasing economic cost of scientific experimentation; these limitations are not scientific in nature (non-scientific events such as a change of government may change their nature) and there is little that can be said about them beyond acknowledging their existence.

Barrow is far more interested in the limitations inherent in modern scientific theories, such as the impossibility of knowing what happens outside the edge of the visible universe. He concentrates on the less well known ideas, rather than ploughing once again the well worn furrow of the popular account of relativity and quantum mechanics. His final section is a brief but sensible account of Gödel's Incompleteness Theorem and its relationship to physics. The problem with this relationship is that it is only possible to determine its nature when the more basic question of how mathematics is embodied in the universe is answered. If mathematical physics is only a description of patterns in the universe, for example, then there is not necessarily any connection. Even if sufficiently complex mathematics is in some way embodied in the universe - you need to have arithmetic with both addition and multiplication - then it is not at all clear what the physical version of a Gödel Undecideable Sentence would be (it would depend on the precise nature of the embodiment, for a start).

Barrow is less polemic than Horgan, more interested in the nature of the various types of scientific impossibility than in ramming home the point that there are limitations to science. Barrow is much more pro-science than Horgan - he is after all a research physicist - which means that his book is less excitingly iconoclastic but perhaps more informative. (The structure of the book also helps here; Horgan's is organised around interviews with prominent scientists which means that his main philosophical points are hidden behind personalities.)