Desmond Sander

I am interested in understanding what happens. It goes without saying, at least for me, that physics — I mean 20th. Century physics — is our best account so far of what happens, very compelling and astonishingly successful. But physics, as is well-known has some deep problems. I have slowly come to realise that the source of those problems is a philosophical mistake, a mistake that is not restricted to physicists but shared by nearly everyone. To put it briefly, it is the belief of nearly everyone that there is just one reality and just one truth, the truth about that reality. I think that physics can be made right, or at least made better, by dropping that faith and accepting that there are many realities, and consequently many times, and that truths about those realities are not given but are reached by agreement.

REVIEW OF: The Symbolic Species - The co-evolution of language and the human brain, by Terrence Deacon, Penguin, 527pp, 1997. Terrence Deacon works at the interface between neurobiology, developmental biology and biological anthropology. He is ideally placed to bring together the insights of the very different sciences of palaeontology and physiology into the nature and origins of language. The pleasures of his book are in the detail, the expert knowledge that the author brings to bear, the lucidity of writing that must at times be quite technical. The reviewer sees a main inadequacy of the book in its cavalier treatment of language itself, and especially of what the author calls "Chomsky's Handstand".

A physics that fails to take account of minds, or account for them, cannot be quite right; a physics that accounts so beautifully and so powerfully for so much of what we observe cannot be quite wrong. This book had that conundrum as its starting point, and resolves it. The mindful physics we need is complementary to the compelling and successful but mind-ignoring physics of today. It is the physics that life, especially human life, has made and is making here on the planet Earth, where brains and minds, and what they do, are located. To accept mindful physics, a resolutely empirical way of thinking is required that differs radically from the classical thinking (often called “realism”) that has held us, like a theology. The book grapples with the difficulties of giving up that faith to reach a more complete understanding of what happens. By embracing each and every individual brain/mind as an empirical phenomenon, a new physics is obtained that accepts and includes the mind-independent physics of the 20th century, greatly extends its power, resolves its deepest issue and brings us closer to a complete coherent account of what happens. Mindful physics throws new light on phenomena, including time and entanglement, that have not been well understood. The author is a winner of the Lester R. Ford Award for mathematics writing of the Mathematical Association of America.

Proof by refutation of a geometry theorem that is not universally true produces a Gröbner basis whose elements, called side polynomials, may be used to give inequations that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the kind of truth of the theorem may be derived from the basis; and that the side polynomials may be classified in a useful way. We analyse the relationship between side polynomials and kinds of truth, and we give a unified algorithmic treatment of side polynomials, with examples generated by an implementation.

REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.