•  118
    Hermann Grassmann and the Creation of Linear Algebra
    The American Mathematical Monthly 86 809-817. 1979.
    One may say without great exaggeration that Grassmann invented linear algebra and, with none at all, that he showed how properly to apply it in geometry.
  •  29
    This is merely the longish abstract of a talk I gave in 2001, that now seems to make more sense than ever.
  •  52
    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 everyo…Read more
  •  10
    Brain/mind — WHY THINKING WORKS
    Aenesidemus Press. 2016.
    This short eBook introduces STRICT EMPIRICISM, an alternative to analytic philosophy, and MINDFUL PHYSICS, the alternative to modern physics that it licenses. Mindful physics illuminates what happens and what is made to happen. If you think that an adequate understanding of consciousness, language, laws, quantum mechanics, time and life will require a new understanding of thinking, then brain/mind is for you.
  •  6
    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 a…Read more
  •  256
    The Kinds of Truth of Geometry Theorems
    with Michael Bulmer and Tim Stokes
    In Jürgen Richter-Gebert & Dongming Wang (eds.), LNCS: Lecture Notes In Computer Science, Springer Verlag. pp. 129-142. 2001.
    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 ana…Read more
  •  95
    The Idea of a Diagram
    In Hassan Ait-Kaci & Maurice Nivat (eds.), Resolution of Equations in Algebraic Structures, Academic Press. 1989.
    A detailed axiomatisation of diagrams (in affine geometry) is presented, which supports typing of geometric objects, calculation of geometric quantities and automated proof of theorems.
  •  48
    Automated Theorem Proving and Its Prospects (review)
    PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2. 1995.
    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…Read more
  •  116
    The Origin of Language (review)
    Human Nature Review 2. 2002.
    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 luci…Read more