
1 August 2005 Myths and mathematics in our vision of the worldDavid Park The Grand Contraption: The World as Myth, Number, and Chance, Princeton, N.J., Princeton University Press, 2005 (331 pp). ISBN 0691121338 (hard cover) RRP $54.95. There was a time when science, myth, and religion were one. Our best theories of the world were a strange mixture of demons, gods, magic, and mathematics. The Babylonians believed in gods and a universe consisting of six disks. Early Christians believed that a single god created the universe in seven days. And Plato believed that the world we see is an imperfect shadow of the real world of forms and numbers. For these early thinkers there was no place where mysticism and religion stopped, and science began. For instance, a great deal of interest in the science of astronomy was as a result of its importance for astrology—even the great astronomer Ptolemy saw astronomy primarily as the servant to astrology. For some, the personification of nature and laws in the form of gods was the only way the world could be brought within human control. This line of thought is expressed very nicely by Epicurus:
In his latest book, The Grand Contraption: The World as Myth, Number, and Chance, David Park takes us on an intriguing journey from the earliest recorded visions of the world, to the latest scientific theories. The book is perhaps best described as a popular essay in the history of ideas. While Park does discuss modern developments—modern cosmology, general relativity, quantum mechanics, and evolutionary theory—his focus is squarely on the intellectual journey that led us to our modern theories. Park spends a great deal of time on early Greek and Egyptian theories and slowly pushes forward through the Middle Ages, to the Renaissance and beyond. The book covers a great deal of territory, though, partly because of its ambition, it doesn’t always do justice to the material covered. Despite Park’s obvious sympathy for the various historical views of the world, he often fails to deliver sufficient detail to give the reader anything more than a glimpse at the worldviews in question. Moreover, these glimpses are unapologetically skewed towards Park’s own interests—primarily mainstream Western thought, though even here the episodes he focuses on are somewhat idiosyncratic.
Mostly I found Park’s idiosyncratic focus excusable, even though the book occasionally threatens to turn into a potted summary of Park’s own recent reading. I did think, however, that there was too much space devoted to Christian thought. After all, Christianity has never offered much by way of a serious theory of the world. And more than once Christianity has been a major obstacle to developing serious theories of the world and our place in it (think of Christianity’s opposition to Galileo and Darwin, for instance). Indeed, it might be argued that Christianity’s main role in understanding our place in the universe has been a negative one. The question of why so much religious thought has survived long past its useby date might have made for a good final section of the book. But instead, Park wraps things up with a rather odd section presenting an environmental message:
While I have sympathy with Park’s environmental message, it seems something of an afterthought and does not sit well with the rest of the book. Park has written an interesting, albeit somewhat frustrating, book. I particularly liked some of the stories and myths that transcended their original cultural contexts (for example, the Mesopotamian and biblical flood stories, pp. 6–25). Perhaps the greatest value of this book, however, lies in some of the questions and issues it raises. I’ll spend the remainder of this essay on a couple of issues that Park raises but does not explore at any length. The first is the matter of the persistent role of mathematics in science and the second, the uneasy relationship between religion and science. Our scientific theories no longer have the need for demons, gods, and magic, but mathematics remains central to the scientific enterprise. Indeed, all that we currently accept of Babylonian science, for instance, is their mathematics. Gone are their gods and the story of the six disks, but the formula for finding the root of a quadratic remains (Kline 1972, vol. 1, p. 8). Why should mathematics alone survive through the millennia? And how does positing strange abstract entities such as numbers sets and functions help us model and explain the universe? Perhaps mathematical objects are part of the world, and mathematics expresses fundamental truths about these objects. This would explain why we are not inclined to revise even mathematics as old as the contributions of the Babylonians—perhaps they were on to something. Plato held that numbers exist in a realm distinct from the physical world. Although the details of his view seem like mysticism nowadays, something like Plato’s view does find modern adherents among philosophers and mathematicians. Modern ‘Platonists’ hold that mathematical sentences, like the Babylonian quadratic formula, are true and thus entail the existence of mathematical objects. What else would explain the applications of mathematics? Science, it seems, cannot get by without positing mathematical objects.
There is an interesting philosophical puzzle here. Either we accept the existence of mathematical objects or we make a mystery of mathematical applications. One popular position in the philosophy of mathematics is to deny the existence of mathematical objects, and endorse a fictional account of mathematics. According to this view, mathematical sentences such as ‘2+2 = 4’ are, strictly speaking, false (since there are no numbers), but these sentences are true in the story of mathematics. In much the same way, we might take the sentence ‘Harry Potter has magical powers’ to be false (because there is no such person as Harry Potter), but accept that the sentence in question is true in J. K. Rowling’s stories. Fictionalism about mathematics allows us to avoid believing in spooky Platonic entities, but, without further work, the applications of mathematics are still a mystery. After all, what’s so special about mathematics? Why shouldn’t other fictions, like Harry Potter, find themselves indispensable to science? There is a great deal that can be said about this (see Field 1989; Shapiro 2000, pp. 226–256) but I’ll resist the temptation to pursue these issues here. Instead, let’s turn to a related question first articulated by the mathematical physicist Eugene Wigner. Wigner (1960) puzzled over why mathematics finds applications at all: ‘[t]he miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve’ (Wigner 1960, p. 14). The problem here can be seen as a clash of methodologies between empirical science and mathematics. Mathematics, by and large, is an a priori discipline—it does not look to the world for its justification—yet science is in the business of describing and explaining the world—it looks towards the world at every opportunity. As Mark Steiner (1995, p. 154) puts it, ‘how does the mathematician—closer to the artist than the explorer—by turning away from nature, arrive at its most appropriate descriptions?’ Very often mathematicians anticipate the needs of empirical scientists without ever intending to. Again we have a philosophical problem worthy of investigation. It is subtly different from the problem outlined earlier. Surprisingly, though, this problem has received much less philosophical attention (though see Steiner 1998 and Colyvan 2001). Let me finish by elaborating a little on a persistent thread of The Grand Contraption: the relationship between science and religion. As Park very nicely reveals, in ancient times science and religion were one, but by the birth of modern science, cracks began to appear in this unity. One particularly interesting aspect of the increasingly uneasy relationship between science and religion is seen in the development of ‘design arguments’. These are arguments that purport to establish the existence of a god (or at least an intelligent designer) by scientific methods. Such arguments employ inference to the best explanation—some feature of the world is in need of explanation and the best explanation for the feature in question is that things were made that way by an intelligent designer. The features of the world invoked in such arguments have changed over the years—first it was the welladapted nature of life and now it is the fine tuning of the values of various physical constants required for a universe with carbonbased life. It turns out, for instance, that, had the value of the electronproton mass ratio been just a little different from the value it actually takes, the universe would be devoid of carbonbased life. Park briefly discusses such arguments (pp. 286–288) and suggests that ‘[i]t seems that in our universe, the values of these numbers were almost miraculously adjusted so that life could develop and evolve’ (p. 287). It is generally thought that it took the genius of Darwin to dispose of the original biological design argument but the modern, finetuning version of the design argument is alive and well (though see Hume (1955) for a more general attack on such arguments).
It is often thought that the only alternative to an intelligent designer is an equally fanciful multiverse. The idea of the latter is to suppose that there are infinitely many universes, each with the various physical constants set to different values. Under this hypothesis, there is no mystery about why at least one of the universes has the values of the constants required for the emergence of carbonbased life. But there are many problems with this whole style of argument (see Colyvan et al. 2005 and Fitelson et al. 1999). One way to see the shortcomings of these arguments is to consider a parody. If the fundamental physical constants took values too different from what they are, we would not have a universe with carbonbased life in it. But notice that a universe with John Howard as Australian Prime Minister is at least as fine tuned as a universe with carbonbased life. Does this prove that the intelligent designer is a Liberal? While no doubt there are some who find the thought of a Liberal in charge of the Universe appealing, others find a Liberal in charge of this small and insignificant corner of the Universe objectionable enough. In any case (and unsurprisingly), the argument is unsound. (I leave it to the reader to find where this and other design arguments go wrong.) Science and religion have had a long and rather tempestuous relationship. Nowadays it is common to see science as the only game in town. Religion is at best a rather quaint reminder of our lessscientific past, and at worst an impediment to serious thought. Park’s book, and its focus on early visions of the world, reminds us that the relationship between science and religion was once a happy and seamless one. While those days are gone, there is much to be learnt about science and religion by recalling a time when both were young. REFERENCESColyvan, M. 2001, ‘The miracle of applied mathematics’, Synthese, vol. 127, no. 3, pp. 401–408. Colyvan, M., Garfield, J.L. & Priest, G. 2005, ‘Problems with the argument from finetuning’, Synthese, vol. 145, no. 3, pp. 325–338. Field, H. 1989, Realism Mathematics and Modality, Blackwell, Oxford. Fitelson, B., Stephens, C. & Sober, E. 1999, ‘How not to detect design’, Philosophy of Science, vol. 66, pp. 472–488. Hume, D. 1955, Dialogues Concerning Natural Religion, ed. H.D. Aiken, Hafner Publishing Co., New York. Kline, M. 1972, Mathematical Thought from Ancient to Modern Times, Oxford University Press, New York. Shapiro, S. 2000, Thinking About Mathematics: The Philosophy of Mathematics, Oxford University Press, Oxford. Steiner, M. 1995, ‘The applicabilities of mathematics’, Philosophia Mathematica, vol. 3, pp. 129–156. Steiner, M. 1998, The Applicability of Mathematics as a Philosophical Problem, Harvard University Press, Cambridge, MA. Wigner, E.P. 1960, ‘The unreasonable effectiveness of mathematics in the natural sciences’, Communications on Pure and Applied Mathematics, vol. 13, pp. 1–14. Mark Colyvan is Professor of Philosophy at the University of Queensland. His interests include logic, decision theory, and philosophy of science and mathematics. He is the author of The Indispensability of Mathematics (Oxford University Press, 2001) and (with Lev Ginzburg) Ecological Orbits: How Planets Move and Populations Grow (Oxford University Press, 2004). View other articles by Mark Colyvan:


