This book is a cultural phenomenology of doing physics. It describes the ways physicists actually do their work--their motives, and their ways of making sense of the world--so that outsiders can understand it. Martin H. Krieger explains that physicists employ a small number of everyday notions to get at the world experimentally and conceptually.

Mathematical theorems are cultural artifacts and may be interpreted much as works of art, literature, and tool-and-craft are interpreted. The Fundamental Theorem of the Calculus, the Central Limit Theorem of Statistics, and the Statistical Continuum Limit of field theories, all show how the world may be put together through the arithmetic addition of suitably prescribed parts (velocities, variances, and renormalizations and scaled blocks, respectively). In the limit — of smoothness, statistical independence, and large N — higher-order parts, such as accelerations, (...) are, for the most, part irrelevant, affirming that, in the end, most of the world's particulars may be averaged over (a very un-Scriptural point of view). (We work out all of this in technical detail, including a nice geometric picture of stochastic integration, and a method of calculating the variance of the sum of dependent random variables using renormalization group ideas.) These fundamental theorems affirm a culture that is additive, ahistorical, Cartesian, and continuist, sharing in what might be called a species of modern culture. We understand mathematical results as useful because, like many other such artifacts, they have been adapted to fit the world, and the world has been adapted to fit their capacities. Such cultural interpretation is in effect motivation for the mathematics, and might well be offered to students as a way of helping them understand what is going on at the blackboard. Philosophy of mathematics might want to pay more attention to the history and detailed technical features of sophisticated mathematics, as a balance to the usual concerns that arise in formalist or even Platonist positions. (shrink)

This chapter studies the scattered career of Prince Frederick August of Augustenburg (1830–1881). Caught between the German-Danish conflict within the Duchies of Schleswig-Holstein, the Prince escaped from parental pressure as well as a lack of perspectives by delving into the riches of the Indian past. As an amateur-Indologist, he reshaped his self-perception and finally wrote the first Western biography of the Mughal emperor Akbar. The study draws on the Prince’s publications and his surviving handwritten documents and tries to highlight India’s (...) role in his process of gaining self-confidence and self-awareness. (shrink)

The ArgumentMost lay users of statistics think in terms of means (averages), variances or the square of the standard deviation, and Gaussians or bell-shaped curves. Such conventions are entrenched by statistical practice, by deep mathematical theorems from probability, and by theorizing in the various natural and social sciences. I am not claiming that the particular conventions (here, the statistics) we adopt are arbitrary. Entrenchment can be rational without its being as well categorical (excluding all other alternatives), even if that entrenchment (...) claims also to provide for categoricity. 1 provide a detailed description of how a science is “normal” and conventionalized. A characteristic feature of this entrenchment of conventions by practice, theorems, and theorizing, is its highly technical form, the canonizing work enabled by apparently formal and esoteric mathematical means. (shrink)

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of (...) mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature. (shrink)

Exact solutions for the partition function of the two-dimensional classical statistical mechanics Ising model may be classified using a scheme of analogy having three moments--analysis, algebra, and arithmetic--developed by Dedekind and Weber in 1882 for providing an algebraic understanding of Riemann’s work. In effect, we have two analogies, a physical one and a mathematical one, coming from very different problems. What is it about the mathematical realm that allows for this threefold analogy, and what is it about the Ising model (...) that allows for such varied modes of solution, and why are the analogies analogous to each other? (shrink)

Krieger revisits the ideas of his now infamous article of some thirty years ago in Science magazine. His aim is to give an account of design, one that experienced designers will say,'Yes, That's just what it is like!' At the same time, Krieger offers an analysis of the tensions that design operates within; between perfection and contingency, between wholes and parts, between the talk we make about the world and the world itself. Krieger takes design—in architecture, landscape, interiors, engineering, and (...) in systems and computer science—to be modeled by traditional theological and artistic problems. And here, he claims, design has traditionally been a redesign of nature. For nature is, as Durkheim would describe it, a totem. Our collective ritual devotion to it allows us to enliven or animate it, and so it may animate us as well. Curiously, much of design and discourse about it now takes place in the computer software engineering world, especially among those concerned with patterns and object- oriented programming. In developing a notion of plastic trees, Krieger probes just what could be wrong with such artifices. As he illustrates, what we call nature is almost always a product of deliberate design. It is as if people make discoveries in exploration, discoveries of places already occupied aboriginally. In essence, he asserts what we actually have is a virtual authenticity, more real than any original could possibly be—since the original was never meant to be sacralized or featured in our lives. A provocative analysis that scholars and students of architecture and planning, environmental studies, engineering and computer science will find stimulating. (shrink)