Published: The Advantages of Bringing Infinity to a Finite Place

Since 2010  I’ve been thinking about how objects like black holes are drawn by physicists. I’ve since published two articles about this, from the perspective of one of the most influential physicists to deal with the physics of black holes: Roger Penrose. The first article was a short, accessible, piece in Endeavour that came out last year. The second has just come out in Historical Studies in the Natural Sciences. It is longer and somewhat more technical in its treatment of the diagrams. Here’s the abstract:

The history of Penrose diagrams in the physics of General Relativity (GR) is presented. It is argued that the diagrams did conceptual work for physicists, providing a literal place for abstract, formal objects. Penrose diagrams were associated with the mathematics of conformal transformations applied to GR. Together the diagrams and formalism reconfigured the basic concepts of the field—notions of space, time, cosmology, and energy. Nor were the meanings of the diagrams themselves stable over time. Their physical and conceptual evolution is traced. This history also demonstrates the tight integration of the contexts of research and pedagogy in the period investigated (1962–66). Diagrams circulated rapidly between research talks and publications and the pedagogical context of summer school lectures for advanced graduate students. Further reception and circulation of the diagrams is briefly examined.


For those interested in the history of physics, relativity, the relationship of pedagogy and research, and thinking with pictures it should be a good read.


Technology, Biology, and Pocahontas

I wanted to like Tim Wu. He’s a professor at Columbia University Law School, and advocates for freedom on the internet (he coined “network neutrality”). But his latest piece in the New Yorker is appalling.

Things get off to a rocky start with the title (written by the NYer, no doubt) “As Technology Gets Better, Will Society Get Worse?” Three immediate problems jump out: Technology gets better? (According to what yardstick?) Society gets worse? (That yardstick problem again.) And, technology and society can be cleanly differentiated? (According to whom?)* This set up flies red flags for those who study Science and Technology Studies, the History and Philosophy of Science, and related disciplines. Some thought reveals that none of these three problems have neat answers.

Pocahontas circa 1870, Library of Congress, via Wikipedia

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Playing with pretty mathematics: Dirac and Mathematical Beauty (2)

The last post in this series explored the question of whether Dirac was “Eddingtonian” in the sense Olivier Darrigol argues for. Did Dirac follow Eddington’s metaphysics and methodological principles? From an analyses of Darrigol’s evidence and a 1931 paper from Dirac, the conclusion was overall “no,” particularly about the metaphysics. The case is stronger when just considering Dirac’s methodological views. This post goes into more detail about Dirac’s methodology and his aesthetics. It takes a closer look at Dirac’s famous 1928 paper that introduced his relativistic theory of the electron to the world.

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Was Dirac Eddingtonian? Dirac and mathematical beauty (1)

This post will be the first in a short series on Paul Adrien Maurice Dirac and his scientific methodology—what I call in my dissertation his “epistemic strategies.” Dirac was famous for his emphasis on the primary role of mathematics in physical theory. According to Dirac, when crafting a new theory, the mathematics should come first. What sort of mathematics? Pretty, or beautiful mathematics. I’m going to use these posts to try to think through some of the historiographical issues here, and would love feedback with links to good sources on the aesthetics of science.


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