17 equations that changed the World (#2)

(continuation of the book review)

“If you placed your finger at that point, the two halves of the string would still be able to vibrate in the sin 2x pattern, but not in the sin x one. This explains the Pythagorean discovery that a string half as long produced a note one octave higher.” (p.143)

The following chapters are all about Physics: the wave equation, Fourier’s transform and the heat equation, Navier-Stokes’ equation(s), Maxwell’s equation(s)—as in  The universe in zero word—, the second law of thermodynamics, E=mc² (of course!), and Schrödinger’s equation. I won’t go so much into details for those chapters, even though they are remarkably written. For instance, the chapter on waves made me understand the notion of harmonics in a much more intuitive and lasting way than previous readings. (This chapter 8 also mentions the “English mathematician Harold Jeffreys“, while Jeffreys was primarily a geophysicist. And a Bayesian statistician with major impact on the field, his Theory of Probability arguably being the first modern Bayesian book. Interestingly, Jeffreys also was the first one to find approximations to the Schrödinger’s equation, however he is not mentioned in this later chapter.) Chapter 9 mentions the heat equation but is truly about Fourier’s transform which he uses as a tool and later became a universal technique. It also covers Lebesgue’s integration theory, wavelets, and JPEG compression. Chapter 10 on Navier-Stokes’ equation also mentions climate sciences, where it takes a (reasonable) stand. Chapter 11 on Maxwell’s equations is a short introduction to electromagnetism, with radio the obvious illustration. (Maybe not the best chapter in the book.)

Core in CiRM [1]

Jean-Michel Marin and myself have thus started our “research in pair” in CIRM, Luminy, for a fortnight. We are working on the second edition of Bayesian Core and, despite working round the clock on the project (except for a one hour run around Mont Puget this morning), we are not going as fast as planned… Today, we worked in parallel on the normal and the regression chapters, looking for a sexy normal dataset to replace the larceny (normaldata) and the large and delicate CMB datasets. We eventually settled for a modern version of the Michelson-Morley dataset (available in R as morley), produced by K.K. Illingworth in 1927. I hope the spectral data and the relevance of the experiment will not be lost on the readers.