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April 10, 2026

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"I want to talk about thought experiments and how they can work, and I want to do that by talking about my favorite example which is Maxwell's equations, the laws of electromagnetism. Again, these are more equations, but it's ok because they're on a T-shirt. So these laws govern the behavior of electric and magnetic fields, but actually, when Maxwell was a boy... there was a missing term. ...When Maxwell got into the field these were the equations, and they had been discovered experimentally, and I want to say a little bit about them. So this bit here is Gauss's law\nabla \cdot \mathbf{D} = \rho_\mathrm{v}it says that electric charges produce electric fields. This bit is Ampere's law\mathbf{\nabla} \times \mathbf{H} = \mathbf{J}it says that a electric currents produce magnetic fields. Faraday's law\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}says that oscillating magnetic fields can also produce electric fields... These were discovered and confirmed by a tremendous amount of data. They were consistent with all known measurements/observations of electromagnetism in Maxwell's day, but there are a problem, and the problem was exposed by a . The thought experiment is simply to consider a rapidly oscillating current with a break in the circuit, a ... and the problem is that if you use those equations to calculate the magnetic field next to the capacitor you don't get definite answer, you get two different answers, depending on how you use the equations. So there is something wrong. Even without doing this experiment you know that there is something wrong with those equations, and from this clue and a lot more reasoning... Maxwell was able to figure out that he could fix this by adding one more term [to Ampere's law]...\nabla \times \mathbf{H} = \mathbf{J} +\frac{\partial \mathbf{D}} {\partial t}and with this the equations are mathematically and physically well posed. They give unambiguous answers to questions like the one I mentioned. Now, Maxwell got a huge bonus because... Faraday's law says that an oscillating magnetic field produces an electric field. Maxwell's new term says that an oscillating electric field produces a magnetic field. So each can produce the other, and so you can get a disturbance which is self-sustaining, and which doesn't just sustain... but moves... Faraday, Maxwell, Faraday, Maxwell... you get a self-sustaining disturbance which moves at a velocity that you get from the equations, and the velocity is the speed of light. So Maxwell got a huge bonus for understanding the unification of electricity and magnetism. He understood the nature of light! When I first heard about this in high school I thought this was the coolest thing, and I still do. It's what we're all trying to do."

- James Clerk Maxwell

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"The advance of technology, together with a culture of caution that transcended ideology, caused the nature of power itself to shift between 1945 and 1991: by the time the Cold War ended, the capacity to fight wars no longer guaranteed the influence of states, or even their continued existence, within the international system. A second escape from determinism involved the discrediting of dictatorships. Tyrants had been around for thousands of years; but George Orwell's great fear, while writing 1984 on his lonely island in 1948, was that the progress made in restraining them in the 18th and 19th centuries had been reversed. Despite the defeats of Nazi Germany and Imperial Japan, it would have been hard to explain the first half of the 20th century without concluding that the currents of history had come to favor authoritarian politics and collectivist economics. Like Irish monks at the edge of their medieval world, Orwell at the edge of his was seeking to preserve what little was left of civilization by showing what a victory of the barbarians would mean. Big Brothers controlled the Soviet Union, China, and half of Europe by the time 1984 came out. It would have been Utopian to expect that they would stop there. But they did: the historical currents during the second half of the 20th century turned decisively against communism. Orwell himself had something to do with this: his anguished writings, together with the later and increasingly self-confident ones of Solzhenitsyn, Sakharov, Havel, and the future pope Karol Wojtyla, advanced a moral and spiritual critique of Marxism-Leninism for which it had no answer. It took time for these sails to catch wind and for these rudders to take hold, but by the late 1970s they had begun to do so. John Paul II and the other actor-leaders of the 1980s then set the course. The most inspirational alternatives the Soviet Union could muster were Leonid Brezhnev, Yuri Andropov, and Konstantin Chernenko, a clear sign that dictatorships were not what they once had been."

- Andrei Sakharov

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