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This picture is not Stephen Butterworth (inventor of the Butterworth filter) to whom the text refers. Stephen Butterworth was my grandfather and this is definitely not him!


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It should not take googling far and wide, a standard college book on physics will give you the details. Basically, Snells law on refraction, tells us that light is a wave. Then as diffraction occurs when diffraction gratings are around the wavelength of the incident light, experiments with known diffraction gratings then tells us the wavelength of specific ...


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It's simply in its natural order of discovery: Cosmology & Mechanics, Electromagnetism and then Relativity and Quantum Mechanics. It's determined by what physicists believe are the most prominent discoveries and theories are. In my own schooling, which will more or less reflect my generation (in Britain), this pedagogical order is reinforced several ...


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Here in the US, public high schools date to 1820, and physics instruction began in high schools. Only later was it adopted as a subject in colleges and universities. The original mode of instruction was that there was no laboratory. Students attended lectures, memorized facts from a textbook, and recited those facts from memory. Physics was seen as a ...


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This is a nice question. As a preliminary, it contains a couple of physics mistakes. It seems to me that once black holes were theorised then the obvious singularity at its centre The singularity of a black hole is not a point at its center, it's a spacelike singularity. one would have to ask where the matter and energy went to, if we are to save the ...


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Actually, the farad was the term used for a unit of charge by Latimer Clark and Charles Bright in 1861 in honour of Michael Faraday. But by 1873, it had become the unit of capacitance and was adopted as such by The British Association for the Advancement of Science by the first report of their Committee for the Selection and Nomenclature of Dynamic and ...


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Not really. Peirce received formal training in chemistry at Harvard, and wrote some manuscripts and papers on the subject in 1860s. One of them, The Pairing of the Elements (Chemical News, 1869), published the same year as Mendeleev's celebrated work, even anticipated the periodic law, but in a way common to chemists of the time (Hinrich, Odling, de ...


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Pierce was educated as a chemist and employed as a scientist. He considered himself primarily as a logician in the American school of analytic philosophy. His biographer Joseph Brent, called him 'he was at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing and subject to violent outbursts of ...


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The Physics Today article shows that Michelson knew of C. S. Peirce's unpublished results on measuring the wavelength of sodium emission: Michelson realized that the interferometer he and Morley had developed and were just then using to detect ether drift could also be used to make precise wavelength measurements. In June 1887, after getting initial results ...


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This sounds like the physics equivalent of the Library of Babel by the Argentine author, Jorge Luis Borges and similarly, as fictive. Perhaps in the future we can imagine some such 'Encyclopadia Principae Physicae' hyperlinked to every journal ever printed and instantly accessible to everyone and running to millions of pages and many thousands of volumes and ...


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Witten gave a spinorial proof of the positive energy theorem in GR. This was originally conjectured by Arnowitt, Deser and Misner in the early 60s. Special cases were then shown by a great many people with the general theorem finally established by Schoen and Yau. Witten also gave a super-symmetric physics proof of the Atiyah-Singer index theorem. This had ...


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The Nagaokan model was suggested by Nagoaka and who called it the Saturnian model. He proposed it in 1904, contra Thomsons 'plum pudding' model. It might have been more accurately called the planetary model. In fact, Rutherford credited Nagaoka with the model in his paper of 1911 where he elaborated on his experimental work that showed Nagaoka was justified ...


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Angular velocity is not a vector and not is it a pseudo-vector. These are in fact abbreviations for the correct notion. A rotation in 3d has an axis of rotation. However, when we look at rotations in higher dimensions, say for example in 4d or 5d, the notion of an axis of rotation does not generalise (we can find one in odd dimensions but not in even ones). ...


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Julian Schwinger said of Feynman diagrams: that they brought QFT to the masses. However, he along with Sin-Itiro Tomonaga independently developed an alternative formalism that is non-perturbative from the beginning, in contrast to Feynmans perturbative approach. Feynmans approach, being perturbative, misses a great deal. One does not need to know QFT to ...


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You don't need calculus to show the relationship that you are pointing out. One only needs to plot distance wrt time. Of course one needs instruments that can accurately measure time which is perhaps where Galileo was helped by his discovery that the pendulum can act as an excellent clock. Calculus is required to demonstrate that relationship follows from ...


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And even before units were introduced in physics, people knew, for example, not to add oranges to say, apples. At least this is what I was taught in primary school, and I imagine that this goes back a long way. Unless some evidence turns up showing that Russell or Whitehead were directly influenced by the notion of dimension in physics, I'd say this is just ...


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Galileo did not derive this law. He discovered it from his experiments with inclined planes. And the law for falling body would make possible to discover Newton's second law, not other way around. But the fact that constant acceleration (i.e. gaining equal amounts of velocity in equal amounts of time) meant that path is proportional to time squared was known ...


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Not really discussing history, but since you asked ... (Bold is vector, normal is magnitude) The position vector is $\mathbf r$, the velocity vector is $\mathbf v$, and $\mathbf \omega$ is the angular velocity vector. We know that the angular velocity and the velocity are related through $v = R\omega$, and, if you look carefully, you will see that $R = r\...


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Indeed they did, the OP story is told by Yau in The Shape of Inner Space, pp.169-70. Calculating the number of twisted cubics in the quintic hypersurface was a big early coup for mirror symmetry that attracted mathematicians' attention to string theory and revitalized enumerative geometry. In A pair of Calabi-Yau manifolds as an exactly soluble ...


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Galileo followed a venerable tradition of distinguishing numbers, magnitudes of different kinds (lengths, times, areas, etc.) and ratios. This is somewhat analogous to the strictures of modern dimensional analysis used in physics, but even stricter, and ancient Greeks did not have dimensional constants to bridge the gaps. They did not even have enough ...


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