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A lamp flickering on and off inspires the math mystery of Thomson's lamp

If you switch a lamp on and off an infinite number of times, will the light end up on or off? Somehow math says both

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Thomson scattering is the scattering of photons by free electrons in an ionized gas. Since the number density of scattered photons and their spectral distribution is directly related to important plasma properties such as ne and Te, it is one of the most prominent techniques in plasma diagnostics.

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