Pauli's conversations with Jung, were, after all, what led Pauli to discover a new property of matter and a new law of nature. What I had first seen as psychobabble had become an avenue of productivity. But those who still believe that the way to save classical music is to reduce it to yet another tawdry entertainment should ponder on these wise words from Stephon Alexander: Words such as cosmology are not the stuff of which click bait is made. In The Jazz of Physics Stephon Alexander links musical forms to cosmology, pointing out that the millions of stars within galaxies are organised into self-similar fractals, just like the fractal structures found in the compositions of Bach and Ligeti, and he uses variants of Feynman diagrams to explain phenomena such as the symmetrical chords that invoke ambivalence in the music of Ravel and others. Stephon Alexander's book is pivotal because it moves the teachings of master veena player and spiritual teacher Hazrat Inayat Khan on the axiomatic role of vibrations - which have influenced many composers including Karlheinz Stockhausen and Jonathan Harvey - from the arena of fuzzy science into scientifically rigorous and peer reviewed academia. String theory is of major importance because it does not just apply to vibrating strings but applies to all matter which is why it has been dubbed 'the theory of everything'. String theory abandons the dogma of traditional physics that a hyper-microscopic view of a vibrating string would show atoms, and instead identifies that there is a fundamental level beyond the atoms which comprises an interlinked network of vibrating strings of energy. (Stephon Alexander is an African American and senior black physicists are as rare as senior black conductors: when he was a PhD student at Brown University in the late 1990s Alexander was one of just three black physics students at PhD level in the U.S.) It is quoted in the recently published The Jazz of Physics by Stephon Alexander, who is a theoretical physicist specializing in string theory and loop quantum gravity and also an accomplished jazz saxophonist. That extract comes from a talk by the theoretical physicist Michio Kaku. The universe is a symphony of vibrating strings. Physics is nothing but the laws of harmony that you can write on vibrating strings. It can be shown by substitution that functions of the form y = A sin (Kx ± ω t) and y = B cos (Kx ± ω t), are solutions to equation (8).The subatomic particles we see in nature, the quarks, the electrons are nothing but musical notes on a tiny vibrating string. Therefore, only those functions for which y (0,t) = 0 = y (L,t) are suitable solutions. The fact that the ends are fixed means that the y amplitude must always be zero at the ends. Now that we know that waves can exist in our system, we can turn our attention to the question of the form of the function y (x,t). The waves will travel with velocity v = (T/μ) 1/2 and the function y(x,t) will be numerically equal to the y displacement at a time t of a point on the string at position x. Therefore, waves can exist in our system. (8) If we let μ/T = 1/v 2, then we see that the equation governing the motion of the string has the same form as the classical wave equation. (7) Realizing that g(x + Δ x) – g(x) Δ x = ∂ g(x) ∂ x = ∂ 2 y ∂ x 2, allows us to rewrite equation (7) in its final form, ∂ 2 y ∂ x 2 - μ T ∂ 2 y ∂ t 2 = 0. Substituting these expressions into equation (6) and rearranging terms yields g(x + Δ x) - g(x) Δ x - μ T ∂ 2 y ∂ t 2 = 0. (6) But m = μ Δ x and a y = ∂ 2 y/ ∂ t 2. (5) Applying Newton's second law gives ma y = T g(x + Δ x) - g(x). Substituting this into equation (4) and rearranging terms yields F y = T g(x + Δ x) - g(x). (4) To make the notation simpler, we define a function g(x) = ∂ y/ ∂ x | x. Substituting these expressions into equation (3) gives F y = T - ∂ y ∂ x x - ∂ y ∂ x x + Δ x. (3) But tan θ = - ∂ y/ ∂ x | x and tan φ = - ∂ y/ ∂ x | x + Δ x. Applying the small angle approximation to equation (2b) yields F y = T tan θ - tan φ. Since cos θ ≈ cos φ ≈ 1, the horizontal forces cancel leaving a net force only in the y direction.
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