Comments by "John Berry" (@user-ud6ui7zt3r) on "This Is the Calculus They Won't Teach You" video.
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Engineers tend to "run over" Mathematics, with about the same disregard that a charging Monster Truck displays towards a parked VW Super Beetle. When that TV show The Big Bang Theory was in production, they always depicted the ongoing rivalry between a Theoretical Physicist and an Engineer, but I think they should have included the classic rivalry that goes on between Engineers and Mathematicians. Afterall, Mathematicians define that...
only a square matrix can possess an inverse
...but meanwhile, Engineers regularly produce non-square matrices, and state that such a matrix suddenly becomes 'singular' (i.e. suddenly possesses no inverse) in the event that one of the rows of the matrix has all of its terms sufficiently approach ZERO (i.e. the matrix "loses rank.") Engineers also unilaterally take it upon themselves to redefine the Euler Angles [that is to say α (alpha), β (beta), and γ (gamma)], so that these angles indicate rotation about the x-axis, rotation about the y-axis, and rotation about the z-axis, respectively. Engineers do this because they are interested in partial differentials and Jacobian matrices, for the purpose of controlling 6DOF (i.e. 6 joint) robots. Meanwhile, back over in "math class", the Euler Angles (α β γ) are always stated with respect to some 3D vector, whose "tail" is at the Origin, and with respect to the angles that such a vector makes relative to the x-axis (this would be α ), relative to the y-axis (this would be β), and relative to the z-axis (this would be γ.) The Mathematicians' definitions for α β γ came FIRST, but the Engineers don't care. Engineers just go ahead AND RE-USE the already defined angle variables α β γ, while simultaneously instantiating COMPLETELY NEW definitions for these variables. In this way, Engineers "run over" Mathematicians.
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