November 1, 2017 — Over the period 1948–1952, Lyndon LaRouche made a series of discoveries in the field of economics. Key to his breakthrough was his developing a fuller understanding of Bernhard Riemann's 1854 Habilitation Dissertation, which re-defined the nature of geometry, physics, and the human mind. In this class, we take up Riemann’s profound work.
Assignment:
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Using the material covered in this class, quiz two people, asking them to define the geometric ideas of “straight” and “flat.” Did you learn anything from the ensuing discussion?
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Now it’s your turn: can you describe what makes a surface “flat” without referring it to other flat things?
Reading for next class: TBA
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could you give an example of the physical meaning of complex numbers? I know that they’re used to calculate electricity, but I don’t know why that’s possible. Do you know any other physical area where imaginary numbers play a role?
And on manifolds: from studying engineering, I learned that engineers treat a flying airplane as an n-fold manifold. I’m thinking of values like speed, altitude, air pressure and temperature, but there could be more physical magnitudes that are necessary to take into account to safely fly a plane. With those 4 mentioned values, the airplane would be treated as a quadruply extended manifold. I can also think of examples like a power plant, where physical processes like pressure, heat, the amount of electrical output etc matter.
And, I really would like very much to see a video, as Jason proposed, on Gauss’ concept of imaginary numbers; and I’m sure many more people would like to see that as well (just think of the huge number of clicks the Riemann habil. diss. video got ;-) )
Best, Jonathan Thron (my account name is another name, I had problems to loggin, so I created a new account)
You’re welcome, Michele!