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 redefined the nature of geometry, physics, and the human mind. In this class, we take up Riemann’s profound work.
Assignment:

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?

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 nfold 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!