5 — Bernhard Riemann and the Shape of Economic Space

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.



  1. 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?

  2. 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


Showing 5 reactions

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  • Benjamin Deniston
    followed this page 2017-11-06 00:45:33 -0500
  • Jonathan Thron
    commented 2017-11-04 06:33:24 -0400
    Dear Basement,

    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)
  • Jason Ross
    commented 2017-11-03 14:55:14 -0400
    Gregory – I hope the answer during the class was helpful. Let me know if you have further questions.

    You’re welcome, Michele!
  • Michele Greene
    commented 2017-11-01 20:55:57 -0400
    The fog is lifting. Great class. Thanks.
  • Gregory Unger
    commented 2017-11-01 20:12:07 -0400
    Can you please explain singly, doubly, and triply extended manifolds again?

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