What Are the Different Spaces Explored by Physicists and Mathematicians?

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Discussion Overview

This thread explores the various mathematical and physical spaces utilized by physicists and mathematicians, including but not limited to the complex plane, quaternions, and different geometrical frameworks. The discussion is open-ended and invites contributions on both theoretical and conceptual aspects of these spaces.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • One participant introduces a poetic perspective on various mathematical spaces, mentioning complex planes, quaternions, and Riemann geometries.
  • Another participant humorously suggests that the initial post could serve as the basis for a textbook on Mathematical Physics.
  • A participant questions whether the discussion should focus on different states of matter or on the concept of space itself.
  • A later reply clarifies that the focus is on different mathematical spaces, providing examples such as the real number line, complex plane, and Euclidean plane.

Areas of Agreement / Disagreement

Contextual Notes

Ben-CS
Do you know the Complex Plane?
Quaternions aren't such a pain!
Do you sing soliloquies
Concerning Reimann Geometries
Of balancing your Tensors,
Spinors and Complex Vectors?
Phase Spaces! Hilbert Spaces!
Oh, so many, many wacky places!



This is an open-ended thread dedicated to the discussion of various spaces used by physicists and mathematicians.
 
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Add a few more lines and you' ve got a brand new university textbook on Mathematical Physics

-----
"Torture him, that's a good idea..."
 
Do you mean that we should discuss different states of matter, that are described by physicists and mathematicians? Or do you mean different concepts of space itself, altogether?
 
I mean different spaces. The real number line (denoted R) is a space. The complex plane (C) and the Euclidean plane (R^2) are other common examples of spaces.
 

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