Cartesian Coordinates in Linear Algebra and Globality

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Discussion Overview

The discussion centers around the historical and theoretical implications of Cartesian coordinates in relation to global applications, particularly in the context of analytic geometry and potential limitations when applied to non-flat geometries.

Discussion Character

  • Debate/contested, Historical, Conceptual clarification

Main Points Raised

  • One participant questions whether Descartes intended his coordinate system to be used globally, referencing a comment about the lack of global application of coordinates.
  • Another participant introduces the concept of longitude and latitude as a counterpoint to the discussion of Cartesian coordinates.
  • A participant expresses confusion regarding the relevance of the previous point about longitude and latitude.
  • It is noted that Cartesian coordinates cannot be applied "on a globe" if they are intended for flat geometries, with a suggestion that this relates to physics and the nature of the universe's geometry.
  • One participant mentions that Cartesian coordinates can exist in any number of dimensions, implying flexibility in their application.
  • A later reply acknowledges that most manifolds require multiple charts, suggesting a connection to the original comment about Descartes' use of coordinates.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Cartesian coordinates in global contexts, with no consensus reached on the historical intent of Descartes or the implications for modern applications.

Contextual Notes

There are unresolved assumptions regarding the definitions of "global" and "flat," as well as the implications of applying Cartesian coordinates to various geometrical contexts.

Bacle
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Hi, Everyone:

I just read recently a comment to the effect that Descartes never intented
his use of coordinates in his layout of analytic geometry to be used globally;
there was also a follow-up comment about " no one really using any coordinates
in a global way. Does anyone know if this is true either way?


( Maybe this is more of a history of Math question, but let me try it here)

Thanks.
 
Physics news on Phys.org
How about longitude and latitude?
 
I'm not sure I get your point.
 
Of course, you cannot use Cartesian Coordinates "on a globe" if it was meant that way!

If you assume a mathematically flat plane, then you can use Cartesian coordinates "globally" but I suspect this is talking about applications to physics in which there is no reason to believe that the universe is "globally" flat.
 
Cartesian Coordinates can be in any dimensions.
 
Yes, I understand most manifolds need more than one chart, but I thought the
comment was related to Descartes' use of coordinates.
 

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