How much of our life is in our minds

  • Thread starter JimmyRay
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  • #26
moving finger said:
a world is not the same as a geometry.
a Euclidean geometry is a geometry. it is not a "world".
a Euclidean geometry may be a self-consistent geometry, but it does not follow from this that a world based on a Euclidean geometry is a self-consistent world.
MF
:smile:
Then please, explain to me what you mean by the term "world." You've given one instance of what a world is not, namely a geometry. I'm not sure I agree with this, but that's not relevant. What exactly, then, is this world you refer to? I can't but help think of it as the geometry of the universe. I guess this is just where mathematicians differ from everyone else. For us, so often, the map is the territory. It does not merely describe the thing, it is the thing. At any rate, what is "world?" Sorry about my digression there.
 
  • #27
89
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lol... okay I understand the axioms...

Whats Euclidean geometry :( .
 
  • #28
JimmyRay said:
lol... okay I understand the axioms...

Whats Euclidean geometry :( .
No worries mate. That's just the regular old geometry you learned in junior-high or high-school. The geometry of the rigid x-y-z axes (I won't bother to generalize it here). Where the interior angles of a triangle sum to [tex]\pi [/tex] radians, or 180 degrees, and all is right with the world. :wink:
 
  • #29
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Ohh I see... so basically this type of geometry is not consistant?

Also, is gravity an axiom, or a proof? Because, it's self-evident but there's nothing to assume...I can see how the number 1 is an axiom because you have to assume it exists since it's abstract... But what about gravity? It is easily seen...
 
  • #30
JimmyRay said:
Ohh I see... so basically this type of geometry is not consistant?

Also, is gravity an axiom, or a proof? Because, it's self-evident but there's nothing to assume...I can see how the number 1 is an axiom because you have to assume it exists since it's abstract... But what about gravity? It is easily seen...
No, Euclidean geometry is completely self-consistent. As are non-Euclidean geometries. Key phrase here is self-consistent. May not be consistent with other models or conceptions of geometry, but self-consistent. That is, you do not arrive at any false statements in the geometry when proceeding logically from the axioms of that geometry. Gravity an axiom or a proof? I don't really understand your question, sorry. Gravity exists. I am sure one of the physicists here would be able to give you some idea of just what it is. I'm sorry that I can't really help you there. :redface:
 

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