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Imaginary Number

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Posts posted by Imaginary Number

  1. To clear this up, lets say that I have a furry sphere with all the hairs combed in the same direction, almost all, will I have a vector that looks like (0)

    (0)

     

    Actually would the same rules apply to "four vectors?"

  2. Energy has always been defined as a scalar quantity since it measures magnitude but, of course has no direction. (E.g. temperature)

    And as we know vectors have magnitude and direction. (E.g: Velocity)

    However, there are 4 dimensions. Our three spacial dimensions and then the fourth: Time. Now as I understand it, everything in the universe is travelling through the fourth dimension at lightspeed. So while energy has no typical direction it has a forwards direction in time. So energy in one place, 3 seconds later, will have traveled forwards (4 dimensionally) by "3 seconds"

    So isn't energy technically a vector?

     

    ;)

  3. Look up vector bundles.

     

    In this context we mean no non-zero globally defined vectors.

     

    In other words, there does not exist an everywhere non-zero tangent vector field on even dimensional spheres. That is at some point(s) on the sphere the vector field will vanish.

     

     

    So if I am understanding you correctly: There has to be somewhere on the sphere where one of the vectors is zero. Is that right?

    I know that a vector is magnitude AND direction, so is the magnitude zero and the direction also zero?

  4. Take a look at Wiki.

     

    It states that there are no non-vanishing continuous vector fields on n-spheres for n even. It is a consequence of the tangent bundle of even dimensional spheres are non-trivial. It has no non-zero global sections.

     

    If you try to comb a "hairy ball" you will always get a tuft.

     

    What do you mean by "non-zero global sections?"

    What are they?

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