Re: Could the 'missing dimensions' be quarks?

Posted by DickT on September 15, 2003 at 06:45:16:

In Reply to: Re: Could the 'missing dimensions' be quarks? posted by rickww on September 14, 2003 at 22:24:28:

Rickww,

Now deflate it without popping it, and it forms a ring with a sheet of rubber across it. If the material could be assumed to have zero thickness, you would have reduced a 3D object to a 2D entity.

No. The balloon, the thin rubber object was two dimensional all the time. For example you could have drawn latitude and longitude lines on it and expressed locations in each coordinate patch with two numbers, just as you can do in the plane. Of course that doesn't work globally; topology shows that you need two coordinate patches. But as long as you can cover an object with a set of overlapping coordinate patches that are "homeomorphic" to the plane and match up on their intersections, you have a two dimensional manifold.

Now when you had the balloon full of water you had a three dimensional object, a "ball", but you threw the water away and were left only with the surface of the ball.

Regards,
Dick

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