How to understand 11 dimensions

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I've read that string theory requires 11 dimensions, our 3 spatial dimensions, time, and then 7 more dimensions that only exist at sub-nuclear distances. They are described as tightly wound up dimensions, much smaller than a proton.

I don't understand this picture. Mathematically, we can pinpoint any location, no matter how small, using the same 3 Cartesian coordinates. So how does the fact that they are very small mean that they are "extra" dimensions?

I've read that space is quantized at very low distances. Are these new dimensions smaller than one quantized unit? Is that why they exist, regardless of Cartesian mathematics? The math is not relevant at such small distances in the physical world?

I'm confused.
 
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I think you're correlating their size with their higher dimensionality. The two traits aren't necessarily intrinsically bound. The fact that they are said to be very small does not mean that extra dimensions emerge due to the size. These dimensions are merely degrees of freedom in movement. The "strings" will vibrate and wind all throughout this higher dimensional space and move through all of those extra dimensions simultaneously. It is indeed a very difficult concept to visualize, I know.
 
hey thanks, that makes a lot more sense.

I notice that popular science articles often use the same phrases, sometime the same words, to describe scientific principles. Its like they are copying off each other. This one about the extra dimensions being curled up inside very small spaces is one. Your explanation was a lot clearer.

Some others:

"A black hole is an object with so much mass than nothing can escape from it, not even light..."

"The weak nuclear force is associated with certain forms of radioactive decay..."

This reminds me of a cartoon I saw once, where a man is listening to the radio and a parrot is perched nearby. The radio says "that piece was performed by The Academy of St Martin in the Field." And the parrot says, "Neville Marriner conducting. BRRRAAAKKK!"
 
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