Spatial dimensions of our universe

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The discussion centers on the compatibility of Max Tegmark's argument against spatial dimensions beyond three and the implications of string theory, which proposes up to 26 dimensions. Tegmark emphasizes that only extended dimensions suitable for life are relevant, contrasting with compactified dimensions that are theorized to exist at a small scale. The conversation raises questions about the effects of additional dimensions on general relativity and gravitation, as well as the predictions of quantum theory regarding these dimensions. It is noted that quantum gravity and string theory are key frameworks attempting to address these complex issues. Ultimately, the relationship between small-scale and large-scale dimensions remains an open question in theoretical physics.
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On the page 17 of this article by Max Tegmark http://arxiv.org/pdf/gr-qc/9704009v2.pdf, in figure 7, it has been argued that why spatial dimensions other than 3, is not possible for our universe. But in string theory, people are talking about 10, 11 or 26 spatial dimensions (even if these dimensions are thought to be in extremely small scale). Are these two contradicting? If no, why?
 
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We are living(!) on a universe that contains life. So our universe has to have 3+1 dimensions then. What is the difference between small scale dimensions and large scale dimensions? For example what would happen to general relativity and gravitation in that case (the universe with more than 3 dimensions)? Again does quantum theory predict these other dimensions?
 
What is the difference between small scale dimensions and large scale dimensions?

size.
The small ones appear to be tightly wrapped...'compactified'.
Nobody knows why some are small and others are large.
For example what would happen to general relativity and gravitation in that case (the universe with more than 3 dimensions)?

quantum gravity and string theory are approaches trying to tackle such questions
Again does quantum theory predict these other dimensions?

String theory suggests that 'particles' are strings...one dimensional extensions of point particles...whose characteristics, like energy,charge, spin are determined by the nature of the extra dimensions. Seems so far ten spatial and one time dimension are needed to account for the particle [string] characteristics we observe.
 
I always thought it was odd that we know dark energy expands our universe, and that we know it has been increasing over time, yet no one ever expressed a "true" size of the universe (not "observable" universe, the ENTIRE universe) by just reversing the process of expansion based on our understanding of its rate through history, to the point where everything would've been in an extremely small region. The more I've looked into it recently, I've come to find that it is due to that "inflation"...

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