Roger Penrose's book "Fashion, Faith and Fantasy in the New Physics of the Universe" is a fascinating (and challenging) read, but while I understand his mathematical points about how additional dimensions would vastly increase the functional freedom of fields (essentially from $\infty^{a\infty^{3}}$ to $\infty^{b\infty^{9}}$ for a 10 dimensional universe as a prediction from string theory) - what I don't follow is his assertion that this would radically alter the observed physical world.

Why would the universe be so different if functional freedom was increased so enormously when the new dimensions would be (we assume) of the Planck length or similar?


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