Spontaneous Dimensional Reduction?

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Several lines of evidence hint that quantum gravity at distances a bit larger than the Planck scale may become effectively two-dimensional.  I will summarize the evidence for this "spontaneous dimensional reduction," and suggest a further argument based on the effect of vacuum fluctuations on light cones.  If this description proves to be correct, it suggests an interesting relationship between small-scale quantum spacetime and the behavior of cosmologies near a spacelike singularity.