So cool! I knew this, but now I'm wondering - is 3 the lowest dimension for which this is true? It's the lowest integral dimension, yes, but in fractal (or Hausdorff) dimensions a little less than 3… - Tom Ritchford

The surprising answer is that for the ant on the fabric (1D) and the ant on the paper (2D) the probability is 1. But for the bird, there is a chance that it wanders off forever without returning. This is also true for dimensions 4,5,6…
Five Paradoxes With Probabilities That Will Puzzle You
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Marcel Moosbrugger
Tom Ritchford
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May 28, 2021
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So cool! I knew this, but now I'm wondering - is 3 the lowest dimension for which this is true?
It's the lowest integral dimension, yes, but in fractal (or Hausdorff) dimensions a little less than 3, is there still a non-zero chance of wandering away from the origin and never coming back?
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Written by Tom Ritchford1.5K Followers
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