Imagine each line of your handwriting as a long tether put on the page, suitably tangled to form the letters but without any knots. If you took the tether by the tips and straightened it out, how longer would it be than the original line? This question is somewhat similar to the How long is the coast of Britain? one frequently used to introduce the concept of fractals.
Speaking of coasts... the left-to-right and back again movement of your hand writing and your eyes reading suggests the movement of waves breaking on the shore. Seen in that light, reading some piece of writing that challenges your worldview is like trying to defend a castle in the sand you took pains to build from the attacks of the rising tide.
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