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Perspective on Time

Author John McPhee offers an interesting analogy for geologic time. First, represent the history of the earth by the width of your outstretched arms. Now, have someone take a nail file and run it once carefully across your furthest fingernail.

McPhee's claim: You have just removed all of human history.

Question: Does this analogy sound correct? That is, check the veracity of the analogy by using some mathematics.