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XFrequentist comments on Punctuality - Arriving on Time and Math - Less Wrong Discussion
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Good post.
A possible difficulty with this is that if you start 65 minutes early as opposed to 45 minutes early, you may end up spending more time on your preparations, since "oh I still have plenty of time". And then the 65 minutes may become equivalent to what was 45 minutes before, since you are doing things slower. So in order to make sure that the math works as you've described, you should remember to not give in to the temptation to take your time, even if you have more of it.
This is a much better description of my own pre-tardy behavior than the Gaussian.