Back-of-the-envelope

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The phrase back-of-the-envelope refers to rough calculations that, while not rigorous, test or support a point. They are far more than a guess but far less than a proof. The phrase is generally used in mathematics and physics, and can also be found in many engineering fields.

The phrase is derived from the practice of quickly jotting down calculations on the piece of paper nearest to hand, which in pre-email days often meant the back of an envelope. Another possible origin for the phrase is a widespread (albeit false) myth that Abraham Lincoln wrote the Gettysburg address on the back of an envelope while on the train to Gettysburg.

Note that the term is an analogy; back-of-the-envelope calculations need not be performed on an envelope, or even written on paper; they could be performed on a computer. The defining factor is the use of simplified, scaled-down models.

Examples

  • When British engineer James Nasmyth was asked to build a bigger hammer after the workpiece was too big for existing fall hammers, Naysmyth, after a little thought, sketched out on a piece of paper the design for the steam hammer.

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