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The phrase back-of-the-envelope calculations (abbreviated "BotEC") 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. A widespread but false urban legend holds Abraham Lincoln wrote the Gettysburg address on the back of an envelope while on the train to Gettysburg.
Note that the term is an idiom; 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.
History
The term back-of-the-envelope calculation was coined by the physicist Enrico Fermi to illustrate that complex scientific equations could be approximated within an order of magnitude using only calculations performed only on the back of an envelope. He went on to develop a series of sample calculations which are called to this day "Fermi Questions" or "Back-of-the-Envelope Calculations". (The idea is that a physicist could make a rough estimate using only the space on the back of an envelope or a cocktail napkin.)
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.
- Fermi was known for getting quick and accurate answers to problems which would stump other people. The most famous instance came during the first atomic bomb test in New Mexico on July 16, 1945. As the blast wave reached him, Fermi dropped bits of paper. By measuring the distance they were blown, he could compare to a previously computed table and thus estimate the bomb energy yield. He estimated 10 kilotons of TNT, the measured result was 18.6. This method of getting approximate and quick answers through "back of the envelope" calculations became informally known as the Fermi method.
External links
"Back-of-the-envelope calculation"