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A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as an envelope. It is more than a guess but less than an accurate calculation or mathematical proof. The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
A similar phrase in the U.S. is "back of a napkin", also used in the business world to describe sketching out a quick, rough idea of a business or product. [1] In British English, a similar idiom is "back of a fag packet".
In the natural sciences, back-of-the-envelope calculation is often associated with physicist Enrico Fermi, [2] who was well known for emphasizing ways that complex scientific equations could be approximated within an order of magnitude using simple calculations. He went on to develop a series of sample calculations, which are called "Fermi Questions" or "Back-of-the-Envelope Calculations" and used to solve Fermi problems. [3] [4]
Fermi was known for getting quick and accurate answers to problems that would stump other people. The most famous instance came during the first atomic bomb test in New Mexico on 16 July 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. [5] [6]
Perhaps the most influential example of such a calculation was carried out over a period of a few hours by Arnold Wilkins after being asked to consider a problem by Robert Watson Watt. Watt had learned that the Germans claimed to have invented a radio-based death ray, but Wilkins' one-page calculations demonstrated that such a thing was almost certainly impossible. When Watt asked what role radio might play, Wilkins replied that it might be useful for detection at long range, a suggestion that led to the rapid development of radar and the Chain Home system. [7]
Another example is Victor Weisskopf's pamphlet Modern Physics from an Elementary Point of View. [8] In these notes Weisskopf used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics.
In a video interview for the University of California, Berkeley on the 50th anniversary of the laser, Nobel laureate Charles Townes described how he pulled an envelope from his pocket while sitting in a park and wrote down calculations during his initial insight into lasers. [9]
During lunch with NFL commissioner Pete Rozelle in 1966, Tiffany & Co. vice president Oscar Riedner made a sketch on a cocktail napkin of what would become the Vince Lombardi Trophy, awarded annually to the winner of the Super Bowl. [10]
An important Internet protocol, the Border Gateway Protocol, was sketched out in 1989 by engineers on the back of "three ketchup-stained napkins", and is still known as the three-napkin protocol. [11]
UTF-8, the dominant character encoding for the World Wide Web, [12] was designed by Ken Thompson and Rob Pike on a placemat. [13]
The Bailey bridge is a type of portable, pre-fabricated, truss bridge and was extensively used by British, Canadian and US military engineering units. Donald Bailey drew the original design for the bridge on the back of an envelope. [14]
The Laffer Curve, which claims to show the relationship between tax cuts and government income, was drawn by Arthur Laffer in 1974 on a bar napkin to show an aide to President Gerald R. Ford why the federal government should cut taxes. [15]
Upon hearing that the S-IV 2nd Stage of the Saturn I would need transport from California to Florida for launch as part of the Apollo program, Jack Conroy sketched the cavernous cargo airplane, the Pregnant Guppy. [16]
The Video Toaster was designed on placemats in a Topeka pizza restaurant. [17]
Robert Metcalfe's early Ethernet diagrams from his days at Xerox PARC back in the early 1970s might be the most famous napkin sketches in the technology industry.
As the prospect of system meltdown loomed, the men began scribbling ideas for a solution onto the back of a ketchup-stained napkin. Then a second. Then a third. The "three-napkins protocol," as its inventors jokingly dubbed it, would soon revolutionize the Internet. And though there were lingering issues, the engineers saw their creation as a "hack" or "kludge," slang for a short-term fix to be replaced as soon as a better alternative arrived.
He sketched the original design for the Bailey Bridge on the back of an envelope as he was being driven to a meeting of Royal Engineers to debate the failure of existing portable bridges
[Conroy] listened to the conversations around him, then picked up a cocktail napkin and a ballpoint pen. And with the precision he'd learned during the brief months he'd attended engineering school many years before, he drew an airplane that had never been built, to carry a rocket that had never been launched, to take man to a place nobody had ever been before. Jack Conroy had just sketched the airplane that would become the Pregnant Guppy.
Montgomery suggested that Jenison meet his friend Brad Carvey, who had been working on projects involving robotic vision. The three of them got together in a pizza restaurant in Topeka and started drawing block diagrams on the placemats.
Enrico Fermi was an Italian and naturalized American physicist, renowned for being the creator of the world's first nuclear reactor, the Chicago Pile-1, and a member of the Manhattan Project. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics and experimental physics. Fermi was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. With his colleagues, Fermi filed several patents related to the use of nuclear power, all of which were taken over by the US government. He made significant contributions to the development of statistical mechanics, quantum theory, and nuclear and particle physics.
Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.
Border Gateway Protocol (BGP) is a standardized exterior gateway protocol designed to exchange routing and reachability information among autonomous systems (AS) on the Internet. BGP is classified as a path-vector routing protocol, and it makes routing decisions based on paths, network policies, or rule-sets configured by a network administrator.
J. Robert Oppenheimer was an American theoretical physicist who served as the director of the Manhattan Project's Los Alamos Laboratory during World War II. He is often called the "father of the atomic bomb" for his role in overseeing the development of the first nuclear weapons.
A sanity check or sanity test is a basic test to quickly evaluate whether a claim or the result of a calculation can possibly be true. It is a simple check to see if the produced material is rational. The point of a sanity test is to rule out certain classes of obviously false results, not to catch every possible error. A rule-of-thumb or back-of-the-envelope calculation may be checked to perform the test. The advantage of performing an initial sanity test is that of speedily evaluating basic function.
A Bailey bridge is a type of portable, pre-fabricated, truss bridge. It was developed in 1940–1941 by the British for military use during the Second World War and saw extensive use by British, Canadian and American military engineering units. A Bailey bridge has the advantages of requiring no special tools or heavy equipment to assemble. The wood and steel bridge elements were small and light enough to be carried in trucks and lifted into place by hand, without the use of a crane. These bridges were strong enough to carry tanks. Bailey bridges continue to be used extensively in civil engineering construction projects and to provide temporary crossings for pedestrian and vehicle traffic.
Frederick Reines was an American physicist. He was awarded the 1995 Nobel Prize in Physics for his co-detection of the neutrino with Clyde Cowan in the neutrino experiment. He may be the only scientist in history "so intimately associated with the discovery of an elementary particle and the subsequent thorough investigation of its fundamental properties."
In physics, mean free path is the average distance over which a moving particle travels before substantially changing its direction or energy, typically as a result of one or more successive collisions with other particles.
Hans Albrecht Bethe was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel Prize in Physics for his work on the theory of stellar nucleosynthesis. For most of his career, Bethe was a professor at Cornell University.
Processor power dissipation or processing unit power dissipation is the process in which computer processors consume electrical energy, and dissipate this energy in the form of heat due to the resistance in the electronic circuits.
Chain Home, or CH for short, was the codename for the ring of coastal early warning radar stations built by the Royal Air Force (RAF) before and during the Second World War to detect and track aircraft. Initially known as RDF, and given the official name Air Ministry Experimental Station Type 1 in 1940, the radar units were also known as Chain Home for most of their life. Chain Home was the first early warning radar network in the world and the first military radar system to reach operational status. Its effect on the war made it one of the most powerful systems of what became known as the "Wizard War".
In physics or engineering education, a Fermi problem, also known as a order-of-magnitude problem, is an estimation problem designed to teach dimensional analysis or approximation of extreme scientific calculations. Fermi problems are usually back-of-the-envelope calculations. The estimation technique is named after physicist Enrico Fermi as he was known for his ability to make good approximate calculations with little or no actual data. Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds. In some cases, order-of-magnitude estimates can also be derived using dimensional analysis.
The Boeing 377 Stratocruiser was a large long-range airliner developed from the C-97 Stratofreighter military transport, itself a derivative of the B-29 Superfortress. The Stratocruiser's first flight was on July 8, 1947. Its design was advanced for its day; its relatively innovative features included two passenger decks and a pressurized cabin. It could carry up to 100 passengers on the main deck plus 14 in the lower deck lounge; typical seating was for 63 or 84 passengers or 28 berthed and five seated passengers.
Chicago Pile-1 (CP-1) was the world's first artificial nuclear reactor. On 2 December 1942, the first human-made self-sustaining nuclear chain reaction was initiated in CP-1 during an experiment led by Enrico Fermi. The secret development of the reactor was the first major technical achievement for the Manhattan Project, the Allied effort to create nuclear weapons during World War II. Developed by the Metallurgical Laboratory at the University of Chicago, CP-1 was built under the west viewing stands of the original Stagg Field. Although the project's civilian and military leaders had misgivings about the possibility of a disastrous runaway reaction, they trusted Fermi's safety calculations and decided they could carry out the experiment in a densely populated area. Fermi described the reactor as "a crude pile of black bricks and wooden timbers".
Guesstimate is an informal English portmanteau of guess and estimate, first used by American statisticians in 1934 or 1935. It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture. Like the words estimate and guess, guesstimate may be used as a verb or a noun. A guesstimate may be a first rough approximation pending a more accurate estimate, or it may be an educated guess at something for which no better information will become available.
Fermi 1 was the United States' only demonstration-scale breeder reactor, built during the 1950s at the Enrico Fermi Nuclear Generating Station on the western shore of Lake Erie south of Detroit, Michigan. It used the sodium-cooled fast reactor cycle, in which liquid sodium metal is used as the primary coolant instead of typical nuclear reactor designs cooled by water. Sodium cooling permits a more compact core, generating surplus neutrons used to produce more fission fuel by converting a surrounding "blanket" of 238U into 239Pu which can be fed back into a reactor. At full power, it would generate 430 MW of heat (MWt), or about 150 MW of electricity (MWe).
Jesse Ernest Wilkins Jr. was an American nuclear scientist, mechanical engineer and mathematician. A child prodigy, he attended the University of Chicago at the age of 13, becoming its youngest ever student. His graduation at a young age resulted in him being hailed as "the Negro Genius" in the national media.
The Los Alamos Primer is a printed version of the first five lectures on the principles of nuclear weapons given to new arrivals at the top-secret Los Alamos laboratory during the Manhattan Project. The five lectures were given by physicist Robert Serber in April 1943. The notes from the lectures which became the Primer were written by Edward Condon.
John Michael Conroy was an American aviator and later businessman, whose company Aero Spacelines developed the Pregnant Guppy, Super Guppy, and Mini Guppy cargo aircraft. He later founded Conroy Aircraft and Specialized Aircraft in Santa Barbara, California.
Kepler is the codename for a GPU microarchitecture developed by Nvidia, first introduced at retail in April 2012, as the successor to the Fermi microarchitecture. Kepler was Nvidia's first microarchitecture to focus on energy efficiency. Most GeForce 600 series, most GeForce 700 series, and some GeForce 800M series GPUs were based on Kepler, all manufactured in 28 nm. Kepler found use in the GK20A, the GPU component of the Tegra K1 SoC, and in the Quadro Kxxx series, the Quadro NVS 510, and Tesla computing modules.
