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In analyzing such problems, precision may be impossible, but you can quickly estimate a range for the right answer. Many problems are too complicated for you to come up with an accurate answer immediate. In a world where we are continuously bombarded with qualitative and quantitative information (and disinformation,) acquiring a solid grounding in numeric literacy has almost become an important intellectual obligation. The ability to reach first-order estimations is an important skill in daily life.
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The Ability to Guesstimate: A Key Problem-Solving Aptitude Before investing a big effort to measure something with precision, problem-solvers can estimate the answer approximately-and only then determine if it’s sensible to do the extra steps to calculate the accurate answers. One distinctive feature of Fermi problems is that precision is impossible to achieve quickly, but it’s easier to arrive at a fast estimate of the range for the right answer. Contestants are asked to estimate unusual assessments (the fraction of the surface area of the United States that’s covered by automobiles, the number of cells in the human body, the number of pizzas ordered this year in the state of California, for example) as closely as they can. The Fermi technique is so popular that math buffs organize competitions in Fermi’s honor. Back-of-Envelope Calculations for Fermi Problems This sequence of thinking, accompanied by a few conversion factors, can lead to an adequate assessment of the number of piano tuners in Chicago. A problem-solver guesstimates the total population of Chicago, then the fraction of families in Chicago that may own a piano, and the frequency of piano-tuning, the time it takes to tune a piano, and so on. The challenge of estimating the number of piano tuners in the city of Chicago is the classical example of a Fermi Problem.
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Classic Fermi Problem: Number of Piano Tuners in the City of Chicagoįermi problems are typically restructured by breaking them up into smaller problems that are easier for the students to approach than the original problem.
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Such approximate calculations were considered necessary to decide if an onerous and lengthy full-blown calculation was required. The historical emphasis on the order-of-magnitude calculation was propelled by the lack of computing power available to solve complex problems. Teaching Physics Students the Fermi Way of Contemplating Open, Non-Standard Problemsīased on Fermi’s technique, at the beginning of many physics courses, professors pose problems such as “how many piano tuners are there in Chicago?” Such questions require students to employ quick reasoning and unsophisticated numerical methods to attack problems without the knowledge of any core physics concepts. A good way to solve physics problems-and complex problems in any line of work-is by coming up with simple shortcuts to make approximate, but meaningful, calculations. Even though Fermi’s estimate appears 50% off, it was a reasonable order-of-magnitude estimate.įermi believed that the ability to guesstimate was an essential skill for physicists. Fermi’s guesstimate of 10 kilotons of TNT was remarkably close to the now-established value of 20 kilotons. After some coarse calculation, Fermi estimated the power of the blast from the motion of the scraps as they fell. In one well-known example, when the first atomic bomb was detonated during the Manhattan Project, Fermi dropped a few scraps of paper as the shock wave from the detonation passed. Physicist Enrico Fermi Was a Master of Guesstimationįermi was celebrated for his ability to make fast, excellent approximate calculations with little or no concrete data. Non-standard problems such as these are called “Fermi problems” after the distinguished Italian-American nuclear physicist Enrico Fermi (1901–54.) Fermi delighted not only in creating and solving them, but also in challenging his fellow scientists with similar problems. What’s the size of the market for razors in China? How many golf balls does it take to fill a Boeing 747 aircraft? How many piano tuners are there in the world?