Fermi-Problem

As Fermi - Fermi problem or question is called a quantitative estimate for a problem in which virtually no data are available initially. It is named after nuclear physicist Enrico Fermi, who was known to be able to deliver spontaneously good estimates despite a lack of information - for example, he threw the first atomic bomb test ( Trinity test ) scraps of paper in the air and watching how far they were blown away by the pressure wave; from which he could directly estimate the approximate explosive force of the bomb site long before sensor measurements were evaluated.

Method

The challenging aspect of such problems is that you have no direct experience of a similar problem, nor the necessary data are available with which one could directly do a calculation. On the other hand, one knows the relationships in the context of the problem quite well and can use this to get an indirect route to a solution.

The prerequisite for the solution of a Fermi problem, then, is a certain general knowledge and " common sense ". Because of this knowledge, however, can not be use directly for the solution, one must quantify this knowledge and thereby justify the assumptions. From these partial estimates, the overall result is then - often only in several stages - determine. The lack of empirical values ​​for the overall problem so we compensated by the fact that empirical values ​​are available for sub-problems; and the absence of data for the calculation are compensated from these estimates for the sub-problems.

The overall result is often surprisingly accurate ( at least in the right order of magnitude ). ( Or could break them even further ), since we know the sub-problems quite well, their estimates are quite good and move around the actual values. In addition, consistently occur no systematic errors, but it is likely that cancel the estimation errors partially cancel each other - if the size was estimated to be too large, another may have been estimated to be too small.

Example: piano tuners in Chicago

The classic example of a Fermi problem is the question of the number of piano tuners in Chicago. Here one has initially neither statistical data with which you can start a calculation (such as the average number of piano tuners per 1000 inhabitants), still experience from other cities that you can extrapolate to Chicago. However, we do quite well, as a piano tuner works; this results in, for example, the following statement.

Assumptions:

• Approximately 3 million people live in Chicago.
• Approximately two people on average live in a household.
• Approximately one in twenty household there is a piano that is tuned regularly.
• Pianos are tuned about once per year.
• It takes about two hours to tune a piano, including travel time.
• A piano tuner has an 8 -hour day, a 5 -day week and works 40 weeks per year.

Hence the number of a year to tune pianos in Chicago:

A piano tuner can handle the following work:

Accordingly, it would have about 100 piano tuners in Chicago give.

This knowledge can, for example, so use: If you want to open a business, the tools for piano tuners sold, and from a further assessment knows that it takes 10,000 potential customers, you can see that as a business, even in a big city like Chicago in far would not be worthwhile. But you can modify its plans and recalculate each time until you encountered a presumably functioning business model.

Application

• Calculations replace: Often one is not equal to the exact result of a calculation is interesting, but would just like to first estimate the order of magnitude. With a good estimate can sometimes abandon the costly computation. Or it may be that an exact calculation is not possible because no data are available - one example is the Drake equation which estimates the number of intelligent civilizations in the Milky Way (see also Fermi paradox).
• Prepare calculations: Instead of performing a mathematical " flying blind ", it is known through an estimate beforehand the magnitude and can judge it, how much effort you have to operate in order to obtain the necessary accuracy. Example, one could estimate the magnitude of velocity and thus assess whether you have to take into account in the accurate calculation of relativistic effects or may neglect this.
• Check Calculations: A calculation error in a complicated calculation does not fall on so fast; with a good estimate can control the outcome, because due to its simplicity there are errors not as likely also the assessment also provides intermediate results. ( It is useful to carry out the assessment first, because you can otherwise easily influenced by the already computed result when estimating. )
• By breaking down into sub-problems with many assumptions, the estimation can be easily improved by sought in each Sub- assessments to more accurate values ​​. If one, however, only a few more complicated basic assumptions, it is usually difficult to improve it.
• By breaking down into sub-problems can specify a lower and upper limit for the overall results with little effort usually by employing the smallest and largest probable value for each sub- problem.
• The procedure for Fermi problems is fundamental to the natural sciences - by solving Fermi problems you learn to break down a complex problem into simpler subproblems, as well as specifying clear of what theories / conditions / assumptions one starts. While it mostly works in science only in small sub-aspects, Fermi problems are usually taken much wider - they require ( for lack of knowledge ) the complete chain of arguments, starting from the description of the basic assumptions; in science are much more popular complete theories as given and only builds on it.