Fermi Estimation for Problem Solving

Fermi Estimation for Problem Solving

From “Training Your Brain Power: Fermi Estimation for Problem Solving“.

Fermi Estimation” is a technique often used in interviews at companies and public institutions overseas. For example, how many telegraph poles are there in Japan? How many dogs are there in the world? For example, how many telegraph poles are there in Japan?

In this book, the author says that Fermi estimation cultivates “brain power = the ability to think. The author categorizes the three types of intelligence into (1) memory power of those who know things, (2) interpersonal sensitivity of those who are tactful, and (3) intelligence power of those who have high thinking ability. By training these three elements, we can obtain the three elements of intuition, logical thinking, and intellectual curiosity that will help us succeed in the future society.

So, how is Fermi estimation actually done? Let’s take the aforementioned question “How many utility poles are there in Japan? I would like to discuss it using “How many utility poles are there in Japan?

First of all, the time given to consider these problems is very short (three minutes), calculators/PCs are not allowed, only paper and writing utensils are used, and no reference to any information is allowed.

What the examiners are really expecting from this question is not the quality of the estimated quantity, but the process used to derive the result. Therefore, what is needed is the “ability to think”, or “brain power”.

In order to think about this problem concretely, let’s subdivide the problem. First, consider a specific area (such as a residential area or a mountainous area) where the number of poles can be imagined. Then, we hypothesize that the density of utility poles differs between urban areas with residential buildings and suburban areas with mountainous terrain, and extend the hypothesis to all of Japan.

If we assume that the number of poles in urban areas is one pole per 50m2 and that in suburban areas is one pole per 200m2, then the number of poles per 1km2 in urban areas is 400 and that in suburban areas is 25.

The next step is to consider the total area of Japan and divide it into urban and suburban areas. The total area of Japan is 380,000 km2, but if you don’t know that, you can use the distance that you can recognize (for example, if you know that the distance between Tokyo and Hakata is 1200 km, you can use that, and if you don’t know that, you can use the time and speed of the Shinkansen (6 hours for 200 km on average) to make a Fermi estimate). Then, approximate 300,000 km2 by drawing a map of Japan and approximating it with some rectangles, say 1500 km x 200 km.

Next, the ratio of urban areas to mountainous areas is also estimated to be 2:8 based on the Japanese map. From the above, we can calculate the estimated value of 300,000 x 0.2 x 400 + 300,000 x 0.8 x 25 = 30 million trees.

The next step is to check the estimated value based on the available real values. (Hypothesis testing by Fermi estimation). Looking at the figures published by the power company and NTT, the total number of units is about 33 million, which confirms that the estimated result was quite good. At this point, another important task of hypothesis testing is to verify what part of the hypothesis was out of line.

Looking at the process of Fermi estimation from the perspective of thinking ability (jidoka-ryoku), the first thing to mention is “hypothetical thinking ability. Here, hypothetical thinking is a pattern of thinking that involves (1) assuming the most likely conclusion (hypothesis) using only the information that is currently available, (2) always keeping it strongly in mind as the ultimate goal, and (3) repeatedly verifying the hypothesis while improving the accuracy of the information to reach the final conclusion while revising the hypothesis.

If we look at Fermi estimation from the perspective of “hypothetical thinking,” we can see that three things are actually used: (1) the attitude of constructing a hypothesis from the least amount of information, (2) the ability to set preconditions and move on, and (3) the ability to set a time limit and come to a conclusion anyway.

What is important in hypothetical thinking is to “reverse the vector from the final destination,” “think from the other side rather than from here,” and “think backwards. This leads to changing the perspective from which we look at the world: thinking from the “end” rather than the “beginning,” thinking from the “purpose” rather than the “means,” thinking from the “what needs to be done” rather than the “what can be done,” and thinking from the “other side” rather than the “self.

People who think in hypotheticals often say things like, “It’s a drop in the bucket” or “It doesn’t matter if it’s a lie. People who are not familiar with hypothetical thinking think that it is inappropriate to think about the “pitfalls” before starting a project or to say “it doesn’t matter if it’s a lie”. If there is a problem with this way of thinking, it is that the “point of no return” is the best place to land at a certain point in time, and it needs to be changed flexibly.

Another important aspect of hypothetical thinking is “digging deep into the hypothesis.” When we reach a “seemingly plausible conclusion” based on the first hypothesis, we end up with a superficial conclusion without sufficient verification. Even if the direction of the verification results is quite close to the original hypothesis, it is possible that it worked by chance due to other factors, so it is important to conduct hypothesis verification with sufficient analysis.

The next important thing in Fermi estimation is to “quantify the results and evaluate them in a visible form. If we make an abstract hypothesis and evaluate it as it is, the guideline for evaluation is unclear and a convenient evaluation can be made. On the other hand, if we reduce the results to some quantitative values and evaluate them in a visible form, we can make an objective evaluation that is not self-serving.

The next thing to consider in terms of intelligence is the ability to “think from the whole” framework. This consists of “big-picture thinking,” which is the ability to see the whole picture of the target issue from a high vantage point, and “decomposition,” which is the ability to cut the whole picture into the most appropriate pieces and further decompose the sections. Furthermore, this decomposition ability is largely divided into “classification” (dividing the whole into appropriate segments without omissions or doubling up) and “factorization” (reducing the whole into a concrete form of numerical calculation).

The important point in framework thinking is to “get rid of the habit of thinking. All of us have habits of thinking based on our past experiences and knowledge, and these habits become barriers when we think of new ideas from scratch or when we communicate with others who do not share the same way of thinking.

What is needed here is to think in “absolute coordinates” that can be understood by everyone, rather than in “relative coordinates” that are in line with each individual’s way of thinking. What is necessary when thinking in “absolute coordinates” is the act of “aligning the coordinate axes,” which can be said to be the act of aligning the definitions of each element in advance.

The act of “looking down on the whole” is also useful in thinking in “absolute coordinates”. This is because the “whole” represents one thing to everyone, while the parts can be selected in an infinite number of ways, and the habit of thinking of the person who selected the part is included in what he or she chose.

In addition, in order to think in a way that is consistent and consistent, it is important to use a group of frameworks called MECE (Mutually Exclusive Collectively Exhautive) (3C, 4C, QCD, KJ method, etc.).

The last thing that can be considered in terms of groundwork is the ability to “simply think” abstractly. This involves three steps: (1) extracting the most important features of the subject, simplifying and modeling it, (2) elucidating the general theory at the abstract level, and (3) concretizing it again to derive an individual solution.

The key words needed to apply this in practice are (1) modeling, (2) truncation of branches and leaves, and (3) analogy (explaining an event from similar ones). In Fermi estimation, where prior information is scarce, the use of analogy (3) is particularly important. Furthermore, from the viewpoint of solving problems in time, (2) truncation of branches and leaves is also an important factor.

When considering the actual business application of Fermi estimation as described above, this book is said to be effective for business people who have the following issues. (1) When asked about the progress of a project by their boss, they cannot answer immediately and say, “Please wait for another XX days” (they try to give an answer only after they have all the information, even though they do not know when they will get the necessary information). (3) “I started with XX for now,” starting with available tools and information without a hypothesis, (4) “I fixate on situations that are not necessarily necessary,” (5) “I don’t think about milestones,” and (6) “I can’t move forward without preconditions,” judging that what I am trying to do is impossible. (5) Not thinking about milestones.

If you or your team members are in this kind of mindset, you may need to think of hypothesis thinking, framework thinking, and abstract thinking, and take a slightly different approach.

Finally, here is an example of Fermi estimation.

• How many tuners are there in Chicago?
• How many pizzas can the world eat in a day?
• How many drops of water are there in Lake Biwa?
• How many golf balls are there in Japan?
• How many no-parking road signs are there in Tokyo?
• How many mailboxes are there in Japan?