Have you tried “creativity by approximation” yet? I will give you a very simple example from last week. My wife picked me up from the airport and during the drive back, said to me, “I meant to vacuum the whole house before you got back from Tokyo but as I was too tired, I just did the heavy-traffic areas”. I was pleased that a readymade example for my creativity “trick” had suddenly dropped in my lap. She approximated the “whole house” by “heavy-traffic” areas, solved the problem, and had energy left over to go out later that night. This is classic day-to-day creativity!
Is there is a *systematic* way to arrive at approximate solutions? There is: a favorite method of mine known as “Fermi Problems”. Author Hans Christian von Baeyer has a classic article on Fermi Problems called, “How Fermi Would Have Fixed It” (Sciences; Sep/Oct88, Vol. 28 Issue 5, pp2-4).
Let me explain the classic Fermi Problem method using an example. When I taught Probability Theory & Stochastic Process to EECS students, the first question I asked them in the very first class of the semester was the following: “How many piano tuners are there in Ann Arbor?” When the class acquired a collective glazed look in their eyes, I took them through these steps:
1. Take a guess at Ann Arbor’s population – say, 300,000 people.
2. Now, assume that an average family contains four members. The number of families in Ann Arbor must therefore be about 75,000.
3. If one in five families owns a piano, there will be 15,000 pianos in Ann Arbor.
4. The average piano tuner:
a. Can service four pianos every day of the week for five days and
b. Has two weeks of vacation during the year
- A typical tuner would service (4 pianos per day X 5 days a week X 50 weeks per year) = 1,000 pianos per year.
- So, there must be about 15 (15,000/1,000) piano tuners in Ann Arbor. Check the telephone directory Yellow Pages and see what you find . . .
The guesses in the first 4 steps are totally unrelated. In statistical terms, these random variables are independent and hence the errors in these guesses tend to “cancel out”. Approximate solutions arrived at using the Fermi Problem method are surprisingly good (within an order of magnitude of accuracy) and hence very useful for practical situations.
What this tells us is that when confronted with a problem, do not be dismayed by a lack of information; Get Creative! – (a) break the problem down into a number of sub-problems and solve the sequence or (b) solve an approximation of the problem.
In the first case, you find approximate solutions to a bunch of exact sub-problems and in the second case, you find an exact solution to an approximation of the problem. In either case, the approximate solution you reach is a creative way out – either when you are in a tough job interview (you may recall the infamous Microsoft and Google interview questions!) or when confronted with a rough practical situation.
Next blog onwards, I will leave the Start Up topic and move on to other interesting issues.
Enjoy the haiku . . . PG