Friday, September 25, 2009

FPOTW The typical Fermi Problem

This weeks "Fermi Problem of the Week" is taken from a previous blog of a similar name. Here the reader is introduced to the concept of the Fermi problem.
Below is a picture of the Fermi problems names sake, Enrico Fermi.



This image is available from the Archival Research Catalog of the National Archives and Records Administration under the ARC Identifier 558578
Linked from Wikipedia





The typical Fermi Problem

Fermi problems, or back of the envelope calculations, are a method of estimating an answer to a question where there is seemingly not enough information to answer the question.

The prototype Fermi Problem is as follows:

How many piano tuners are in the city of New York?

One might think there is not enough information to answer this question.
However, by using a bit of common sense and a few reasonable guesses, one can estimate the answer.
For instance, one could go about tackling this question as follows:

First, how many people are in NYC?
We can estimate this as about 8 million.

How many people have a piano? 1 in 10? 1 in 20? Lets use 1 in 50.

That gives us the number of pianos in NYC as 160000.

Lets suppose a piano needs tuned once every 4 years. This means that each year about 40000 pianos need tuned.
Suppose an average piano tuner can tune 4 pianos a day, and works 200 days a year, this means that the average piano tuner tunes 800 pianos a year.

Therefore there are about 40000/800 = 50 piano tuners in NYC.

This seems to be a reasonable number, as 5 would be far to low and 500 would be too many.

A Fermi problem solution is also known as an order of magnitude answer, meaning it is accurate to a power of 10, or at best a factor of 2 or 3.

Try this problem on your home town, then afterward check the phone book. You will find that your answer will be remarkably close.

Thursday, September 24, 2009

Scientific Illiteracy! (RUN!)


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In this day and age (it could be argued for any day and age), an ability to think critically is exceedingly important.
Being able to think critically can save one headaches in paying bills for un-needed items that promise to lengthen your penis, to save you panic on reading the latest alarmist news stories, and could even save your life. Heck, one could propose that critical thinking is the entrance exam and the placement exam for life.

Although this blog is about scientific illiteracy, what is at the heart of matter is actually the ability to think critically.

You see, many people think that they need to know something about science in order to understand and judge the validity of a statement that is couched in scientific terms.
Nothing can be further from the truth.

You don't need to know the periodic table of elements, or Newtons laws, or how electricity "works" in order to question what you read, see and hear. Rather, you simply need to acquire and become facile in the use of a few simple tools.

This blog will introduce the reader to those essential tools, and through discussions on current events, give readers a chance to apply those tools in deciding for themselves how to let the promises of con artists, swindlers, or the well meaning uninformed affect their daily lives.

Of course, being a physicist means that science is a subject near and dear to me. I will be discussing science. I will be using the scientific method in my discussions. But know that many of the socio-political issues discussed, even if they are rooted in science, can still be tackled using critical thinking skills.

By the way, the scientific method is one of the tools you will soon have at your disposal. Don't let the word "scientific" scare you, because it is not technical, or abstract, or even very hard, but simply a recipie if you will... a prescription for organizing the questions you ask and evaluating the answers you get.

Finally, a very important thing about critical thinking should be noted:

Thinking critically about a topic does not guarantee that your conclusions are right.

P.S.  How cool is it that critical thinking 101 is a course you can take again for credit?



 * Image used without permission. Located at: http://www.sciteam.ubc.ca/~sciteam/w/images/Critical_thinking.jpg