Category : Science and Math

A Theory of Movies

For a variety of reasons, I don’t review books. The biggest is that I might run into the author in a dark alley or at a conference.

But I have no such restriction on movie reviews. Hence my review of A THEORY OF EVERYTHING. In a nutshell:

1. Amazing performances by all the principals. In case you’re wondering if Emily Watson is old enough to be the mother of Felicity Jones—she is, barely, older by 16 years.

2. Great cinematography, if that’s the word for beautiful views of Cambridge.

So far so good, but WHERE’S THE BEEF? SCIENCE?

I know the movie is being billed as the story of the relationship between Stephen Hawking and his first wife, Jane, but couldn’t there be SOME science? Maybe 10 minutes worth instead of the 4 we were treated to? One potato-and-pea analogy does not science make.

I can’t help thinking that if we were watching the story of a “brilliant” athlete, we’d be treated to scene after scene of tackles, hoops, swings, twirls, and goals.

Maybe quantum mechanics doesn’t lend itself to such action shots, but how about head shots for a change? Maybe someone can figure out how to show multicolored brain activity while explaining worm holes and general relativity?

I’m going to try THE IMITATION GAME next. It’s billed as English mathematician and logician, Alan Turing, helps crack the Enigma code during World War II.

Let’s see how much mathematics and logic have been allowed to seep in.

Fermi Problems

I think of September as Enrico Fermi’s month. His birthday is 9/29/1901. It’s a little early to sing, but I thought I’d introduce my own favorite aspect of Fermi’s contribution to science—his problem solving technique.

The problem:

How many piano tuners are there in Chicago?

This is the legendary problem presented to his classes by the Nobel Prize winning Italian-American physicist. It’s the original of a category of problems called “Fermi problems,” meant to be solved by putting together reasonable estimates for each step of the solution.

At first glance, Fermi problems seem to be impossible to solve without research. The technique is to break them down into manageable parts, and answer each part with logic and common sense, rather than reference books or, these days, the Internet. By doing this systematically, we arrive at an answer that comes remarkably close to the exact answer. By the end of this calculation, we also see what advantages it has over looking up the answer on Google.

Here’s the way Fermi taught his students to solve the piano tuner problem:

1) Assume that Chicago doesn’t have more piano tuners than it can keep busy tuning pianos.

2) Estimate the total population of Chicago.

At that time, there were about 3,000,000 people in Chicago.

3) Estimate how many families that population represents.

The average family consisted of four members, so the number of families was approximately 750,000.

4) Assume that about one third of all families owns a piano.

That gives us 250,000 pianos in Chicago.

5) Assume that each piano should be tuned about every 10 years.

That gives us about 25,000 tunings per year in the city.

6) Assume that each piano tuner can service four pianos per day, and works about 250 days a year.

Each piano tuner would perform 1,000 tunings per year.

Summary: In any given year, pianos in Chicago need 25,000 tunings; each tuner can do 1,000 tunings, therefore we need 25 piano tuners.

The answer was within a few of being the number in the yellow pages of the time.

Why not just count the listings in the yellow pages in the first place? A good idea, until we remember that “solving a problem” is an exciting, challenging word to people like Fermi and to scientists in general. Difficult problems are even better opportunities to test their minds and their ability to calculate.

Another of Fermi’s motivations in giving this problem was to illustrate properties of statistics and the law of probabilities. He used the lesson to teach something about errors made in estimating, and how they tend to cancel each other out.

If you assumed that pianos are tuned every five years, for example, you might also have assumed that every sixth family owns a piano instead of every third. Your errors would then balance and cancel each other out. It’s statistically improbable that all your errors would be in the same direction (either all overestimates or all underestimates), so the final results will always lean towards the right number.

Fermi, present at the time, was able to get a preliminary estimate of the amount of energy released by the atomic bomb—he sprinkled small pieces of paper in the air and observed what happened when the shock wave reached them.

A whole cult has been built up around “Fermi questions:”

• how much popcorn would it take to fill your family room?

• how many pencils would you use up if you drew a line around the earth at the equator?

• how many rejection letters would it take to wallpaper a writer’s office? (oops, too personal?)

For Fermi, there was great reward in independent discoveries and inventions.

Many contemporary scientists and engineers respond the same way. Looking up an answer or letting someone else find it impoverishes them, robbing them of a creative experience that boosts self-confidence and enhances their mental life.

Could this also be why they don’t ask for directions when they’re lost?


I’m in a cutting corners kind of place — very busy, so why bother folding pajamas, when you’re just going to have to unfold them to wear them? Have you been there?

That intro is by way of saying, this piece on Fairy Tales is being re-blogged, from the LadyKillers where I also show up. If you’ve read it there and are aggravated at the repeat, let me know, and I’ll never do it again!

A Fairy Tale

It’s been a long time since I’ve read a fairy tale. But if I remember correctly, most of them are scary, with disastrous endings for some, if not all, of the characters, sometimes my favorites. Like the step-mother in Cinderella. Doesn’t she get carted off to jail by CPS? I’m a step-mother, so I wasn’t pleased by that.

I went on a search for “Grimm’s Fairy Tales” to see if there were any with happy endings. I learned that the book contains 209 tales! I clicked on a few, with mixed success, until I came upon this one. At last, a fairy tale that I can use in a math or physics class! Here it is, The Shepherd Boy:


There was once upon a time a shepherd boy whose fame spread

far and wide because of the wise answers which he gave to every


The king of the country heard of it likewise, but

did not believe it, and sent for the boy. Then he said to

him, if you can give me an answer to three questions which I

will ask you, I will look on you as my own child, and you shall

dwell with me in my royal palace.

The boy said, what are the three questions.

The king said, the first is, how many drops

of water are there in the ocean.  The shepherd boy answered, lord

king, if you will have all the rivers on earth dammed up so that

not a single drop runs from them into the sea until I have

counted it, I will tell you how many drops there are in the sea.

The king said, the next question is, how many stars are there

in the sky.  The shepherd boy said, give me a great sheet of

white paper, and then he made so many fine points on it with a

pen that they could scarcely be seen,

and it was all but impossible to count them,

any one who looked at them would have lost his sight.  Then he

said, there are as many stars in the sky as there are points

on the paper.  Just count them.  But no one was able to do it.

The king said, the third question is, how many seconds of time

are there in eternity.  Then said the shepherd boy, in

lower pomerania is the diamond mountain, which is two miles

high, two miles wide, and two miles deep.  Every hundred

years a little bird comes and sharpens its beak on it, and

when the whole mountain is worn away by this, then the first

second of eternity will be over.

The king said, you have answered the three questions like a

wise man, and shall henceforth dwell with me in my royal

palace, and I will regard you as my own child.


If you have a better explanation for infinity, or for the limits in calculus, or for the great theological questions, let’s hear them!

Girls Only

April 24, Take Your Son and Daughter to Work Day!

The day began in 1993 to give adolescent girls additional attention and an insight into work-world opportunities available to them. When boys realized that they were in school as usual while the girls were out having fun, the day turned into Take your Son and Daughter to Work Day. Much better.

Too bad it wasn’t planned that way in the first place. Isn’t it just as (or more) important for adolescent boys to see both women and men in the workplace? Aren’t “boys” still the ones at the top, who do the screening and the hiring?

Years ago, I was part of a similar program, XYZ, to give girls an extra push by having a day of science, for girls only, taught by female scientists. Sounds good, right? Wrong. First, there was the giggle factor – boys, young and old, giggling over the fact that girls had to be taken aside and given special attention to learn science. They just weren’t good enough to take science with the boys.

They were right—that’s how it looked.

That should have been enough to kill the program, but it didn’t. I tried several times to change the course of the program, simply by inviting boys to the classes. Let the boys experience female scientists, too. (see above for why that’s important!) I continued to volunteer in the program, constantly petitioning for a change of philosophy and was shot down each time, until I finally quit. I realized that sexism was still rampant, and the powers that be would always consider that girls need special TLC to learn the hard stuff.

Last time I checked (4/22/14) the program is alive and running, and still girls only. I found an interesting FAQ on their website:

Q (paraphrasing): Why is there such a thing as the XYZ conference?

A (in part): Because girls and women are still underrepresented in science and technology fields.

I might pose it in the opposite way.

Q: Why are girls and women still underrepresented in science and technology fields?

A: Because programs like XYZ that have existed for more than 30 years, and are still encouraging people to think girls can’t cut it in the normal learning environment. Because boys who are left out will still go on to be the CEOs, Research Directors, who will pass over those girls.

Oh, the pressure!

Interesting conversation with a young art graduate student the other night: He’s not thrilled with his classes, especially with the exercises his professor assigns. Bottom line—he just wants to be able to go into the classroom/studio and do his own artist-thing. Nothing should be right or wrong in an art class.

Can the same be said for physics classes? The discussion prompted me to resurrect an old physics story. As the legend goes, a physics teacher posed this question on an exam and got surprising results.

Show how it’s possible to determine the height of a tall building with the aid of a barometer.

One student answered this way:

“Take the barometer to the top of the building and attach a long piece of rope to it. Lower the barometer until it hits the sidewalk, then pull it up and measure the length of the rope, which will give you the height of the building.”

What? The teacher expected a different answer, using an equation involving the difference in pressure at the top and bottom of the building.

ΔP/Δh = (-mg/kT)/P

When challenged to come up with “the right answer,” the student gave several. Among them:

1. Take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building. Using simple proportion, determine the height of the building.

2. Take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units.

And so on.

My favorite remains this one:

“Take the barometer to the basement and knock on the superintendent’s door. When the superintendent answers, say: ‘Mr. Superintendent, if you will tell me the height of this building, I will give you this barometer.'”

How would you grade this student?

** Legend has it that the student was Niels Bohr (1885-1962, Nobel Prize in physics, 1922), but then a legend can say anything and get away with it.