Fermi problems represent a method of thinking... a place where you can be creative and playful. Many a pleasant lunch break have I spent with friends coming up with Fermi problems. The silly ones, the political ones, the environmental.
And don't think that only physics geeks spend time contemplating the Fermi. After a short introduction to the concept many of my non-physics friends become enamored with Fermi problems. One of my ex girlfriends became quite good at positing such problems!
However, one can always find company who will phoo phoo the whole concept, try and argue over the minutia, and in general act like an utter ass about the whole thing.
Take for instance my Aunt.
A few days ago I was invited to dinner by my grandmother, a sort of going away dinner since she was moving to California to live near her daughter (my Aunt).
We went to the old perennial, the Olive Garden, where I decided to order a Martini. The olives on this particular drink were skewered by this huge twizzle stick. Clear emerald green plastic in the shape of the crystal used by Superman in the first movie to create the fortress of solitude. It was monstrous, HUGE!
I comment that due to its size, the restaurant could probably wash it with the dishes and reuse it.
Now, my aunt is the kind of person who will argue the color of the sky and the smell of dog shit. She likes to argue, period. She also is the type who likes to attempt to show off her intelligence whenever she can. She does this not by making meaningful observations, or witty comments, but by... you guessed it... arguing. Her idea of wit is put people down while she argues. This is one smart lady.
After suggesting the recycling of the twizzle stick, she of course says that this is against health code and this it was a stupid idea to suggest.
Now, my Grandmother, who is sitting quietly in the corner of the booth starts looking distressed. I can see why, after all, she is leaving the only home she has had for the last 50 or so years. Leaving all her friends, etc. The last thing she needs is to witness an argument.
So rather than playing to my Aunt's game and partake in an argument, I try to lighten up the mood and say. Hey, lets Fermi the twizzle!
"Who is Fermi?" My Aunt asks.
"He was a very famous physicist in the early half of the 20th century. They named the Fermi labs after him. He worked on the atomic bomb. More importantly, he has had a a type of Gedanken experiment name for him, where you use order of magnitude estimates to solve seemingly difficult problems." I rather long windedly respond.
"Humm, well... I never heard of him," She responds: "so he must not have been all the famous or important."
Now, one thing you must realize here is that my Aunt said all this in a rather pretentious and snooty British accent. The funny part is that she is white bread WASP American. Born and raised in the good old USA in the late 60's, her nickname (self endowed) in high school was DICA, which explains her stunning lack of IQ. The reason she has acquired the affectation of mumbling in a pseudo English accent is because she married a British/Welsh mathematician much older than she, who's only claim to fame was that he was drinking buddies with Stephen Hawking. Not the fact that good old Hawking would not even remember my Uncle does not keep my Uncle from resting on Hawking's laurels. But I digress.
So, one must be able to empathize with my feelings and be astounded at my self control after hearing that because my Aunt has never heard of Fermi, that he must have been an obscure nobody.
I respond: "Humm, well... anyhow... lets consider how many twizzle sticks are used each day in the US. Lets assume that on average each person uses 2 of them a week so..."
"That number seems way to large... that is a silly assumption." My Aunt interrupts belligerently.
"Well" I politely respond, "A Fermi problem is order of magnitude. So I can range from one to ten and still be ok, considering that later when we estimate the size of the average twizzle..."
"What if the average use was 0.45 per person?" She interrupts.
"Well, that still might be ok since we are averaging the size which..." I start.
"We can just as well assume that 22.3 of them are used per person a day... so this is a stupid problem since we cannot exactly determine the number of twizzle sticks!" She pontificates.
I look into her bovine face with disgust and think to myself that if she and her lush of a husband were to go out and drink commensurately with their in house consumption of booze, that the national average usage of twizzle sticks might indeed be 20 per person per day. But I hold my tongue.
My Grandmother at this time decides that the best way to end this is to take the side of her daughter and say: "Well, this is a boring topic... how was your snowboarding trip last week Mike?"
In all fairness to my Grandmother this was the best tack to take. After all, her daughter would not be satisfied until she won the argument, and my Grandmother realized that although in the short term I might feel put down a bit, in the end I would live. Plus, my grandmother had to deal with her daughter for the rest of the week during the move, and live close by in California for the rest of her life.
I conceded the victory to my Aunt via silence, and spent the rest of the evening listening to her whine and moan about how much she hates her job (computer programming, go figure), hates the lack of water in Santa Barbra, hates her weight, hates her life and hates her brother.
However, I had to wonder if perhaps my choice of Fermi problem was indeed silly and boring. To test this I brought up the topic the next day at the coffee shop, and received a vastly different attitude and response.
To see how fun a Fermi problem can be, I will outline how the general flow of how the discussion went.
First we discussed the average size of the Twizzle stick. This lead to a digression of the various types of twizzle sticks each person has seen. One friend of mine mentioned that at her friends bachelorette party the twizzle sticks were in the shape of a penis. Which led to how hard it is to make twizzle sticks in the shape of breasts, and a discussion of the phallic connotations of twizzle sticks in general.
After discussing the various shapes and sizes we agreed to the "average length" and size of twizzle sticks and proceeded to estimate that there were probably 3 to 6 hundred million of them used in the US per week. It was agreed that 3 billion a week was too high and perhaps 30 million of them were too little. There was no recrimination or posturing during this estimation as after all, it was order of magnitude.
From there we estimated the volume of plastic used in the creation of the Twizzle, and one person asked how big of an olive could be skewered by a giant twizzle stick made from all that plastic. A friend from Turkey jokingly asked what would happen to Greece if that olive was dropped from orbit onto the tiny island. This lead to discussion of orbital food fights which led to how astronaut piss could crack the windows of the shuttle which lead to... well... you get the idea.
The solution of a Fermi problem is not its own end, but a way to have fun, to be a little silly, to use ones mind. It can bring friends together (but perhaps not family), and can be a great icebreaker and flirtation device. A good Fermi problem can lighten the mood dragged down by the violence and abject stupidity proliferating in the world.
So perhaps the perils of the Fermi problem are overwhelmed by its benefits.