Wednesday, September 5, 2018

SearchResearch Challenge (9/5/18): Can you be a Fermi estimator?

Are you a good estimator? 

How tall was Enrico Fermi, the physicist?  How would you estimate?  Assume he doesn't have extraordinarily long legs.  
An important skill in a lot of skilled reading (or fact checking, or just being a skilled SearchResearcher) is being able to do quick estimates of values by just doing a bit of thinking about them.  

This estimation technique is often called Fermi Estimation, after the famous physicist who was known for his ability to good approximate calculations with little or no actual data.  These are sometimes called "back-of-the-envelope calculations," but great Fermi Estimators don't actually do this without any data--they need to start somewhere... but they know a few key facts, and then work forward from what they know towards an estimate. Fermi estimationg problems typically involve making reasonable guesses about quantities, their variances, the upper and lower bounds, and how to combine guesses together to lead to a useful insight.  

This came up for me recently when the shopper in front of me at the grocery store insisted that she wanted 1.00 pounds of ground hamburger.  When the butcher dropped a lump of ground beef onto the scale, she insisted on NOT paying for the 1.05 pounds, but she really wanted 1.0o pounds.  

The butcher rolled his eyes and removed a tiny bit of meat to get it exactly to 1.00 pounds.  

I immediately thought of this as a Fermi Estimation question:  About how big a lump of meat is 0.05 pounds?  Would it be the size of your hand?  Would it be the size of your little finger?  

If you assume that ground beef is about the same weight as water, then if we know how many ounces are in 0.05 pounds, then we can estimate the volume of meat that represents.  

Here's the Fermi Estimation I did in my head:  

In the US, 1 pound is 16 ounces.  In particular, 1 pound of meat (which weighs about the same as water) is 16 ounces.  First I converted that number into a ratio I could work with.  I realized that 0.05 of 1 pound is half of 0.1 of a pound... and that's half of 1.6 ounces, or 0.8 ounces.  Luckily, an ounce of water weighs the same as 1 fluid ounce of water. So..  0.8 ounces is just under one fluid ounce of water.  1 fluid ounce which is 2 tablespoons of water, so 8/10ths of 2 tablespoons is close to 1.5 tablespoons of water... around the size of my little finger!  

(Of course, doing this in grams is SO much easier. Imagine if the shopper wanted exactly 500 grams, and not 530 grams of ground meat.  About how big is 30 grams of meat?   1 gram of water is 1 milliliter, so we'd be looking at 30 ml of meat..) 

As Enrico Fermi might say:  non tanto! (not much!)  

This leads us to our Challenges for this week--the first is a true Fermi estimation?  

1.  Can you estimate how tall Enrico Fermi was?  

2.  Can you estimate (without looking up the answer!) how many people in the United States are over 80 years old?  (For extra credit, how many people worldwide are over 80 years old?)   

3.  To do Fermi Estimates you actually need to know a few basic facts (e.g., about how many people live in the US).  This brings up a great meta-question for Fermi Estimation and sensemaking of data that you see presented in the news... What facts do you need to know to be a good Fermi Estimator?  (There's no perfect answer for this; just tell us what facts you've used to do your own Fermi Estimates!)  

What I want you to think about is how you do estimates in your everyday life.  When you read an article that claims something that seems excessive, what kind of thinking should you be doing in order to sanity-check the assertion? 

Have you seen any recent examples of assertions that fall apart under a Fermi Estimation?  What do you have to know in order to Fermi-check the claim? 

Let us know in the comments!  

Search (and estimate!) on! 


  1. 1. Can you estimate how tall Enrico Fermi was?

    I think it was Mr Calder our high school physics teacher who told us about this estimating business; and to get the answers in the correct units too. In the centuries since I have used Fermi's technique many times, For instance, when my floors were to be refinished I estimated $3000. The job came to %2900. A trip to the vet: I took along oldest grandson and told him 'Watch how fast 200 bucks vanishes.' The bill was $196.97.

    So, I estimated Fermi was an average sized man in his day; about 5ft 6". [height of average Italian male born 1900] finds the perfect data at Height and the Normal Distribution: Evidence from Italian Military Data. Reading thru that I find, I think, for his cohort born ca 1900 at adult was 165cm or 5' 5".

  2. I was thinking about the Challenge and for these questions, I will use Anthropomorphic measures, Ergonomics and Normal distribution. I remember that head measure helped to determine the height of a human. I don't remember very well, so I need to check. I think average human size is 7 times the size of the head or something similar. And with Normal distribution, as humans fit in this probability distribution, we can estimate those data.

    1. Thinking about how to answer, after posting my message, thought if someone already answered that. The answer is no. At least not found by me. But, found this site that also has estimations by visitors. But doesn't say how or why they shared those numbers.

      160 or 183 centimeters. That is 63 or 72 inches

      I think Jon estimate is great. Glad you have that talent, Jon! I think he is right taking into account Dr. Russell's mention about legs.

      On other topics, yesterday watched "Paul Hollywood City Bakes" Reykjavík. And remember a lot our Challenge about kaymak. Have any of you already visited Iceland?

      They have lots of different dishes. For example, improved versions of French Croissant, breads cooked with geothermic ovens, Skyr yoghurt and

      lamb’s blood meringue!

  3. "(There's no perfect answer for this; just tell us what facts you've used to do your own Fermi Estimates!)" that's a good thing!
    …searched for a full length photo of Enrico - hopefully with something that would provide scale - I was lucky enough to run across this photo
    of the Via Panisperna boys that included King LeBron (I had no idea of his work in physics… although he certainly defies physics at times)
    …anyway, knowing that LeBron is 6'8"/203.2cm - I would have to estimate that Enrico was ~ 7'5/226.06cm in his street shoes…??
    can only conclude it was the uranium/radiation exposure - one of the unintended consequences of the atomic age… my back-of-the-envelope calculations/methods may not be to Fermi standards…;P
    Mr. James height SERP
    …or it may be attributable to alien encounters?
    Via Panisperna boys

  4. 2 Can you estimate (without looking up the answer!) how many people in the United States are over 80 years old? I Fermiated 4%; turns out its (by the same source and same page as below) 9,000,000 which is just under 3%

    (For extra credit, how many people worldwide are over 80 years old?) I had thought it would be lower than USA numbers but I Inadvertently spotted this answer before I fermiated the answer which turns out to be 3.8% worldwide according to

  5. What facts do you need to know to be a good Fermi Estimator? Having some esxperience with the topic helps I guess. For my floor job I had no experience just a feeling that the cost would be in that region of 3 grand. The vet is totally experience based with many visits to Dr Helen over 2 decades. I am having an anti wildfire smoke air cleaner installed. I fermiated $2100, which as it turned out, would have been pretty close except They have a unit different from what I was thinking of for $1200 which does an even better job.

  6. I haven't tried the challenges but I would normally make estimates by breaking down the quoted figure into a smaller unit (like your ground beef example) to see if it sounds reasonable. Our mayor recently stated that a particular street attracted 400 cyclists an hour at peak times. Breaking that down, it's 40 cyclists every 6 minutes, or 6 or 7 cyclists per minute - and I don't believe it! I love Jon's word 'fermiate'.

  7. I just found an article, that I am sure many will like and that made me remember previous SRS Challenges about the same topic: In pictures: Spectacular super bloom transforms South African desert

    Also, was wondering about YouTube videos so searched [how to know if YouTube video is available worldwide] and yes, there is a tool for that.