## guesstimation (1+2)

I received very recently this book, Guesstimation 2.0, written by Lawrence Weinstein from Princeton University Press for review in CHANCE and decided to check the first (2008 )volume, Guesstimation, co-written by Lawrence Weinstein and John A. Adam. (Discovering in the process that they both had a daughter named Rachel, like my daughter!)

The title may be deemed to be very misleading for (unsuspecting) statisticians as, on the one hand, the book does not deal at all with estimation in our sense but with approximation to the right order of magnitude of an unknown quantity. It is thus closer to Innumeracy than to Statistics for Dummies, in that it tries to induce people to take the extra step of evaluating, even roughly, numerical amounts (rather than shying away from it or, worse, of trusting the experts!). For instance, how much area could we cover with the pizza boxes Americans use every year? About the area of New York City. (On the other hand, because Guesstimation forces the reader to quantify one’s guesses about a certain quantity, it has a flavour of prior elicitation and thus this guesstimation could well pass for prior estimation!)

In about 80 questions, Lawrence Weinstein [with John A. Adam in Guesstimation] explains how to roughly “estimate”, i.e. guess, quantities that seem beyond a layman’s reach. Not all questions are interesting, in fact I would argue they are mostly uninteresting per se (e.g., what is the surface of toilet paper used in the U.S.A. over one year? how much could a 1km meteorite impacting the Earth change the length of the day? How many cosmic rays would have passed through a 30 million-year-old bacterium?), as well as very much centred on U.S. idiosyncrasies (i.e., money, food, cars, and cataclysms), and some clearly require more background in physics or mechanics than you could expect from the layman (e.g., the energy of the Sun or of a photon, P=mgh/t, L=mvr (angular momentum), neutrino enery depletion, microwave wavelength, etc. At least the book does not shy away from formulas!) So Guesstimation and Guesstimation 2.0 do not make for a good bedtime read or even for a pleasant linear read. Except between two metro stations. Or when flying to Des Moines next to a drunk woman… However, they provide a large source of diverse examples useful when you teach your kids about sizes and magnitudes (it took me years to convince Rachel that 1 cubic meter was the same as 1000 liters!, she now keeps a post-it over her desk with this equation!), your students about quick and dirty computing, or anyone about their ability to look critically at figures provided in the newsy, the local journal, or the global politician. Or when you suddenly wonder about the energy produced by a Sun made of… gerbils! (This is Problem 8.5 in Guesstimation and the answer is as mind-boggling as the question!)

To help with this reasoning and the recovery of (magnitude) numeracy, Lawrence Weinstein added an appendix called “Pegs to hang on” where he lists equivalent objects for a range of lengths, weights, etc. (The equivalent can be found in Guesstimation.) The books both start with a similar section on how to make crude evaluations by bounding the quantity and taking the geometric mean. I also like the way he battles for using metric units and powers of 10 in calculation, and join us in fighting against extra digits, claiming they are lies, not precision, which is true! Illustrating the point with the following xkcd strip:

A few problems in Guesstimation 2.0 irked me, including all related to recycling because they only gave the monetary gain in recycling a bottle, a can, etc., versus the time required for an individual to dump this object in the right bin: not the most constructive approach to recycling (see, instead, David McKay’s Sustainable Energy Without the Hot Air much more coherent evaluation). The same was true for the landfill question in Guesstimation: the volume of trash produced by Americans over 100 years may well fit in a 100m high hill over 10⁶ square meters, but landfills are definitely not the solution to garbage production! There are also one or two probability related problems: for instance the one about getting a baseball ball inside one’s beer glass during a game. Lawrence Weinstein goes from the probability of getting one foul ball being 3×10-4 to the probability of getting one of the forty foul balls during one game equal to 10 -2 without the beginning of an explanation. (This is true but how does he get there?!) I also found very amazing the computation that climbing 6 flights of stairs (what I usually do to get to my office in Paris-Dauphine, sometimes several times a day) consumes (roughly) 100W, which is twice an average daiily intake. Am I missing something? The relation does not seem right. (By the way, it seems question 7.10 did not make it to Guesstimation 2.0 as it reads as a quick intro to angular momentum, a recap usually found. at the start of a chapter.)

And what about the comparison between Guesstimation 2.0 and Guesstimation? Well, as you can guess (!), they are quite similar. Overall, I would tend to find Guesstimation more engaging and funnier (like the joke about advising against storing a cubic meter of uranium under your kitchen table!), as well as more diverse in its choice of questions (with a section on risk, e.g., computing that smoking a cigarette costs you in life expectancy the time it takes to smoke it, similar to the evaluation that driving a car cost you in working hours the time you are driving) but, again, these books are not primarily designed for linear reading, so they both come as a good resource for numeracy tests and quizzes, Guesstimation 2.0 simply adding to the pool. Note also that, in addition to the 80 questions processed in Guesstimation, the book concludes with a list of 30 unanswered questions. (I liked the one about the potential energy of a raindrop in a cloud as it reminded me of a recent entry in Le Monde science addition about the strategy of mosquitoes for avoiding being flattened by those drops!)

### 2 Responses to “guesstimation (1+2)”

1. The answer to your question about “climbing 6 flights of stairs”, 100 W, and “twice daily consumption”, is that it sounds like the author (1) hasn’t done a good job of helping the reader understand the difference between energy and power (see the opening chapters of “Sustainable Energy – without the hot air” (available free online)); and (2) has introduced a red herring by talking about 6 floors. While you are going steadily up stairs, no matter how many floors, you are delivering a power of about 100 W. That is (unsurprisingly) bigger than your average power output. Hope this helps! David MacKay

• Thanks, David, this is most helpful!