[chairleader]

Any resources for learning the Fermi estimation techniques listed there? Seems like a collection of complementary skills, each of which could be improved:

memorizing useful facts, selecting facts that lead to a meaningful estimate, the mental math to compute the final result

https://en.wikipedia.org/wiki/Fermi_problem

[sidlls]

Mainly the list you stated.

Practicing basic arithmetic and judicious application of the distributive property (much like decomposing complicated problems into smaller subproblems) will take one very far in this sort of thing.

I was introduced to dimensional analysis in my high school physics class. We generated an expression off by just a constant for some property (which I don't recall) of a large scale dust cloud simply by identifying pertinent quantities (e.g. density, the classical gravitational constant) and resolving the powers each quantity must have in order to yield the correct units (corrected due to below comments; thanks) of the property. It made an impression on me, and I used the technique often as a guesstimate to "motivate" or provide a calibration for a solution to various problems all the way through grad school. It's not infallible, and can even be wildly misleading, but it's a fantastic tool.

[chairleader]

Good point. Dimensional analysis is a great "space" to traverse to get answers. It's a great grounding for your thinking, in addition to helping you get to within the right order of magnitude.

I suppose I was wondering if there are any good drills, exercises or puzzles to help internalize these skills. Instead of a daily crossword, maybe there's a daily estimation puzzle somewhere.

[konschubert]

However, dimensional analysis is for when you need to figure out the formula.

"Estimating" is when you have the formula and fill it with estimates to obtain a combined estimate.

[imcoconut]

Could you elaborate on this? By "resolving the powers" do you mean magnitude of interacting forces? And by correct dimensions do you mean spatial dimensions?

[btouellette]

By dimensions he means units. So taking into account the units of density/the gravitational constant (and any other pertinent quantities) and the units of the quantity you are calculating for you can derive an approximate formula just by looking at it and saying okay this unit needs ^2 and this one needs ^-1 and this one needs ^-3 for the end units to work out.

https://en.wikipedia.org/wiki/Dimensional_analysis

[jostylr]

I teach a Quantitative Methods course and in it, I have students read through the Guesstimation book by Weinstein and Adams (listed on that wiki page). There is also a second volume.

They do 11 blog entries each on modifying a question from each chapter and then computing it out.

I also have them watch TED talks and come up with guesstimation critiques of the talks, also in the form of 11 blog entries.

These are highly effective exercises. I recommend doing something similar. If you can, find some others who are interested in doing the same. Reading each other's questions and answers is very valuable in detecting mistakes and comparing your own technique to theirs.

Fundamentally, you just have to do it.

The mental facts needed to memorize are surprisingly minimal. The Guesstimation book lists some good suggested ones. Often you will find you already have some sense of a number. By taking reasonable boundaries on either end of the plausible range and then taking the geometric mean, you can get a decent approximation.

The mental math is also fairly minimal. It just requires two digit arithmetic for the most part along with being comfortable with powers of 10. There are books on mental math, but I think practice is sufficient for two digits: http://arithmetic.zetamac.com

[chairleader]

Fantastic! Thanks!

[sn9]

The two books by Sanjoy Mahajan, freely available as pdfs from the publisher, teach precisely this subject: https://mitpress.mit.edu/authors/sanjoy-mahajan

[jtraffic]

Try Superforecasting by Philip Tetlock.

https://www.amazon.com/Superforecasting-Science-Prediction-P...

[nobody09182343]

https://ocw.mit.edu/courses/mathematics/18-098-street-fighti...

[wglb]

In engineering school, we learned BOEC, useful in the time of slide rules. That is Back Of The Envelope Calculation.