Back of the Envelope Calculations [pdf]

What are the alternatives though? (to powerpoint)

I love chalk and talk but it puts a lot of load on the speaker. My Electricity and Magnetism professor basically pushed it to the limit I think. He had a carefully cultivated temper that was bad enough to keep 100 students totally silent for 50 minutes and he used about five different colors of chalk, but there are limits to what you can scrawl out on a blackboard.

You can distribute written documents, this gives you maximum opportunity to convey information, but you can't force people to actually read them. Going from a paper memo to email exacerbates this I think. Best case scenario, you can present very clear and well structured information but if you go past two pages you have to wonder if anyone is really paying that much attention. As a "best case example" I'd look at something like this memo that Robert McNamara wrote to LBJ about a month after LBJ took office: https://www.mtholyoke.edu/acad/intrel/pentagon3/doc156.htm . A benefit of written work is that you are committed to your words. But: creating a concise and readable written document that will effectively spread your thoughts is excruciatingly difficult. You can't write a book of background info every time you have a staff meeting.

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About remembering that you have a rough model though, I think the key thing is that when you realize that there is something you are interested in measuring and once you have a model then you can start looking for quantities you can actually measure to (in)validate and tighten the model. Always be model checking.

But that's a broad category. There are a lot of instruments that need repairs and maintenance that are not pianos, and they tend not to cross instrument categories, or even individual instruments. A flute repair person will not likely also repair oboes, for instance. Also, piano repairs and piano tuning are not always done by the same people.

This is strictly true, but doesn't account for the fact that errors tend to cancel one another. For instance, if 2 of the 5 independent estimates are high, one is right on, and 2 are low, you can end up with a number very close to the actual number. And, by "very close," I mean usually within 1-2 orders of magnitude, depending on the quality of the component estimates.

And yet it typically yields the right answer (in the hands of an expert). I wonder why?

If this was Reddit this would pretty much be /thread, however I propose the following question:

While this may be a good estimate, what about businesses not on Yelp?

"Professional Piano tuner" doesn't seem the most technologically advanced profession, so I think it's safe to assume that there are several, if not dozens more in existence in the NY area.

This is actually not a very good estimate. It has many inaccuracies, and those inaccuracies are harder to nail down than the original problem, so you made it harder on yourself.

Some questions about your result: How many piano tuners work at any of those piano tuner companies? How many piano tuner companies are not on yelp? How many piano tuners are employees of instrument stores instead of working freelance/for a tuner company?

Those are all harder to answer without industry information than the simple deductions the handout makes from common sense/knowledge.

I have the feeling it is important that people understand the limits of technology. Even though we like to say something doesn't exist if it isn't on Google, things very often do irregardless.

Sweet! My guess was 6. I proceeded by estimating the number of pianos per person (my guess was 7000 in NYC), then by estimating the frequency of tuning. I came up with ~20 pianos/day needing tuning and guessing the average tuner could handle 3 pianos / day (when I was a kid I recall the tuner taking a couple of hours.) some edge cases like Carnegie Hall (where the piano is probably tuned quite frequently) probably skew the numbers somewhat. Also, I would guess that a city with mostly single family homes, say, Houston, has more pianos/capita than NY or Chicago, based on the pain in the assedness of moving a piano into an apartment, though that may be offset by the number of music schools and cultural institutions.

It's the well known 'this graph is true because it has unexplainable data in it' bump.

It's certainly true in statistics and machine learning that adding variables with unreliable estimates lowers the whole model's accuracy after some point.

Knowing the correct order of magnitude is seldom trivial. Getting the correct order of magnitude quickly will make you a better decision maker (not to mention impress people whose opinion matters).

An imbalance of supply can increase/decrease the population by maybe as much as 2x (or .5x). An order of magnitude can be the difference between a market that's worth considering and one that's too small to currently be serviceable.

This is important because in business getting a right(ish) answer quickly is often more important than getting a precisely correct answer slowly. While you're measuring precise supply and demand, FermiCo has already concluded that the market is too small and moved on.

p.s. irregardless is a great word.

If there is a 1 year backlog it is a temporary market state. The prices will rise, which will attract competition, which means more tuners, which means elimination of backlog. Free market etc.

I think it has to do with how you phrase the question. People go to job interviews knowing that they're going to be tested for their knowledge, and phrasing the question like that triggers a "how am I supposed to know that?" response.

But you're not actually asking them to know it, you're asking them to reason about it. So perhaps instead of asking "How many gas stations do you think are in this town?" try asking "Could you give me a reasonable estimate of the amount of gas stations in this town?".

I think a lot of people just lock up when they're asked something they don't know in a synthetic situation even when in a real situation they would actually make very good judgements since in any real situation the context is often so much more clear, unless you like to keep your employees in the dark..

How often do you really need these kinds of caluclations? And if you use them wouldn't it be faster / more precise in most cases to just google it?

Honest question.

The problem I see is that for most of these you at least need SOME information (e.g. the number of inhabitants of NYC) to start from.

To get that initial information you'll most likely use a search engine anyway, so why not just invest a little more effort to find a exact number?

I think the problem with a question like "How many gas stations do you think are in this town" is it is too simple to reach the answer, and the approximations are too vague. The solution for everyone is to google it. The approximation method requires some big assumptions about how many gas stations there are per-capita, or per-car, or per-area. I don't think anyone would be able to easily approach that off the top of their head and expect to get a reasonable answer. Just as approximation is a useful tool, knowing when it doesn't work is also useful.

What would your approach be to work out how many gas stations are in your town? Have you done that calculation, and come out with a reasonable answer? What assumptions did you have to make?

Really, I had him a couple years ago. I'm in CompEng, what field are you in, we might know each other ;).