I’ve run meetups on this topic twice now. Every time I do, it’s difficult to convince people it’s a useful skill. More words about when estimation is useful would be nice.
In most exercises that you can find on Fermi calculations, you can also actually find the right answer, written down somewhere online. And, well, being able to quickly find information is probably a more useful skill to practice than estimation; because it works for non-quantified information too. I understand why this is; you want to be able to show that these estimates aren’t very far off, and for that you need to be able to find the actual numbers somehow. But that means that your examples don’t actually motivate the effort of practicing, they only demonstrate how.
I suspect the following kinds of situations are fruitful for estimation:
Deciding in unfamiliar situations, because you don’t know how things will turn out for you. If you’re in a really novel situation, you can’t even find out how the same decision has worked for other people before, and so you have to guess at expected value using the best information that you can find.
Value of information calculations, like here and here, where you cannot possibly know the expected value of things, because you’re trying to decide if you should pay for information about their value.
Deciding when you’re not online, because this makes accessing information more expensive than computation.
Decisions where you have unusual information for a particular situation—the internet might have excellent base-rate information about your general situation, but it’s unlikely to give you the precise odds so that you can incorporate the extra information that you have in this specific situation.
Looking smart. It’s nice to look smart sometimes.
Others? Does anyone have examples of when Fermi calculations helped them make a decision?
Fermi’s seem essential for business to me. Others agree; they’re taught in standard MBA programs. For example:
Can our business (or our non-profit) afford to hire an extra person right now? E.g., if they require the same training time before usefulness that others required, will they bring in more revenue in time to make up for the loss of runway?
If it turns out that product X is a success, how much money might it make—is it enough to justify investigating the market?
Is it cheaper (given the cost of time) to use disposable dishes or to wash the dishes?
Is it better to process payments via paypal or checks, given the fees involved in paypal vs. the delays, hassles, and associated risks of non-payment involved in checks?
And on and on. I use them several times a day for CFAR and they seem essential there.
They’re useful also for one’s own practical life: commute time vs. rent tradeoffs; visualizing “do I want to have a kid? how would the time and dollar cost actually impact me?”, realizing that macademia nuts are actually a cheap food and not an expensive food (once I think “per calorie” and not “per apparent size of the container”), and so on and so on.
Oh, right! I actually did the comute time vs. rent computation when I moved four months ago! And wound up with a surprising enough number that I thought about it very closely, and decided that number was about right, and changed how I was looking for apartments. How did I forget that?
realizing that macademia nuts are actually a cheap food and not an expensive food (once I think “per calorie” and not “per apparent size of the container”),
But calories aren’t the only thing you care about—the ability to satiate you also matters. (Seed oil is even cheaper per calorie.)
The main use I put Fermi estimates to is fact-checking: when I see a statistic quoted, I would like to know if it is reasonable (especially if I suspect that it has been misquoted somehow).
I’ve run meetups on this topic twice now. Every time I do, it’s difficult to convince people it’s a useful skill. More words about when estimation is useful would be nice.
In most exercises that you can find on Fermi calculations, you can also actually find the right answer, written down somewhere online. And, well, being able to quickly find information is probably a more useful skill to practice than estimation; because it works for non-quantified information too. I understand why this is; you want to be able to show that these estimates aren’t very far off, and for that you need to be able to find the actual numbers somehow. But that means that your examples don’t actually motivate the effort of practicing, they only demonstrate how.
I suspect the following kinds of situations are fruitful for estimation:
Deciding in unfamiliar situations, because you don’t know how things will turn out for you. If you’re in a really novel situation, you can’t even find out how the same decision has worked for other people before, and so you have to guess at expected value using the best information that you can find.
Value of information calculations, like here and here, where you cannot possibly know the expected value of things, because you’re trying to decide if you should pay for information about their value.
Deciding when you’re not online, because this makes accessing information more expensive than computation.
Decisions where you have unusual information for a particular situation—the internet might have excellent base-rate information about your general situation, but it’s unlikely to give you the precise odds so that you can incorporate the extra information that you have in this specific situation.
Looking smart. It’s nice to look smart sometimes.
Others? Does anyone have examples of when Fermi calculations helped them make a decision?
Fermi’s seem essential for business to me. Others agree; they’re taught in standard MBA programs. For example:
Can our business (or our non-profit) afford to hire an extra person right now? E.g., if they require the same training time before usefulness that others required, will they bring in more revenue in time to make up for the loss of runway?
If it turns out that product X is a success, how much money might it make—is it enough to justify investigating the market?
Is it cheaper (given the cost of time) to use disposable dishes or to wash the dishes?
Is it better to process payments via paypal or checks, given the fees involved in paypal vs. the delays, hassles, and associated risks of non-payment involved in checks?
And on and on. I use them several times a day for CFAR and they seem essential there.
They’re useful also for one’s own practical life: commute time vs. rent tradeoffs; visualizing “do I want to have a kid? how would the time and dollar cost actually impact me?”, realizing that macademia nuts are actually a cheap food and not an expensive food (once I think “per calorie” and not “per apparent size of the container”), and so on and so on.
Oh, right! I actually did the comute time vs. rent computation when I moved four months ago! And wound up with a surprising enough number that I thought about it very closely, and decided that number was about right, and changed how I was looking for apartments. How did I forget that?
Thanks!
But calories aren’t the only thing you care about—the ability to satiate you also matters. (Seed oil is even cheaper per calorie.)
The main use I put Fermi estimates to is fact-checking: when I see a statistic quoted, I would like to know if it is reasonable (especially if I suspect that it has been misquoted somehow).
Qiaochu adds:
I also think Fermi calculations are just fun. It makes me feel totally awesome to be able to conjure approximate answers to questions out of thin air.