I think this is an error. (And so are “significant figures” as commonly used.) 2.4 +- 2 and 2.0 +- 2 are quite different estimates even though you wouldn’t (according to conventional wisdom) be justified in giving more than one “significant figure” for either.
Using the number of digits you quote to indicate how accurately you think you know the figure as well as to say what the number is is a hack. It’s a convenient hack sometimes, but that’s all it is. Everyone knows not to round intermediate results even when starting with low-precision numbers. Well, your final result might be used by someone else as an intermediate result in some bigger calculation.
The same goes for probabilities. It is very important to know when your estimate of a probability is very inaccurate—but that’s no reason to refuse to estimate an actual probability. Even if you just pulled it out of your arse: doing that makes it a very unreliable probability estimate but it’s still a probability estimate.
I won’t deny that significant figures are a crap implementation of the principle I’m talking about. But you have to propagate the uncertainty and include it, in some way, in your final answer, either numerically or via some explanation that might let me figure out how precise your answer is.
Don’t say “1% probability of FAI success by 2100.” Say ”.01-10% probability of FAI success by 100 based on XYZ.” Or if there’s no numerical process behind it that can support even a range like that, just say “FAI success by 2100 seems unlikely.”
Agreed. Though in the latter case you might still do best to give numbers: “Somewhere around 1%, but this is a wild guess so don’t take it too seriously.” This is not the same statement as the corresponding one with 2% instead of 1%, even though both might be reasonably accurately paraphrased as “unlikely” or even “very unlikely”.
I think this is an error. (And so are “significant figures” as commonly used.) 2.4 +- 2 and 2.0 +- 2 are quite different estimates even though you wouldn’t (according to conventional wisdom) be justified in giving more than one “significant figure” for either.
Using the number of digits you quote to indicate how accurately you think you know the figure as well as to say what the number is is a hack. It’s a convenient hack sometimes, but that’s all it is. Everyone knows not to round intermediate results even when starting with low-precision numbers. Well, your final result might be used by someone else as an intermediate result in some bigger calculation.
The same goes for probabilities. It is very important to know when your estimate of a probability is very inaccurate—but that’s no reason to refuse to estimate an actual probability. Even if you just pulled it out of your arse: doing that makes it a very unreliable probability estimate but it’s still a probability estimate.
I won’t deny that significant figures are a crap implementation of the principle I’m talking about. But you have to propagate the uncertainty and include it, in some way, in your final answer, either numerically or via some explanation that might let me figure out how precise your answer is.
Don’t say “1% probability of FAI success by 2100.” Say ”.01-10% probability of FAI success by 100 based on XYZ.” Or if there’s no numerical process behind it that can support even a range like that, just say “FAI success by 2100 seems unlikely.”
Agreed. Though in the latter case you might still do best to give numbers: “Somewhere around 1%, but this is a wild guess so don’t take it too seriously.” This is not the same statement as the corresponding one with 2% instead of 1%, even though both might be reasonably accurately paraphrased as “unlikely” or even “very unlikely”.