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sixes_and_sevens comments on True numbers and fake numbers - Less Wrong
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Comments (128)
Why do those criteria form a gold standard for a "true" number? I can invent formal, mathematical or empirical definitions for things all day long that don't correspond to anything useful or meaningful or remotely "real" outside of the most tautological sense.
Let's say the Woowah of a sample is the log of its mean minus the lowest number in the sample. If I sample the heights of fifty men aged 18-30, that sample has a mathematically well-defined Woowah. There's even an underlying true value for the Woowah of the population, but so what? When I talk about the Woowah, I'm not really talking about anything.
Meanwhile a population's carrying capacity (currently the most "fake" number in the poll) isn't something I can directly observe. I have to infer it through observation. (For all practical purposes I have to infer the Woowah through observation too, but in principle I could sample the entire population and find the true Woowah). I can't directly measure the carrying capacity because it isn't a direct property of the population. It's a parameter in a model of the population which happens to refer to a property that population would have in a specific and probably counterfactual case. It's questionable whether there is an underlying "true" population carrying capacity, but it's definitely talking about something important and meaningful.
The OP's definition of a "true" number isn't that it's useful, meaningful or corresponding to something "real". It's merely that it's objectively measurable and actually measured..
But why is this an interesting property that's worthy of consideration?
It's a specific failure mode that's useful to talk about because it might let us recognize real-world failure in some "false" numbers. That's not intended to imply there aren't other failure modes; it's not a sufficient test for the quality of a 'number'.