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sixes_and_sevens comments on True numbers and fake numbers - Less Wrong
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Some anecdotal and meandering gubbins.
I am occasionally called upon to defend what an interlocutor thinks of as a "fake number". The way I typically do this is to think of some other measure, parameter, or abstraction my interlocutor doesn't think is "fake", but has analogous characteristics to the "fake number" in question, and proceed with an argument from parallel reasoning.
(Centre of mass is actually a very good go-to candidate for this, because most people are satisfied it's a "real", "physical" thing, but have their intuitions violated when they discover their centre of mass can exist outside of their body volume. If this isn't obvious, try and visualise the centre of mass of a toroid.)
Some of the above are this sort of parallel measure I have used in the past, either with each other or with some other measures and values mentioned in comments on this post. I'm quite pleased at how divisive some of them are, though I'm surprised at the near-unanimity of food calories, which I would have expected to be more politicised.
My conclusions to date have been that the "reality" of a measure has a strong psychological component, which is strongly formed by peoples' intuitions about, and exposure to, abstract concepts with robust, well-understood or useful behaviour.
How is the fact that the center of mass can exist outside the body volume supposed to make center of mass "fake" in any way shape or form?
To clarify, my position is that whether someone finds an abstract measure to be "fake" or not depends on how comfortable they are with abstractions. Some abstractions wear very concrete disguises, and people are generally fine with these.
My experience is that people's folk-physics interpretation of their centre of mass is that it's an actual part of their body that the rest of their body moves around. A lot of dancers, for example, will talk about their "core", their "centre" and their "centre of gravity" as interchangeable concepts. When confronted with the idea that it's an abstraction which can be located outside of their body, they're often forced to concede that this intangible thing is nonetheless an important and useful concept. If that's true of centre of mass, maybe they should think a little bit harder about market equilibria or standard deviation.
As Dan pointed out here cousin_it's definition of "fake number" has a very concrete meaning. The most your example shows is that the folk-physics notion "center of gravity" as opposed to the actual physics notion is a fake number.
While his definition of "true number" is fairly concrete, his definition of "fake number" is less so, and importantly is not disjoint with "true number".
ETA: Having thought about it a bit and looked over it, I'm fairly sure we're just talking past each other and there's no coherent point of dispute in this discussion. I suggest we stop having it.
Some of these things have formal, mathematical or empirical definitions and that's the gold standard for a true number. I don't want to point out which ones, as that would ruin the poll.
A formal or mathematical definition isn't good enough if it's inputs can't be similarly computed.
That's true. And only some of those things can be computed, and some are inexact. But I'm surprised that some people voted for 'fake' on every item except for the center of mass (only one vote for 'fake').
A while has passed since the poll, so I guess we can discus this now:
Food calories: the energy that human metabolism can free from a food. 1 food calorie = 4200 J. The definition is precise, and can be measured exactly with a calorimeter.
Digestion and metabolism can deviate from that definition. Wikipedia notes that "alterations in the structure of the material consumed can cause modifications in the amount of energy that can be derived from the food; i.e. caloric value depends on the surface area and volume of a food." People also have individual metabolic differences. Still, it's a useful unit of measure.
The position of an object's centre of mass has a strict definition. To calculate it you need to know the distribution of mass in an object, but you do know it for many objects.
The population mean is defined by Wikipedia as equal to the arithmetic mean over the whole population - for a finite population. That seems simple enough that I'm confused that some people voted it was 'false'.
It can be a fake number if we have no practical way to survey every member of the population.
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'.
I'm not personally sold on "true" and "fake" numbers, but I do think it's going in an interesting direction.