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.
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..
you come up with some numerical quantity, discover interesting facts about it, use it to analyze real-world situations—but never actually get around to measuring it. I call such things “theoretical quantities” or “fake numbers”,
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’.
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’.
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.
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.
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’.
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.