An example of a “true number” is mass. We can measure the mass of a person or a car, and we use these values in engineering all the time. An example of a “fake number” is utility. I’ve never seen a concrete utility value used anywhere, though I always hear about nice mathematical laws that it must obey.
It is interesting that you choose mass as your prototypical “true” number. You say we can “measure” the mass of a person or car. This is true in the sense that we have a complex physical model of reality, and in one of the most superficial levels of this model (Newtonian mechanics) there exist some abstract numbers which characterise the motions of “objects” in response to “forces”. So “measuring” mass seems to only mean that we collect some data, fit this Newtonian model to that data, and extract relatively precise values for this parameter we call “mass”.
Most of your examples of “fake” numbers seem to be to be definable in exactly analogous terms. Your main gripe seems to be that different people try to use the same word to describe parameters in different models, or perhaps that there do not even exist mathematical models for some of them; do you agree? To use a fun phrase I saw recently, the problem is that we are wasting time with “linguistic warfare” when we should be busy building better models?
Perhaps, though, you could argue it differently. I have been trying to understand so-called “operational” subjective statical methods recently (as advocated by Frank Lad and his friends), and he is insisting on only calling a thing a [meaningful, I guess] “quantity” when there is some well-defined operational procedure for measuring what it is. Where for him “measuring” does not rely on a model, he is refering to reading numbers off some device or other, I think. I don’t quite understand him yet, since it seems to me that the numbers reported by devices all rely on some model or other to define them, but maybe one can argue their way out of this...
It is interesting that you choose mass as your prototypical “true” number. You say we can “measure” the mass of a person or car. This is true in the sense that we have a complex physical model of reality, and in one of the most superficial levels of this model (Newtonian mechanics) there exist some abstract numbers which characterise the motions of “objects” in response to “forces”. So “measuring” mass seems to only mean that we collect some data, fit this Newtonian model to that data, and extract relatively precise values for this parameter we call “mass”.
Most of your examples of “fake” numbers seem to be to be definable in exactly analogous terms. Your main gripe seems to be that different people try to use the same word to describe parameters in different models, or perhaps that there do not even exist mathematical models for some of them; do you agree? To use a fun phrase I saw recently, the problem is that we are wasting time with “linguistic warfare” when we should be busy building better models?
Yeah, that sounds right. You could say that a “true” number is a model parameter that fits the observed data well.
Perhaps, though, you could argue it differently. I have been trying to understand so-called “operational” subjective statical methods recently (as advocated by Frank Lad and his friends), and he is insisting on only calling a thing a [meaningful, I guess] “quantity” when there is some well-defined operational procedure for measuring what it is. Where for him “measuring” does not rely on a model, he is refering to reading numbers off some device or other, I think. I don’t quite understand him yet, since it seems to me that the numbers reported by devices all rely on some model or other to define them, but maybe one can argue their way out of this...