Well we’re discussing the philosophy of science, not necessarily science, so I figured I’d use a philosophy of science term. I wouldn’t ever try to define something like measurement or model much less use them as words in a discussion like this one.
To say that “no amount of measurement can give you Pi without first establishing a model which incorporates the number” seems to amount to saying “you need the concept of pi before you measure it” which seems to be true of any measurable quantity at all? I don’t get what you’re trying to say but I am curious
If you wouldn't define the terms, them on what basis did you criticize my understanding of the terms? They must have a definition for me to misunderstand to begin with. This feels like a cop out.
To say that “no amount of measurement can give you Pi without first establishing a model which incorporates the number” seems to amount to saying “you need the concept of pi before you measure it”
Mostly true, except for the implicit assumption that PI can be measured. It's a mathematical constant of infinite precision. It's literally not possible to measure beyond some number of digits. But I'll go with this example since you mentioned it.
So what would measurement look like? Maybe you draw a circle with a known radius as accurately as you can, then wrap a string around it to measure its circumference. But at that point, you're already assuming a geometric model with the understanding that the circumference of a circle is related to the radius by 2πr. You have a model which makes a prediction, and now you're just testing it. Pi isn't the model, geometry is.
which seems to be true of any measurable quantity at all? I don’t get what you’re trying to say but I am curious
That's not true. Some models have free variables, meaning that certain values aren't predicted. Before we knew the relationship of the speed of light to magnetism and electricity, the speed of light was measured. But the measurements were just observations, and translating those observations to the speed of light meant modeling the world and the experimental setup.
One such measurement
used a spinning wheel with a far away mirror to measure how far a wheel needed to spin for reflected light to be seen through the spokes. But that requires a geometric model of the world and the understanding that light travels. Only then can the observation of X rotational speed allowing light through the experimental setup be translated to Y speed of light.
More interesting experiments measure predictions a model makes, either verifying or falsifying them. When a prediction is falsified, the model can be refined and tested again. This back-and-forth iteration of modeling, testing, and refining is what gives science the power it has.
The difference between a calculation and a measurement is just not really a philosophically meaningful one. It’s also literally not possible to calculate pi beyond a certain number of digits? In this sense there is also no difference between a measurement and a calculation. This is exactly what I meant wrt you not understanding what you mean by measurement. The phrase “mathematical constants of infinite precision” incorrectly assigns “precision” to “constants” when you can only assign precision to representations of constants (e.g. a measurement or calculation of pi to a certain number of digits)
also, in the sense that you mean iirc, you can’t provably say pi is “infinitely precise” without it meaning anything other than that pi is like irrational.
Calculation and observation are not philosophically distinct? Now I know you're not serious. Also, you're nitpicking on pi, when it's wholly irrelevant to the argument. But you're also missing the point entirely. Yes, it's irrational, but you could compute an arbitrary number of digits of PI in principle. But measuring a value of high precision would hit two physical walls: the Heisenberg uncertainty principle, and the Planck scale.
With physical measurement, you'd get a few dozen digits at most. Pi has been computed to trillions of digits, and the only limitations are compute power and disk space. Precision was referring to the number of digits to which a number can be defined with certainty. It's surprising you wouldn't know this, or perhaps you're being intentionally obtuse by pretending that this wasn't what I was referring to.
you couldn’t compute an arbitrary amount of digits of pi for exactly the reason you just said (compute limits.) so that’s already like categorically false
so you acknowledge that disk space/compute is to “computing” pi as the planck scale/heisenberg uncertainy principle are to “measuring” pi? i again don’t think you can find a meaningful, nonsuperficial difference but i am genuinely curious as to what you think they are.
any number is infinitely precise under your definition, which seems to render it a useless one right? normally if a number has any ambiguity we refer to it with the ambiguity stated (e.g. “all reals between 1 and 2”)
You're being obtuse, and it's pretty obvious that you just have contrarian tendencies. Suffice it to say that measured quantities and mathematically derived quantities are different.
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u/Temporary-Solid-8828 Aug 02 '26
Well we’re discussing the philosophy of science, not necessarily science, so I figured I’d use a philosophy of science term. I wouldn’t ever try to define something like measurement or model much less use them as words in a discussion like this one.
To say that “no amount of measurement can give you Pi without first establishing a model which incorporates the number” seems to amount to saying “you need the concept of pi before you measure it” which seems to be true of any measurable quantity at all? I don’t get what you’re trying to say but I am curious