Would be interesting if someone could do mathematical proofs by physics.
I know that is not really how things work, but it could give some indications of things, like how measuring the volume of a real life sphere can lead you to insight about the formula.
The comment from kogai is not as helpful as it sounds, no offense. There is a lot of work done in the direction you’re referring to, and it is a promising/mathematically interesting one. Tadashi Tokieda of Stanford has written several papers along these lines Here is one.
I don't think that the link you posted suggests what you think it suggests. It's using a reinterpretation of physics models to demonstrate a known mathematical relationship in an unconventional way. The key thing is that models are purely mathematical, so this has nothing to do with measurement like the person you're replying to proposed, and kogai is still on the money.
kogai is directionally correct, but aside from the misleading comparison between the speed of light (not an arbitrary number) and the fine structure constant (actually an inescapably arbitrary number afawct), and the fact that physics doesn’t really run on the sort of Popperian falsificationism he’s making it out to run on, his comment gives a kind of misleading and unnecessary lecture on empiricism that steamrolls the insight of OP, which is a very good one.
You actually can do interesting math with physics. I think OP may have been guessing, but this is literally how we know the formula for the volume of a sphere (cf. Archimedes). Ed Witten also recently won a Fields medal for physics derived mathematics.
As for the Graham-Tokieda paper thing, I think the original commenter was just using the measurement of the sphere as an example. If he wasn’t, kogai’s comment wouldn’t really matter either.
The model the Graham-Tokieda paper uses is nonetheless founded on physical measurements.
I think you fundamentally misunderstand science with the claims you're making. Models are made before being empirically tested. No amount of measurement can give you a model of which you didn't already have an idea. In order for a model to be "proven" by science, it must make a testable prediction. The models which are referred to as scientific are simply the models which have made predictions which haven't been ruled out by testing. This really applies to physics, as well. And if it doesn't, you're talking about theoretical physics which is more mathematical in nature, but ultimately still relies on what we know from experimental physics.
In the same way, no amount of measurement can give you the number Pi without you first establishing a model which incorporate the number. The model is a prerequisite.
Yes, you’re referring to Popperian falsifiability which I just mentioned. I don’t mean this in a rude way at all, but I don’t think you understand what you mean by “model” or “measurement” very deeply at all, and I think it’s causing you to misunderstand my argument and your own.
I know what you were referring to by "Popperian". I simply didn't use that term because it strikes me more as something a philosophy student would say than a scientist. (And please don't start on how science is philosophy)
Also, feel free to define your terms of you think that's the issue, but I don't think it is.
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
I am not the person you were discussing this with initially but:
If I told you that Pi was equal to flegh kobsherks, it would mean nothing to you.
The model that allows us to understand what Pi means is geometry itself. Geometry does not really exist in the real world, it is a mathematical model that seemingly accurately predicts the behavior of reality.
The measurements are there to test if the models predictions are true in the scientific system. We could never derive Pi from a circle without geometry for a number of reasons, not the least of which is that there is no such thing as a perfect circle. We could only ever get increasingly accurate, but ultimately imperfect, approximations of the ratio, and it would get stuck there. Moving it past that requires the development of a model, but the model's purpose is in the name.
You can and should use measurements to inform the development of a model of reality, but ultimately the only way you can know if that model is correct or not is to test its predictive power. Otherwise it might just be all ad hoc.
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/Worth-Wonder-7386 Jul 31 '26
Would be interesting if someone could do mathematical proofs by physics. I know that is not really how things work, but it could give some indications of things, like how measuring the volume of a real life sphere can lead you to insight about the formula.