[xaa]

Your overall point is correct, but I would add that there is no such thing as a non-statistical model or prediction in any science or aspect of physical reality IMO. For two reasons: A) reality is inherently statistical at the quantum level, and B) measurement error will always exist.

Thus even our models of planetary orbits are statistical. The inverse-square law, GM1M2/r^2, even if it perfectly describes reality (probably, but not entirely certain! see [1]), will have some degree of measurement error in M1, M2, and r (not to mention G) and so the resulting Fg will be a distribution, not a single number technically speaking.

It seems that the situations where physics can best describe things with very high accuracy is when it can abstract away many relatively homogeneous particles or entities into a bigger "thing" with aggregate properties. For example, in fluid dynamics or gravity, you don't attempt to determine the behavior of individual particles, which would be subject to enormous uncertainty, only the behavior of the system-as-a-whole. By the law of large numbers then the uncertainties decrease dramatically.

[1] https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics

[godelski]

Yes, but you're implying "predictive" means 100% accurate. No science, no math, no language, will ever be 100% accurate. We say things have predictive power if we can, to a reasonable degree, if our results reflect our prediction. This is definitely true. And most those equations involve a pi. Pi doesn't have an end. There is ALWAYS and WILL ALWAYS be some uncertainty to our predictions. But is it that big of a deal if we can predict a planet's location down to the nm? Would you even say that it isn't predictive if we were off by 10km? No, you wouldn't. Because it is a planet and if you are looking for a planet and off by 10km you will still find the planet because the error is small. It would also be unreasonable to calculate the location of a planet down to the plank scale.

And to your mention of everything being statistical because quantum, well there's a reason Newton's methods didn't require them to be powerful (useful or predictive). Because the likelihood of quantum like events happening on a macro scale is basically zero. Sure, your hand could quantum tunnel through a wall, but would we ever expect to see it within the lifetime of the universe?

We're talking about the relativity of wrong here[1]. Physics wouldn't have become so popular if it wasn't predictive. We don't need to be 100% to be predictive nor useful. Accuracy and predictiveness are two different things.

[1] http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm

[xaa]

> Yes, but you're implying "predictive" means 100% accurate.

No, I'm not. Or I didn't intend to, in fact I intended quite the opposite. I completely agree that "wrongness" is relative. "Wrongness" could be more accurately described as the amount of variance in a predictive model plus that model's divergence from reality.

My point was that all models and predictions are statistical/probabilistic, but not all have even the same order of magnitude of error. For shorthand, we pretend that models with very low variance/error are "exact" solutions, but in actual reality, they are not, they are just solutions that have a negligible error rate for the purpose at hand.

I am not implying anything like "well, psychology and physics both have probabilistic models, so they're equally valid". Their variance and error rate are very far apart. I agree physics is very predictive and has high accuracy but it is still probabilistic.

[godelski]

> My point was that all models and predictions are statistical/probabilistic, but not all have even the same order of magnitude of error.

Definitely not. The models used in undergraduate physics classes, or even to high school physics are not statistical. A good example is ohm's law. When building circuits this is necessary to use. Works just great. Now this is different from any attempts at GUT, but that's a different ball game. And those are different models.

> For shorthand, we pretend that models with very low variance/error are "exact" solutions

Maybe the public, but not the actual scientists. For shorthand we generally say "is" instead of "to an error we can't measure" because it is easier to say. But if you read the research papers errors are always included. But that's just language. Doing otherwise would be pedantic. Yes, the public gets confused, but for all they are concerned with these predictions might as well be "exact". When the public starts venturing out of their realm without learning they get confused with other more important ideas like "observer" and "information". Don't get me started on how many people believe stupid quantum stuff.

> they are just solutions that have a negligible error rate for the purpose at hand.

This demonstrates that you understand my point too. Or that you don't understand what negligible is. But I think you understand. At a certain point we stop worrying. Why would you care if you could predict the location of a planet down to the 10^-40m? I get doing it just for fun and because you want to, but there is no practical purpose. Anything this accurate might as well be exact.

[xaa]

> The models used in undergraduate physics classes, or even to high school physics are not statistical.

You are correct insofar as they are not presented as being statistical. But in reality, they are. Ohm's law is a good example. Resistors in reality do not have the exact resistance specified on the package, but rather are constructed within a certain tolerance, so that the final behavior of the circuit will be, again, a distribution. This would be an example of measurement error. The quantum effects also exist, as Intel will affirm as they are trying to build very small transistors, and the behavior of such transistors is probabilistic.

> Maybe the public, but not the actual scientists...

Ehh, I'm an "actual scientist". I work in bioinformatics & medical research. I don't care about what the public thinks for the purposes of this conversation. Even actual scientists will sometimes use this shorthand if the error is small enough, which is fine by me.

> At a certain point we stop worrying...but there is no practical purpose.

You're right. When we talk about the error rate in predicting planetary orbits, there is no practical purpose. My only point in my original reply was that the "exact" is a special case and a simplification of the statistical model, which is ubiquitous. If we are wanting to be technically correct, however, I stand by my assertion that all physical laws are inherently statistical.

I think we don't really disagree. This all started because you asserted there are phenomena which are "not statistical in nature", which I disagree with at a pedantic level.

[godelski]

> which I disagree with at a pedantic leve

I think we'll agree there. Because while you are technically correct you aren't practically.

Like how the Newtonian equations taught to undergrads literally don't have statistics. It isn't that it isn't presented to them that way, it is that they are using a different model. Going through physics (because this is the experience I have) you just keep learning better and better models.

As for Intel, you're confusing micro and macro scales. With the ohm's law you just measure the resistor before applying. This would be common procedure, depending on application. But this conversation is really arguing extremely fine points.