The model F=GMm/r^2, for example, has a causal and ontological semantics: F is a force, M a mass etc. these are pieces of reality. And this formula (though actual a little suspicious in many ways, GR fixes this) nevertheless says there is a force between masses that has certain properties etc.
Now you can say that astrologers who recorded positions of the stars in books helped 'create' this model in the sense that this data was inspiration to newton. But he didnt derive the model from this data: there are an infinite number of (causal) models consistent with the data (statistical models).
Rather newton played around with creating geometries, just like the vase-makers in plato's cave. Newton built various ways the world might be first, projected data out of them, and compared that to 'the statistical data of his day' (ie., astrology).
There's nothing in the data to tell Newton he was right. Indeed, vast amounts of it told him it was wrong: such a law does not describe the known solar system at his time, very far away from it.
Nevertheless 'modelling shadows' isnt science; and his job was science. So one has to compare actual explanatory models, and his was the best.
What you're describing above is hypothesis testing which occurs long after theory building. Broader theories create causal models, causal models create sets of predictions, we call some subset a hypothesis and by hypothesis testing we can select, in an often psuedoscientific way, between causal models.
This technique occurs long after the invention of science, arises out of explanatorily bankrupt areas, as a way of 'giving researchers something to do'. It's wholly pointless without theory-building, it is just averaging shadows.
The science we think of when using the term 'Science' owes very very little to the modern practice of hypothesis testing. Comparing hypotheses is an intellectual part of assessing explanations -- identifiable formal statistical methods entered in the early 20th C.
For almost all of scientific history 'data' functions much more like reductio-ad-absurdum premises in philosophical arguments than as sets of numbers from which to derive distributions.
That latter system, in most cases, fails. It provies a wholly illusory sense that data can decide matters; and applies in cases requiring extreme non-physical assumptions (eg., of the normalcy of the underlying data, or of a fast rate of convergence of the central limit theorem).
Much real-world phenomena studied by stats cannot really be studied by data analysis at all; and the whole method of 20th C. statistical hypothesis testing is the opening sales pitch to entire fields of pseudoscience.
And this model is based on the observations of Newton himself and those that came before him. There is nothing magic about observing the attraction between objects and deriving a model from that. Why are they magically "pieces of reality"? How do you know that? What differentiates mass from "funny-mass" that I just thought up and actually repels other "funny-mass"? Maybe the fact that we can test the effects described by that first model and therefore verify it as the most likely candidate?
> But he didnt derive the model from this data: there are an infinite number of (causal) models consistent with the data (statistical models).
He did derive it either from that data or his own experiences. It's true that you can construct infinite models to explain an observation, which is why the scientific method includes an Occam's razor-esque tenet to select the simplest possible model. Complex models risk contradictions with new observations, which is why you choose the one with the least assumptions. With that rule, the model to select becomes quite clear.
> There's nothing in the data to tell Newton he was right. Indeed, vast amounts of it told him it was wrong: such a law does not describe the known solar system at his time, very far away from it.
No, most of it told him he was right, unless you want to claim Newton was an idiot that stumbled onto the right model by accident. With "most" I obviously mean most reasonable data, people telling him he's wrong is obviously excluded from this list, if his evidence contradicted those claims.
> Nevertheless 'modelling shadows' isnt science; and his job was science. So one has to compare actual explanatory models, and his was the best.
And we compare those models by...?
> What you're describing above is hypothesis testing which occurs long after theory building. Broader theories create causal models, causal models create sets of predictions, we call some subset a hypothesis and by hypothesis testing we can select, in an often psuedoscientific way, between causal models.
You yourself just correctly made the point that we can construct endless models, well, we can create endless theories as well. And all of these theories are exactly worthless unless we test them. There is nothing "pseudo-scientific" about testing, it is literally the core of the scientific method. By your reasoning, are some crackpots coming up with the newest flat earth theory pure and unsullied by the lower demands of verification, and therefore way more scientific?
> identifiable formal statistical methods entered in the early 20th C.
Formal is the important word here, statistics has been used in an informal manner from the inception of life. Formal mathematics, as in mathematics on a formal axiomatic framework, has also only been introduced in the 19th century. So what? Science owes everything to informal statistics, as does engineering and art. Rules of thumb used by engineers and creation of art that satisfies our aesthetic preferences requires sampling and approximation.
> That latter system, in most cases, fails. It provides a wholly illusory sense that data can decide matters; and applies in cases requiring extreme non-physical assumptions
It literally doesn't and no, it doesn't need those assumptions either. The reason why normalcy is usually assumed is that it often can be assumed without significant deterioration in predictive power. That doesn't mean it needs to be assumed, in fact, it often isn't.
You constantly reference theory building, but how do you think those theories get created exactly? Through mathematical reasoning? How do you know mathematics is valid? Through logical deduction? How do you know logical deduction is valid? Through knowledge? How do you know knowledge... and so on.
Fact is, we only use these tools because they have proven their validity through being tested over and over and over again. And if you look at modern pseudoscience, it always seems to coincide with a proclivity for theory building, with very little hypothesis testing involved.
We first suppose that the universe is something like a glass sphere -- because we've created that. And if it is, then we derive some consequences -- if those line up, we proceed with that view until a better one comes along.
Eventually after the glass sphere view is understood, we either derive contradictions with observation; or we end up unable to derive novel consequences. Here observation is essentially singular, and indeed, the rarer reason we reject a theory. We mostly reject scientific theories because of their explanatory limits, not disagreement with observation. (Rarely can we observe enough for observation even to matter.)
In the case of the system of spheres, we built spinning devices on that basis and this motion -- along with the hydraulics and kinematic devices of the time -- was part of the development of an independent notion of force.
With some imagination, you can start to peel away material from our creations and see certain abstract causal patterns (and the like) and you then get to, eg., the universal law of gravity.
Absent this process we do not have any explanatory ideas, we cannot explain observations -- hence it takes thousands of years to get anywhere.
Applying 'statistics' to do the data to arrive at statistical models is pseudoscience; it doesnt give you any account of anything.
'Statistics' doesnt own 'testing', nor does 'science' own experiment -- theologians had their experiments (prayer, say) and scientists collected data without statistical methods.
What I am talking about is the 20th C. discipline of statistics, as a novel apparent 'core' to science -- this is ahistorical, and largely only true of pseudoscientific disciplines.
As Ernest Rutherford said, “if you need statistics to do science, then it's not science.”
It is in Rutherfod's sense of stats and of science that I speak.
Not some bizarre historical back-projection by which when Aristotle analysed cases of sea creatures, "Really", he was engaged in stats.
By this light i can just claim "Testing" is as owned by science. And so of course science requires testing -- it was the *scientific method* as developed by bacon and others that created the very conditions for "statistical methods" to derive from these
Is it that LLMs specifically don't have this same property of being able to approximate such functions? Is it that a neural network wouldn't learn that model if you gave it real world measurements (because I think it would, but such a thing should be fairly easily testable)?
The issue is that to prepare the dataset from which that formula is learnt requires already knowing it. This is the triviality of applications of universal function approximators to science -- empirical data modelling isnt new, and neural networks are just one example of it; not all that special.
All observational data on the solar system, at any point in time, would not yield this formula via empirical function approximation. there really isnt "observational data" to collect, in this sense
This is what I mean about rigging -- there is no 'bare dataset' which tells you what the world is like. to construct experiments which yield data that 'presents' scientific laws as if statistical patterns requires millenia of theory-building science
science uncovers the necessary causal relations between objects and their properties, as determined by extremely controlled experiments which take millenia of engineering and theory-building to even conceive, let alone execute
stats is the dumb 'accounting' of this data -- by the time you actually have it all the science (and indeed, all the intelligence) is done
what can be automated at this point is 'stamp collecting' as rutherford said
Why is that? Are you saying that universal function approximators can't invent higher level models? Isn't that what happens in the hidden layers when an neural network is trying to predict things that require those higher level models?
you'd need to measure the force between planets, the distance between them, etc. no such direct measurements have taken place to my knowledge, certainly not at newton's time
All "universal fn approximator" means is that given any dataset which is sampled from a function, you can recover that function with enough data points. It does not mean, eg., that given a 2D dataset you can derive a 3D function -- you cannot, this is impossible.
So you need to be sampling from F=GMm/r^2 to find that function. So you need to know the answer before you begin. Fn approximators are only useful for empirical refinements to existing knowledge.
In order to construct such datasets you need to do science; hence experiments, etc.
With Plato's cave, the scientists do not put literally every possible object in front of the light, they sample the shadow representation and, again, construct a model around those samples.
Also, you're describing statistics in an incredibly dismissive way. Stats is decidedly not just "taking the average". At the very least not in this brainless, first-order way you describe here.
Let's explore this with an thought experiment:
A model of some process has been confirmed across the globe, at least 5000 studies show the same result. Yet, one day, a study is published that fails to demonstrate the desired effect. Without using statistics, please tell me which action should be taken next:
A: The stray result is investigated for experimental failures.
B: The entire model of the process is immediately dismissed and we start from scratch.
By the way, you're welcome to call me uninformed, but I'd ask you to at least provide either your credentials or research that directly contradicts me.
Oh, I almost forgot. I know all of these definitions, please actually engage with what I'm saying instead of insinuating that I'm missing information.