Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
You don't have something to teach us, you have almost everything to learn, and I recommend you go get started by doing your homework. The most elementary aspect of your idea is common property to all modelers, not original, and is the only part of what you are talking about that is clear or correct. The only thing you are adding is blindness to other bits, and unawareness of the prior work of others. You confuse the resulting myopic view, with something original, because you have not seen that myopia exactly reproduced before.
You asked whether your overall presentation makes sense or is gibberish, and I am telling you. Told you on the first post, told you on the second, and on the third. I'll tell you in any level of detail you require, but the answer isn't going to change. You are clearly interested enough in these questions that it would be worth your while to actually go learn the relevant literature. You are clearly not well enough informed about the subject that you have anything to teach us before you have done so. Sorry, I can be polite a few iterations but sometimes the point is simply not grasped unless one is blunt.
Now in detail -
"I meant that the model is defined only by unobservables."
Equivocation on "defined by". Any model posits some underlying terms, rules, mechanisms, equations, what have you. Those have consequences in their own formal terms. Any model tells you how its posited underlyings map to observations (directly, by being averaged, by being sampled, whatever), or it fails to show any relation, let alone the relation of accurate correspondance, to the observations. No model *defines* a sequence of observables.
"None of the values within the model are observable."
Equivocation on "within the model". That which the model implies for a variable it predicts will be observable, is part of the model. It just is a different variable than some underlying or hidden one. You can't make a model with all the variables hidden or you don't have a map to observations, don't say anything about observations, and therefore do not say anything. "All my underlying variables flap about this way. I've no idea how they are connected to the observable sequence". Then they have no relation to it, you haven't modeled anything.
A model is a map from something posited to a set of observables, however restricted a map. The underlying can have a billion billion states, and the observable can have only two, one of which obtains 99% of the time. But if there isn't a map from the underlyings to an observable difference there isn't a model at all. And if there is, then the statement that none of the values within the model are observable is false. The model says, F of this underlying goes to, equals, follows, is, this observable.
"As far as I know, no scientific model does that."
And I am telling you, how far you know is not very far at all, because you are just wrong. Every model does this, not none.
Kepler does some math and predicts Jupiter will be here next Wednesday night. That is a map from some ellipse equation, which you can't observe, to the position of a dot in the night sky, which isn't a number. Any model already does this.
Any *hidden variable* model does more than this, it asserts that you can't measure something that is really going on, but can measure some resultant of it. It may say, for instance, you can't see the position and velocity of all of these particles I've posited as existing in this box of gas, but you can measure the pressure they exert on average on this wall of it. And then I can explain why that pressure goes up, when I put hotter gas in the box. The ensemble state of the gas is not an observable, the pressure is. The observable is predicted to reflect the ensemble state in a uniform way. The ensemble state is, further, expected on plausible but not certain arguments, to usually follow this or that statistical relation to another observable (some velocity distribution according to temperature).
A model posits an underlying formal system without requiring it to be observable, provides a map from any such system observable or not to a set of observables, and thereby tries to relate the sequence of observables to some formal system. No relation to observables at the top end means no model. But nowhere is it ever required that anything the model posits, must be observable. And in practice, practically no scientific model predicts everything it posits or refers to, will be observable. Nor does it try to fit every wiggle of the observed. It tries to get some potentially noisy and lossy map from some posited underlying formalism, to a selected, few-aspects-only, series of observations.
Don't congratulate yourself on reinventing the wheel, learn a little about how much is already known about these problems.
"But with my model you *can* predict the outcome of an experiment, it just isn't as simple as reading the result of a calculation as a value."
Um, of course it is, "calculation" just means more than you think it does. First I evolve the model, then I apply the underlying to "observable" map, to every scrap of it. What you are calling "the calculation" means state (t2) as some function g of state (t1), t2 = g (t1). But perpendicular to that, I also have another function f that takes state at t1 and state at t2 or anything like them, to observable at t1 - f ( t1 ) and f (g ( t1 ) ) aka f ( t2 ). f may be lossy - it may lump different things together; f may be noisy - it may introduce slight differences even when provided the same underlying. But no f provided, means the observable consequence left unspecified, means nothing modeled. A model maps something to observations or it fails to model. Nothing original is being said in this paragraph, this is news to no one, it is not an original idea, it is something everybody already knows.
"Say you measure your height to be 6 feet tall. That is an observable, a measurement. Correct?"
Strictly speaking, to be six feet tall means a succession of measurements by fair tape measures results in an equivalence class of visual inspections in which some pencil mark or what not is always within half an inch of this many ticks from where I started. Each of those is an observation, the posited external reality that rolls them all together is not an observation but a fact (except the right answer is 5 feet 9 inches in my case), and no model or theory has been advanced in the process. Some have been assumed or used in the deduction, such as I am not growing rapidly, tape measures are not wildly fluctuating, all pragmatically dismissed etc.
"is there a "6" in the values of the universe that somehow, during measurement, leaves the logical system and enters our conscious experience?"
Red herrring and a basic philosophical confusion, ascribed to others if not actually suffered. No model has anything to do with this. I prescribe Santayana and Popper in addition to the black box problem and the theory of hidden variable modeling and inference already suggested.
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