Real quick while I barf:
***I finally sat down my wife (who knew no physics at all) and explained the derivation line by line (trying to do it in terms she could follow) -***
Sounds like a fun date. I bet you were the catch of all the girls. Sorry, couldn't resist.
***The meaning of correct is vague. We must do our best to avoid relying on context as the context itself may be misconstrued. That is why I move to context free labels provided by numbers. (This appears to be an issue beyond Harv's comprehension!)***
No, what you do not comprehend Dick about my comments is that you cannot have it both ways. You cannot be a pure mathematician using numbers and such, and then in the same breath, you use concepts that mean something in the world (e.g., knowable and unknowable). These concepts are meaningless in mathematics, but yet you wish to use them. That's fine if you define those terms, and that you create a model whereby you make predictions. That's what science does, and that's how science justifies its use of mathematics. If science made no predictions, then the use of mathematics would be entirely suspect since many scientists have developed many theories that were apparently consistent with mathematics, but they were wrong. Just matching the physics that's already constructed is not good enough as Bible Codes show.
***I presume you understand here that the set of numbers are nothing except a representation of a message in meaningless labels and that we possess no information not provided by that message. Again, as an aside, I fully realize that I am using a mental model created by my subconscious for the purpose of discussing and thinking about the problem. Now Harv barfs all over me for that. My position is that if one takes Harv's advise, there is simply nothing which can be done as logic itself vanishes from our vocabulary. Harv's advise amounts to telling us to leave the solution up to our subconscious.***
No, this is not what Harv is saying. I'm saying that you are approaching this problem from a metaphysical perspective where your model is an ontological theory (i.e., true because it is self-consistent). The solution, regardless of what you do, is up to your 'subconscious' (i.e., our direct experiences of the world). What you want to do is pretend that somehow you've surpassed this limitation simply because you've moved to definitions and mathematical processes, but as I showed in a previous post a few days ago, any definition or mathematical process that you can imagine is all built on your direct experiences of the world (i.e., what you call the 'subconscious'). Call it what you want, but if your model is assuming that your 'subconscious' is correct by coming up with a self-consistent method (e.g., mathematics or logic), then you are just as reliant on the 'subconscious' as you are had you just relied on scientific observations compared to theory in establishing the 'truths' of the universe. Your whole argument boils down to what deduce from what your 'subconscious' believes, and yet you cannot comprehend this basic fact.
***I really don't know how to make the idea of "knowable" and "unknowable" classifications clear enough to avoid Harv's tendency to barf all over what I say. His complaint here is that there exists no way to identify the "knowables". He is of course correct; however, what he misses is that the conclusion is not dependent upon being able to make that identification and I have no idea of how to make that fact clear to him.***
My contention is more than identification of the 'knowables'. You simply cannot even define the terms without assuming the very observations that you wish to reject as part of meanderings of the 'subconscious mind'. This is why you cannot define 'knowables' since to do so you must accept the 'subconscious' model of the world. If you only define it using common language then we have no idea what you are talking about (e.g., "everyone knows what a knowable is, its what we know - are you saying we don't know anything?"). If you thoroughly defined your terms, you'd see how much you rely on your 'subconscious' even in terms of defining and going about solving the so-called 'problem' that you talk about, then you see that you are doing something no more elabore than tail-chasing (e.g., when a dog chases its own tail).
***Now Harv always barfs on that concept because it is clear that we fundamentally do not have the power to determine if any given idea belongs to one or the other category; however, I hold that the two different categories require different logical consequences. That issue has no bearing whatsoever on whether the categories exist or not.***
Dick, here is a classic quote. If you forget everything else I tell you, then remember this:
If the issue has no bearing whatsoever on whether the categories exist, then your conclusions, even in the best possible scenario, have no bearing whatsoever on how the world is, and therefore the results are meaningless. That's the best case. The worst case is that they are just mistaken altogether since you might have set-up the problem in a manner such that an Emmy Noether (or related) proof emerges, if so, then you have proved nothing extraordinary that wasn't already known.
If you forget everything else, just remember this. It is, in essence, what is wrong with your model's fundamental assumptions.
***So, from that perspective, one can understand that as science advances, there are two things which can change. Actual facts (the knowables) cannot change, but both the "unknowables" (what we think exist) and "what we think the rules are" can change. As scientists, we are free to create any "unknowables" we wish so long as all the "knowables" and "unknowables" (all the things we think exist) obey "all the rules". And we are free to theorize any "rules" we wish so long as all the "knowables" and "unknowables" (all the things we think exist) obey "all the rules". This is no more than an abstract statement of what scientists do all the time. They continually invent new entities which provide explanation of the phenomena they examine and then check to see if those invented entities obey the rules they believe to be true. At the same time, they occasionally change the rules a little. (On some very rare occasions, the rules have changed quite a little and I guess I am proposing a basic change in the rules.)***
What if there are no 'knowables' or 'actual facts'? What if all that is 'true' is all built on a human conceptual framework. I'll use this example again. If someone said that 'chairs do not actually exist' Fred Sanford (fictional character from tv series "Sanford and Son") might say "that is false, how can you be that stupid?, of course they exist since I'm sitting on one right now - you big dummy". In Fred's mind the chair existing is true. But, what Fred doesn't consider is that the term 'chair' is a term from modern human conceptual frameworks. An ET alien might have no concept of a 'chair' and might look at such an 'object' and say: "ah, it is a multiple structure composed of wheels, a seat, handrests, etc", or "ah, a collection of quarks and leptons organized in some new and bizarre fashion...". The point is that the term 'true' or 'actual fact' does not apply necessarily to a 'chair' and it might be that there are no such 'actual facts' - at least from our human logic way of thinking. I know this is tough and easy to mock such a comment, but this so far has been our experience of the universe. So far, we haven't found one model of science that hasn't broken down in its attempt to describe the universe, and this might just be how the universe is. We cannot assume we are correct if we say otherwise.
***Getting back to what I have done: I have explicitly proved that, if you accept that both the rules and the entities are variable (that is, subject to change by advancement of science), then it is always possible to put the rules in the form of a solution to the expression F=0. That is, there exists a very specific rule for the functioning of the universe which does not constrain the universe in any way. That rule is in fact my fundamental equation. The result of that constraint is that the only question left to answer is "what entities actually exist?" The equation itself is entirely content free and imposes no constraints whatsoever on the universe.***
Terms like 'explicitly proved', 'rules and the entities', 'always possible', 'rules in the form', 'expression F=0', 'there exists', 'functioning of the universe', 'constrain the universe', 'fundamental equation', etc, must be treated as meaningless terms with respect to the way the universe actually is (for the reasons above). It is a math exercise that went to far in its ambitions. Where no exact definitions are provided, you cannot obtain any conclusion with respect to the world. Too bad this is over your head, but maybe its not over Tim's head.