Since Paul has described this as a great post, I felt it deserved a critical response for 'equal time':
***This I leave open as I have no way of proving that any meaning which I attach to any of those labels is correct! I only wish Harv could understand that. I use numerical labels because they possess no connotations at all and the problem of connotations in the English language (and probably all other "languages") is what I want to avoid at all costs. The problem with those connotations is that they imply more relationships then can be checked (for consistency) on a conscious level.***
Here is an area where we have fundamentally disagreement. Paul and I debated this issue, and it seems he and I also fundamentally disagree as well. Let me attempt to explain again (as futile as this attempt will be at successfully making my point clear).
When we talk about mathematics there are different interpretations to the terms and meaning of terms as used in math. For example, if you treat mathematics as a game, then one doesn't have to provide meaning to the undefined terms in math. A mathematician merely states that certain terms are undefined, and provides the rules by which apply to those undefined terms, and you're off to the races. This is mathematics.
What Paul and you are confused about is when mathematics is brought out of the classroom and used in describing the world or our position and relation with the world. This is using mathematics as models of what occurs in the real world: applied mathematics. In applied math you try to make isomorphic relations between the terms of mathematics with the terms we identify in the world. For example, an empty field on a plain in the United States can be represented mathematically as a 'plane'. The term 'plane' has been provided meaning. This doesn't mean that we are saying that the plain is actually a mathematical plane, but only that it can be represented as a mathematical plane. We deal in approximations. Now, the basis of applied math is that these isomorphic approximations between mathematics and the world are useful to our purposes, and we are able to construct mathematical models that provide new information about the world that we didn't have prior to. Hence, we use the mathematical models for pragmatic purposes. Unfortunately, all mathematical models are not useful. Some mathematical models are crude and the approximations are not really reliable, and others are just altogether wrong (i.e., so unusable that we don't even consider them as viable models that provide useful results).
Hence, in applied math applications, the terms we use in our math model must have meaning in order to know exactly whether the model is useful or not. This doesn't mean that we cannot use abstract terms that we do not know what they mean in terms of reality (e.g., imaginary numbers in quantum physics or electromagnetic theory), however our model must have enough meaningful reallife terms that we made isomorphic with the mathematical terms (e.g., plain with mathematical plane), otherwise the model is completely useless and says absolutely nothing about reality (i.e., it has any practically no useful applications with respect to our experience with reality).
This is a major failing of your model. You do not define any of your terms that are to link your model with reality. You fail to define any term with any retrospect to the world of experience. You simply assume that by throwing certain terms out there that you have represented enough terms to make it a viable mathematical model of some subset of reality (i.e., the world of experience). When, in fact, you have failed at doing so. Terms you use in your model (like time, space, reality, known, unknown, etc) are completely non-isomorphic to the things we identify those terms in practical usage. You just assume that these terms have the same isomorphic meaning as used in the real world, but they do not. So, this is not some mere problem of having terms where their physical meaning is not understood (e.g., imaginary numbers). No, this is a problem of having every term as having no such meaning. As a result, your model doesn't represent reality in any precise (i.e., epistemologically so) fashion, hence your epistemological conclusions can only be taken with a grain of salt. We simply cannot properly interpret the meaning of your mathematics with respect to the world. Had you come up with some predictions on how the world is, then we can sacrifice some of the explanatory merit of a good model in exchange for some predictivity merit. But, this predictivity merit is also lacking. So, we can only judge your work based on explanatory merit in terms of epistemology, and as I and others have pointed out, there isn't much.
***That issue is the fact that all information available to us is obtained through our senses. That we have absolutely no way to check the veracity of our perceptions by any means outside of our perceptions themselves. Now I am totally astonished that everyone in the scientific community is not immediately bothered by that truth (a truth which seems to me to be accepted by everyone).***
This statement, if you fully understood what you are asking, is ludicrous. Every possible thought that you have ever entertained is made possible by your sense impressions. Checking to see whether your sense impressions are valid is to first assume that your sense impressions are valid, and that whatever means you use to check these sense impressions are based on the original set of sense impressions that a) got you to ask the question in the first place, and b) gave you the idea on how to answer the question, and c) provided you with the resources necessary to make you believe that you accurately found another way to check your sense impressions. Without assuming your sense impressions are valid in the first place, these (a)-(c) steps would be meaningless endeavors.
That's not to say that we can at least check some of our sense impressions, and this is what science does. But, we are simply at a loss to check everything without at least assuming that some of our sense impressions are accurate enough to construct useful scientific models. Whether they are actually correct in terms of the way the world is, is actually outside the goals of science. I wish I could get you to understand this very basic point.
***Whenever I bring this issue up the most common barf I obtain is "well, if you are going to take that position, then everything is "illusion!" I say there is no more proof of that than there is that it isn't "illusion". My personal opinion of the reaction is that people like Harv just don't like to think about the problem and use that common response to cut off debate.***
I don't recall making this point, maybe I have. But, the main issue is that you are deluded into thinking that you have found a more reliable means to understand reality than science. If you had, you would be telling science the theories of the future. Obviously, you haven't done so, so why is it that you think you have something of significance? The answer you provide is that the 'math works' and you have obtained 'most of physics'. The justification beyond this point is very weak from you, and this is why you have not justified to me the significance of your work.
***The issue of this discussion is the fact that the problem we face is one of deciphering the puzzle which is reality.***
NO, NO, NO. This is metaphysics and even philosophers stay away from this issue. The issue of this discussion is the fact that the problem we face is one of deciphering the puzzle which is how do we best represent reality so that we can take as much advantage of reality as much as is humanly possible. This is a major lapse in your ability to understand why your model is faulty.
***The only thing I do know about reality itself is that (if it is communicable) it can be presented as a set of numbers.***
It can be represented as musical notes too, but that doesn't mean that I should think about doing it. I have to get my head out of the clouds and focus on understanding nature in a manner that yields the most promising results. Understanding reality is a pipe dream, at least it has been to date and I don't see any end in sight to that pipe dream. Don't smoke that pipe Dick.
***Now Harv may want me to name each of these things but I don't know how to come up with that many names. How about we just give them numerical labels Harv?***
You can just label them Dick, but that doesn't mean anything if none of the terms in your model have any physical significance. This is what a mathematical model is supposed to do in order to explain things better. It should also predict things to establish it as a successful model, but I've given up on convincing you of that criteria for a good math model.
***That procedure involves careful definition of a number of particular terms. The definitions begin with the primary definition: "reality is a set of numbers". Harv, those are the meaningless numerical labels attached to the "things" which go to make up the "observations" my second defined term. The Ontology is very simple: those labels are labels for the things which actually exist! What comes out of the pipeline? Things I think exist (plus a whole lot of defined ideas so complex that I cannot even begin to enumerate them).***
I might have said this before, but the problem with numbering reality is that it automatically qunatifies reality. When you say the "ontology is very simple: those labels are labels for the things which actually exist", you have assumed that reality is quantifiable. That might not be the case. The ontology might not be so simple. This is what I mean that you go back and forth between ontology and epistemology in a sloppy fashion. Where I respect Frieden is that he seems to steer clear from ontology and focus on scientific epistemology which doesn't even get involved in non-physics discourse (e.g., subconscious renderings). He stays away from psychology altogether. You would be much better off if you followed suit.
***The things I think exist are clearly made up of two components: things which really do exist (reality) and things which do not really exist (illusions created in the pipeline). I refer to these two different components as "knowable" data and "unknowable" data (just names I attach to the conceptually different components). The "unknowable" data is, by definition, not part of reality (that is, it is illusion) so it must be created by the pipeline itself. Clearly, it can be done as we all possess a mental image. The real puzzle is, how can such a thing be done?***
You can't define things that exist (i.e., knowable) in any meaningful fashion with regard to your epistemological approach. This is another fundamental mistake by you.
***The first step in this puzzle is to realize that the freedom to add illusory information to the actual data obtained from reality allows one to specify the rules which control our illusions to be specified as a solution to the equation F=0 without making any constraint at all on what set of numbers appear in the original observation (and Harv, not being able to obtain that original observation has absolutely nothing to do with this conclusion).***
I didn't ever say I disagree with that. Here you are talking mathematics and every mathematically possible pattern that can mathematically exist. The open question is whether the parameters which you initially set-up are valid with regard to how we actually experience and make-up our understanding of the world. The only way that I know that you have done so successfully is when you can predict what our sciences will anticipate next. This is why I said that Frieden was close in doing so since he came up with all of our physics (including the standard model). That's pretty close, but so far, far away. Without a predictive model applying for the future science (made before the fact and not after), I cannot accept that the model was constructed properly in terms of the parameters by which we actually experience the world (and thereby prove that our sciences will unfold according to those initial conditions of our conscious/subconscious experiences). You need predictions, not just good math, to demonstrate this result.
***I will quote myself again,***
Is it just me thinking so, or do you actually get a little emotional perk whenever you quote yourself? Just wondering.