Let us get simple. I fell into what I discovered 30 years ago. At the time I was a physicist and I thought what I was doing was science! In my head I was looking at a very specific problem (a problem no other physicist had any interest in but a specific problem none the less). I was astonished when I stumbled over the solution and the only thing more astonishing in my life was the total lack of interest in what I had found.
When I tried to publish, every journal I submitted it to said that it was outside the field they represented. About a year ago I was told that what I had done was in the field of metaphysics. Ok, let it be metaphysics then I could care less. I have discovered something quite fundamental and it has far reaching consequences. Call it anything you want, classification is not the issue.
You of all people should comprehend the central issue. First, what do you know? The only rational answer to that question is "nothing". The problem with that answer is though it may be true, it doesn't provide anything to work with.
What do I want? I want something, that I can be confident cannot be disproved. Ok, that's easy: God did everything and it is the way it is because he wanted it that way. You can't disprove that but it sure doesn't provide much from a scientific perspective.
Let us suppose you do have something to work with! I don't know what it is; you don't know what it is! But there is something to work with -- call it anything you want -- I happen to call it reality but I intend no content in the meaning. If it doesn't exist then let's go home because the answer to all your problems is in the previous paragraph.
But, if we do have something to work with then let us try to work with it! We have no idea what it is so our work must be totally abstract. Do we have any tools to work with? I do not know. Maybe not but, if that is the case, go home and forget it; paragraph 4 is the only rational answer.
Suppose mathematics can be depended on as a collection of internally self-consistent structures; i.e., that the truth of the defined concepts lead to the truth of the deductions. Notice that I have not said the defined concepts are true, I have said that if the defined concepts are true then the deductions are true (these are very different statements). It seems to me that that is exactly the issue struggled with by the professional mathematicians. If that is the case, and I presume it is, then I will leave that aspect of the problem in their hands. That is, I will take mathematics as a valid useable tool.
I would say at this point that if mathematics is not a useable tool then "we might as well go home and forget it as paragraph 4 is the only rational answer". There is certainly no other collection of decently defined concepts that may be depended on.
So, I have a tool and I have something to work with. If I am going to use the tool than the thing I am going to work with better be expressible in terms of mathematics. If it isn't then 'we might as well ….4…".
On the other hand, that doesn't seem to be all that bad an idea. Certainly, anything you and I can discuss can be represented by numbers (consider this e-mail or any future e-mails). So I come upon my first definition "reality" is "a set of numbers". If your concept of reality (what we have to work with--which, at this point, I will presume is the correct answer) cannot be translated into numbers than we "might as well ….4…".
Thus the situation resolves itself into the following, you generate the correct set of numbers (what we have to work with) and e-mail them to me. But you cannot do that because you don't know what we have to work with either. All you have is some verbal construct that I can't be sure I understand. So I will let you (and everybody else) spout that out and analyze what I get.
This is how I get to the picture of an undefined data set transformed by an undefined process. In my paper I refer to my the undefined source as "reality" and the transformation process as my "subconscious". Again, there is no intention of content in the definitions other than reference tags on information.
The problem is essentially one of decoding. That is, if we have anything at all to work with and if the problem can be solved, the problem of understanding reality is, in essence, a decoding problem. We must find patterns which occur and tag them (define the patterns as concepts???). Then identify the rules of the system: what patterns are related to what patterns and in what way. The names we give to the patterns is totally immaterial.
As you well know symmetries in physics are very powerful tools. What the physicist does is to postulate a symmetry and then work out the consequences. He is left with the question "why that symmetry?". The power of my analysis is that postulating the symmetry is totally unnecessary. In the picture I present (a totally undefined data set transformed by a totally undefined transformation) any symmetry which can be generated by a transformation cannot be assigned to the underlying data. It must be presumed bogus as there is no way to prove it exists in the underlying reality.
There is an interesting parallelism here between what I am saying above and a certain simple mathematical concept: the idea of a "basis". A "basis" may be thought of as the minimum data necessary to describe something. In a certain respect, the underlying reality above may be thought of as a basis in that all symmetries have been removed from consideration via assigning them to the transformation.
Having removed all symmetries from consideration (notice that instead of being considered, they are instead imbedded in the representation, i.e., presumed to be in the transformation) any patterns which remain must correspond to patterns in the underlying data. If such a correspondence exists (if the decoding is possible) then what name was given to the pattern is immaterial. If we have named it in one side of the transcription, it is named in the other.
Notice that at no point have I proposed any solution at all. Everything I present is an abstract representation of the problem. However, given that abstract representation of the problem, there are certain "bogus" relations generated by the "undefined" transformation. Before one begins to search for those patterns discussed in the previous paragraph, one should make every attempt to remove those "bogus" relations.
What are these "bogus" relations? Classical mechanics, quantum mechanics, relativity, etc. These are relations which must exist in any representation of reality. Think of them as analogous to Newton's pseudo forces generated by being in the wrong coordinate system. Am I saying they are not real? That the science is incorrect? No, I am not. What I am saying is that you cannot create an internally self consistent model of reality where these sciences are false. (Except in the case where they are in error! Which is why I just happen to catch Einstein.)
If you e-mail me an address
I will send you a copy of a paper I wrote in 93 (also unpublished) which clearly expresses my complaints about Einstein and the errors in his approach.
Have fun -- Dick