Thanks for your response! I appreciate your thoughtful comments. I only referred to the Maxwell/Boltzmann attack as an example how circular reasoning can indeed produce concrete results: i.e., just because something is based on circular reasoning does not make the reasoning itself illogical. In my case, I show that what you want constrains what you will accept (think about that a little).
Early on we had what was probably a miscommunication concerning the issue of symmetries. Perhaps if I tried again, you could understand why the symmetries are required by the problem itself. After this last year, it has become clear to me that a lot of things which seem obvious to me are not so clear to others; I am not the great communicator. You are in a considerably better position to understand what I have done than others.
The necessity for the symmetry (actually, the necessity for all conceivable symmetries) flows from the fact that entirety of "something B" is an abstract construct of my mind. Imbedded in that construct is a representation of "something A", that which is to be explained. Now, the explanation (once it is conceived of) must include that subset I have called my senses which must, by the very definition of the concepts, stand between that representation of "something A" (called by me, the knowable data) and the explanation in its entirety!
Now, from the structure of the relationships between these various concepts imbedded in that explanation, the image of "something A" must be "knowable". Anything which can be attributed to hypothesis and can not actually be proved necessary, cannot be part of that image of "something A". That is, by the definitions of the categories, anything which can be attributed to the senses (that unknown transformation) must be so attributed.
Since the entire structure "something B", is an artificial construct anyway, including the senses, any symmetry which we can credit to those senses must be so attributed as a possibility. To do otherwise would require the symmetry to be a part of that which is knowable; if I can conceive of a transformation which would produce the illusion of that symmetry then I certainly cannot prove the symmetry is necessary and it cannot be part of the image of "something A".
Now, given the fact that my entire analysis must be based on information on the opposite side of the transformation from the image of "something A" and the fact that that transformation can be anything, it makes complete logical sense to include the possibility of all possible symmetries. To do otherwise would complicate my life very severely as I would then have to consider each apparent symmetry in the observed data as a special case and introduce a mechanism to remove that symmetry explicitly unless I could prove it had to exist in "something A". Since I have made the simplifying decision to count all symmetries as created by the transformation, they absolutely must be included as part of the explanation (this flows from a rational decision, and is not an assumption). As you well know, a lot of physics then flows right out of those symmetries.
I take personal credit for a number of major breakthroughs here.
First, the fact that all symmetries should be attributed to the transformation accomplished by our senses. That is, the fundamental fact that the symmetries are an illusion is required by the two step nature of the analysis: our explanation is based on our senses which are part of the explanation.
Secondly, working out the consequences of a symmetry completely ignored by the scientific community. Namely, scale invariance which requires that the Dirac delta function interaction is the only interaction possible and leads directly to the requirement of special and general relativity.
And finally, a mathematical representation which takes into account the entire universe: i.e., a fully holistic representation of the universe.
Now, let me entertain your question!
Do your numbers have to be static or stable in some other manner.
In a very specific manner, yes! That manner is very specific and is expressed in the idea of the "observations". These "observations" are completely static and do not change in any way. They constitute what you call the past. Remember my definition of time? The purpose of the whole operation was to predict an observation not part of the collection upon which your analysis was based: i.e., predict the future from what you presently know!
What I essentially said was that, if your explanation is to be consistent with what you know then the algorithm which you should use to give the probability of that unknown observation, must be a solution to my fundamental equation. I then go on to show that what you call quantum mechanics is nothing more than an approximation to my equation.
One significant difference between Loop theory and yours is that it seems to me that you are assuming that your numbers are in a background space-time.
No, I again argue with your use of the word "assuming". What I do is invent the coordinated system to plot my numbers. What I am trying to do is to transform my totally unconstrained model of the information (that set of numbers) into the common everyday image of reality.
But perhaps your theory does not require any background if it's just a set of numbers. But you do say that it does not matter where you put the zero point of the coordinate system- the notorious shift symmetry. Is it possible that you could get the same result without using a coordinate system. After all, it's just a set of numbers.
Yes of course; all you have to do is realize that you can add a constant to all the numbers. The result is totally equivalent to moving the zero point if you were to plot the data. The scale invariance is equivalent to multiplying all the numbers by a constant. Again, the sole purpose of the coordinate system is to transform the mental picture from a set of numbers to something which looks more like your common perception of reality (objects in space).
Thanks for your attention -- Dick
PS Why don't you call me "Dick"; it's what I go by!