Perhaps the following is a little more comprehensible. Maybe someone out there might comprehend where I am coming from. I try to put things as simply as possible but I seldom comment on what made me think the way I do.

In many respects, modern physics is a religion, not a science! I went into physics for the very simple reason that math and physics were the only fields where my teachers made a real effort to logically back up their explanations. Now mathematics is a logical construct based entirely on internal definitions thus, though mathematical arguments are used through out physics, math really has to do with logic and not reality. So physics it was which I wanted to understand.

Now physicists always made significant efforts to explain things to me but there were incidents where my questions were answered with "you will have to talk to someone with a more advanced education because I do not know the answer to that question! That is exactly what brought me to graduate school. Now graduate school was a great disappointment to me as I have never met a faculty member who had any interest in understanding reality; their interest seemed rather to be recognized for their authoritative knowledge. (A very strong symptom of religion.)

As a graduate student I had a bad habit when it came to reading journals. Whenever my class work required reading a referenced article, I would read the referenced journal volume cover to cover. When one does that, one gets a very different impression from what one gets if they read only the referenced articles. If one reads only the referenced articles one gets the impression that they are dealing with intelligent people. If one reads the entire journal one gets the impression that most of the publications are not worth the paper they are printed on. Common journal articles are seldom well thought out.

As a result, I had little interest in publishing. I decided that I would make no effort to publish unless I had something serious to bring up; understanding the universe was my real interest. Thus I have only three official publications to my name. My thesis, and two publications related to my first employment after receiving my Ph.D in January 1971. (I ended up earning my living outside physics, thinking about physics issues on my own time.)

I tried to publish on a number of occasions but was totally blocked by the "peer review process". In 1982, I tried to publish what I felt was a rather important insight but was rejected by every physics journal I sent it to. I don't think it ever saw a referee as the response was too quick to allow anyone to read the thing. Their responses were almost identical: they said what I had written was philosophy and not physics and was of no interest to physicists.

I took it to my thesis advisor for help in getting it published but he refused to even look at it with the comment: "Stafford, no one will ever read your stuff because you haven't paid your dues!" He made it quite clear that not publishing was an unforgivable slight to the academy.

It is funny but, because of the physics response, a couple of years later I sent it to several philosophy journals and received the response: "this is mathematics and not philosophy and is of no interest to philosophers." I showed it to some mathematicians I knew and obtained the response, "there is no new math here, this is physics and would be of no interest to mathematicians." So I have apparently discovered something of no interest to any scientific field. I will present another version of my thoughts which might be comprehensible to someone here.

**I contend that there exists a specific mathematical relationship that must be a valid constraint on any self consistent explanation of anything. **(That opening equation on this thread.)

There exists only one universal constraint which applies to absolutely all theories. That would be the fact that any acceptable theory must be internally self consistent. The only way to examine the consequences of that constraint is to first establish an absolutely general notation capable of representing absolutely any collection of facts.

That notation must be capable of representing the language necessary to express any possible explanation, without knowing what that language might be. That fact brings up two very important points that are explicitly under focus in my analysis.

Before one can even discuss a theory, one must first learn the language necessary to express that theory. The intellectual process of learning that language is identical to the intellectual process of learning the facts to be explained. If the notation must be capable of representing any language, without knowing what that language might be, the underlying information required to comprehend the language must be included in the complete body of facts to be explained: i.e., the notation itself can make absolutely no presumptions whatsoever.

A second significant fact under focus is that all explantations must be based on a finite volume of information. If the information required to learn such an explanation together with the required language were infinite, it could not be learned and thus could not be understood. Thus it is that the only underlying requirement is that the proposed notation can represent absolutely any finite collection of information.

The entire collection of information can be divided into two categories. I will refer to the two different categories with the labels "elements" and "facts". Elements will consist of the collection of all information which can each be represented by means of a single concept significant to the theory of interest. Note that this is exactly the roll played by words in the required language but that it is not necessarily constrained to actual words. There are often concepts embedded in a theory which require more than one word to express; however they may nonetheless be represented by a definition which is the specific representation of an elemental idea embedded in the represented information.

Facts will consist of any information representable by a structured collection of those elements. You should comprehend that the definitions of the elements constitute "facts". You should also comprehend that, if there exist facts which can not be expressed via a structured collection of elements, the language designed to express the explanation is insufficient to its purpose. In essence this is no more than an expression of the fact that, If a theory can not be expressed through use of the fundamental concepts of the language, it can not be explained and is thus beyond representation.

Given the above one can examine the problem of representing a specific theory. The first point is that one cannot represent a theory without knowing that theory. It follows that, if one knew the specific theory to be represented, the required elements (together with the specific facts constituting the definitions of those elements) could be listed and numerically labeled. Once that list has been created, any specific elemental concept required to explain that theory may then be represented by a specific number which I will represent by "x": i.e., "x" is no more than that elements numerical label in the created list.

One can mentally picture that as essentially a complete list of all entries in every relevant dictionary in existence at the time the specific theory is understood. That would essentially be the entire set of possible concepts which could be used to clarify the theory of interest. Again, It must be understood that the definitions are relevant facts and not elemental information.

The next step is to use those numerical labels to represent any factual information presumed by the theory. The represented facts can be seen as a collection of statements in the relevant language specified by means of the numerical labels "x". The actual statements of interest can be single sentences, whole contents of books or even perhaps an entire library or collections of libraries. The single most important point here is that the collection of known facts is finite. The only issue of significance is that each and every fact can be specifically represented by the notation (x_{1},x_{2},…,x_{n}): i.e., an ordered list of elements. (Assertions are expressed with words.)

Of particular interest to this analysis is the fact that the truth of the relevant statement can not be a function of the order with which the facts are considered and must be represented by the statement itself. If a different result is obtained via an alternate order of consideration of facts, the system is, by definition, "internally inconsistent".

A second issue of interest arises if one opens up the set of possible representations. If one allows all possibilities which are representable by the notation (x_{1},x_{2},…,x_{n}), constrained only by the specific definitions of the numerical label "x", two important categories are added to the representation. These additions can be seen as no more than new expressions in the relevant language which are not part of the factual information presumed by the theory.

The complete collection of expressions now being represented can be divided into three categories: a finite set which represents the facts on which the theory is based, a second set which represent assertions which could be valid under the represented theory and a third set which constitute a collection of assertions which are either meaningless garbage or totally inconsistent with the relevant theory. In essence the third category constitutes expressions which can not possibly be valid.

Probabilities can be assigned to each of those three categories consistent with the theory being represented. First, those which constitute the facts on which the theory is based must be true. Second, those which represent assertions which are meaningless or totally inconsistent with the relevant theory must be false. And third, those which represent assertions which could possibly be valid under the theory (issues predicted by the theory but not yet confirmed) can be seen as having a probability bounded by zero and one.

The complete set of probabilities just brought up can be represented (within the proposed representation) by the expression P(x_{1},x_{2},…,x_{n}), where "P" represents the probability that the represented assertion is true. It follows that the entire collection of probabilities constitutes a complete representation of the specific theory of interest. Under this definition people who have different mental concepts of a theory would be considering a different theory: i.e., under my definitions, the theory is specifically represented by this set of probabilities.

At this point I contend that I have developed "an absolutely general notation capable of representing any conceivable theory**"**.

Using this notation, I can prove that there exists a specific mathematical relationship that must be a valid constraint on any self consistent explanation of anything**. **I will present here only the first step of that proof as the entire proof is too long to specify here.

There is a very interesting fact embedded in the representation just defined. The assignment of the numerical labels "x" is an absolutely arbitrary process. The actual numerical labeling is of no consequence. Consider two lists of exactly the same required elements numerically labeled via a totally different procedure. Let "x" represent a numerical label of a concept in the first list and let "y" represent the numerical label of exactly the same concept in the second list. In that specific case, the probability represented by P(x_{1},x_{2},…,x_{n}) must be exactly the same as the probability represented by P(y_{1},y_{2},…,y_{n}).

At this point a very interesting consequence appears. If one examines the rather simple alteration where y_{i}=x_{i}+a, it must be absolutely true that the derivative of P(y_{1},y_{2},…,y_{n}) with respect to "a" must vanish exactly by the very definition of a derivative. This would be a very significant observation were P(x_{1},x_{2},…,x_{n}) a mathematical expression. Note that although It may look like a mathematical expression, in fact it certainly is not.

The expression P(x_{1},x_{2},…,x_{n}) arose from a defined mechanism capable of representing "all possible theories" and it's creation must be carefully understood. It does not qualify as a mathematical expression for several reasons. First, if it were a mathematical expression, the number "n" would be the same for every assertion under consideration and, second, if it were a mathematical expression, the numerical labels "x_{i}" would be variables. In this representation they are fixed constants and not variables.

The idea of shift symmetry (the phenomena represented by y_{i}=x_{i}+a) together with the arbitrary nature of the labeling procedure should lead one to think about possible alterations in the representation which might transform it into a valid mathematical representation.

If such a notational shift could be achieved it would open a massive collection of deductive possibilities. Performing that notational shift is in fac, the second step of my proof. Achieving that transformation without introducing a constraint which would invalidate the issue of representing "any conceivable theory**" **requires a complex analysis too involved to be presented here. I will nonetheless give a very rough sketch of my attack.

The first possible step is to convert the expression, (x_{1},x_{2},…,x_{n}), into a collection of points plotted on an "X" axis. This representation certainly satisfies the required shift symmetry and, in a certain sense, converts the** **"x_{i}" into variables. At the same time such a conversion creates a number of other serious problems which need to be handled.

It should be clear that important information contained in the original representation is lost in the proposed conversion. The original definition of the representation made no constraint that an elemental concept (think "a word") could be used only once in a given assertion. If an elemental concept were used more than once, multiple entries in (x_{1},x_{2},…,x_{n}) would plot to exactly the same point and the existence of multiple occurrences in the original notation would be lost information.

Another factor in the original representation which would be lost is the order of the elements in the expression (x_{1},x_{2},…,x_{n}). The order in the proposed plot would end up being the actual value of the numerical label "x_{i}" and would not represent the indicated subscript.

It turns out that repetitions, order and specific number of elements can all be handled by a rather simple change in the definition of the relevant concepts. Note that these concepts can be thought of as "elements" of the language. It turns out that the addition of "hypothetical" concepts can be used to restore the lost information brought up in the previous paragraphs.

An example would be converting this graphical plot to a two dimensional plot by adding an additional hypothetical position information for every element, essentially converting each "x_{i}" to a vector in that two dimensional space. This allows elements which would otherwise plot to exactly the same x coordinate to be separated in that hypothetical dimension.

Similarly, the order problem may be solved by adding a hypothetical ordering parameter. And finally "n" can also be made to be the same in all expressions through the addition of a sufficient number of hypothetical elements.

The actual process required to achieve the desired result is far from trivial and extreme care must be taken to assure that the final representation can indeed represent absolutely all possible theories without making any constraints beyond internal consistency.

I would very much like to find someone in the world who would be willing to take the time to follow what I have to say. If I have made an error in my deduction, I would very much like to have that error pointed out to me.

I would love to find someone interested in thinking -- Richard Stafford, Ph.D. in theoretical physics.