I am of the opinion that I have made a discovery which totally unravels the flaws in modern scientific thought. A discovery which no one seems to comprehend. I have a very strong feeling that my problem is that they misinterpret what I am saying. This note is no more than another attempt to clarify my position.

If one looks at the history of science carefully, one will discover that most all of the major advances occurred when someone recognized that an assumption being made in the accepted explanation was wrong. That there was another interpretation of what was known which opened doors not yet examined.

If one examines the structure of scientific exploration itself, it is quite clear that "research" is based on the assumption that current theories are correct. Anyone who believes that the current theories are without flawed assumptions is simply gullible. Removing all assumptions is the basis of my attack.

The only solution to removing all assumptions is to design a method of representing the presumed facts which is capable of representing absolutely all possibilities, even possibilities which have not yet been conceived. It should be clear that the thought process being examined must include absolutely all possible solutions. Imbedded in that idea is the fact that learning a language necessary to express the presumed facts is a fundamental part of the problem. That issue is omitted from every scientific analysis of which I am aware.

Understanding the universe includes understanding a means of representing that understanding even if that understanding is being communicated to no one except ourselves: i.e., one can not even think about one's perceptions without a means of representing those perceptions. This is the issue I am trying to convey.

That issue brings language itself to the forefront. Without comprehension of a language, we cannot even begin to think about anything. That is the reason no one ever makes any attempt to explain Einstein's theory of relativity (or anything else for that matter) to a new born child. In fact, I find it astonishing that children manage to solve the problem of understanding vocal communication so quickly.

It follows that, if we wish to represent the problem of "understanding" reality itself we need a means of representing totally undefined information which makes absolutely no presumptions as to what relationships are being represented.. A clue to that difficulty is embedded in the structure of language itself.

Every conceivable language requires a collection of defined words. The definitions of some words must be understood before any relationship may be expressed. It follows from that fact that the presumed meanings of these words is the first presumption made in that long string of assumptions standing behind our "understanding of reality" (I have simply defined reality to be "the universe" as that is what I mean by the two terms).

At any point in the process of "learning to understand reality", one has presumed the meaning of a finite number of words (if the required number were infinite, they could not be learned). This is the starting point of my analysis. Since the number of words under discussion is finite, they can be listed and that list may be enumerated (that means they may listed and labeled with a numerical label).

Note that, at this point, I am presuming mathematics itself is an internally consistent collection of relationships carefully analyzed and described by thoughtful individuals. As mathematics is a field unconcerned with "reality" the presumptions in mathematics have no bearing on the analysis I am discussing. Mathematics is a representation system designed to generate internally consistent conclusions and makes no assumptions beyond its own definitions..

Thus it is that I can represent each and every word under discussion with it's numerical label in that list which I will represent as "x" (the common mathematical symbol for an unknown). Note that I have made no presumptions as to the meaning of any word in that learned set thus no presumptions have been made in my supposed understanding of reality. Again, in the interest of simplicity, I will refer to words as "fundamental concepts" as, when I use the term "word" I will be referring to the concept represented by that word.

Fundamental, as expressing one's understanding would be impossible without those concepts.

However, the meaning of those words was deduced from experience where the experience constitutes the collection of interactions with reality which were presumed to yield the meaning of those words. Since the set of words can be used to express the presumed understanding of those interactions, it follows that the individual interactions themselves can be expressed by the notation (x_{1},x_{2},…,x_{n}), i.e., an ordered collection of a finite number of understood concepts.

At this point I have developed a notation for representing each and every presumed interaction with reality via a set of concepts created internally consistent with those interactions.

If they are not internally consistent with those interactions, I assert that they do not constitute a valid understanding. If the reader disagrees with me, I would suggest they put forth their reasons for that disagreement.

Essentially, I have now put forth a representation of any and all understandings of any possible collection of interactions. This representation makes utterly no presumptions regarding that understanding of reality. The next step is quite trivial. Now that they have the necessary collection of "fundamental concepts" (think words) to express their understanding of reality, they also have the capability of explaining that understanding. The explanation can be seen as representable by a collection of interaction specified by the notation (x_{1},x_{2},…,x_{n}).

That adds a valuable additional component to the representation. It is possible to represent an interaction which is not part of the collection of interactions experienced by the person providing the explanation. The expression (x_{1},x_{2},…,x_{n}), even if the "x_{i}" are understood concepts, might not yield an actual known interaction. In fact, all possible expressions (x_{1},x_{2},…,x_{n}) can be divided into three sets: first, the set of actual known interactions, second, the set of comprehendible interactions not experienced and third, the collection of interactions inconceivable under the understanding being expressed.

Seen as an ordered collection of words, that third set can be seen as meaningless.

That brings up the final step in my representation. If P(x_{1},x_{2},…,x_{n}) can be seen as representing the probability that (x_{1},x_{2},…,x_{n}) is a valid known interaction, then the complete collection of possible expressions P(x_{1},x_{2},…,x_{n}) can be seen as representing the understanding the individual has achieved.

It must be understood that I have presented a universal representation of any possible explanation of any collection of facts (facts are interactions known to be true). I have not presented an explanation of anything. That is to say, if you want to use my notation to represent an explanation you would like to represent, you need to first possess and understand some explanation.

The first step would be to list all the words required to express that understanding and second, list all the facts necessary to defend that explanation (including a sufficient number of facts required to deduce the meanings of all the required words). One could then refer to every word with its numerical label in the list of words and express every known fact with P(x_{1},x_{2},…,x_{n}) =1: i.e., that ordered collection of words expresses a truth.

The above is entirely trivial and would be of utterly no use except for a very astonishing consequence of that notation. The underlying issue of significance is the fact that the numerical labels given to those fundamental concepts are of no significance whatsoever. That leads to the fact that if one creates a second set of numerical labels "y_{i}" where "y_{i}"refers to exactly the same concept referred to by "x_{i}", it must be true that P(y_{1},y_{2},…,y_{n}) =P(x_{1},x_{2},…,x_{n}).

If one choses the set y_{i}=x_{i}+a then the derivative of P(y_{1},y_{2},…,y_{n}) with respect to "a" must vanish by definition. If P(y_{1},y_{2},…,y_{n}) were to be a bonafide mathematical expression, that fact would guarantee that

[math]\LARGE{\sum_i^n\frac{\partial \;\; }{\partial x_i}}\large{ P(x_1,x_2,\cdots,x_n)=0.}[/math]

If that were true, it would imply some very significant and far reaching facts about any explanation represented by my notation P(x_{1},x_{2},…,x_{n}). Since my representation is absolutely universal, those facts apply to any internally consistent explanation of anything.

However, P(x_{1},x_{2},…,x_{n}) can not be a mathematical expression for several reasons. First "n" (the number of words in a specific assertion) varies from assertion to assertion and second, the set of numbers specified by "x_{i}" are not variables but are rather constants.

It turns out that there exist changes in my representation which overcome those problems; however, those changes and the problems they introduce are far from simple. The above is essentially another expression of chapter I of my book. The changes in representation which overcome those problems constitute chapter II.

A pdf copy of that book may be found at http://foundationsof...cs.blogspot.com .

I am available for any questions concerning the above.

Thanks -- Dick

**Edited by Doctordick, 04 September 2015 - 02:09 PM.**