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Perhaps Something Easier To Understand.

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I am interested in comments on this presentation of the problem I claim to have unraveled. Any suggestions regarding clarification would be appreciated.

Part I – Representing the Situation:

There exist four concepts in the English language which need to be carefully examined in order to comprehend how they influence the fundamental aspects of all scientific studies. Those four words are “information”, “understanding”, “explanation” and “communication”. The central issue of any scientific endeavor is to understand the problem confronting one. One can refer to what is to be understood as “information” and the purpose of understanding is to provide an “explanation”. Finally, without communication, understanding is to a great extent rather worthless. In my definition of “communication” I include what one could call self communication which essentially amounts to consciously thinking about the issue to be explained.

Since my purpose here is to create a mathematical representation of all four concepts, the first step is to come up with a mathematical representation of “information” which makes no constraints whatsoever on any aspects of communicating that information. I will use an approach somewhat related to the concepts behind the the idea of TCP/IP internet packets. Internet packets essentially amount to collections of numerical labels for particular elements essential to the intended communication, the actual meaning of those labels is established by the design of the TCP/IP packets. I will use a collection of such numerical labels to denote what I call specific circumstances. The idea here is that any communications can be represented by a collection of such “circumstances”: i.e., any communication can be seen as a collection of meaningful elements. If every meaningful element is labelled with a specific numerical label, then the communication can be see as a collection of such numerical labels.

I intentionally omit any information as to what each of those labels actually mean as coming up with a meaning is very much a central aspect of the problem to be represented here. Learning the meaning of the communication symbols is the first step of solving any problem and is a process involving a great many assumptions to be avoided. That is, if we assign meaning to those labels, we are presuming what they represent is known. My intention is to include all possible interpretations of those given numerical labels and a presumption that we know their meanings amounts to a total failure to include absolutely all possibilities. .

That brings up a second extremely important issue. It is a very common presumption that there exists but one interpretation of of what “understanding the represented information” means. Understanding the represented information is ordinarily interpreted to mean that the examiner knows exactly what was intended by the creator of that message (whoever it was that assigned those labels). The fact that a serious unwarranted assumption has been made there should be recognized by the reader.

There clearly exists no way of proving that one's “understanding” of a specific message is actually what the sender intended (if there were, secret codes could not exist). The only process available to clarify misunderstandings involves further communication. That is exactly the process used by teachers to determine if the communication of a subject is understood by their students. It is by the means of questions and answers that the character of “an understanding” is determined. Again we are confronted with the problem of representing all possible questions via an acceptable mathematical notation. Once again, Alan Turing and computer technology comes to our rescue.

Today it has been shown quite clearly that any question on any subject may be represented by a finite collection of true/false questions expressed by means of exactly the same language used to present the original "information" which we are interested in understanding. It follows that the desired questions can be represented by exactly the same kind of circumstances used to represent the information to be explained: i.e., collections of circumstances represented by specified sets of numerical labels.

Essentially, what I have just pointed out is the fact that one's “understanding” of a given collection of circumstances can be represented by assigning true/false values to a collection of numerical labels written as $(x_1, x_2,\cdots, x_n)$. This brings up another subtle issue. As any teacher well knows, the answers can be a function of the context the student has in mind; essentially, the same question can be asked multiple times and the answer may vary. Since I wish to be very careful to include all possibilities I will include allowing fractional answers between zero (for false) and one (for true) which are to indicate the probability the understanding will yield a true answer for the circumstance represented by a specific set of numerical labels.

Now the first issue to be clarified regarding my analysis is the fact that everyone makes the erroneous assumption that there exists but one “understanding” of any given set of information (often referred to as the “correct” understanding). It should be clear to the reader that it is impossible to prove a specific understanding is correct. So long as the volume of information on which the understanding is based is less than all possible information, the possibility exists that there exists a piece of information not yet examined which will invalidate that understanding.

From the above, I will assert that there exists a function $P(x_1, x_2,\cdots, x_n)$ which expresses exactly what the probability which a specific understanding gives to the truth of the circumstance represented by $(x_1, x_2,\cdots, x_n)$: i.e., the probability it could be a member of the body of information to be explained. It should be recognized here that (at this point in the discussion) everything is finite. The number of elements in a “circumstance” is finite, the number of known circumstances making up the information of interest is finite and the number of known cases for values of “P” is finite: i.e., the best we can possibly do is to create a table expressing values of “P” for specific circumstances $(x_1, x_2,\cdots, x_n)$.

The issue now is the idea that every possible understanding of any possible collection of information can be represented by a particular table of “P”. There are two issues of significance here. Is there indeed a one to one mapping between all possible understandings and all possible such tables of “P”? Clearly if two thinking entities produce exactly the same table of answers for “P”, there exists no evidence that their understanding of the subject differs in any way. On the other hand, one different answer is sufficient to imply the understanding of the two entities is different in some way. This suggests that, the moment a different value of $P(x_1, x_2,\cdots, x_n)$ is found, that table of "P" can be taken to indicate a possibly different understanding.

Thus all possible understandings of any possible information can be represented by the given functional notation,

$P(x_1, x_2,\cdots, x_n)$

which, at this point, is represented as a finite table of entries.

Does anyone find any part of that unintelligible?

Thank you -- Dick

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Does anyone find any part of that unintelligible?

Yeah, all of it. Each idea in your post leads to energy storage, and I don't see how you are converting synaptic energy storage into mathematics.

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• 2 weeks later...

Well, I am saddened by the fact that no one appears to have the intellect to follow what I have said; or at least, if they do, they have no interest in letting me know of the fact. Part I was quite simple. The only thing which was presented was an argument that any understanding (or explanation if one prefers) of any body of information can be represented by the mathematical notation of a function where $(x_1,x_2,\cdots,x_n)$ represents a possible “circumstance” expressed in a language represented by n meaningful elements and $P(x_1,x_2,\cdots,x_n)$ represents the validity of the hypothetical circumstance being represented. It really shouldn't be that mentally taxing.

In hopes that someone out there does comprehend the representation, I will step off to Part II, examining the problem confronted by the existence of some unknown and unexplained information.

Part II: The problem of actually finding an explanation.

The very first step in solving any problem (finding an explanation for the undefined information) is to assign some presumed meaning to those unknown elements. What must be taken into account is the fact that it is that very step which amounts to essentially converting the “circumstances” into a language (a step the consequences of which scientists apparently never even consider). What is important here is that the conversion into a language actually amounts to “a hypothetical solution” to the meaning of the circumstances and that very step itself violates the first supposed constraint on our investigation (that no assumptions are to be made). It should be clear to the reader that presuming we understand the meaning of any element of a language is an assumption. (It is a pretty obvious fact that people misinterpret words all the time.)

The fact that the first step in the solution to be found cannot be taken might seem to be an absolute barrier to ever discovering a solution; however, a subtle aspect of language allows a step to be taken which otherwise might go forever unnoticed. If you look at the "1.a." definition of “language” given by the “free dictionary by farlex” you will find the following: “Communication of thoughts and feelings through a system of arbitrary signals, such as voice sounds, gestures, or written symbols”.

The existence of that word “arbitrary” there requires some subtle relationships to exist within the representation $P(x_1,x_2,\cdots,x_n)$ in any language. It is in fact the freedom expressed with that word which removes that apparent absolute barrier to examination which would otherwise plague any truly open minded approach. Anyone truly interested in understanding anything should put a little thought into the following conundrum.

Is it possible that an explanation of something of interest to you can exist in a language you do not understand?

If your answer to that question is “no” then you are wasting your time reading this. The problem being discussed is so far outside your comprehension that you will never understand it.

That word “arbitrary” says that the meanings referred to by the numerical labels represented by “x” are not only unknown but that the specific connection is immaterial. That implies that the meaning itself is embedded in the totality of information represented by the known circumstances $(x_1,x_2,\cdots,x_n)$: i.e., solving the problem requires your learning a language which is capable of expressing those circumstances. One important issue embedded in that situation is the fact that there might exist explanations, for the information you are concerned with explaining, that require understanding a language you do not yet know. That is an issue people tend to brush aside without a second thought. In actual fact, it has some very serious consequences.

Keeping the language issue in mind, let us get back to analyzing the problem confronting us. That problem is, “exactly what constraints are imposed on $P(x_1,x_2,\cdots,x_n)$ by the definition of the representation so far laid out”. One very interesting constraint pops out almost immediately. If one were to have two entities who possessed exactly the same understanding of exactly the same collection of known circumstances including exactly the same understanding of the language necessary to express that understanding, we still have that arbitrary aspect of the numerical labeling used in $(x_1,x_2,\cdots,x_n)$ to examine.

The representation of their understanding cannot be a function of the specific numerical labels used to represent that understanding. All that is actually required is that the entire collection of numerical labels form an internally consistent labeling of those elements. Other than the need for overall consistent use, the actual numerical labels used is totally immaterial. If one were to add five to each and every numerical label in the entire collection of labels, that act in no way changes the meaning implied by the understanding represented by $P(x_1,x_2,\cdots,x_n)$. This fact implies a rather interesting embedded relationship in that function.

$P(x_1,x_2,\cdots,x_n) \equiv P(x_1+5,x_2+5,\cdots,x_n+5)$

Of course, this relationship is not constrained to using “five”. The number I used could have been any number and in fact could be any sum of numbers. In particular I would like you the think about adding two very specific possibilities. First, to the left hand side of the above, add the number “a” and to the right hand side, add the sum of the number “a” and a second number I will call $\Delta a$. The equality will clearly still hold but now we have a rather interesting equation:

$P(x_1+a,x_2+a,\cdots,x_n+a) \equiv P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a+\Delta a)$

or

$P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a+\Delta a)-P(x_1+a,x_2+a,\cdots,x_n+a) \equiv 0$

If we then divide that expression by $\Delta a$, we have

$\frac{P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a+\Delta a)-P(x_1+a,x_2+a,\cdots,x_n+a)}{\Delta a} \equiv 0$

Which should look quite familiar to anyone who has ever studied calculus. What is unusual is the fact that it is zero even when $\Delta a \neq 0$. That fact leads directly to the absolute validity of the expression,

$\lim_{\Delta a \to 0 }\frac{P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a+\Delta a)-P(x_1+a,x_2+a,\cdots,x_n+a)}{\Delta a} \equiv 0,$

the left hand side of which is the very definition of a differential. Requiring the notation to include the existence of that "a" can be removed by a rather simple mathematical procedure. To simplify the notation a bit, define a new collection of “numerical labels z” as $z_i = x_i + a$. One can then write:

$\frac{d}{da}P(z_1,z_2,\cdots,z_n) \equiv 0$

Which, if the reader understands partial differentiation and the chain rule of partial differentiation, allows one more simple step . Since $\frac{\partial}{\partial a} z_i = 1$ (as the numerical label x is not a function of “a”) one can write

$\frac{d}{da}P(z_1,z_2,\cdots,z_n) \equiv \sum_{i=1}^n \frac{\partial P}{\partial z_i}\frac{\partial z_i}{\partial a} \equiv \sum_{i=1}^n \frac{\partial}{\partial z_i}P(z_1,z_2,\cdots,z_n) \equiv 0.$

But, with regard to the representation, there is no real difference between using “z” or “x” to represent the numerical labels, we know that the expression above must be valid for all possible explanations of the underlying information: i.e., the expression

$\sum_{i=1}^n \frac{\partial}{\partial x_i}P(x_1,x_2,\cdots,x_n) \equiv 0$

must be an absolutely valid constraint on all possible explanations of any possible collection of information. What must be comprehended here is that the constraint is not a constraint on what is being explained; it is instead, a constraint on the explanation itself, quite a different matter. It must always be remembered that the “known information” supporting any explanation constitutes a finite collection of information but that the explanation itself can provide information beyond what is known. When we have an explanation (an algorithm capable of answering one's questions) the amount of information “explained” is quite easily infinite; however, one must always keep in mind the fact that some of those answers may, someday, be found to be wrong.

When an explanation is found to be wrong, the fact that it is wrong is due to the discovery of an incorrect answer: i.e., the total “known information” is still finite. In essence, all we ever actually have to work with is a collection of known non-zero entries to a table of values for that function $P(x_1,x_2,\cdots,x_n)$. Picking what we think is the correct explanation is actually a question of deciding upon the interpolation we are going to use to predict values outside the known facts (picking a shape for the function "P" outside the known circumstances). What I have just shown is that the interpolation implied by the constraint

$\sum_1^n \frac{\partial}{\partial x_i}P(x_1,x_2,\cdots,x_n) \equiv 0$

is the only interpolation consistent with the arbitrary nature of the symbology used to fabricate a language capable of expressing that understanding.

Now I am quite sure there are those reading this who will hold that the symbology used in language are not arbitrary but, if that were the case, why would any peoples speak or write in different languages?

Have fun -- Dick

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Hi Doctordick,

Now I am quite sure there are those reading this who will hold that the symbology used in language are not arbitrary but, if that were the case, why would any peoples speak or write in different languages?

Bill Clinton might have been interested but that was over a decade ago.

represents the validity of the hypothetical circumstance being represented

You just have to google boolean differentials to see how this works in its correct context.

This short introduction into the Boolean Differential Calculus and the presentation of some applications show the usefulness of this theory. If it is combined with the appropriate software and a high-level description of the problems to be solved, then it can be highly important for many applications of logic functions, particularly for the design and analysis of hardware in many areas. The inclusion into courses and educational processes of Engineers and Computer Scientists should be self-evident.
Edited by LaurieAG
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• 2 weeks later...

Hi Dick!

So you have been writing since the eighties... And here you do a rewrite and want comments.

I see no harm in that, Ill give it an honest try, but I should warn you that Im a bit on the slow side

and prefere to digest new scenarios piece by piece.

Here is what Ive read so far :)

Part I – Representing the Situation:

There exist four concepts in the English language which need to be carefully examined in order to comprehend how they influence the fundamental aspects of all scientific studies.

Those four words are “information”, “understanding”, “explanation” and “communication”.

The central issue of any scientific endeavor is to understand the problem confronting one.

One can refer to what is to be understood as “information” and the purpose of understanding is to provide an “explanation”.

Finally, without communication, understanding is to a great extent rather worthless. In my definition of “communication” I include what one could call self communication which essentially amounts to consciously thinking about the issue to be explained.

I find a clear text with nothing to disagree with.

I like the words: to understand the problem confronting one

I noticed you are going to use rather complicated formulas to represent information later on...

Maybe its a good idea to exemplify?

A Problem

Is the following claim true?

(1) Claim 1 is not true.

Understanding the problem

To illustrate your method by selecting what may be the most difficult problem there is (at least among the short and easily formulated problems) might in itself create new problems, but you are surely not analysing only problems with obvious solutions. Right?

Maybe I should be careful and try to index the problems?

1. Understanding "Perhaps Something Easier To Understand."

So far I see no problem: If im not mistaken it has been said that information needs understanding which explains and communicates it.

A lot should be said about that and I expect to do some editing here later, but for now Im eager to understand what follows...

2.Dick continues:

"Since my purpose here is to create a mathematical representation of all four concepts, the first step is to come up with a mathematical representation of “information” which makes no constraints whatsoever on any aspects of communicating that information. I will use an approach somewhat related to the concepts behind the the idea of TCP/IP internet packets. Internet packets essentially amount to collections of numerical labels for particular elements essential to the intended communication, the actual meaning of those labels is established by the design of the TCP/IP packets. I will use a collection of such numerical labels to denote what I call specific circumstances. The idea here is that any communications can be represented by a collection of such “circumstances”: i.e., any communication can be seen as a collection of meaningful elements. If every meaningful element is labelled with a specific numerical label, then the communication can be see as a collection of such numerical labels."

I take away what I dont understand...

"Since my purpose here is to create a mathematical representation of all four concepts, the first step is to come up with a mathematical representation of “information” which makes no constraints whatsoever on any aspects of communicating that information.

I will use a collection of numerical labels to denote what I call specific circumstances. The idea here is that any communication can be represented by a collection of such “circumstances”: i.e., any communication can be seen as a collection of meaningful elements. If every meaningful element is labelled with a specific numerical label, then the communication can be seen as a collection of such numerical labels."

Im beginning to worry about a possible confusion of information with its communication ...

"I intentionally omit any information as to what each of those labels actually mean as coming up with a meaning is very much a central aspect of the problem to be represented here.

Learning the meaning of the communication symbols is the first step of solving any problem and is a process involving a great many assumptions to be avoided. That is, if we assign meaning to those labels, we are presuming what they represent is known.

My intention is to include all possible interpretations of those given numerical labels and a presumption that we know their meanings amounts to a total failure to include absolutely all possibilities."

You are predicting what you will do... not actually doing it , and I must think it over some... Ill be back ;)

Edited by sigurdV
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Hi Dick!

So you have been writing since the eighties... And here you do a rewrite and want comments.

Yeah, I guess I am not very clear in what I say as, to date, AnssiH is the only person who seems to possess an inkling of what I am talking about. I have read your post and I am afraid that you are also missing the central point. Don't feel bad as you are apparently in excellent company.

I see no harm in that, Ill give it an honest try, but I should warn you that Im a bit on the slow side

and prefere to digest new scenarios piece by piece.

Slow isn't really the problem. The real problem is in the area of comprehension of what I am doing.

I find a clear text with nothing to disagree with.

I like the words: to understand the problem confronting one

I noticed you are going to use rather complicated formulas to represent information later on...

Maybe its a good idea to exemplify?

Not really because what I am saying is quite abstract and the simplest decent example would require a basis of more information than you could possibly write down in a life time. You need to comprehend the characteristics of the fundamental problem confronting one.

I am looking at only the constraints imposed on an explanation by the definition of an explanation (“the explanation provides answers to the questions which can be asked about the information to be explained”). There are two very important issues concerning that problem: first, the information to be explained must be finite (if it is infinite, no matter how much you have acquired, there is some left you are ignorant of) and second, the language used to explain is defined as “Communication of thoughts and feelings through a system of arbitrary signals, such as voice sounds, gestures, or written symbols”. The issue regarding that word "arbitrary" being there is that the first step of finding an explanation is coming up with a language to express what information is being explained. Human beings usually require roughly a year to come up with meanings for the sounds they here (children are not born understanding English).

What you should understand is that I am talking about the collection of all possible explanations of that “information to be explained”; what most people don't seem to comprehend is that the problem includes coming up with a meaningful language expressing exactly what that information is. If the constraints are to be proved absolutely general, all this must be done without making any assumptions whatsoever and thinking you understand the language being used is an assumption (think about the possibility of secret codes). I will try to show you how your example goes astray of the problem.

A Problem

Is the following claim true?

(1) Claim 1 is not true.

You have totally overlooked an unbelievable number of interpretations of the problem you have presented. First of all, you apparently mean that the information to be explained is, “(1) Claim 1 is not true”. My statement was that the explanation yielded the validity of the hypothetical circumstance being represented.

What is the circumstance being represented? A pattern of pixels on my monitor? A pattern of binary numbers in a TCP/IP packet or possibly the chemical deposits on a piece of paper (if I print it out). Those are all valid possibilities. I am quite sure that wasn't your intention. Your intention is obviously to work under the umbrella of a known language, English. If that is your goal you have already violated the “no assumption” condition: you have assumed the English language is a major component of your solution.

Think of it this way; suppose you had nothing except a message by some alien in some alien language you had never seen or heard of before, how much more information would you need to have to even start to come up with an explanation of that message? It is entirely possible that he intended to say “(1) Claim 1 is not true” but what he intended is certainly not part of the information available to you.

In fact, even my above generalization of the problem you present essentially presumes a great body of information (which has not be expressed) is not only understood but that the specific understanding is the only possible interpretation of the information being given. You should think of the problem as constituting a universe: i.e., no information whatsoever exists outside the body of information you are trying to explain.

To illustrate your method by selecting what may be the most difficult problem there is (at least among the short and easily formulated problems) might in itself create new problems, but you are surely not analysing only problems with obvious solutions. Right?

I am not analyzing the any problems at all! What I am doing is extending the constraints implied by the definitions of “explanation”, “circumstances” and “language” as they bear upon possible “explanations”.

Im beginning to worry about a possible confusion of information with its communication ...

Information is what is being communicated. You are presuming the information has meaning whereas, meaning is itself part of your explanation of the information.

You are predicting what you will do... not actually doing it , and I must think it over some... Ill be back ;)

Will do??? I am talking about showing that my representation constitutes a valid constraint on the explanation of any body of information. It is essentially a proof and when I say “I will”, I am talking about steps in that proof. The total issue here is that the definition of “an explanation” (it answers questions), the finite nature of the underlying facts behind the explanation (what you are basing your explanation on) and the arbitrary nature of language (that the actual symbols used to represent meaning are arbitrary) yield some major constraints on the representation of “an explanation”. How these constraints are interpreted is another matter entirely. The whole thing is a totally abstract representation.

What is astounding about my proof is the fact that the constraint I deduce yields almost exactly all of the physics developed in the last three thousand years. That says something rather remarkable.

Have fun -- Dick

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• 2 weeks later...

It is not "the central issue in science to understand a problem to be solved" [claim of Doctordick, Part 1]. Thus, given that the thread topic begins with this false assumption about the fundamental nature of science, it is easy to understand why few take anything presented by the author seriously. Richard Feynman concluded that no physicist understands quantum events or the problems it solves, yet quantum theory has resulted in many problems being solved based on knowledge [not understanding] of experimental results related to quantum events.

 See also this statement..."It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. Niels Bohr". The author of the thread [DD] has a false understanding of the "task of physics"; it is NOT to "understand a problem" or "find out how nature is", the task is to gain knowledge of nature, that is, to see what can be communicated to self and others about nature.

There is a fundamental difference between understanding and knowledge, science has little to do with the first, everything to do with the second. By definition, science is uncertain knowledge. The author of this thread correctly concludes the thread with the statement that "knowledge is power" yet fails to include "knowledge" as being one of his four most important "words" related to science. My advice, eliminate "understanding" from the list of 4 important words in Part 1 and substitute "knowledge" Then rewrite the entire presentation from a philosophic uncertain "knowledge" (e.g., science) perspective as relates to explanation. Best of luck to you.

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QUOTE OF AUTHOR DD:

"The only thing which was presented was an argument that any understanding (or explanation if one prefers) of any body of information can be represented by the mathematical notation of a function where (x_1,x_2,\cdots,x_n) represents a possible “circumstance” expressed in a language represented by n meaningful elements"

Well, here is another problem with the presentation, the claim above is false. It is false because the author cannot present a single example of an argument where a known circumstance can be represented by any such function.

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• 1 year later...

What happens if the student only wants a root with the teacher?

ie, I don't care for the lesson - just the EXPERIENCE!

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• 1 year later...

I was just looking around today and saw this "Easier to Understand" piece I wrote a number of years ago. I guess it wasn't "easier to understand".

In recent years I have somewhat come to understand why everyone seems to fail to understand just what it is that I am talking about. A short time ago I became aware of a publication called "Constructivist Foundations" edited by Alexander Riegler. The publication seemed to have some interest in thinking about alternate approaches to scientific thought and I corresponded with Dr. Riegler for a short period of time. The exchange was quite interesting in that he also totally misunderstood what I was attempting to say and ended up deciding I was a nut case! This led me to examine others misunderstandings and I suspect I am beginning to comprehend the difficulty.

Essentially everyone presumes I am presenting a theory of some sort. I am beginning to comprehend that this is exactly where the difficulty arises, Riegler brought up Heinz von Foerster's "Principle of the Double Blind", "The blind spot: one does not see what one does not see". He was essentially expressing the opinion that I was the one subject to that principle. To quote Dr. Riegler, "You want to present a most general definition of an explanation and a most general method of to arrive at explaining anything, a way that forgoes a-priori assumptions themselves." Then complains that I make assumptions that I know what what "truth and facts" are.

When looking at others responses to what I say, I finally realized that everyone makes the presumption that I am presenting a theory of some sort. I am not! I am presenting a representation of "an explanation" (a mere notational representation). There are indeed three things which need to be "represented": explanations, facts and truth!

What people apparently miss is the fact that I am not making any assumptions concerning those three concepts; I am instead defining what "I mean"when I use those words.

I "define" "an explanation" to be anything which provides answers to some collection of questions. Please, can anyone suggest an explanation which answers no questions? It seems to me that my definition is pretty well universal.

The central idea which I need to represent is "an assertion". I don't need to define it but only need a way of representing it. I hold that every possible "assertion" can be represented by an ordered series concepts. Now I do need to define what I mean by a concept. I "define" "a concept" to be anything representable by a language symbol (essentially a specific expression in a language. Again I ask, can anyone suggest a concept which can not be represented by a language?   It seems to me that my definition is pretty well universal. Notice that the issue of the language is left entirely open (the desired concept might not exist in any presently known language but, if it can be expressed, a relevant future language must be able to express it).

This leaves one with the issue of "facts" and "truth". I merely define "a fact" to be an assertion which is "true". So "a fact" becomes a category of assertions. A category to which I will attach the label "true". How do I determine the "truth" of an assertion? Is that not the purpose of "an explanation"? In other words, I do not need to define when something is true, that issue is taken care of by the explanation.

My ONLY concern is representing "concepts", "assertions" and "explanations" in a way which excludes no possibilities. That is, I need not know what they are so long as I can represent them without making any assumptions as to what they are. Everyone wants me to give them examples. Giving examples amounts to making assumptions as to what they are; the only issue to be avoided here.

On the other hand, if the reader can give me an example which fails to be included in my definitions above, that would be a significant issue.

Please let me know if anyone finds the above incomprehensible!

Have fun -- Dick

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I agree that it is very easy for everyone to assume you are presenting a theory about the world in some sense, because everyone are so used to thinking in that "mode". We are not naturally tuned to think about things in general abstraction, and especially when the discussion turns into explanations or world views, it is easy to interpret things as ontological arguments. Even most of physics is almost invariably communicated with ontological terminology even if the original work has actually risen from deliberately epistemological reasoning (like, say, quarks), and most people are oblivious to the misdirection that causes.

I think the reason why your repeated statements, that you are not presenting a theory, fall into deaf ears is because of the simple fact that, the world is full of crackpots who are representing a theory as "the final truth". Saying, exactly with the same words, that they are not presenting a theory, they are merely exposing falsehoods of existing theories. The definition of a crackpot is a person who doesn't recognize that - contrary to their claim - they are merely talking about consequences of tacit assumptions that they happen to believe are the only possibilities. For instance the paragraph where you are commenting about your definitions of "facts" and "truths", skim that text and notice how similar it "looks like" to a text written by a person who is in fact trying to say that he knows "the truth" and wants to somehow "prove" an unprovable thing.

How then can a reader make a difference between an actual crackpot, and someone who is talking about a different abstraction level entirely? Almost always, they can't

I wonder if people might find the word "theorem" more useful in this context... maybe, maybe not. Just a like a pythagorean theorem should be viewed just as a tautology of some other statements, your presentation should be viewed as a proof of two seemingly different things being actually restatements of each others. But on the other hand, perhaps that is also in its own ways misleading.

Anyway, all that just amounts to semantics over a word, and there's a more serious issue that should be addressed...

Of course, it is important to define exactly what one means by his words (as much as such a thing can be achieved), but a very serious issue that rises is that the presentation contains very many definitions that need to become interpreted correctly in the mind of a reader before the whole argument can become understood at all. And despite the voluminous efforts, until the reader is far enough along in understanding the thing, it is almost completely impossible to make correct interpretation of all that communication leading there. I don't think this is because the definitions are badly stated (at least I could not do any better), I think it's just an error in strategy.

I remember this problem held true to me too, but I think what helped me was that, in my line of work, I'm used to continuously re-invent a personal explanation to some coherent system as I move along understanding it better. The same skill is pretty much required if your presentation is read from start to finish, and it takes a lot of work and effort and re-thinking of ideas previously thought true (but in light of new statements completely false). Let's face it, logical thinking is HARD WORK. So hard that most of mankind just never really bothers. So, most people cannot be even asked to put that much effort into a thing that they suspect can well be another crackpot idea in a sea of crackpot ideas.

As an alternative strategy, I have found more than once that fast forwarding someone to the point where Schrödinger's Equation appears, is quite useful. It was when I reached that point that I would say I first had a complete enough set of communications from you, that I was able to interpret it correctly enough to understand what the point of the excercise was at all. I.e. that is the moment when the last necessary "paradigm shift" for your communication occured in my mind.

So if the reader even has a crude idea that the arguments given in the early part of the presentation somehow relate to a fact that the exact form of Schrödinger's Equation will appears into plain view, it is much easier to interpret what is being said in more meaningful way on the way there. And it's much harder to mis-interpret things as ontological arguments.

What I'm trying to do with the blog posts at http://foundationsofphysics.blogspot.com is to give a succint enough account of the steps leading into the physical relationships. Even though that account cannot be viewed as an exact argument of the matter, it can give the reader the idea that; what this whole thing is, is argument of a purely logical equality between seemingly unrelated things, and that that equality says something about what aspects of our views are purely epistemological, removing all logical reasons of taking those things also as ontological. That I think really helps in communication of your work.

-Anssi

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• 3 months later...

What people apparently miss is the fact that I am not making any assumptions concerning those three concepts; I am instead defining what "I mean"when I use those words.

I "define" "an explanation" to be anything which provides answers to some collection of questions. .....How do I determine the "truth" of an assertion? Is that not the purpose of "an explanation"? In other words, I do not need to define when something is true, that issue is taken care of by the explanation.

The purpose of an explanation is not to determine the truth of an assertion, not as the term explanation is defined in your presentation.  Because you define an explanation to be 'anything' that provides an answer to some collection of questions, a false 'anything' must be allowed to serve as an answer, as well as a true 'anything', including the logical possible outcome that the 'anything' is both true and false simultaneously, or neither true nor false.

You claim that you are not making any assumptions concerning concepts, which is correct thinking because one should only offer logical definitions of concepts based on the associated facts of reality, not assumptions.  However, you offer an illogical definition of a concept (e.g., the concept true), which then leads you to make the false claim that you "do not need to define when something is true".

So, given that a truth statement is not taken care of by your proposed definition of the explanation process, how exactly do you define when any knowledge statement you make is true ?

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• 1 month later...

You claim that you are not making any assumptions concerning concepts, which is correct thinking because one should only offer logical definitions of concepts based on the associated facts of reality, not assumptions.  However, you offer an illogical definition of a concept (e.g., the concept true), which then leads you to make the false claim that you "do not need to define when something is true".

So, given that a truth statement is not taken care of by your proposed definition of the explanation process, how exactly do you define when any knowledge statement you make is true ?

I do not need to define when something is true for the very simple reason that it is "your explanation" which must specify when any specific knowledge statement is true! I am merely putting forth a notation system capable of representing any given explanation (no matter what that explanation happens to be).

Nowhere must I define when any knowledge statement being represented is true! That is the job of your explanation. The explanation's purpose is to provide that information via what ever representation the explainer has chosen to use.

Given a finite number of concepts required (and provided by the explanation) those concepts may be numerically labeled. That "finite set of concepts" can thus be represented by those numerical labels (each specific concept being represented by $x_i$). And from that fact the second fact I put forth is that every fact (proposed to be true by that explanation) may be represented by $(x_1,x_2,\cdots,x_n)$ via the expression $P(x_1,x_2,\cdots,x_n)=1$ (the probability that specific ordered collection of concepts represents a true statement).

It appears that this is totally beyond your comprehension. You keep asking me how I determine the truth of things! I don't! That is the job of your explanation! Any explanation which fails to provide any such assertions is a pretty worthless explanation!

Have fun -- Dick

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• 2 weeks later...

I do not need to define when something is true for the very simple reason that it is "your explanation" which must specify when any specific knowledge statement is true!

Have fun -- Dick

Nonsense.  You just DEFINED explanation to be:  " anything which provides answers to some collection of questions".

The definition of explanation you use for your presentation does not require that the provided answers MUST SPECIFY when the any specific knowledge statement is true or false.   What appears to be totally beyond your comprehension is that the concepts of truth or falsity do not reside solely in mental judgements as you define explanation.  Your answer reveals that you have no idea exactly what your definition of explanation is logically missing before you can claim any representation with truth or falsity.    So once again, how do you define the concept truth ?

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• 4 weeks later...

Nonsense.  You just DEFINED explanation to be:  " anything which provides answers to some collection of questions".

The definition of explanation you use for your presentation does not require that the provided answers MUST SPECIFY when the any specific knowledge statement is true or false.   What appears to be totally beyond your comprehension is that the concepts of truth or falsity do not reside solely in mental judgements as you define explanation.  Your answer reveals that you have no idea exactly what your definition of explanation is logically missing before you can claim any representation with truth or falsity.    So once again, how do you define the concept truth ?

I apologize for not quickly responding to your note. It is quite clear that you have absolutely no inkling of what I am saying. Since people are still apparently reading this thread, I will try my best to make the issue a little more clear. One thing that I feel most everyone fails to comprehend is that I am in no way proposing a theory of any kind. What I am presenting is a vast, practically unbelievable, tautological construct. (I definitely take mathematics to be a well defined collection of tautological constructs understood by any reasonably intelligent person.)

Claude Levi-Strauss once said, "The scientist is not a person who gives the right answers, he is one who asks the right questions." Regarding that issue, I have asked a question which I suspect no one else has made any attempt to answer. My question is, "What can one say about reality without making any assumptions whatsoever?"

To my knowledge only one person other than myself has ever put any serious thought into that question. That would be Sir Arthur Eddington via his 1935 publication "New Pathways in Science" In his opening chapter he made it quite clear that he was well aware of the vast number of unexamined assumptions embedded in any world view. In that book, he examines that very problem and comes to the conclusion that one cannot study the recurrence of signs and indications without first identifying the signs and indications to be studied. As he saw the issue, the development of those signs and indications are absolutely necessary opening assumptions and thus are impossible to avoid. After considerable thought, he simply defended placing the problem into philosophy and outside the interest of physical scientists. As far as I know, neither he nor anyone else (save myself) has ever brought up the issue up again. it should be clear to you that "English" is insufficient to the problem. Learning English itself requires a great number of assumptions to be made.

I agree with Sir Aurthur one hundred percent; however, I suggest there exists another question which should be seriously considered. If one totally lays aside the issue of actually finding any scientific explanations, (a process which must include inventing those required underlying assumptions), one can still ask: "what can one say about those explanations without making any assumptions whatsoever?" That is actually a rather different question than the one Sir Arthur was considering.

Of importance here is the fact that we are not born as competent scientific investigators. There is a path of learning and comprehension which we must all endure long before we can even begin any serious scientific study of reality. One of the most serious problems confronting any newborn child is that of, "fabricating a mental construct consistent with their experiences". If the person claiming a solution has not solved that problem then then there is no need to represent their solution.

In essence, the problem I am trying to discuss revolves around the problem confronting any entity possessing no concept of reality whatsoever. On the surface that seems to be an insoluble problem; however, in this case one can totally ignore what Sir Arthur and the scientific community are concerned with and instead consider only the the totally undefined information to be explained. That was what led me to look at the problem of inventing a language from scratch. It appears that my thoughts on that issue constitute a presentation which most can not even begin comprehend.

The first point everyone seems to omit is that I am concerned with absolutely nothing beyond coming up with a representation of a supposed success achieved by such an entity.

Now the central issue of such a representation is that it can be used to communicate that supposed successful fabrication of a mental construct consistent with their experiences. Now, in order to communicate my thoughts  on the question of representation, I need a way of representing my thoughts on the subject (creating a representation). It should be obvious to you that "English" constitutes the best representation of my thoughts in any communications I attempt with you or anyone else on this forum.

What everyone seems to miss is that I am talking about "a representation" and have utterly no interest in what it is that is being represented! I am using "English" to represent my thoughts on the subject because that is about the best communication mechanism I possess. In no way do I suggest that your interpretations of the words I use are identical to my interpretations. (Learning any language involves making presumptions as to the meaning of the words one uses.) In particular your worry about the definition of "truth" and my supposed definition of "an explanation".

If the person who has "fabricated a mental construct consistent with their experiences" can provide no description of that "reality" then I have no interest in learning it. However, if they can provide some kind of description then I could very well be interested in understanding that description (particularly if it happens to be internally consistent). Now, do you have any problems in understanding that English representation of my interests?

Now, if I go to the trouble of learning his "description of reality" then I should be able to represent it. What shall I call what I am representing?  In this admittedly inexact "English" means of communication I am using here, I suspect "true facts" would be a useful representation. And I would presume that somewhere in his description of reality there would be some definition at least somewhat equivalent to that English expression.

In his description these "true facts" must be represented in some way. Once I learn them I certainly can list them. (If the entire list is infinite, I certainly cannot list them and learning them would be impossible.)

That is all you need to accept to understand my presentation.

Have fun --Dick

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