Philosophical Foundations of Physics

[Doctordick]

Dear Sirs,

I am posting here for one reason and one reason only. There are apparently a great number of powerful people on the main forum who would like me to go away. If they were the only people on the forum, I would certainly do so; however, I think leaving would do a great disservice to the readers on the forum. Physics is a very important subject with far reaching implications and, as such I think careful thought about its foundations is worthwhile to any student (or professor) of the field.

I originally posted to the quantum mechanics thread because I thought the probability of reaching cognizant minds with an interest in the foundations of their field was higher there than anywhere else. My original thread was immediately moved to "Theory Development" which I accepted as a prerogative of the powers; however, I have now been locked out of posting to that sub forum.

I have tried to present a very simple point to which absolutely no one on the physics forum has yet responded. The point can be broken into two issues. In the interest keeping things simple, would someone competent please respond to my first issue which is the extent of the applicability of the expression

[tex]
P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv
[/tex]​

It is clearly an expression of far reaching consequences in quantum mechanics; however, it is my position that the expression is of far deeper significance than is ordinarily attributed to it. I hold that there exists no algorithm which will yield (as a result of that algorithm) a real number between zero and one which cannot be represented by that expression.

The proof of that statement is quite straight forward.

1) Anything which can be referenced can be represented by a set of numbers.

2) An algorithm is defined to be a procedure which transforms something into something else: i.e. from the above, this can be represented by one set of numbers being transformed into a second set of numbers.

3) Both [itex](\vec{x},t)[/itex] and [itex]\vec\Psi[/itex] can be used to represent an arbitrary set of numbers.

4) Given [itex]\Psi[/itex], it is always possible to define [itex]\vec{\Psi}^{\dagger}[/itex] such that the inner product, [itex]
\vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)
[/itex], is a real number greater than or equal to zero.

5.) Probability is defined to be a real number between zero and one.

It follows that there exists no statement of probability of an occurrence which cannot be written in the form given above.

Either what I have just said is true or false: i.e., the proof is valid or it is not.

As an aside (issue #2), it follows that the correct answer to any question concievable resolves down to finding the algorithm [itex]\vec{\Psi}[/itex] which will yield the probability of each and every possible answer (represented by the expression for the argument of [itex]\vec{\Psi}[/itex])

Given the possible importance of that fundamental representation, I would appreciate it if anyone who sees an error in my proof, would please point it out to me. If you believe my proof holds water, I refer you to the locked thread:

https://www.physicsforums.com/showthread.php?t=39508

In particular, that thread was locked before I could comment on some of the posts made there which I would like very much to answer.

Russell, referring to

https://www.physicsforums.com/showthread.php?p=291013#post291013

You seem to missing a very important issue when you bring up the validity of my representation of probability. That statement is a mathematical statement, not a physics statement. If you can follow my proof, the central issue of that particular statement (and the reason I presented it) is that there exists no algorithm for determining any expectation of anything which cannot be put in that form.

The point is that this statement contains absolutely no physical information. Without knowing the dynamical field equation and boundary conditions that determine [itex]\vec{\Psi}(\vec{x},t)[/itex], there is no way to argue either for or against the equation.

What Tom is missing is the fact that I am not discussing any particular problem here. His statement goes to the issue of the value of the expression with regard to the solution of a particular physics problem. He is absolutely correct: the statement contains utterly no physical information at all. The entire issue of interest to physics is: does it apply to a specific problem of interest?

The simple answer is, of course, yes it does! We have a great number of specific problems whose answer is expressed exactly in that form. Since Tom sees the issue in terms of the problems he has learned to solve, his "intuitive" position on the validity of the expression is: "I have to know the problem before I can answer the question of its validity!". When he does that, he misses the entire point of my presentation.

There's a line in "Harry Potter and the Order of the Phoenix" which just seems to fit this situation exactly. Hagrid, speaking of the giants, says, "overload them with information an' they'll kill yeh jus' to simplify things".

I think Tom finds my presentation overloads his ability to think things out. I conclude that because he supports BaffledMatt's statement, "Why else does he hide the logic of his arguments by making his written theory so incomprehensible?" with the comment, "He did make a point, and he is right".

Check it all out and see if you can comprehend what I am getting at.

By the way, I have made no presentation of a theory in any way.

Have fun -- Dick

 

[selfAdjoint]

It follows that there exists no statement of probability of an occurrence which cannot be written in the form given above.

True but trivial. It can be restated, every probability between 0 and 1 can be derived from some wave function. As to an algorithm for generating the wave functions, there are as you just proved, at least a power of the contunuum valid wave functions (in fact i think there are aleph-1 of them). There will be then untold infinities of candidate algortithms. And So?

 

[quantumdude]

I have tried to present a very simple point to which absolutely no one on the physics forum has yet responded.

That's not true, both BaffledMatt and myself have responded. It's your problem if you don't like the responses.

The point can be broken into two issues. In the interest keeping things simple, would someone competent please respond to my first issue which is the extent of the applicability of the expression

[tex]
P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv
[/tex]​

It is clearly an expression of far reaching consequences in quantum mechanics; however, it is my position that the expression is of far deeper significance than is ordinarily attributed to it.

No, it's not clearly an expression of far reaching consequences in any discipline. Not one of those symbols has been defined. Later on you say that the multiplication is an "inner product", which is a start. But without knowing what vector space we are looking at, and what sort of adjoining process the dagger represents, all you have here is a dot product of two arbitrary vectors.

In other words, the expression is empty in both a mathematical and a physical context.

I hold that there exists no algorithm which will yield (as a result of that algorithm) a real number between zero and one which cannot be represented by that expression.

This is trivially true, because you can define those symbols to yield a real number between zero and one. This is not a matter of proof, it's a matter of definition.

The proof of that statement is quite straight forward.

1) Anything which can be referenced can be represented by a set of numbers.

Comment: This is not a self-evident truth, but a definition of referenceable objects.

2) An algorithm is defined to be a procedure which transforms something into something else: i.e. from the above, this can be represented by one set of numbers being transformed into a second set of numbers.

Comment: This is just the definition of a function f:C-->C.

3) Both [itex](\vec{x},t)[/itex] and [itex]\vec\Psi[/itex] can be used to represent an arbitrary set of numbers.

Comment: This is just part of the definition of x, t, and Ψ.

4) Given [itex]\Psi[/itex], it is always possible to define [itex]\vec{\Psi}^{\dagger}[/itex] such that the inner product, [itex]
\vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)
[/itex], is a real number greater than or equal to zero.

Comment: This is just the definition of a normalzable function.

5.) Probability is defined to be a real number between zero and one.

This is just the definition of a probability.

It follows that there exists no statement of probability of an occurrence which cannot be written in the form given above.

So in short, it's always possible to construct a normalizable function to serve as a probability density, and to separate it into two factors such that one is the adjoint of the other, and that the inner product of the factors yields the probability density. Certainly no one would argue with that.

Now all you have to do is define the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors. Then, you'll have something.

Either what I have just said is true or false: i.e., the proof is valid or it is not.

You don't have a proof. What you have written is true, by definition.

As an aside (issue #2), it follows that the correct answer to any question concievable resolves down to finding the algorithm [itex]\vec{\Psi}[/itex] which will yield the probability of each and every possible answer (represented by the expression for the argument of [itex]\vec{\Psi}[/itex])

You can't just write down an empty identity and then claim that it can answer every possible question.

Given the possible importance of that fundamental representation,

The problem with your whole argument is that you are ignoring the fact that what you have posted is not a representation of anything at all! Not as written, anyway. As I said, no physics is contained in that statement until you define the terms, and state the dynamical equation whose solution is the function [itex]\Psi[/itex]. Any fool can write down an expression like the one you have here. It takes a theorist to get the dynamics right. Without that, you don't have anything.

You seem to missing a very important issue when you bring up the validity of my representation of probability. That statement is a mathematical statement, not a physics statement.

If you can follow my proof, the central issue of that particular statement (and the reason I presented it) is that there exists no algorithm for determining any expectation of anything which cannot be put in that form.

It's not even a mathematical statement, because none of the terms means anything. It doesn't matter that any probability density can be put in "that form" if "that form" has no meaning in and of itself. Define the function Ψ, define what it means to adjoin the function Ψ, and define the inner product. Then, you'll have a mathematical statement.

What Tom is missing is the fact that I am not discussing any particular problem here. His statement goes to the issue of the value of the expression with regard to the solution of a particular physics problem.

That's true, my statement does say that. And now I'm saying that your equation contains no mathematical information, either.

He is absolutely correct: the statement contains utterly no physical information at all. The entire issue of interest to physics is: does it apply to a specific problem of interest?

The simple answer is, of course, yes it does! We have a great number of specific problems whose answer is expressed exactly in that form.

That may be the simple answer, but it is not the correct one. The correct answer is that what you have written has no meaning from either a mathematical or physical point of view. In view of that, there is no way that it can be used to solve any problems. Without the definitions I mentioned, your expression is a body in search of a soul.

Since Tom sees the issue in terms of the problems he has learned to solve, his "intuitive" position on the validity of the expression is: "I have to know the problem before I can answer the question of its validity!". When he does that, he misses the entire point of my presentation.

There's a line in "Harry Potter and the Order of the Phoenix" which just seems to fit this situation exactly. Hagrid, speaking of the giants, says, "overload them with information an' they'll kill yeh jus' to simplify things".

I think Tom finds my presentation overloads his ability to think things out. I conclude that because he supports BaffledMatt's statement, "Why else does he hide the logic of his arguments by making his written theory so incomprehensible?" with the comment, "He did make a point, and he is right".

Doctordick, go read a math book. Specifically, read a linear algebra book. You're quite obviously rusty at this stuff. It's not that I can't figure out what you're doing here, it's that you have not posted anything that is well-defined enough to analyze.

 

[Doctordick]

We are still not communicating!

So in short, it's always possible to construct a normalizable function to serve as a probability density, and to separate it into two factors such that one is the adjoint of the other, and that the inner product of the factors yields the probability density. Certainly no one would argue with that.

Now all you have to do is define the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors. Then, you'll have something.

Right here you are agreeing completely with what I am trying to communicate as issue #1. I agree with you absolutely one hundred percent.

As you say, now all one has to do is define the vectors, the adjoint, the parameters and the equation and boundary conditions which generate the vectors. You will then have something of value! That is indeed the obvious description of the steps required to achieve a valid theory, but I am not proposing a theory. Nevertheless, there is one more issue I am interested in presenting. I would like to get to that issue; however, there is another insight (one I feel is just as "obvious" as the one you have just agreed to) which we should touch upon first.

That has to do with my aside regarding issue #2. I am glad I inserted it here as I didn't realize the difficulty you would have understanding what I was saying.

You can't just write down an empty identity and then claim that it can answer every possible question.

The difficulty here is the fact that, although you may thinkthat is what I am claiming, that is not at all what I am saying. What I am saying is actually quite different. I will try to restate it to help you understand:

The answer to every possible question can be cast in a form where that answer is a solution to the identity being discussed. The necessity of that follows directly from the fact that it is always possible to cast the answer to any question into the probability of specific answer being true (or, lacking a single correct answer, the probabilities of each of a set of possible answers). "All one has to do is to define the vectors, the adjoint, the parameters, and the equations and the boundary conditions which generate the vectors."

I have never said I ever proposed a theory of any kind, neither did I ever say that the process I was talking about was trivial. What I said was that it had to exist! That is a totally different statement.

If you cannot comprehend the correctness of that statement then try thinking about communications via twenty questions only make the number of questions infinite. My statement is false only if there exists a communicable answer to a question which cannot be communicated via an infinite set of true false statements. In my mind, if the answer is not communicable, there is no answer to discuss.

No, it's not clearly an expression of far reaching consequences in any discipline. Not one of those symbols has been defined. Later on you say that the multiplication is an "inner product", which is a start.

You are making an undefendable assertion here. To me it is clear. To you it may not be clear but I think that is because you are putting emphasis on the definition of the symbols.

I do not think you understand my proposition. Essentially, to disagree with my proposition, you would have to assert that there exists no definition of those symbols which would make the identity in question true. Are you willing to make that assertion?

With regard to your initial comment:

That's not true, both BaffledMatt and myself have responded. It's your problem if you don't like the responses.

It is my position that both of you responded to what you thought I was saying, not what I was saying! You both seem to have a very strong compulsion to add things to what I am saying. That is your intuition talking, not your analytical logic.

Have fun -- Dick

 

[quantumdude]

The answer to every possible question can be cast in a form where that answer is a solution to the identity being discussed.

What is "the identity being discussed"? Is it P=Ψ⁺Ψ? If so, then in what sense does it have "solutions"?

The necessity of that follows directly from the fact that it is always possible to cast the answer to any question into the probability of specific answer being true (or, lacking a single correct answer, the probabilities of each of a set of possible answers).

You never proved that it is possible to cast the answer to every question in the form you stated. You showed (by stating definitions) that the answer to any question that can be answered in terms of a probability density can be put in that form.

I have never said I ever proposed a theory of any kind, neither did I ever say that the process I was talking about was trivial. What I said was that it had to exist! That is a totally different statement.

I know you didn't say it was trivial. I said it was trivial. And furthermore, you still don't have an existence proof, so at best the above could be called a conjecture.

If you cannot comprehend the correctness of that statement then try thinking about communications via twenty questions only make the number of questions infinite. My statement is false only if there exists a communicable answer to a question which cannot be communicated via an infinite set of true false statements. In my mind, if the answer is not communicable, there is no answer to discuss.

This is bogus, as it is just argumentum ad ignorantiam--argument from ignorance. It is the logical fallacy that says, "If it hasn't been proven false, it must be true!". Since the method you have outlined above requires an infinite number of steps to prove a statement false, it is not a valid method of proof. You'll have to try something else.

Tom: No, it's not clearly an expression of far reaching consequences in any discipline. Not one of those symbols has been defined. Later on you say that the multiplication is an "inner product", which is a start.

Doctordick: You are making an undefendable assertion here. To me it is clear.

LOL, so when you say it is clear--without proof--it is defendable?

It's not clear, simple as that. It will be clear when your terms are well-defined and your inferences are valid.

To you it may not be clear but I think that is because you are putting emphasis on the definition of the symbols.

If symbols are undefined, then there is no point in stating them. You may as well have said that the answer to any conceivable question can be put in the form: asopfduaowiog;lnawljgl.

But fine: You say that your argument doesn't depend on the symbols of that pseudomathematical relation. The definintion problem remains however, because the terms you do rely on are not well defined.

I do not think you understand my proposition. Essentially, to disagree with my proposition, you would have to assert that there exists no definition of those symbols which would make the identity in question true. Are you willing to make that assertion?

I haven't said that your proposition is false, I said that it is meaningless, which is a fact.

It is my position that both of you responded to what you thought I was saying, not what I was saying! You both seem to have a very strong compulsion to add things to what I am saying. That is your intuition talking, not your analytical logic.

And it is my position that BaffledMatt was right when he said that you state things in ways that are incomprehensible. And I am not trying to add things to what you are saying, I am trying to get you to say things that are not ill-defined.

 

[Russell E. Rierson]

I have tried to present a very simple point to which absolutely no one on the physics forum has yet responded. The point can be broken into two issues. In the interest keeping things simple, would someone competent please respond to my first issue which is the extent of the applicability of the expression

[tex]
P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv
[/tex]​

It is clearly an expression of far reaching consequences in quantum mechanics; however, it is my position that the expression is of far deeper significance than is ordinarily attributed to it. I hold that there exists no algorithm which will yield (as a result of that algorithm) a real number between zero and one which cannot be represented by that expression.

The proof of that statement is quite straight forward.

1) Anything which can be referenced can be represented by a set of numbers.

2) An algorithm is defined to be a procedure which transforms something into something else: i.e. from the above, this can be represented by one set of numbers being transformed into a second set of numbers.

3) Both [itex](\vec{x},t)[/itex] and [itex]\vec\Psi[/itex] can be used to represent an arbitrary set of numbers.

4) Given [itex]\Psi[/itex], it is always possible to define [itex]\vec{\Psi}^{\dagger}[/itex] such that the inner product, [itex]
\vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)
[/itex], is a real number greater than or equal to zero.

5.) Probability is defined to be a real number between zero and one.

It follows that there exists no statement of probability of an occurrence which cannot be written in the form given above.

Either what I have just said is true or false: i.e., the proof is valid or it is not.

It looks like you have derived a general relationship that is tautologically true by definition. It can yield the probability of any occurence.[as far as I can understand your presentation Dr. D ]

Specifying boundary conditions & constraints, corresponding to physical existence, would be taking a "risk" but that is probably what is required.

That is the real challenge.

I am still wondering if it is possible to define a limit that converges for an isomorphism between physical existence and mathematical existence...?

 

[Russell E. Rierson]

...define the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors.

There is also the "No-Boundary Proposal":


http://www.hawking.org.uk/lectures/quantum.html

But cosmology is still not a proper science, in the sense that as usually practiced, it has no predictive power. Our observations tell us the present state of the universe, and we can run the equations backward, to calculate what the universe was like at earlier times. But all that tells us is that the universe is as it is now, because it was as it was then. To go further, and be a real science, cosmology would have to predict how the universe should be. We could then test its predictions against observation, like in any other science.

[...]

...It therefore seems more natural to adopt what Jim Hartle and I called the no boundary proposal. The quantum state of the universe is defined by a Euclidean path integral over compact metrics. In other words, the boundary condition of the universe is that it has no boundary.

 

[Doctordick]

What is "the identity being discussed"? Is it P=[itex]\Psi^{\dagger}\Psi[/itex]? If so, then in what sense does it have "solutions"?

I didn't say "it" had a solution. What I said was that there exists an algorithm [itex]\vec{\Psi}[/itex] which will yield the P which is the correct solution to the problem whatever the problem happens to be. You have already admitted that!

So in short, it's always possible to construct a normalizable function to serve as a probability density, and to separate it into two factors such that one is the adjoint of the other, and that the inner product of the factors yields the probability density. Certainly no one would argue with that.

You never proved that it is possible to cast the answer to every question in the form you stated. You showed (by stating definitions) that the answer to any question that can be answered in terms of a probability density can be put in that form.

What? Are you stating that I have to prove to you that every question can be answered in the form of a set of probabilities assigned to a set of possible answers?

I think you are nit picking on issues for the sole purpose of defending your intuitive position that what I am doing could not possibly be significant. Ok, you want to hold out on the fact that, out there somewhere, there just might be a question which is answerable which could not be put in the form of a probability density of correct answers, I'll let you have that though I think you are being intentionally blind. The existence of such a question is not critical to my presentation anyway as there are certainly enough to make the entirety of the set which can be so answered a significant set of problems.

I know you didn't say it was trivial. I said it was trivial. And furthermore, you still don't have an existence proof, so at best the above could be called a conjecture.

Again, I get a distinct feeling that this post is purely for the purpose of confusing anyone who happens to read this thread. A chance for you to use your subtle apparent confusion in the object of the word "it" to sow confusion. When I said it was not trivial, I was referring to the process of defining the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors which will yield the result that [itex]\vec{\Psi}[itex] does indeed generate the solutions desired (that set of probabilities which describe the correct solution).

I have no idea what "existence proof" you are referring to here. Neither do I understand what you are referring to as trivial. Or what conjecture this is that you are referring to. Please, take my statements one at a time, don't make sweeping critical statements without any basis or, if you have a basis, please make that basis clear.

This is bogus, as it is just argumentum ad ignorantiam--argument from ignorance. It is the logical fallacy that says, "If it hasn't been proven false, it must be true!". Since the method you have outlined above requires an infinite number of steps to prove a statement false, it is not a valid method of proof. You'll have to try something else.

Again, I have no idea what argument you are referring to. It certainly can not be the central issue of the post which, as I said, you have already agreed to, I can only conclude that you are referring to my aside (regarding issue #2). If that is indeed the thing you are referring to, I must comment that it was nothing but an aside, placed there to help the reader comprehend where I am going. If that is the crux of your problem, than forget it, the general truth of it (though I certainly believe it is true in general) is not at all necessary.

There are certainly enough problems already solved where the answer to the problem can be specified in terms of a probability density! But, let us not even worry about that, let us instead worry about what can be done with what has been presented.

LOL, so when you say it is clear--without proof--it is defendable?

Tom, this was an aside. I was stating that seeing answers of general questions in terms of probabilities is a concept which is very clear to me. It is no more than a statement of how I see things. If the concept of seeing answers from that perspective is unclear to you then I am simply prevented from using that concept in our discussion. That will merely make my presentation a little more difficult to make, but not impossible. Thank you for letting me know that you found the view too alien to comprehend.

It's not clear, simple as that. It will be clear when your terms are well-defined and your inferences are valid.

Again you use the pronoun "it" when I am not sure exactly what is being referred to. If you are referring to the fact that the procedure of finding solutions is not clear, I certainly agree with you. I never said I was presenting a procedure for finding a solution to any specific physics problem. As you said earlier, that involves defining the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors used to calculate the referenced probability density. (By the way, the problem of changing the notation from an apparent continuous form to a discrete form is not a serious issue, so please don't confuse the issue by bringing up that cavil.)

On the other hand, if (when you say its not clear) you are referring to what I am doing, than you are not being truthful. You have already agreed with the central presentation of this thread; I can only conclude that you must mean that, to you, it is unclear where I am going. That is totally understandable. If it were clear to you where I am going, I wouldn't have to show you.

If symbols are undefined, then there is no point in stating them. You may as well have said that the answer to any conceivable question can be put in the form: asopfduaowiog;lnawljgl.

I agree with you completely: there is no more meaning in what I have put forward than there is in the expression asopfduaowiog;lnawljgl. What is important is where can you go from there? I know of no use for the expression you gave but I do have more to discuss about my expression.

But fine: You say that your argument doesn't depend on the symbols of that pseudo mathematical relation. The definition problem remains however, because the terms you do rely on are not well defined.

I am at a loss as to what terms you are referring to here! Again, you cannot possibly be referring to the definitions of the vectors, the adjoint, the parameters, and the equation and boundary conditions, as I have already laid those things aside as needing to be done to solve any specific problem. It occurs to me that perhaps your problem is the order in which I attack these issues. I do not know what your real problem is or I would clear it up for you.

I haven't said that your proposition is false, I said that it is meaningless, which is a fact.

And I agree with you, so long as the vectors, the adjoint, the parameters, and the equation and boundary conditions are not defined, the expression is certainly meaningless; however, if those things were defined, will you agree that the expression could become meaningful?

If you will, is it possible that we could step forward to issue #2? As far as I can see, you have agreed with the truth of issue #1, your only complaint seems to be that you think it is trivial. That's fine with me, I always thought it was trivial.

I am very serious; the real problem here may really be no more than your intuitive feeling that I am attacking the definitions of things in the wrong order. Certainly it is not the order we are taught, but can you really say it is the wrong order? But perhaps I still misunderstand your complaint about what I have said. I am really trying to be as clear as I can be.

If you still have complaints with what I have said, suppose we take them one at a time as these posts are getting a little long and I don' think that does anything to clear things up.

Have fun -- Dick

 

[Doctordick]

Hi Russel,

Thank you for your interest in what I am trying to say.

It looks like you have derived a general relationship that is tautologically true by definition. It can yield the probability of any occurence.[as far as I can understand your presentation Dr. D ]

"It can yield" is not really the correct phrase to use here. You have the cart in front of the horse, so to speak. What I have shown is that any algorithm which can yield a result which can be interpreted as a probability can be written as an inner product of a more general category of algorithm. In fact, that category is as general as you can get; the category is "any algorithm" and no possibility is outlawed.

The central issue here is that the search for solutions to problems has to start somewhere. If your intention is to explain the universe (a TOE so to speak) it is a fairly trivial observation that the search begins with absolutely nothing: i.e., your explanation must begin from "nothing". Since, no matter how much you know, you must include the possibility that new information may prove some part of that "knowledge" erroneous, you can never do better than to estimate the probability a particular piece of information is valid. That is, in the final analysis, all answers to all problems must be stated in terms of probabilities. To state that you know anything for sure is simply foolish.

If follows that predictions of expectations become the only possible venue capable of stating the outcome of that universal TOE. If that is the case, it is important to make sure that no stone is left unturned. If a way exists to produce an expectation for a given circumstance which we have overlooked then, no matter how sophisticated that TOE is, it is possible it is based on incomplete analysis.

The point of all this is that the problem of finding an algorithm which yields the probability of interest to you (whatever that interest might be) maps directly into the problem of finding a correct [itex]\vec{\Psi}[/itex] which will yield (by virtue of that inner product) that probability. If an algorithm which answers your problem exists, the required Psi algorithm exists. (The latex program would not allow me to repeat the latex representation of Psi: i.e. the preview worked, the post didn't.)

The importance of such a thing is that the perspective guarantees an effective barrier to unobjective bias. The range of possibilities is complete: any algorithm is any algorithm and one has not biased one's perspective so as to omit a possible solution. As Tom Mattson has stated, there is utterly no physics whatsoever contained in the statement. The sole strength of the statement consists of the fact that, if nothing is being said, it certainly cannot be a biased statement. As Tom might say, that's a pretty trivial observation; however, the mistake Tom makes is that he uses triviality as a reason for not thinking about the issue. In Tom's mind, if it is trivial, thinking about it is a waste of time; that, I am afraid, is an opinion and not a scientific truth!

Specifying boundary conditions & constraints, corresponding to physical existence, would be taking a "risk" but that is probably what is required.

That is the real challenge.

Yes, that is exactly what is required if you are looking to solve a specific problem. And it is most certainly a real challenge. However, the central concern of my presentation is the fundamental foundations under physics, not the performance of physics itself. I went into physics because I wanted to understand the universe I found myself in and physics seemed to have a better handle on the problem than any other field. What I discovered is that they didn't really understand what they were doing either.

The great majority just lay the foundation problem aside with the comment, look it works, don't worry about it! The problem with that statement is "it works" can be replaced with "it appears to work" which changes the character of the statement substantially. I have looked where others refuse to look and I have discovered some very interesting facts. The only reason no one else has discovered those same facts is that they simply refuse to look. They all know there is nothing down that path.

Apparently you are the only person with any serious interest in what I am trying to communicate (at least you have evidently read a great deal of the presentation); however, even in your case, from the comments you have made, I think you have missed the fundamental issues underlying my work. I thought I had Tom Mattson's attention there for a moment but it appears that I was mistaken. Nevertheless, the character of his comments gave me pause to think on the reasons I get so much flack from the people with a technical background sufficient to seriously follow my thoughts.

They seem to think that my purpose is to argue with the accomplishments of physics. They could not be more wrong. I agree with the entirety of physics; including the fact that some of the theoretical stuff is still questionable and that some subtle difficulties still exist. Anyone who holds that there exist no unsettled questions in physics is simply ignorant. I applaud the efforts of those who are making a serious effort to settle those questions and I think some of what I have discovered is directly applicable to some of their problems. But we certainly have to lay the foundations of my work before we can consider the applications to physics.

But, back to Tom. In a sense, he has now responded to a post of mine.

So in short, it's always possible to construct a normalizable function to serve as a probability density, and to separate it into two factors such that one is the adjoint of the other, and that the inner product of the factors yields the probability density. Certainly no one would argue with that.

Now all you have to do is define the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors. Then, you'll have something.

He clearly does not disagree with what I say but he does go out of the way to emphasize the triviality of that agreement implying he wants out of the discussion. He is apparently retreating from the fray with the personal conviction that he has settled the issue: what Dick is saying is trivial and therefore there is no reason to think about it. And he certainly doesn't want to look into it any deeper.

Notice that he does not disagree with the need to define things (though he doesn't want to discuss the subject). In fact, he wants me to "define vectors, the adjoint, the parameters and the equation and boundary conditions". Apparently what he does disagree with is the order in which I define them. In balking at that issue, he has clearly failed to comprehend purpose of my presentation. My purpose is to avoid, as long as possible, the actual insertion of physical content. I want to maintain as much generality as possible (hopefully total generality but I know that statement will draw enough flack to blot out the sun so I will not say it).

The purpose of attacking the problem by avoiding insertion of known solutions is to build a foundation which still functions when some aspect of those known solutions is found to be invalid. Certainly some aspects of my attack may be found to be invalid and then those foundations will have to be rebuilt and I am sorry for that deficiency, but I am doing my best and no one else seems to have any interest in the problem.

Continued below -- Dick

 

[Doctordick]

Back to Tom's complaints.

With regard to defining the "vector", I will go no further than saying that I use the vector notation because it serves a purpose. Any conceivable algorithm generates a set of numbers. In order to guarantee that the final result will be a positive real number, I define the adjoint to be exactly the same algorithm with the additional operation that each and every number generated is replaced with its complex conjugate. If the original set of numbers is viewed as specific coordinates in an n dimensional space then the operation needed to generate a positive definite number is exactly what is commonly called a vector inner product (or a dot product). So I am talking about nothing except a particular operation to be performed on the output of that unknown algorithm.

At this point, if the algorithm were defined, the vector, the adjoint and the inner product would all also be defined. That is again a trivial statement and is entirely general: no physics whatsoever is implied. Please notice that at this point I have introduced a few powerful procedures commonly used in physics and have defined those procedures in a way such that they are totally empty of physical content (probability, a wave function, and a vector dot product).

Following Tom's rather excellent list of the missing definitions, we need yet to define the parameters (that would be the arguments of the above mentioned algorithms) and "the equation and boundary conditions which generate the vectors". And I would agree with him: once those things are defined, as Tom says, "you'll have something".

Well, the parameters I have defined! They are a set of real numbers. But I am sure Tom would be dissatisfied with that. He wants something with physical content. My position is that the set of numbers can have any physical content you wish. There exists no information which cannot be transformed into a set of numbers (at least we can't talk about any). (Anyone who cannot comprehend that statement should get a book on TCP/IP protocols.)

I will leave the boundary conditions aside as all that tells you is which of the possible solutions to the equation are the ones you are interested in. In essence, I hold that definition of the boundary conditions cannot be done without specifically attaching physical content to the parameters and is the essence of insertion of physical interpretation! Since that is the specific issue I want to postpone as long as possible, I am left with "the equation!"

Now, generating a truly general equation without actually putting any constraints on the parameters (i.e., introducing any physical content) is not a straight forward issue. I would appreciate critical analysis of my solution of that problem. The fundamental procedure can be found in my paper "An Analytical Model of Explanation Itself". I hope some of you take the trouble of examining that essay.

http://home.jam.rr.com/dicksfiles/Explain/Explain.htm

Again, within that paper (which generates a generally applicable equation without introducing any physical content) I also introduce representation of another powerful procedure common to every science. That would be the introduction of hypothetical inputs to the algorithm (the possibility of invented entities), without actually establishing any physical interpretation of those entities).

When I introduce those hypothetical inputs (set D in the paper) I require they obey exactly the same rules imposed on "non-hypothetical" inputs. This is essentially the common scientific definition of "it exists!" That is, when the existence of the hypothetical entity is one hundred percent consistent with all experiments which can be performed (the experiments obey all the rules defined by the theory) and absence of the entity is inconsistent with the self-same experiments, it is taken as prima fascia evidence that the entity exists.

The scientist should note a certain subtle aspect of that conviction. It is based on the idea that the explanation of the phenomena being examined is the correct explanation. In fact, exactly the self same evidence is used as proof that the explanation is correct! This fact has important unexamined consequences. The problem is that the solution of the difficulty cannot be discussed without a decent appreciation of my presentation.

And Russell, you are absolutely correct, in the final analysis, the boundary conditions of a TOE must vanish.

Have fun -- Dick

 

[arildno]

Hi, DrDick:
I have followed your posts for some time, and I am deeply intrigued by your attempt to formalize in a mathematical manner the distinction between assumptions and received information.

In particular, I am impressed with your struggling of:
What do we mean when we assume that reality as perceived is comprehensible and, to some extent, explainable in a predictive manner?
In particular, how should we best formalize in a mathematical way this fundamental assumption; will, there, for example naturally appear constraints on what may be considered an explanation?

I have chosen to defer commenting this until now, primarily due to my (almost) entire lack of knowledge (and, hence, probable lack of understanding) of QM&GR.

I do have various questions though, but at first I'd like ask to you one you might well snort with derision of:

I cannot help sensing a (very slight) resemblance of your efforts with Im. Kant's "Transcendental Deduction of Reality", i.e, his efforts at trying to elucidate:
"What phenomena/aspects of reality as we perceive it must be necessarily true/present?"

Is my "sensing" way off?

 

[Doctordick]

You sound very rational to me!

Hi arildno,

I cannot express how happy I am to hear from you for several reasons: first, from your profile you appear to have an education which requires competency in mathematics, second, you appear to have a good idea of what I am talking about and third, you are young enough for it to make a difference.

Just an aside, my wife and I were in Oslo last year and we enjoyed your city very much. We were very disappointed to hear of the robbery of the museum; we enjoyed the exhibit very much.

I have chosen to defer commenting this until now, primarily due to my (almost) entire lack of knowledge (and, hence, probable lack of understanding) of QM&GR.

I am sure Tom Mattson would disagree with me but I am of the opinion that understanding is much more valuable than knowledge as it is not rare to discover that knowledge is flawed. That reminds me of a joke I used to always tell.

When we are young, we have to be careful to think everything out in detail or we will certainly screw up. As we begin to learn how the world works, we are able to accomplish more and more without thinking. If we live long enough, we can eventually learn enough that we know the answers to all the questions without thinking at all. That final stage is called senility!

I seldom snort with derision about much of anything (well, maybe my wife would disagree with that) {She just said, "you don't snort with derision, you just call them idiots".}

With regard to your question, philosophy is probably my weakest subject. As a physicist, I suspect I was trained to believe philosophers couldn't think. At any rate, I have no familiarity with Im. Kant's work at all. If I free up some time, I will see if I can find a copy of "Transcendental Deduction of Reality"; it sounds very interesting.

"What phenomena/aspects of reality as we perceive it must be necessarily true/present?"

I, personally don't believe that is an answerable question. If you stand back and look at what I have done as a whole, you should be able to comprehend that, other then requiring different constraints on two categories (one can change, the other cannot), my approach totally avoids the problem of identifying which is which. In fact, in the final analysis, the difference is immaterial.

You might notice that at the end of my development of a model of explanation, I comment on the fact that "I have established a fundamental means of communication". The thought behind that statement is the fact that, if my model is valid, there exists a mapping between any possible model of reality and the common model presently conceived of as "physical Reality". There is a very subtle consequence of that which I would love to discuss with someone. Physical reality becomes a basis for rational communication but need not be a unique coherent interpretation.

This is in direct opposition to the common position that there exists only one coherent interpretation of reality. Looking forward to hearing from you again.

Have fun -- Dick

 

[quantumdude]

I didn't say "it" had a solution. What I said was that there exists an algorithm [itex]\vec{\Psi}[/itex] which will yield the P which is the correct solution to the problem whatever the problem happens to be. You have already admitted that!

Look at your sentence again.

"The answer to every possible question can be cast in a form where that answer is a solution to the identity being discussed."

What I asked you was: What is the identity being discussed?

Why not just answer it?

What? Are you stating that I have to prove to you that every question can be answered in the form of a set of probabilities assigned to a set of possible answers?

No, I'm stating that you never proved that it is possible to answer any question with an answer of the form P=Ψ⁺Ψ. That's what it means when you say that "it is always possible to cast the answer to any question into the probability of specific answer being true (or, lacking a single correct answer, the probabilities of each of a set of possible answers)."

But now I think you're actually saying something different. Now that you've given it some exposition, I think you are saying something different. You seem to be saying that to any question Q, there is a set S of answers, each of whose probability P being true is representable as a function that can be expressed in the form P=Ψ⁺Ψ.

I think you are nit picking on issues for the sole purpose of defending your intuitive position that what I am doing could not possibly be significant. Ok, you want to hold out on the fact that, out there somewhere, there just might be a question which is answerable which could not be put in the form of a probability density of correct answers, I'll let you have that though I think you are being intentionally blind.

I'm not being intentionally blind. I'm taking you at your own words, but your words are not very clear.

Why do you feel the need to attach a motive to what I've written? How would you like it if I said that by your strange way of writing about mathematics, you were being intentionally obfuscating?

Seriously, you write about math as if you've never taken a math course in your life.

Again, I get a distinct feeling that this post is purely for the purpose of confusing anyone who happens to read this thread. A chance for you to use your subtle apparent confusion in the object of the word "it" to sow confusion. When I said it was not trivial, I was referring to the process of defining the vectors, the adjoint, the parameters, and the equation and boundary conditions which generate the vectors which will yield the result that [itex]\vec{\Psi}[itex] does indeed generate the solutions desired (that set of probabilities which describe the correct solution).

And here it is again. You would do well to stop your irritating habit of imputing motives to others, and to simply deal with what is written.

I have no idea what "existence proof" you are referring to here.

You said: "What I said was that it (edit: the probability distribution) had to exist!"

That requires an "existence proof". You call it nit picking, but hey, you're the one claiming that your statement is mathematical.

Neither do I understand what you are referring to as trivial.

I think it is a trivial result that any probability distribution can be written in a form that has no meaning.

Or what conjecture this is that you are referring to.

The conjecture is that the probability distribution "has to exist", without making an existence proof.

Please, take my statements one at a time, don't make sweeping critical statements without any basis or, if you have a basis, please make that basis clear.

I hope you find the above clear enough.

Again, I have no idea what argument you are referring to.

For Pete's sake, it's the argument that I quoted and commented on. It appears right above my remark!

It certainly can not be the central issue of the post which, as I said, you have already agreed to, I can only conclude that you are referring to my aside (regarding issue #2). If that is indeed the thing you are referring to, I must comment that it was nothing but an aside, placed there to help the reader comprehend where I am going. If that is the crux of your problem, than forget it, the general truth of it (though I certainly believe it is true in general) is not at all necessary.

There are certainly enough problems already solved where the answer to the problem can be specified in terms of a probability density! But, let us not even worry about that, let us instead worry about what can be done with what has been presented.

OK, fine.

Tom, this was an aside. I was stating that seeing answers of general questions in terms of probabilities is a concept which is very clear to me.

It's clear to me, too. It just wasn't clear to me that that was what you were saying. I thought you were saying that the answer to any conceivable question can be cast in the form P=Ψ⁺Ψ. But what you were really saying is that P is a function that can characterize the set of answers to the question, vis a vis a probability distribution.

 

[quantumdude]

I am sure Tom Mattson would disagree with me but I am of the opinion that understanding is much more valuable than knowledge as it is not rare to discover that knowledge is flawed.

What on Earth makes you think that I would disagree with that?

 

[Russell E. Rierson]

Hi Russel,

Thank you for your interest in what I am trying to say.

"It can yield" is not really the correct phrase to use here. You have the cart in front of the horse, so to speak. What I have shown is that any algorithm which can yield a result which can be interpreted as a probability can be written as an inner product of a more general category of algorithm. In fact, that category is as general as you can get; the category is "any algorithm" and no possibility is outlawed.

The central issue here is that the search for solutions to problems has to start somewhere. If your intention is to explain the universe (a TOE so to speak) it is a fairly trivial observation that the search begins with absolutely nothing: i.e., your explanation must begin from "nothing". Since, no matter how much you know, you must include the possibility that new information may prove some part of that "knowledge" erroneous, you can never do better than to estimate the probability a particular piece of information is valid. That is, in the final analysis, all answers to all problems must be stated in terms of probabilities. To state that you know anything for sure is simply foolish.

You are beginning to make more and more sense to me Dr. D.

Stephen Hawking has derived the "wave-function of the universe" and it appears that you have derived something similar, that has no constraints whatsoever? It is valid for all possible universes?

From what I read, Einstein valiantly struggled to derive a unified field theory.

http://www.lrz-muenchen.de/~aunzicker/rep2.html

Please forgive me for "jumping ahead". I am being greedy

Einstein:

The case of the absence of an electromagnetic field is characterized by the vanishing of rho_mu. In this case (7) is in first order equivalent to the equation

R_ab = 0


used as yet in the theory of general relativity (R_ab = contracted Riemann tensor). With this it is proved that our new theory yields correctly the law of a pure gravitational field in first approximation .

Mathematician John Nash derives something similar:


http://www.stat.psu.edu/~babu/nash/intereq.pdf

It was discovered only recently by me that the scalar equation naturally derived from the tensor equation for vacuum, particularly in the case of 4 space-time dimensions, has a form extremely suggestive of waves. The scalar derived equation can be obtained by formally contracting the general vacuum equation with the metric tensor. This results at first in
an equation involving G (the scalar derived from the Einstein tensor) and the Ricci tensor and the scalar curvature R. And G, being the scalar trace of the Einstein tensor, can be expressed in term of R but this expression involves the number of dimensions, n. So we get as the scalar equation derived from the original vacuum equation this result:


[]R + [(n-4)/(2n-4)] [2R^ps R_ps - R^2] = 0


And now two things are notable about the form of this resulting scalar equation: (1): If n = 2 there is a singularity and this simply corresponds to the fact that the Einstein G-tensor is identically vanishing if n = 2, so there isn't any derived scalar equation of this type for two dimensions. (2): For n = 4 we find the nice surprise that the scalar equation entirely simplifies and then asserts simply that the scalar curvature satisfiees the wave operator (which is a dAlembertian if we think in terms of 3 + 1 dimensions).
So the scalar equation is

[]R = 0 PROVIDED that n = 4:

And further remarks that can be made are that it turns out, in 4 dimensions, that this scalar equation is satisfied by any vacuum solution of the Einstein (tensor) equation for space- time (with any value of the cosmological constant" [itex]lambda[/itex]).

 

[Doctordick]

Perhaps we can bury the hatchet!

How would you like it if I said that by your strange way of writing about mathematics, you were being intentionally obfuscating?

I am sorry but I had the impression that it was exactly what you were doing!

I think we have been having a great deal of difficulty communicating. From my perspective, no real communication has yet occurred and, as I feel no purpose is served by worrying about whose fault it is, why don't we just drop the recriminations and deal with the scientific issues themselves.

I will readily admit that I really don't do a very good job of communicating my thoughts. I have always thought that the reason was because my views are so askew of the norm but perhaps that is not the correct answer. In that case, I apologize for my inept struggles at communicating.

If you can understand what I am getting at in my "Model of Explanation" at

http://home.jam.rr.com/dicksfiles/Explain/Explain.htm

I would appreciate any constructive criticism. I know it has no content, but that is the central issue; it has been purposely designed as a template for the display of any possible explanation of anything and thus cannot have any content in and of itself.

Is it useful? I would suggest that question be delayed until the model is understood.

Thank you for your indulgence -- Dick

 

[Doctordick]

arildno, please talk to me!

Hi arildno,

How about a private message or an e-mail so that I know who you actually are. I checked into Kant by googleing "Transcendental Deduction of Reality". Sorry it took me so long; I'm a busy boy most of the time. Anyway, the first return I got was

http://www.philosophypages.com/hy/5g.htm

which yielded some very interesting points. To quote the source, "Thus, Kant supposed that the philosophical concept of substance (reflected in the scientific assumption of an external world of material objects) is an a priori condition for our experience." with which I agree completely. And I further feel it demands some serious thought.

Furthermore, in paragraph two, he says, "Thus, Kant responded to Hume's skepticism by maintaining that the concept of cause is one of the synthetic conditions we determine for ourselves prior to all experience." Again, I find this man a soul with my own thoughts. If you look at my work carefully, you will find that, in my analysis, causality is a constraint imposed on our solution to the problem, not an essence of reality.

To kind of stomp the result into a contra-intuitive proposition, he says, "Finally, the experience of a world of coexisting things requires not only the experiences of each individually but also the presumption of their mutual interaction….Thus, on Kant's view, the notion of the natural world as a closed system of reciprocal forces is another a priori condition for the intelligibility of experience." God, I wish I could talk to this guy. He seem to comprehend the essence of the issues I want to talk about.

Let us merely analyze the circumstance we find ourselves in; are they not exactly expressed by, "Since the thing in itself (Ding an sich) would by definition be entirely independent of our experience of it, we are utterly ignorant of the noumenal realm." Do I agree with this man? Do bears sh** in the woods?


The web page I refer to above says that, "According to Kant, then, the rational human faculties lead us to the very boundaries of what can be known, by clarifying the conditions under which experience of the world as we know it is possible. But beyond those boundaries our faculties are useless. The shape of the boundary itself, as evidenced in the Paralogisms and Antinomies, naturally impels us to postulate that the unknown does indeed have certain features, but these further speculations are inherently unjustifiable." Now here, I have a few differences with him. Yes, certainly these further speculations are inherently unjustifiable but it seems to me that a little thought should lead to concepts which are justifiable. They just don't happen to be the ones the current scientific academy pushes.

The site goes further to state that "The only legitimate, "scientific" metaphysics that the future may hold, Kant therefore held, would be a thoroughly critical, non-speculative examination of the bounds of pure reason, a careful description of what we can know accompanied by a clear recognition that our transcendental concepts (however useful they may seem) are entirely unreliable as guides to the nature of reality.”

Unreliable is one thing, logical analysis is another. Let us analyze carefully what we can and cannot know. The article puts forth the idea that "pure reason inevitably reaches for what it cannot grasp." I would rather that pure reason reaches for what it can grasp and the difference should be comprehendible. I personally would love to debate the issues and would like serious criticism of what I have already put forth (which is directly applicable to this entire realm.

Somebody please respond!

Looking to talk to someone – Dick

 

[arildno]

I'm sorry I haven't replied to you as yet.
I have read your paper on explanation, and compared it to the introduction and first parts of your first chapter in "Foundations o. R.".
I think the material is at a level of abstractness which require careful thought, but precisely for that reason, ideas and questions needs to mature a bit before getting the correct precision level (that's how I think about it, anyway..)
Please bear with me; I'll get back to this in a few days when I've sorted out the primary questions I have..

 

[Doctordick]

I'll get back to this in a few days when I've sorted out the primary questions I have..

Do you need to amend that to "a few weeks"? I have a strong suspicion that you are making some attempt to fathom my presentation on an intuitive level. That is: that you want to understand it sufficiently well to make use of your innate ability to see the consequences without a detailed logical examination of every specific step. I am afraid that is a result not easily achieved and, as a matter of fact, is exactly what I would like to talk about. Facts is facts -- and that is what I have put before you -- nothing more! Anything more requires some very careful thought.

You never commented on my post concerning the character of thought. I presume that means you have not read it (if you have, please excuse my presumptions). I think it applies very much to the situation you currently find yourself in.

https://www.physicsforums.com/showthread.php?t=28396

If I judge you in error, please excuse me.

Have fun -- Dick

 

[Doctordick]

Just out of pure curiosity, is there anyone here who comprehends why I made the post about thought?

https://www.physicsforums.com/showthread.php?t=28396

Does anyone here comprehend the essense of rational thought? Please respond if you have an inkling of what I am talking about.

Just trying to find out if anyone out there is interested in thinking -- Dick

 

[juju]

hi,

There should be only one philosophy about physics. That is to created a model with its associated mathematics that can be mapped, as close as possible, one to one onto reality.

For sure, these models will evolve as our objective knowledge of reality increases.

juju

 

[Doctordick]

How about a general model, capable of representing anything?

That is to [create] a model with its associated mathematics that can be mapped, as close as possible, one to one onto reality.

For sure, these models will evolve as our objective knowledge of reality increases.

Why does a "valid model which has associated mathematics which can be mapped one to one into any reality" have to evolve?

http://home.jam.rr.com/dicksfiles/Explain/Explain.htm

Spend a little time thinking about it!

Have fun -- Dick

 

[juju]

Why does a "valid model which has associated mathematics which can be mapped one to one into any reality" have to evolve?

The model has to evolve because our qualitative/quantitative knowledge and perception of reality are not complete.

juju

 

[Doctordick]

That is the central issue of my model!

The model has to evolve because our qualitative/quantitative knowledge and perception of reality are not complete.

Go read the reference I gave you! The model therein described includes the fact that the knowledge and perception or reality are not complete. If you cannot understand that, you do not understand the model.

Spend a little time thinking about it!

Have fun -- Dick

 

[juju]

hey doctor dick,

It seems to me you are describing a general meta-model that describes how a model evolves and incorporates new information and truth discovered by the use of the model.

I have looked at it like this.

Initial data, information, pattern, initial Model (or paradigm), more data, information, pattern, change of Model(or paradigm), back to more data.

This cycle is a model also.

juju

 

[Doctordick]

Perhaps "meta-model" is a better discription of your model!

It seems to me you are describing a general meta-model that describes how a model evolves and incorporates new information and truth discovered by the use of the model.

No, I don't think the adjective "meta-model" is an appropriate description of what I have constructed. Let A be the set of symbols required to specify an arbitrary explanation of anything (including, of course, the collection of all symbols sufficient to interpret the intended meanings of those symbols). In that case, I have laid out an exact procedure to construct a specific model of that explanation which can be applied to any such set of symbols and discovered that there exist some very simple basic relationships imbedded in any conceivable explanation of anything.

I have looked at it like this.

Initial data, information, pattern, initial Model (or paradigm), more data, information, pattern, change of Model(or paradigm), back to more data.

This cycle is a model also.

Yes it is; but your model is, and has been, the standard model of explanation for eons and has, after thousands of years of analysis, yielded no predictions in and of itself at all. Of what value is a model if it yields no testable deductions?

My model is certainly superior to yours as mine at least puts forth some testable deductions. Now, if you can show that there exists a set which cannot be modeled by my procedure; or if you can show a specific error in my deduction (that would be my deduction of that fundamental formula) then you would have reason to prefer your ancient perspective to mine. Why don't you give it a little serious thought?

Have fun -- Dick

 

[juju]

Of what value is a model if it yields no testable deductions?

I suppose the cycle requires a modification.

Initial data, information, pattern, initial Model (or paradigm), predictions (outside of the original data set), more data, information, pattern, change of Model(or paradigm), predictions (outside of the previous data sets), back to more data.

juju