What are the constraints for definitions in The Foundations of Reality?

[moving finger]

I don't claim it; I simply define the future to be "what I do not 'know'". C is what I know which is absolutely true. What I think I know is defined to be the set C + D. I have been very careful never to even allude to the idea that we can tell the difference between C and D. Somehow you simply seem to overlook that fact.

Dear Dick, I have overlooked nothing of the sort. What YOU are overlooking is that you are inconsistent – the above "definition of knowledge" is not only inconsistent with the JTB definition of knowledge that you agreed to way back in post #3, it is also inconsistent with your own definition of D.

Under JTB, I can know things about the future – but in post #1 you are quoted as claiming :

the future is completely unknown

If you now have a different definition of knowledge, perhaps you could explain what it is so that we stop going round in circles?

If so, may I ask you to define just what you do mean by “knowledge”?

I simply define it to be C + D.

D represents everything one thinks is true which may not be true.

This does not say that D cannot contain propositions about the future. If I can think it is true that the sun will rise tomorrow (which in my case I do), then this is clearly within D. But this is a proposition about the future. Therefore if you define knowledge to be C + D (which you do) then one can know things about the future, which is yet again inconsistent with both of your your claims :

the future is completely unknown

And

I simply define the future to be "what I do not 'know'"

Ok, then tell me how you would like to adjust in my proposed goal, which is, by the way, find a mechanism for constraining explanations to be consistent with what is known.

I have simply stated, in post #12, that I believe your point (4) should read :

(4) The perfect explanation can not change as more information is added. That is, the "perfect model" must be valid at all times past, present and future. But in striving to arrive at this “perfect model” we may need to pass through many “imperfect models”.

Which in post #15 you seemed to take exception to, claiming that the original point (4) was not yours anyway.

I have defined an explanation to be method of obtaining expectations from given known information. The "meaner" certainly has some expectations and one would assume those expectations are based on something: so an explanation is a way (at least modeling the procedure of the "meaner") of getting from "what those expectations are based on" to the expectations of the "meaner".

Agreed. This shows that all the essential components (information, explanation, expectations, meaner) are essential to derive any meaning, because meaning is derived from the inter-relationships between the components – each component in isolation has no meaning. “Explanation” is no more fundamental in this than any of the other essential components.

No, the central issue is the existence of ignorance and the fact that the problem cannot be solved without assuming the "absence of ignorance on that particular issue". The need to make that assumption has very real consequences.

Of course – we cannot derive any expectations without assumptions. In the example of the arbitrary measurement of position that you gave in post #3, one cannot arrive at any expectations of velocity or momentum or position unless and until one defines a coordinate system against which to measure such quantities. But in absence of any other physical reference point, the definition of this coordinate system is arbitrary – there IS no preferred frame of reference. And if two non-communicating people make their independent measurements on the particle, there is no a priori reason to expect that their results will be correlated in any way at all.

This, however, imho does not (as you seem to claim in Post #3) then lead to a derivation of the law of “conservation of momentum”.

There exists no internally self consistent explanation of any possible world which cannot be interpreted (when taken in total, including the definitions of all concepts used in that explanation) as satisfying my fundamental equation.

This may indeed be true, but I’m sorry that I don’t understand your maths enough to agree or disagree.

It has nothing to do with the "creation assumptions" of the agent; it has everything to do with creating an internally consistent explanation from a finite amount of information.

I view “creation assumptions” as another term for “boundary conditions” or “premises”

Thus you are saying there are no premises in your model, apart from consistency itself?

Best Regards

 

[Canute]

If D vanishes, then no choice exists in determining your expectations (they depend entirely on C, what you know which is absolutely true) and, since D can never exist, your expectations can not be wrong. Sounds like religion to me.

I'm afraid I can't figure out how this is connected with anything I've said or asked.

Anytime you have a question let me hear it; it probably arises from a misunderstanding somewhere.

I asked some in my last post which are unanswered. But there's too much going on here for you to deal with the issues I wanted to focus on. As I'm not going to get to grips with your idea this way I'm going to drop out. Sorry about this, but it would be wasting your time for me to continue. I may ask some questions by PM if that's ok.

regards
Canute

 

[Doctordick]

This does not say that D cannot contain propositions about the future. If I can think it is true that the sun will rise tomorrow (which in my case I do), then this is clearly within D. But this is a proposition about the future. Therefore if you define knowledge to be C + D (which you do) then one can know things about the future, which is yet again inconsistent with both of your your claims :

You simply do not understand what C and D are. Let me call E = C + D. Then E stands for the set of all things you believe to be true. In any analysis, you must include the entire set as any expression of a single element is meaningless without understanding the the rest of the elements. That is to say, E must include all references to the word "If[/color]" which you believe to be valid, all references to "I[/color]" which you believe to be valid, all references to "can[/color]" which you believe to be valid, all references to "think[/color]" which you believe to be valid, all references to "it[/color]" which you believe to be valid, all references to "is[/color]" which you believe to be valid, all references to "true[/color]" which you believe to be valid, all references to "that[/color]" which you believe to be valid, all references to "the[/color]" which you believe to be valid, all references to "sun[/color]" which you believe to be valid, all references to "will[/color]" which you believe to be valid, all references to "rise[/color]" which you believe to be valid, all references to "tomorrow[/color]" which you believe to be valid, all references to "([/color]" which you believe to be valid, all references to "which[/color]" which you believe to be valid, all references to "in[/color]" ... (you should be able to complete the list) plus all references to any words used in the references you are going to include in E. When I attempt to understand your references, the past consists of the collection of references I have and the future consists of references I do not yet have (unknown to me). Exactly the same problem confronts you whenever you attempt to understand anything.

The meaning of the phrase, "But this is a proposition about the future." must be obtained through analysis of E. The meaning is only established when the explanation is "understood" and that "understanding" will include assumptions (as your explanation of what you mean must be finite). In addition, it must always be held in mind that my understanding of what you mean "could be" wrong. On the other hand, if my understanding of your meaning is inconsistent with what you have already said, my understanding "is" wrong. What I am trying to explain to you is that I am speaking in abstract terms which seem to be beyond your comprehension; certainly the number of required elements of E is beyond any conscious comprehension of anyone.

The issue here is to separate "could be" from "is". That horrendous list of references (which I merely number for reference) plus my assumptions (also numbered for reference) if plotted to an (x,tau,t) space must satisfy my equation or those assumptions are in error. That is, if the set of references so viewed do not satisfy my equation, the presumed understanding "is" wrong; if the set of references so viewed do satisfy my equation, the presumed understanding "could be" wrong, but no information is available to prove it wrong. I am sorry but it is a rather abstract proof.

I view “creation assumptions” as another term for “boundary conditions” or “premises”

You are viewing things from a perspective of "having a solution" to what E consists of; you are not "looking for an explanation" you are instead "defending an explanation" you have already concluded is correct. I, on the other hand, can only conclude it is in the collection "could be wrong".

What is significant here is that the class "is wrong" is determined by the failure to satisfy my equation and, with regard to that issue, I think it is quite significant that all of modern physics constitute approximate solutions to that equation. That puts modern physics in the "could be wrong" collection but not in the "is wrong" collection (at least not so long as one accepts the accuracy of those required approximations).

Thus you are saying there are no premises in your model, apart from consistency itself?

Essentially, yes!

Sorry about this, but it would be wasting your time for me to continue. I may ask some questions by PM if that's ok.

That's fine by me.

Have fun -- Dick

 

[Paul Martin]

Thus you are saying there are no premises in your model, apart from consistency itself?

Essentially, yes!

I have to add my two cents worth here and clarify "essentially".

Dick has added or introduced no new premises in the construction of his model. He has only introduced definitions and drawn inferences from them.

But...and this is something Dick only briefly mentions, he has assumed and thus incorporated the premises upon which the mathematical system of analysis is founded. Dick usually says something like, "I assume mathematics, and I will let the mathematicians worry about that."

What needs to be pointed out is that the premises which undergird the mathematical system of Analysis, are not the only premises which lead to a consistent branch of mathematics. It is true that physicists use Analysis, and have used it ever since Newton and Leibniz invented the calculus of real numbers, to describe their theories. As extensions of Analysis, implied by the definition of the imaginary number i, led to the system of Complex Analysis, this was also used by phyicists to describe some of their theories. Dick is no exception here; his theorem is based on Complex Analysis. But it is important to keep in mind that Dick has added no additional axioms whatsoever. He has only defined some specific terms in terms that have already been defined within the system.

Physicists have also begun to use mathematical systems that are separate from Analysis, such as Group Theory, a component of Galois Theory. There are other esoteric systems that have been considered, but Analysis is the workhorse, and that is all that Dick uses.

So, apart from consistency itself and the premises underlying Mathematical Analysis, there are no premises in Dick's model.

Warm regards,

Paul

 

[Eric England]

He has only defined some specific terms in terms that have already been defined within the system.
So, apart from consistency itself and the premises underlying Mathematical Analysis, there are no premises in Dick's model.

Could you list the specific terms, without defining them?
And is Dick defining consistency or referring to it as a pre-existent given?

 

[Eric England]

Here's another thought I've been having.

Is Dick possibly saying that nobody has REALLY explained anything yet and that is his finding?

 

[Outlandish_Existence]

Dick... I'm right there with you. Keep up the good work. I just see one thing... the word reality... what is reality? Is reality an illusion or is illusion a reality? Whether we are being in reality or illusion; all things are still existential. "The Foundations of Existence"?

Or as Einstein wrongly stated... "Reality is merely an illusion, albeit a very persistent one."

Contradiction : Illusions don't exist... the illusion is within the illusion itself. To say that reality is an illusion is to say that we see illusions within an illusion. Illusions are merely a fancy concept for nothing or things that are not existing. Existence is the only route of truth. Regardless of if we are existing inside of reality or illusion; we are still existing.

Anyway, you all keep up your great thinking(Believe and you will be). Peace and love my fellow humans. Try and help each other out every now and then.

 

[Eric England]

There is an existence between actual and not – doesn't actually, but doesn't not.

I think if you put (to us) after reality, you will find that Einstein wasn't wrong.

 

[Paul Martin]

Could you list the specific terms, without defining them?
And is Dick defining consistency or referring to it as a pre-existent given?

The specific definitions he starts with are the sets A, B, and C. In his paper he gave the set A the name 'reality' which got a lot of readers off to a bad start and I think it hurt his chances of getting his paper read. But lately he has stuck with A, B, and C. He also defines certain functions along the way during his development, but these get pretty technical.

The concept of consistency is pre-existent. He does not define it.

Warm regards,

Paul

 

[Paul Martin]

Here's another thought I've been having.

Is Dick possibly saying that nobody has REALLY explained anything yet and that is his finding?

I don't think so. I think what he is saying is that no matter what consistent explanation anyone comes up with for anything, it must be constrained in a very specific way. It must look a lot like physics.

Warm regards,,

Paul

 

[Eric England]

I don't think so. I think what he is saying is that no matter what consistent explanation anyone comes up with for anything, it must be constrained in a very specific way. It must look a lot like physics.

That, of course, is a very common belief. A very specific constraint is necessary and it might look a lot "like Physics", but is Physics a constraint in itself? Can it answer the "what and why"?

I don't want to be hurtful, but I think Dick has been inadvertantly trying to pass off the obvious, as unobvious.

I sincerely think a re-thinking rather than a re-hashing, is called for. I would suggest discussing the constraint itself.

 

[Paul Martin]

I sincerely think a re-thinking rather than a re-hashing, is called for. I would suggest discussing the constraint itself.

OK, but the constraint itself is a VERY hairy looking differential equation. I would be delighted if you, or anyone else for that matter, were both competent to discuss it and willing to do so.

Warm regards,

Paul

 

[Eric England]

I don't think so. I think what he is saying is that no matter what consistent explanation anyone comes up with for anything, it must be constrained in a very specific way. It must look a lot like physics.

OK, but the constraint itself is a VERY hairy looking differential equation.

I would still like to get clear on the "constraint" and not the equation. Are you actually saying, by saying these two things, that his equation satisfies and will satisfy, all consistent explanations (including those that explain inconsistentcies) in Physics?

That his equation is the constraint, within which, Pysics is constrained?

 

[Doctordick]

OK, but the constraint itself is a VERY hairy looking differential equation.

"VERY hairy looking"? I think it's pretty simple looking compared to a lot of differential equations in common use by modern physicists! What is hairy, is finding solutions to it. So far, every solution I have found has turned out to be a fundamental "law of physics". That would include Classical Mechanics, Quantum Mechanics, Electrodynamics, Nuclear Theory, Relativity (both special and general). I can show that the following well accepted physical relationships are all approximate solutions to my "hairy looking" differential equation.
Newton's equations, Schroedinger's equation, Dirac's equation, Maxwell's equations, Bose and Fermi statistics and, last but not least, Schwarzschild's solutions to Einstein's representation of General relativity.

Though I have not actually proved that absolutely everything we know follows from our definitions, I have shown that the idea is consistent with the great bulk of "scientific" research. I have certainly proved that the great majority of experimental scientific work done to date amounts to little more than answering the question "does water run downhill" after defining downhill to be the direction water runs. What is left is not known solidly enough to even presume to hold that those "facts" tell us anything about the universe we find ourselves in. They amount to little more than a complex method of keeping track of the facts (a sort of Dewey decimal system of relating our expectations to what we know).

The fault does not lie with the experimentalists. Their concern is directly with the accuracy of the prediction (the theory), not the design of that prediction (the theory). An experimentalist loves inconsistencies as it gives him something to check. The theorists however should be expected to be more careful. It is evident they have spent little time considering the real problem confronting them. As I have said elsewhere. "The great minds [of this world] should have spent a little more time considering the basis of their beliefs before charging forward with new "theories". It is high time they did a little homework." I think I have defended my position and that I have, in actual fact, provided them with a substantial start on that project.

I would be delighted if you, or anyone else for that matter, were both competent to discuss it and willing to do so.

Oh, I would so love to run into such a person.

Is Dick possibly saying that nobody has REALLY explained anything yet and that is his finding?

Yes, I think that is a pretty good summary of what I have said! Though I wouldn't really say what they have done is worthless; have you ever tried to keep track of a library without a cataloging system? In the same way, you could not possibly keep track of your experiences without a system? The system you use is called "a mental image of physical reality" and the only real constraint is that it has to consistently express what you think to be true. Only the scientists have worked out a decently internally consistent system which makes really accurate pronouncements: i.e., all the "non-scientific" systems are pretty sloppy with their pronouncements of what will or will not happen. God may very well destroy the terrorists but you can't be very sure of it.

I don't want to be hurtful, but I think Dick has been inadvertantly trying to pass off the obvious, as unobvious.

Now, to this I would disagree. I am saying that my presentation is quite obvious if one takes the time to examine it. From my perspective, it is the scientific community which is trying to pass off the obvious as unobvious as they have not taken the trouble to examine the problem of understanding the universe carefully. You should take a look at a post I have made to "hypography.com". You needn't take the trouble to follow the algebra, just look at the conclusions at the end.

That his equation is the constraint, within which, Pysics is constrained?

No, my equation expresses the constraints which must be obeyed by the fundamental elements of any internally consistent argument! Again, that statement is clarified in the conclusion of my post on "hypography.com".

Have fun -- Dick

 

[selfAdjoint]

No, my equation expresses the constraints which must be obeyed by the fundamental elements of any internally consistent argument! Again, that statement is clarified in the conclusion of my post on "hypography.com".

Hey, DD, you've piqued my interest! I went to hypography.com and printed off that thread, which has the title "Is 'time' a measurable variable?". And my comment concerns that very issue.

You explain that the (\vec{x},t), independent variables in your equation, contitute "The entirety of information available to us". But the fact that you have set up a differential equation over the set of these information items, and propose to solve it, assumes that all this information is measureable. And what warrant do you have for this?

Given your over all skeptical stance, how can you assume our information about reality is limited to a measurable continuum? After we only ever can measure a finite number of digits. Someone recently, a Brit (Paul Davies?), has asserted on this basis that all our variables should be regarded as elements of Q, the rational numbers. But there is no warrant for THAT, either! A finite-digit approximant, with an error bar, could represent a rational, or an irrational. It could also (we can't tell) represent a member of some exaotic, unmeasureable subset of the reals.

So isn't a little arithmetical skepticism in order along with the rest?

 

[Eric England]

"Is Dick possibly saying that nobody has REALLY explained anything yet and that is his finding?" – Yes, I think that is a pretty good summary of what I have said! Though I wouldn't really say what they have done is worthless...

Understood. I was only trying to arrive at a "bottom line" and wasn't meaning to imply a judgement on your part.

"...I think Dick has been inadvertantly trying to pass off the obvious, as unobvious." – Now, to this I would disagree. I am saying that my presentation is quite obvious... it is the scientific community which is trying to pass off the obvious as unobvious...

I will assume that I have hit on another "bottom line", although the two viewpoints (yours and theirs) are (in context) at odds.

I would say their "passing off" is no more intentional than yours (if yours happens to be one). I think taking a value judgement out of the
relationship would be helpful, although I fully understand the frustration that can lead to one.

As for theirs, I would go back to my first point, which is that some, but not all, pretend (for ulitimately innocent reasons) that they have really established something. Something other than, that which can only be applied relatively, to a yet to be defined, "arena". The problem of "re-normalization" is fully admitted by many, but is not necessarily understood as being applicable to ALL contingents, not just GR and Quantum. If I'm not mistaken.

No, my equation expresses the constraints which must be obeyed by the fundamental elements of any internally consistent argument!

Is your equation the "arena" and if not, where in the crowd of relatives does it stand? Surrounded by, in amongst or overlooking?

 

[Doctordick]

You explain that the (\vec{x},t), independent variables in your equation, contitute "The entirety of information available to us".

If you want to understand what I am saying, you can't just jump in and make comments on issues taken out of context. If you had read the majority of what I have said, you would understand that I use mathematics as a language. As such, I take the terms and procedures defined within the realm of mathematics as understood concepts and my fundamental equation is to be understood within that context. You should go back and read my paper "http://home.jam.rr.com/dicksfiles/Explain/Explain.htm " carefully. If you do that, you will see that I operate with the common meanings of mathematical expressions together with the following specific definitions:
A is what is to be explained, B(t) is a change in what is known of A, C is the total of what is known and D what the explanation needs to assume exists. The function Psi of B(t) stated as a function of references to the fundamental elements we presume exist (which go to make up C+D) defines the expectations consistent with that explanation via the defined normalized inner product of Psi with itself. Those are the only defined objects of interest. The resultant fundamental equation yields the internal relationships necessary to make that collection of elements consistent with our explanation (the function Psi).

But the fact that you have set up a differential equation over the set of these information items, and propose to solve it, assumes that all this information is measureable.

"Measureable" is not a defined object within the context of mathematics. You have suggested this concept and, if you wish to talk about it as a "mathematical" term, you will need to first define it in mathematical terms. I need no warrant for something I have not said.

Given your over all skeptical stance, how can you assume our information about reality is limited to a measurable continuum?

That is not the assumption I have made. The assumption I have made is that your explanation of reality is expressed via a finite collection of concepts which can (as they are finite) be enumerated. The continuum (the x, tau and t axes) are in my imagination as a foundation within which to embed those finite references. At no point do I ever make an assumption that any of those numbers can be uniquely defined. It is, in fact, your assumption that those references can be uniquely defined which is in error.

In fact, the whole issue of http://home.jam.rr.com/dicksfiles/Explain/appendex/noteone.htm constitutes the consequences of making the assumption that those references can be uniquely specified within your explanation.

So isn't a little arithmetical skepticism in order along with the rest?

Again I state that I use mathematics as a language to express defined entities and procedures. What I am concerned with is that the procedures I lay out are sufficiently accurately defined and specified to allow another (familiar with the language of mathematics) to be led to the same results which I intended to lead them to: i.e., that they will find the defined procedures comprehendable (that would be the algebra necessary to solve the equation). The only issue of interest to me is the fact that mathematics is no where near as vague and undefined as is English.

I will assume that I have hit on another "bottom line", although the two viewpoints (yours and theirs) are (in context) at odds.

I wonder if you have any inkling as to exactly where my view and their's are at odds. We certainly are not at odds with regard to the experimental results as we all agree. What we are at odds is with the issue of the implications of those experimental results. The scientists think that their results justify the idea that they have "discovered some laws of physics"; whereas, my conclusion is that those very same results merely justify a belief that their ideas are close to being internally consistent. If you examine my definition of "an explanation" (stated as an analytical truth) with a little care, you will discover that all my fundamental equation states is that the explanation represented by Psi must be an internally consistent representation of what you know.

Is your equation the "arena" and if not, where in the crowd of relatives does it stand? Surrounded by, in amongst or overlooking?

As I have said many times, English is an extremely vague and undefined mechanism of communication and, with regard to your question, I have no idea as to what you are asking.

Have fun -- Dick

 

[Rade]

Originally Posted by Doctordick...my equation expresses the constraints which must be obeyed by the fundamental elements of any internally consistent argument

Question--does your equation express the constraints that must be obeyed by the internally consistent mathematical argument of "chaos theory" ? If yes, exactly how many constraints are expressed ? If no, why not ?

 

[Doctordick]

Question--does your equation express the constraints that must be obeyed by the internally consistent mathematical argument of "chaos theory" ? If yes, exactly how many constraints are expressed ? If no, why not ?

Yes! And that would be however many are needed.

I am afraid you simply do not understand the basis of my equation. If you understand mathematics, I would suggest you go back over my deduction carefully so that you might understand exactly what is being said.

Have fun -- Dick

 

[Eric England]

The only issue of interest to me is the fact that mathematics is no where near as vague and undefined as is English...as I have said many times, English is an extremely vague and undefined mechanism of communication and, with regard to your question, I have no idea as to what you are asking.

First, let's get this one straightened out. The English language, taken all the way back to its roots, and with all of its inter-implications recognized, is a about as vague as a bullet in the head.

As for my understanding of mathematics, I will bow to you any day.

I wonder if you have any inkling as to exactly where my view and their's are at odds.

I might.

We certainly are not at odds with regard to the experimental results as we all agree.

Are you saying that you agree with their experimental results, or do have some of your own as well?

The scientists think that their results justify the idea that they have "discovered some laws of physics"; whereas, my conclusion is that those very same results merely justify a belief that their ideas are close to being internally consistent... an internally consistent representation of what you know.

I may very well be misinterpreting "internally consistent", but if it can be directly compare to "externally consistent", then I would gather there is something someone "knows", that is "outside" of that which is "inside". In any case, what is "known"?

I think I'll go back to my earlier statement, that you in principle, agreed with. That your finding is, that although their ideas are not worthless, they don't REALLY know anything. I would agree with that. So what do you know or any of us know, that they don't?

Are you possibly stating that mathematics knows, and physics and philosophy (language) doesn't?

Let me ask you a couple of mathematical questions, if I may. What are the confines of infinity? If 1 is a dimensionless number, what is 0?

 

[selfAdjoint]

"Measureable" is not a defined object within the context of mathematics. You have suggested this concept and, if you wish to talk about it as a "mathematical" term, you will need to first define it in mathematical terms. I need no warrant for something I have not said.

This claim amazes me. You have a doctorate and don't know http://en.wikipedia.org/wiki/Lebesgue_measure" ?

(although I concede that I misspelled measurable).

Whatever you say you claim, at the end of the day you present a differential equation in the (\vec{x},t) and that equation is just meaningless over any set of (\vec{x},t) that is not measurable.

 

[Rade]

Yes! And that would be however many are needed. Originally Posted by Rade
Question--does your equation express the constraints that must be obeyed by the internally consistent mathematical argument of "chaos theory" ? If yes, exactly how many constraints are expressed ? If no, why not ?

Well, yes indeed. So I take it then that you cannot use your equation to calculate the exact number of constraints that are present in the internally consistent mathematical argument of "chaos theory" --that is, you cannot show me here how your equation would yield the explanation to the real number--would that be correct ?
Also, are you aware that others offer mathematical models that claim to do exactly what your equation claims--that is, they would claim that your equation is nothing more than a subset of their equation--how do you falsify such claims--why should I accept your equation and not their equation ?--see these links:
http://www.cs.cornell.edu/home/halpern/papers/expl.pdf
http://yudkowsky.net/bayes/technical.html
http://philsci-archive.pitt.edu/arc...ything_a_TM_and_Does_It_Matter_Publish_12.doc

 

[Doctordick]

First, let's get this one straightened out. The English language, taken all the way back to its roots, and with all of its inter-implications recognized, is a about as vague as a bullet in the head.

Now do you put that forth as an opinion or are you prepared to prove it? I am of the opinion that you are misinterpreting what I meant by vague. When I say the English language is vague, I mean that it is rampant with opportunities to be misinterpreted. I find these forums (which are in English for the most part) consist of exchanges which often include misunderstandings. Ergo, I think you are wrong.

Now mathematical notation can also be occasionally misinterpreted; however, it is much less susceptible to misunderstanding than is English.

This claim amazes me. You have a doctorate and don't know http://en.wikipedia.org/wiki/Lebesgue_measure" ?

I apologize; I thought you were referring to measurable as used by the physics community, a very physical concept.

But the fact that you have set up a differential equation over the set of these information items, and propose to solve it, assumes that all this information is measurable.

You apparently miss the point that I enumerate the information (which must be communicated via a finite number of references) first and then embed that information in the real (x,tau,t) space. The mathematical concept of "measurable" certainly includes the standard definition of the Euclidean axis itself. If there are indeed problems with the concept, I will leave the difficulties to the professional mathematicians as my only interest in mathematics consists of using it as a communication device: i.e., that my definitions of entities, properties and procedures can be understood.

My work initially began entirely with finite sets of numbers (used as symbols to refer to specific concepts) in which case, probabilities are defined purely by the number of repetitions of specific patterns divided by the total number of patterns examined (I could go through that analysis if you think it would be worthwhile). As such, the Psi's also become finite sets and don't really confront the issue of mathematical "measure". It is only when I extend D to cover the entire axis that the issue could even possibly arise; however, the results required to insure consistency still reduce to a finite set in any checkable circumstance so that the presumption that Psi is a measurable function (in the mathematical sense) is of no real consequence (as all it is ever used for, in the final analysis, is the construction of finite tables). Continuity does nothing more or less then provide us with an interpolation mechanism for our expectations not on the known tables.

Remember, we are not talking about truth here, we are talking about a decent method of obtaining our expectations consistent with what is known; a method, once established, which will yield expectations for future events. I am not saying that my method is the only way of generating expectations consistent with what we know, what I am saying is that it is a method which will do so and it is quite simple. Furthermore, if you attempt to explain to me a better method, I can use my method to establish an understanding of what you are trying to tell me. That is, I can certainly judge my understanding of you via support of the validity of my expectations as obtained from my understanding thus my method of interpreting your explanation will work just fine.

Well, yes indeed. So I take it then that you cannot use your equation to calculate the exact number of constraints that are present in the internally consistent mathematical argument of "chaos theory" --that is, you cannot show me here how your equation would yield the explanation to the real number--would that be correct ?

You misunderstand what my equation represents. It is a constraint upon any internally self consistent explanation of anything. As such, failure to satisfy the equation is evidence that an explanation is not internally self consistent. You give me your explanation of "the internally consistent mathematical argument of 'chaos theory'" in its absolute entirety (where no possible questions concerning any issues related to the argument could be asked), and I will show you how to determine if that explanation is internally self consistent. I will also point out to you that an effort to follow that procedure would be pretty worthless.

Also, are you aware that others offer mathematical models that claim to do exactly what your equation claims--that is, they would claim that your equation is nothing more than a subset of their equation--how do you falsify such claims--why should I accept your equation and not their equation ?--see these links:
http://www.cs.cornell.edu/home/halpern/papers/expl.pdf
http://yudkowsky.net/bayes/technical.html
http://philsci-archive.pitt.edu/arc...ything_a_TM_and_Does_It_Matter_Publish_12.doc

No, I am not aware of any such claims. I looked at your links and read the first two. The third is so poorly presented by my browser that it is very difficult to read so I didn't bother to read it.

Neither of the other two make any attempt to present any absolute constraint applicable to all explanations of anything. You should have noticed that fact when you read the Chajewska and Halpern paper as they make the comment, "Clearly the appropriateness of a notion of an explanation will depend in large part on the intended application." That is not the statement of someone intent on maintaining absolute generality. In fact, they state their concern as bearing on the issue of probabilistic inference. Yudkowsky, on the other hand is concerned with common mistaken concepts of probability and he very definitely brings up the very issues which are important to my analysis; however, he does not back up to the underlying problem but rather makes exactly the same assumption as everyone else: i.e., he assumes his understanding of the universe is correct and tries to specify detailed consistency under that presumption. And he provides no equations thus it is meaningless to even suggest could my equation could be a subset of his.

You have to comprehend that my analysis is based on the analytic truth (that would be truth by definition) that "An explanation" is a method of obtaining expectations from given known information. That definition was arrived at by considering the answer to the question, "exactly how does one know that they understand something?" To quote Yudkowsky, "since the beginning, not one unusual thing has ever happened": i.e., if you understood everything, your statistical expectations would match the statistics of what happened exactly. It follows from that, that the alignment of your expectations with what happens is exactly the criteria by which one judges their understanding.

Any explanation of anything (even when you are explaining it to yourself) consists of a collection of concepts, things, events observations, experiences ... (whatever you want to call them) which you have at your disposal. The very definition of those things must be arrived at via your explanation. You must realize that some of those things are irreducible and others are explicable in terms of the fundamentals (they are what is referred to as "emergent" phenomena). My equation specifies a required relationship between the fundamental entities; required only by the fact that the explanation (the method of obtaining those statistical expectations) must be in perfect alignment with what actually happened. The "emergent" phenomena must also be in perfect alignment with that equation as it is no more than collections of fundamental phenomena; however, a detailed analysis of "emergent" phenomena is far beyond the mental capabilities of anyone. With regard to "emergent" phenomena, the only method available to us at the moment is "by guess and by golly". Someday, we may have computers powerful enough to perform the required detailed analysis but, until then, working on that stuff is not science, it's entertainment.

My problem with your question (and almost every question raised by everyone) is that they are all based upon "emergent" phenomena which, by its very existence, presumes your explanation of the underlying fundamental phenomena is correct. My concerns are with the fundamental phenomena but my conclusions apply just as well to the "emergent" phenomena.

I hope someone has understood what I have just said.

Have fun -- Dick

 

[octelcogopod]

That was.. Difficult..

So, what you are saying is that any explanation of anything, will always be lacking, because every little factor and detail and event must be calculated for emergent phenomena?

While you have somehow come up with an equation that details the relationship between the emergent phenomena and the fundamental one?

So in a way (and I may be way off base but screw it) the aspired state is to be god, who can see all fundamental and emergent phenomena?

Furthermore, what are these fundamental phenomena?
And could you explain a little bit how you separate these two, aren't they really made in our heads?
And wouldn't that make your explanation of everything, actually an interpretation of everything?

Or maybe these are all emergent questions again.
Heh.

 

[Eric England]

... When I say the English language is vague, I mean that it is rampant with opportunities to be misinterpreted. I find these forums (which are in English for the most part) consist of exchanges which often include misunderstandings. Ergo, I think you are wrong. Now mathematical notation can also be occasionally misinterpreted; however, it is much less susceptible to misunderstanding than is English.

I would think it fair to say, that you were vague in how you presented your judgement of the English language.

You must realize that some of those things are irreducible...

What is there in math or physics that is irreducible? I think you are saying there is no irreducible. I certainly know physics hasn't found it and in math I am not so certain, so I would really like to know.

... and others are explicable in terms of the fundamentals (they are what is referred to as "emergent" phenomena).

An accurate emergence theory, certainly has to be based on an irreducible fundamental, and if there is more than one of them, the relationship between them, has to be irreducible as well.

My equation specifies a required relationship between the fundamental entities; required only by the fact that the explanation (the method of obtaining those statistical expectations) must be in perfect alignment with what actually happened.

Arriving at fundamental entities and the fundamental realtionship between them, doesn't necessarily lead to "actually happened".

The "emergent" phenomena must also be in perfect alignment with that equation as it is no more than collections of fundamental phenomena; however, a detailed analysis of "emergent" phenomena is far beyond the mental capabilities of anyone.

I would choose to describe emergent, as something other than, "no more than collections of fundamental". A collection doesn't imply the necessary hierarchal sturcture involved.

...however, a detailed analysis of "emergent" phenomena is far beyond the mental capabilities of anyone.

There is no fundament, upon which the impossiblity of the emergence of someone with the requisite mental capabilities, can said to be true. It may take someone with something more than mental capabilities, but that is beside the point, if that is not your point.

... they are all based upon "emergent" phenomena which, by its very existence, presumes your explanation of the underlying fundamental phenomena is correct. My concerns are with the fundamental phenomena but my conclusions apply just as well to the "emergent" phenomena.

Have you found a truth about fundamental (irreducible) phenomenon? If so, then I dare say we need to know it. If not, then I dare suggest, that you are saying that no irreducible has been found, so all emergent reducibles are suspect. If so, are you saying you have an equation that proves this to be so, which otherwise is common sense to many, but not to those who would rather... "working on that stuff is not science, it's entertainment."?

I hope someone has understood what I have just said.

 

[Rade]

...My equation specifies a required relationship between the fundamental entities; required only by the fact that the explanation (the method of obtaining those statistical expectations) must be in perfect alignment with what actually happened...

But, so also does this equation A = A. Note, this equation specifies a required relationship between a fundamental entity and itself for nothing is more fundamental for an entity than to say that it exists as itself. And note that the relationship is in perfect alignment with what actually happened, that is, there is 100% statistical expectation that A exists as itself. Thus, using Occam's Razor I would suggest that your equation is but a much unnecessary expanded attempt to derive the equation for the Law of Identity, A = A--but I'm sure you will correct my error.

 

[Rade]

...You give me your explanation of "the internally consistent mathematical argument of 'chaos theory'" in its absolute entirety (where no possible questions concerning any issues related to the argument could be asked), and I will show you how to determine if that explanation is internally self consistent. I will also point out to you that an effort to follow that procedure would be pretty worthless.

The text in this thread so just so convoluted--but I would swear that you have just "explained" to me that my attempt to use "your equation" to determine if my explanation of chaos theory was "internally self consistent" would be "worthless", that is, you have just offered an explanation of a thing (your equation) where you conclude that practical application of that thing is a "worthless" activity --would that be a correct understanding of the worth of your equation to my problem ?

Second, you do understand do you not that it is not possible for me to provide you an explanation of chaos theory in "absolute entirety"--in fact, it is an axiom of science that absolute knowledge is not possible via scientific explanation since by definition science is "uncertain knowledge". So, we appear to be at a logical dead end--before you can show me how to put your equation to work you request that I provide you the impossible, an explanation of chaos theory with 100% certainty. Now, since it is then clear that your equation is of no value for the explanation I seek, how then can you claim that your equation is universal for all explanation ?

 

[Doctordick]

Now, since it is then clear that your equation is of no value for the explanation I seek, how then can you claim that your equation is universal for all explanation?

You are completely correct, my equation is of utterly no value in "finding" any explanation of anything. No more than the Dewey decimal system will tell you anything about how to write a book for the library of Congress. Like the Dewey decimal system, it is designed to be entirely general: i.e., it is designed to be "universally applicable" in that no explanation exists which cannot be cast into the specified form (so long as the explanation is internally consistent). You must discover the explanation yourself (in the same vein, once you write a book, the only purpose the Dewey decimal system serves is to decide where to place the book within the library). My equation is no more than a designed constraint that any explanation must obey unless it's internally inconsistent. My equation is a restatement (in mathematical terms) that an explanation must be internally self consistent with what is being explained.

C constitutes all of the information on which the explanation is based and that "ALL" includes the information necessary to define all the elements of C (if the explanation is to be in English, C must include every reference necessary to define Eric's English language, taken all the way back to its roots sufficient to allow deduction of the meanings of those arbitrary numerical references: think of the problem of decoding). Internal to that structure, it specifies internal consistency via a required relationship which must be obeyed by the fundamental entities upon which the explanation is based.

What is astonishing about my equation is that every solution I have found seems to represent a fundamental law of physics. As I said earlier, I can show that Newton's equations, Schroedinger's equation, Dirac's equation, Maxwell's equations, Bose and Fermi statistics and, last but not least, Schwarzschild's solutions to Einstein's representation of General relativity are all approximate solutions to my equation. If my equation expresses nothing except internal self consistency, then what do these "approximate solutions" express? How can a solution of my equation contain any information beyond "internal self consistency"?

On the other hand, that result certainly implies that all explanations must be "emergent" phenomena based upon the laws of physics. Finally, with regard to "emergent" phenomena, either the concepts being used are based on fundamental concepts (in which case they must directly obey my equation) or they are not. If the concepts being used to explain a phenomena are not fundamental, they must be explainable in terms of more fundamental concepts and that is the very definition of "emergent" phenomena.

Have fun -- Dick

 

[Rade]

Thank you for the clarity Dr. Dick. But should we be all that surprised that laws of nature are solutions to your equation since any invariant over a set of phenomena implies a constraint (for the simple reason that the full range of variety does not occur) and laws of nature by definition imply the existence of an invariant.

 

[Doctordick]

Thank you for the clarity Dr. Dick. But should we be all that surprised that laws of nature are solutions to your equation since any invariant over a set of phenomena implies a constraint (for the simple reason that the full range of variety does not occur) and laws of nature by definition imply the existence of an invariant.

I think you miss the point. I am not surprised that all the laws of nature are solutions to my equation as they clearly would not be accepted if they were not as that would mean they were internally inconsistent. What I am surprised by is the fact that every solution to my equation which I have uncovered corresponds to an accepted law of nature. What this means is that I can find no evidence of any truth in science above and beyond the constraint that it be consistent with our definitions. If, indeed, science is telling us something about reality other than "our explanations are internally consistent", there should be solutions to my equation which are not seen in reality: i.e., it should not be true that any internally self consistent explanation will do as well as any other. You should be able to comprehend the enormity of such a contention.

Have fun -- Dick