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

[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

 

[Rade]

.. 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...

Yes, I agree, but of course definitions can evolve (as do laws and thus scientific truth) whereas knowledge of those concepts linked to definitions is the task of science, e.g., science is defined as search for uncertain knowledge of concepts--not definitions--and of course concepts are a mathematical construct formed by the calculus (e.g., differentiation and integration) within the mind. Thus, imo, if your equation concerns only the constraint of definitions and not the constraint of concepts defined, it would seem to me your equation misses the point of truth in science--but perhaps I just do not understand your logical argument.

 

[roamer]

Doctordick,
Are you saying the only solutions to your differential equation are laws of physics?? This would leave the conclusion that only physics has produced or discovered internally consistent explanations, right??

I didn't review your math nor could I, but it seems that if we accept your definition of an internally consistent explanation we at this point would have accept that the only known internally consistent explanations are those offered by the laws of physics. Do you forsee that there might be some more complicated solutions to this equation, do you think that these solutions or explanations would be new laws of physics?

 

[Doctordick]

Thus, imo, if your equation concerns only the constraint of definitions and not the constraint of concepts defined ...

Just exactly what are the constraints of definition if they are not constraints on the concepts defined?

but perhaps I just do not understand your logical argument.

I have thought about it for several days and I cannot come up with another explanation for your response.

Are you saying the only solutions to your differential equation are laws of physics??

I am saying that, each and every solution that I have found correspond to the known laws of physics and that the set includes all the laws of physics I am aware of. And yes, this would seem to lead to the conclusion that physics has produced or discovered nothing more than a collection of internally consistent explanations. But there is a very subtle consequence beyond that which no one seems to have picked up on.

Do you foresee that there might be some more complicated solutions to this equation, do you think that these solutions or explanations would be new laws of physics?

I do not know. That is for others to determine. I am an old man and I do not foresee my discovering much more than what I have already discovered. Discovery is for the young.

Have fun -- Dick

 

[Rade]

Just exactly what are the constraints of definition if they are not constraints on the concepts defined?

I think of the constraints for the concepts as being the number of units subsumed to form the concept (e.g., 2 units, 3, 4, etc.), whereas the constraints for the definitions are the contextual ways that the units can be mentally united. Thus two different types of constraints--those dealing with number of units, and those dealing with units united. It would appear (please correct me if I error) that your equation deals only with how units that form concept are united.