# The Foundations of Reality

Paul Martin said:
The definition of 'God' as used here is the most general idea of an agent which caused, or is responsible for the existence of, all of reality, assuming that there is (or was) such an entity.
Let's assume for the moment there is, was, and will be such an agent. A "secret agent" as it were (is and will be).

the laws of physics will (according to Dick's discovery) always be valid no matter how that agent (God) might have caused or constructed the universe, as long as the resulting universe is communicable.
I would paraphrase this to say – "that the laws of physics have to absolutely reflect the way in which the agent caused or constructed the universe, and that the agent does include in this construction, a way for the agent to communicate this to us, and thereby to each other.

'Communicable' means that the phenomena to be interpreted can all be represented by sets of numbers.
I would first have to say, that the "phenomena" isn't necessarily limited to the universe. There may be additional "principles" at work (in play), that exist between the agent and the "universe", that need to be included to "proof" the universe.

As for this being "represented by sets of numbers", I would suggest that any set(s) of numbers, no matter how thorough and exacting, they and their interrelationship are; need to be contained within two "points" that need be located absolutely, both as a quantity (1 & 0) and a quality (true & false).

I believe that under concise and thorough scrutiny, any theory will result in a relative ad infinitum (towards infinitesimal or infinite), if it is not contained within an absolute "proof" of 1 (true) and 0 (false).

As for God's relationship to the interpretation, Dick and his result don't have much comment (I don't think). Since the interpretation is done by human beings, the relationship you ask for is the relationship between humans and God. This, of course, is a very contentious issue and it is not generally resolved.
As I mention earlier, the relationship between humans and God goes in both directions.

I hope this helps, and I hope I haven't misrepresented Dick too badly.
It helped tremendously. Thank you.

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Paul Martin said:
the laws of physics will (according to Dick's discovery) always be valid no matter how that agent (God) might have caused or constructed the universe, as long as the resulting universe is communicable.
I’m not sure what you are trying to say here, Paul.

Are you saying that, given the way the agent created a communicable universe, the laws of physics (whatever they are) will always be the laws of physics? Which seems obviously but trivially true – a law of physics (given a universe) is by definition spatially and temporally invariant - how can we call something a law of physics if it will not always be a law of physics (in that given universe)?

Or are you saying that, given the way the agent created a communicable universe, the laws of physics (whatever they are) are necessarily true (ie they follow necessarily from the assumptions implicit in the creation)? (In other words, there is no other possible world where the agent could have used the same "creation assumptions" and ended up with a different set of laws of physics).

Best Regards

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moving finger said:
.. a law of physics (given a universe) is by definition spatially and temporally invariant - how can we call something a law of physics if it will not always be a law of physics (in that given universe)?
Laws of physics like laws of human society can change (be modified) over time--one need only consider Newton's law of gravity--no law at all under conditions of a vacuum--and vacuum is a state within our universe. IMO, any hypothesis about foundation of reality that is derived from a premise that laws of nature are invariant is a false hypothesis--the premise is false.

The Reality and Laws of Existence? Brought to us by what? Meant to be understood when? Meant to be understood how? Meant to be understood why?

moving finger said:
The belief that we possess knowledge is a fallible belief, no matter whether that belief is about past or future events. ... It does not follow from this that the future is “completely unknown” as you claim.
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.
moving finger said:
If so, may I ask you to define just what you do mean by “knowledge”?
I simply define it to be C + D. Any definition beyond that depends upon your explanation; i.e., "the method or means by which you achieve your expectations".
moving finger said:
I believe that getting there will be in incremental steps – and that in doing so we may even adjust the idea of where we (think) we want to be.
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.
moving finger said:
But explanation without a “meaner” is meaningless.
True, but who wants to talk about explanation in the absence of a "meaner". 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".
moving finger said:
I agree they must refer to an axis – but not to the same axis. This is the point. In your analysis you seem to treat them as if they both refer to the same axis.
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.
Canute said:
I though C was 'what we know', are you saying it's 'everything that can be known'.
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.
Canute said:
I've still a couple of outstanding questions from the previous essay so won't ask any more for the moment. Here is next one anyway so we can start pondering on it.
Anytime you have a question let me hear it; it probably arises from a misunderstanding somewhere.

Now this second essay is not a quote of my writings as it contains a comment I would never make.
Paul said:
If we look at the problem of understanding our universe, we realize that all we have to work with are sense impressions.
We do not even have "sense impressions" to work with! The idea of "sense impressions" are part and parcel of the most basic explanation of the universe we can currently conceive of. That is why I say "all we have to work with is C". What C actually is, is whatever our explanation requires C to be. That is, the actual definition of C arises in your explanation.
Paul said:
He has proved that any such set of numbers whatsoever must conform to a particular differential equation which describes the behavior of the probability density of any rule which might describe some order present in subsets of the numbers.
True and not true. The issue has to do with the fact that any explanation consists of two very different components: "what exists" and "what rules must be obeyed". It should be clear to any reasoning person that a change in one component quite often necessitates changes in the other (I would say almost always). What they don't realize is that there exists a very simple rule which will yield an explanation for absolutely anything (that "explanation" being a method of matching the statistical occurrence of the elements in C no matter what the elements of C might be).

Once one understands the method, then the future can be predicted under the simple assumption that the future will look a lot like the past: i.e., the occurrence of a particular "defined event" has a probability directly related to similarity of the surrounding events to the occurrences of those surrounding events in the past. That direct relationship is expressly dictated by my deduced "fundamental equation". What is surprising is the fact that the commonly accepted physical relationships held forth as the "laws of physics" are actually approximate solutions to that deduced equation.

To put it another way, I am aware of no known experiment which constitutes a violation of that equation and, as that equation is a tautological relation, I take that fact as evidence that modern physics is a tautology.
Paul said:
God can do nothing to make that interpretation invalid.
The problem God has (if he were to attempt to create a universe within which that equation was invalid) is that the past consists of so much data (compared to the present) that making the next moment totally inconsistent with the past is close to impossible. If the past contains anything bearing any resemblance to the present at all, my equation tells you how to compare the "future at that past moment" to the "future at the present moment". The point being that, if your explanation of the situation does not conform to my equation, it will not conform to the past on which it is based. Thus it must be your explanation which is invalid.

The best god could do is to create a universe which could not be explained: i.e., contained no repetitive events of any kind. This would mean that everything would have to be absolutely random and no sequence of events which existed within that universe could ever repeat, no matter how short the sequence might be. Think about it, a random number table where no mathematical pattern of any kind existed more than once within any set of three digits would be very difficult to create.
Paul said:
... as long as the resulting universe is communicable. 'Communicable' means that the phenomena to be interpreted can all be represented by sets of numbers.
It is not "as long as the resulting universe is communicable" but rather "as long as the resulting 'explanation' is communicable". That is a wholly different statement.
moving finger said:
(In other words, there is no other possible world where the agent could have used the same "creation assumptions" and ended up with a different set of laws of physics).
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. 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.

Have fun -- Dick

Doctordick said:
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 :

Doctordick said:
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?

moving finger said:
If so, may I ask you to define just what you do mean by “knowledge”?
Doctordick said:
I simply define it to be C + D.
Doctordick said:
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 :

Doctordick said:
the future is completely unknown
And

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

moving finger said:
(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.

Doctordick said:
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.

Doctordick said:
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”.

Doctordick said:
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.

Doctordick said:
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

DoctorDick said:
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

moving finger said:
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" which you believe to be valid, all references to "I" which you believe to be valid, all references to "can" which you believe to be valid, all references to "think" which you believe to be valid, all references to "it" which you believe to be valid, all references to "is" which you believe to be valid, all references to "true" which you believe to be valid, all references to "that" which you believe to be valid, all references to "the" which you believe to be valid, all references to "sun" which you believe to be valid, all references to "will" which you believe to be valid, all references to "rise" which you believe to be valid, all references to "tomorrow" which you believe to be valid, all references to "(" which you believe to be valid, all references to "which" which you believe to be valid, all references to "in" ... (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.
moving finger said:
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).
moving finger said:
Thus you are saying there are no premises in your model, apart from consistency itself?
Essentially, yes!
Canute said:
That's fine by me.

Have fun -- Dick

moving finger said:
Thus you are saying there are no premises in your model, apart from consistency itself?
Doctordick said:
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

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Paul Martin said:
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 refering to it as a pre-existent given?

Here's another thought I've been having.

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

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.

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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.

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Eric England said:
Could you list the specific terms, without defining them?
And is Dick defining consistency or refering 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

Eric England said:
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

Paul Martin said:
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.

Eric England said:
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

Paul Martin said:
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?

Paul Martin said:
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.
Paul Martin said:
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.
Eric England said:
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. :rofl: :rofl: :rofl: :rofl:
Eric England said:
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.
Eric England said:
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

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Gold Member
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Doctordick said:
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?

"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?

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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 [Broken]" 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 [Broken] 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.
Eric England said:
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.
Eric England said:
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

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Doctordick said:
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 ?

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. :rofl: :rofl: :rofl:

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

Doctordick said:
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?

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