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

[Canute]

The purpose of this thread is to explore Dr. Richard Stafford's paper 'The Foundations of Reality' in order that I (and anyone else who wants to try) can come to some understanding of it. I'll quote from some introductory essays written by the author and also by Paul Martin, who has spent some time getting to grip with Dick's ideas, and ask questions of the two essayists as they arise.

These essays are available at http://paulandellen.com/ideas/tfor2.htm and are quoted with permission.

The Starting Point of "The Foundations of Reality"

by: Richard D. Stafford, Ph.D.

1) We know what we know whatever that might be! Of significance is the fact that it is all in the past and that the future is completely unknown!

2) We want to understand what we know! That means we are looking for an explanation of what we know. An explanation can be thought of as a collection of ideas which, taken as a whole will make describing what we know as easy as possible. Such a collection of ideas is called a mental model of reality.

3) A useable mental model of reality must be self consistent as, if it is not, it will not serve its purpose. It may give a different answer to the same question depending on the attack taken.

4) Finally, the explanation can not change as more information is added. That is, the "model" must be valid, no matter what the future consists of.

My entire presentation is based on those simple four ideas and it will "explain" any conceivable reality.

Paul/Dick

Q1: How is 'self-consistent' defined here? Specifically, would quantum theory qualify as a self-consistent (mental or otherwise) model despite the contradiction at the heart of it?

Q2: For 'explanation' my dictionary is not very helpful. It equates explaining with rendering comprensible. But the explanation of Nature given by physics is incomprehensible to us according to most physicists. Does this create a problem for the definition here or not? Is 'explanation' given a more precise definition later?

I'm ok with the rest.

Canute

 

[moving finger]

1) We know what we know whatever that might be! Of significance is the fact that it is all in the past and that the future is completely unknown!

2) We want to understand what we know! That means we are looking for an explanation of what we know. An explanation can be thought of as a collection of ideas which, taken as a whole will make describing what we know as easy as possible. Such a collection of ideas is called a mental model of reality.

3) A useable mental model of reality must be self consistent as, if it is not, it will not serve its purpose. It may give a different answer to the same question depending on the attack taken.

4) Finally, the explanation can not change as more information is added. That is, the "model" must be valid, no matter what the future consists of.

Some clarifications needed, so we don’t go off in different directions.

How is “knowledge” defined as used above? Should we assume the Justified True Belief (JTB) definition? (if so, then some of the above is incorrect).

(4) presumes that we can arrive at the perfect explanation at the outset. This is not how progress in understanding is normally made – normally we start with one explanation and adapt and evolve it as more information is added (eg Newtonian Mechanics being replaced by Relativity) – that our explanations evolve and change as we understand more is something we should accept.

Best Regards

 

[Doctordick]

Sorry for dropping out for a while. We have a brand new grand daughter and there are more important things to do. At the same time, I kind of lost heart in the idea of reaching anyone when everyone seemed to want to understand the universe without understanding mathematics. Even Paul, who I know has a masters in mathematics, made the comment, "as far as we can get without 'going mathematical'" which bothered me quite a little considering the source. As you all should know by this time, I regard mathematics as a language constructed by people concerned with exact meaning; as such, I agree with Feynman that "mathematics is the distilled essence of logic. Essentially, Paul's comment had exactly the same impact on me as would the comment "as far as we can get without "being logical".

Add to that the fact that another thread which I thought was at least developing a little interest on another forum encountered a rather extreme reaction and was terminated in a thread lock when I referred to their physics expert an http://www.scienceforums.net/forums/showthread.php?t=20615&page=3 . Actually, his reaction was quite similar to most all professional reactions; I think they have too much invested in being right to think about any other possibilities.

However, barring my declining interest in butting my head against a stone wall, I was surprised to find you all still at least a little interested in what I was talking about and thought I might answer your questions.

Q1: How is 'self-consistent' defined here? Specifically, would quantum theory qualify as a self-consistent (mental or otherwise) model despite the contradiction at the heart of it?

As I said above, I regard mathematics as the only decently defined language. Mathematics consists of complex systems of defined objects and procedures which allow us to make large numbers of relational statements. Such a "mathematical" system is deemed "self-consistent" when the constructed statements within the system are not a function of the procedure used to arrive at the statement when multiple procedures leading to the same statement exist. If English were a well defined construct, then the concept self consistent would have meaning in English; however, in my opinion, English is far to vague to provide one with internal self consistency over any substantial range of logic.

Q2: For 'explanation' my dictionary is not very helpful. It equates explaining with rendering comprehensible. But the explanation of Nature given by physics is incomprehensible to us according to most physicists. Does this create a problem for the definition here or not? Is 'explanation' given a more precise definition later?

I define "An explanation" to be a method of obtaining expectations from given known information. That is my definition and I think it is quite precise. My entire presentation is based on that definition and my conclusions follow directly from that definition. If it is your intention to call my definition into question, I would appreciate your giving me an explanation which does not provide you with any expectations or a logical procedure for producing expectations which can not be seen as an explanation.

How is “knowledge” defined as used above? Should we assume the Justified True Belief (JTB) definition?

As far as I am concerned, using that definition is fine; however, by bringing the question up you point out that you are missing perhaps the single most important aspect of the presentation: i.e., the deduction is not a function of the definition of "what is known" (the elements which go to make up C are intentionally undefined).

(if so, then some of the above is incorrect).

You will need point out exactly what you are referring to before I can comment on that statement.

(4) presumes that we can arrive at the perfect explanation at the outset.

I think that is a function of your point of view. From my point of view the assumption is that, if it is impossible to arrive at the perfect explanation, we will fail to find one: i.e., it can't hurt to look.

This is not how progress in understanding is normally made – normally we start with one explanation and adapt and evolve it as more information is added (eg Newtonian Mechanics being replaced by Relativity) – that our explanations evolve and change as we understand more is something we should accept.

And you are putting this forth as a reason for not looking at the big picture in a coherent manner? There are lots and lots of people attempting to understand the universe via the "normal" approach. I call it the "by guess and by golly" approach.

My whole development began with an attempt to understand how the problem should be approached intelligently. I was actually quite surprised to discover that all the equations of modern physics were approximate solutions to my "fundamental equation". Clearly, since my development is nothing more than a tautology based on the definition of an explanation, it appears that the entire field of physics tells us nothing about reality. If their results are no more than the logical consequences of an internally consistent explanation how can there be any real content? Now that is an issue really worthy of serious discussion.

I personally believe the resolution of this conundrum lies in essence of symmetry arguments. Paul has brought up Noether's theorem several times. Most scientists see Noether's theorem as the fundamental foundation of symmetry arguments but I think there is more there than they think. An excellent discourse on the common scientific view of Noether's theorem can be found on [URL='https://www.physicsforums.com/insights/author/john-baez/']John Baez's website[/url].

Symmetry arguments are often referred to as the most powerful arguments extant. I have heard them referred to as the only arguments which can produce something from nothing. The general introduction to a symmetry argument begins by supposing a symmetry and then logically deducing the consequence. In general, little time is spent on the issue of a general definition of a symmetry. At least Baez tells us what he means by a symmetry: "Next, suppose the Lagrangian L has a symmetry, meaning that it doesn't change when you apply some one-parameter family of transformations sending q to some new position q(s)[/color]." He then progresses through a pretty standard deduction of the relevant conserved quantity.

What I would like to point out is the fact that no mathematical deduction of any kind can produce a result which is not embedded in the axioms relevant to that deduction. That is, all proofs are tautological in nature as there is nothing in the result which was not stated in the original axioms: i.e., they amount to "saying the same thing twice", the essential definition of a tautology. To me it seems worthwhile to examine exactly how those conservation effects are embedded in the axioms. I think that the issue can be cleared up by examining the definition of symmetry carefully.

Just for the fun of it, let's take shift symmetry as an example. Shift symmetry has to do with the case where the analysis of a problem cannot depend upon our selection of the origin. The symmetry argument then leads to conservation of momentum. The real problem here is that, if shifting the origin has no impact on the problem to be solved, then the solution of that problem cannot depend upon the selection of the origin. That being the case, if I give the problem to two different students (one of them could be God himself) if they can find a correct answer, their answers must be exactly the same no matter what origin I select when I hand them the problem. In fact, I should not even have to tell them what point I selected as the origin when I composed the problem.

It should be clear to everyone that, under the description of the problem as I have given it here, any problem concerning the position of an object cannot be solved. It is absolutely necessary that the student make some selection of an origin before he can even express the position of the object. When he makes that selection, he is assuming something he cannot possibly know. But what he assumes cannot have any bearing on the solution thus the probability the object will be found at some position (x-a) (obtained by student number one, who's origin differs from mine by a) must be identical to the probability the object will be found at some position (x-b) (obtained by student number two, who's origin differs from mine by b). This means that P(x+c+d) must be identical to P(x+c) or the solution is an invalid solution (clearly c can be set to -a and d to a-b). As this relationship has absolutely nothing to do with what a or b is chosen, anyone familiar with calculus should see that the derivative of the probability with respect to the shift must vanish. (The derivative is simply defined to be limit, as d goes to zero, of the quantity (P(x+c+d)-P(x+c)) divided by d so it cannot be anything but zero.) All that is left is to define what we are going to call the differential. The concept "momentum" can be defined in terms of that differential and, by this means, one is able to obtain "conservation of momentum".

So let's review exactly what has happened here. Essentially, the problem was unsolvable as given as any solution had to presume the existence of a meaningful (yet unknowable) concept called "the origin". Thus the statement of a symmetry is really a statement of an assumption in the representation of the problem[/color] which has no bearing on the real problem. The solution of the problem thus involves an unstated assumption. It is that assumption which is exactly equivalent to asserting that the specified derivative vanishes. As moving finger has stated many times, one cannot make any deductions without making some assumptions. What I have actually shown is that those assumptions must include assumptions which are equivalent to differential relationships.

To put it another way, what I have shown (in my paper, http://home.jam.rr.com/dicksfiles/Explain/Explain.htm )
is that you cannot solve the problem of explaining anything without making the assumption that my fundamental equation is a valid relationship; it is a pure consequence of your assumption of a basis of representation of your ideas. (Physicists have essentially made that very assumption and the assumption fundamentally constitutes the assumption that physics correctly explains the universe.) Now I find that a very interesting thing to think about.

Have fun -- Dick

 

[Eric England]

... any problem concerning the position of an object cannot be solved. It is absolutely necessary that the student make some selection of an origin before he can even express the position of the object. When he makes that selection, he is assuming something he cannot possibly know.

The position of a point, is as you say, dependent on establishing its origin.

Saying the origin is unknowable, however, isn't necessarily true.

The origin of all dependent points is an independent point with no location. It has no outside whatsoever (of or to itself). It is a literal point.

Is this description logically accessible? Yes. Why? Because the point is invisible. We are allowed to look through it and see that it has no outside, and why. We can't, however, step outside of it to turn around and look.

From the inside, however, we can see it has a quantity and quality. Its quantity is one and its quality is existence.

Inside of a point with no location, there is only one possible literal postion – the center. The center is the only place, so it is everywhere.

At the center is another literal point – zero. It has no inside whatsoever.

Between these two literal points, which are both invisible and indivisible, is a relative "reality" of figurative points. These points "appear" to move from the center and take on dimension, but in fact, no matter how far they seem to move from center, they are always equally moving towards it, so they never actually do.

 

[Canute]

Dick

Congratulations on the addition to the family.

I take your point about mathematics. I agree it is a vital tool in studying the universe. However, not all of us can be mathematicians and I do not believe this entails that not all of us can understand the universe. For example, I have almost no understanding of Godel's mathematics, but this does not prevent me from having a reasonable understanding his results. Similarly, although I will not understand your mathematics, I may come to understand the form of your argument and your results.

I wrote something earlier that I realized later you might misinterpret. Can I add then I have no interest in whether or not you are a crank, and certainly none in trying to prove it. I've no doubt at all that many people here think I'm a crank.

I define "An explanation" to be a method of obtaining expectations from given known information. That is my definition and I think it is quite precise. My entire presentation is based on that definition and my conclusions follow directly from that definition. If it is your intention to call my definition into question, I would appreciate your giving me an explanation which does not provide you with any expectations or a logical procedure for producing expectations which can not be seen as an explanation.

I'm not going to object to your definitions. They are your definitions and as such are given. However, I would like to be clear about them, otherwise when I say 'explanation' I will not mean what you mean, which will cause chaos.

Would you equate 'explanation' with 'theory' and 'description'?

Is 'expectation' here equivalent to 'prediction'?

I find the phrase 'given known information' a bit ambiguous. Do you mean information that is either known or assumed to be true?

i.e., the deduction is not a function of the definition of "what is known" (the elements which go to make up C are intentionally undefined).

This may answer my previous question, but I'm not sure. Are you saying that your argument holds whatever the chosen axiom-set? (Does C represent the axiom-set?

Clearly, since my development is nothing more than a tautology based on the definition of an explanation, it appears that the entire field of physics tells us nothing about reality. If their results are no more than the logical consequences of an internally consistent explanation how can there be any real content? Now that is an issue really worthy of serious discussion.

I couldn't agree more, although I get very confused when I consider this issue. It seems to relate to a recently published article (in New Scientist if I remember right) mentioned on another thread, in which the author argues the laws of physics are the same as the laws of nothing.

What I would like to point out is the fact that no mathematical deduction of any kind can produce a result which is not embedded in the axioms relevant to that deduction.

That seems true to me.

That is, all proofs are tautological in nature as there is nothing in the result which was not stated in the original axioms: i.e., they amount to "saying the same thing twice", the essential definition of a tautology.

What about reductio proofs like Euclid's that there is no highest prime? In other words, what about proofs of the falsity of the axioms?

As moving finger has stated many times, one cannot make any deductions without making some assumptions.

Hmm. It probably doesn't matter here but I think there are exceptional cases in which this statement is not true. I certainly wouldn't want to move on leaving this as an assumption if it is going to be important later.

Regards
Canute

 

[Paul Martin]

Even Paul, who I know has a masters in mathematics, made the comment, "as far as we can get without 'going mathematical'" which bothered me quite a little considering the source.

My sincere apologies. I did not mean to bother or disparage you. I agree with you that we can't really understand reality without understanding the mathematics, but on the other hand, few of you are equipped to understand the mathematics. The rest of us have to do the best we can by understanding as much math as we can, and then trying to remain logical and consistent when we use language. Given the nature of language, this can't be achieved completely as I think you would agree.

Essentially, Paul's comment had exactly the same impact on me as would the comment "as far as we can get without "being logical".

Sorry about the impact, but I think that the only change I would make would be to say "as far as we can get without being "completely" logical. I just don't think you can be rigorous in natural languages. Even in mathematics, I think rigor is achieved only with great difficulty.

I applaud your approach of using mathematics to derive your result. That is why I insist on calling it a theorem. I am convinced that it deserves either recognition or serious refutation. It is either correct or incorrect and I wish someone qualified would confirm or deny its correctness.

Warm regards,

Paul

 

[sneez]

we can't really understand reality without understanding the mathematics

while almost everybody will agree that mathematics is of the utmost importance in studying reality i would like to remind us that the source of inspiration for the new direction in which this great investigative tool navigate comes harldy ONLY from mathematics/physics. This is especially true when we talk about physics and reality.

Most of initial "gut" intuition (or whatever one wants to call it) to start working on certain problem certain way comes from metaphysics/philosophy.

We may in our effort to root out any trace of metaphysics from science deprive ourselves of our very important source of inspiration. Even more so, there is great number of assumption in physics which when scrutinized do not come from known physics but from metaphysics. (a great book: "https://www.amazon.com/gp/product/1402002335/?tag=pfamazon01-20")

So while i agree (as physics grad student) the crucial importance of mathematics in study of nature, i do not agree that its the only language to convey our understanding of it. Let's just look how we learn from childhood before we get to the level of mathematics of Ph.D, ie, the power of metaphors in study of physics and math...,(for example)

imho

 

[Eric England]

... the power of metaphors in study of physics and math...

In my of thinking anyway, it might be more accurate to describe it as the figurative and the literal.

Very important distinction in any discipline.

 

[Paul Martin]

We may in our effort to root out any trace of metaphysics from science deprive ourselves of our very important source of inspiration.

I agree. I would not advocate eliminating metaphysics from science. You are correct that it provides us with inspiration to ask the right questions.

So while i agree (as physics grad student) the crucial importance of mathematics in study of nature, i do not agree that its the only language to convey our understanding of it. Let's just look how we learn from childhood before we get to the level of mathematics of Ph.D, ie, the power of metaphors in study of physics and math...,(for example)

I think you have the emphasis backwards. I think that our child-like wonder at nature, our experience at living in the world, and the reflections of metaphysical thought are all of crucial importance to the study of nature. But when it comes time to carefully formulate statements about how nature behaves, and in particular when it comes time to convey our understanding of it to others, then mathematics becomes crucially important. I think there is no other useful way.

Poets and artists, for centuries, have tried to convey to others their understanding of nature. But their attempts, when compared against those of the scientists of the past two or three hundred years, have been nearly useless in solving any human problems.

Warm regards,

Paul

 

[Doctordick]

However, not all of us can be mathematicians and I do not believe this entails that not all of us can understand the universe.

I think that very much depends upon your definition of "understand" and that is another issue which could require a lifetime to resolve.

I'm not going to object to your definitions. They are your definitions and as such are given. However, I would like to be clear about them, otherwise when I say 'explanation' I will not mean what you mean, which will cause chaos. Would you equate 'explanation' with 'theory' and 'description'?

No, I don't think so. As I said, I define "An explanation" to be a method of obtaining expectations from given known information. A theory seems to qualify as such a thing as it provides one's expectations; however, the common concept of a description seems to be little more than a list of information: i.e., a way of representing something you think you know ("given known information").

Is 'expectation' here equivalent to 'prediction'?

A "description of what you expect" seems to me to be quite similar to "predicting what you expect". The only real difference between the two concepts seems to me to be the issue of solidarity. "Predicting what you expect" seems to imply a static assertion whereas the idea of a "description of what you expect" implies a more dynamic assertion: i.e., your expectations can be seen as changing from moment to moment. But, as I say English is a rather vague mechanism for communication and I can not be at all sure that the same ideas cross your mind as cross my mind when I hear those words.

This may answer my previous question, but I'm not sure. Are you saying that your argument holds whatever the chosen axiom-set? (Does C represent the axiom-set?

Except for the mathematics presented (which I regard as a mechanism for communication established by others having nothing else to do with my presentation) C represents everything known which is absolutely true. D represents everything one thinks is true which may not be true. C + D represents everything thought to be true. As such, they would seem to include any axioms presumed to be valid. They are part of your explanation are they not?

As I have said many times, there exists no way of separating C from C + D other than its failure to be yielded by the explanation: i.e., things which are eliminated via invalidity of expectations are certainly members of D and never members of C. The new explanation must continue to explain all of C. The fact that Solipsism can not be invalidated is no more than the fact that one cannot prove C does not vanish; however, it is just as true to state that you cannot prove C vanishes so, a rational statement of the circumstance needs to include both possibilities. That is exactly why the set C is included.

I couldn't agree more, although I get very confused when I consider this issue.

Now, from my perspective, your confusion arises from your attempt to understand without understanding mathematics. Sans mathematics, your logic can carry you no farther than a few meager steps. You need to look at what I wrote to moving finger as to the difference between "logical thought" and what I like to call "squirrel thought". "Squirrel thought" (analogous to intuition or Zen) provides one with rational steps when the information relevant to the step is too complex to be processed logically (which is the most common situation one runs into).

What about reductio proofs like Euclid's that there is no highest prime? In other words, what about proofs of the falsity of the axioms?

The fact that a set of axioms are false is contained in the set of axioms!

I certainly wouldn't want to move on leaving this as an assumption if it is going to be important later.

It gets quite important later but not in the way you and/or moving finger comprehend the issue. We will perhaps get to that issue sometime later.

My sincere apologies. I did not mean to bother or disparage you.

Paul, you owe me no apologies and I did not take it as being disparaging in any way.

Even in mathematics, I think rigor is achieved only with great difficulty.

I agree with you completely; that's why I always doge the issue: I will leave it to others much more brilliant than I. After all, I really don't use much difficult mathematics. None of what I use goes even close to the bleeding edge of mathematics development. Most everything I use is in common usage throughout the hard scientific fields. As I say, I use it for exact communication and little more.

i do not agree that its the only language to convey our understanding of it.

As I said to Canute, that depends very much on your definition of "understanding". If the only purpose of your "understanding" is to provide you with direction when the information relevant to the next step is too complex to be deduced logically from your circumstance (i.e., a rule of thumb useful to your current situation) then "gut" intuition or some convenient metaphor may be the most valuable thing you have. That's fine for a working system to obtain useful results applicable to a given circumstance but I certainly would not set that definition equal to "understanding the universe".

The philosophical concept of "understanding the universe" is unachievable in the absence of mathematics as without mathematics, the extent of your logic is limited to the number of steps you have time to list and the universe is far to complex an entity to even begin to compile the relevant information. A philosopher without mathematics is analogous to a quadriplegic wanting to compete in an Olympic 100 yard dash, he can't even get out of the starting blocks.

I don't think anyone here has any real concept of the complexity achievable from very simple propositions via what is commonly referred to as "emergent" phenomena. Only mathematics can easily develop such results: take a look at the Mandelbrot set. (Google Mandelbrot for a lot more information.) I have a rather simple geometrical proof which displays some rather astounding (and unbelievable) "emergent" phenomena which I am tempted to post. Next week I may just write it up for the fun of it. All you need to know is a little geometry and common trigonometry but you have to be able to understand and follow logic.

Have fun -- Dick

 

[sneez]

As I said to Canute, that depends very much on your definition of "understanding".

Let us look at it from this view. i can have dr. hawking and to him similar quenching math that is beyond me even to begin to phantom for me coming with some conclusions which (like 11 dimension and other "unbelievable" stuff) are not accessible to 99% of population living. Now, what good is it, if the 99% of population simply cannot appreciate, or even begin to understand it? Would not the 99% of population create their own understanding of universe/reality? Sure the would, and they do. 40% of US believes that Earth is 6000yr old.

Plus, scientists are dependent on funds. Well, what business is going to support science which for them is magic? Just like i would not fund magic projects that would be telling me that they are really how universe works, the same goes for ordinary ppl who perceive it the same way.

I think we got the point I am trying to stress here. While we need precision of math to investigate universe, we have to be able to find a language and forms to convey the information to the 99% of ppl. Otherwise, we just have white coat "crazy” scientists who throw at themselves some Masonic jargon which is useless to rest of the world.

As one may see, human begins have different interests and talents. If i spent my life time crunching math i must be able to intelligently narrate it to a poet or musician. Science should create bridge, not border around different group of ppl that will feel, naturally, hostility due to misunderstandings in their views about reality. Science (math) has its limits (talking about physical world), so does poetry, but those are two different domains.

To summarize this, understanding i mean to talk about finding of science in other than math language, or approach ppl on their level of math thinking. Being falsely proud or rigid in thinking in one way limits our own understanding.

 

[moving finger]

another thread which I thought was at least developing a little interest on another forum encountered a rather extreme reaction and was terminated in a thread lock when I referred to their physics expert an advocate of ignorance.

That was rather unsubtle of you, Dr Dick. That’s not normally like you, is it?

How is “knowledge” defined as used above? Should we assume the Justified True Belief (JTB) definition?

As far as I am concerned, using that definition is fine

Then it follows that your statement “the future is completely unknown” is false. I can justifiably believe on July 4th that the statement “the sun rises on July 5th” is a true statement, and indeed “the sun rises on July 5th” may be a true statement, in which case by definition (the definition you accept) I know on July 4th that “the sun rises on July 5th”. Hence, the future is not completely unknown.

(if so, then some of the above is incorrect).

You will need point out exactly what you are referring to before I can comment on that statement.

See above.

(4) presumes that we can arrive at the perfect explanation at the outset.

I think that is a function of your point of view. From my point of view the assumption is that, if it is impossible to arrive at the perfect explanation, we will fail to find one: i.e., it can't hurt to look.

Your latter statement “if it is impossible to arrive at the perfect explanation, we will fail to find one” is an analytic truth, but this is NOT the same as “we must have the perfect explanation at the outset”.

In other words, “having an imperfect explanation to start with” is compatible with “arriving at the perfect explanation in the end”. But “arriving at the perfect explanation in the end” does not entail “having a perfect explanation to start with”.

Thus imho your (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”.

This is not how progress in understanding is normally made – normally we start with one explanation and adapt and evolve it as more information is added (eg Newtonian Mechanics being replaced by Relativity) – that our explanations evolve and change as we understand more is something we should accept.

And you are putting this forth as a reason for not looking at the big picture in a coherent manner? There are lots and lots of people attempting to understand the universe via the "normal" approach. I call it the "by guess and by golly" approach.

No, I am not putting this forth as a reason for not looking at the big picture in a coherent manner. I am saying that the ultimate goal may be the “perfect explanation”, but our journey towards that goal will entail working with imperfect explanations on the way.

What I would like to point out is the fact that no mathematical deduction of any kind can produce a result which is not embedded in the axioms relevant to that deduction. That is, all proofs are tautological in nature as there is nothing in the result which was not stated in the original axioms: i.e., they amount to "saying the same thing twice", the essential definition of a tautology.

Agreed. This is the definition of an analytic truth. All proofs by deduction fall into this category. Hence my point that we must first make assumptions before we can arrive at any meaningful understanding or meaningful explanation.

Just for the fun of it, let's take shift symmetry as an example. Shift symmetry has to do with the case where the analysis of a problem cannot depend upon our selection of the origin. The symmetry argument then leads to conservation of momentum. The real problem here is that, if shifting the origin has no impact on the problem to be solved, then the solution of that problem cannot depend upon the selection of the origin. That being the case, if I give the problem to two different students (one of them could be God himself) if they can find a correct answer, their answers must be exactly the same no matter what origin I select when I hand them the problem. In fact, I should not even have to tell them what point I selected as the origin when I composed the problem.

It should be clear to everyone that, under the description of the problem as I have given it here, any problem concerning the position of an object cannot be solved. It is absolutely necessary that the student make some selection of an origin before he can even express the position of the object. When he makes that selection, he is assuming something he cannot possibly know. But what he assumes cannot have any bearing on the solution thus the probability the object will be found at some position (x-a) (obtained by student number one, who's origin differs from mine by a) must be identical to the probability the object will be found at some position (x-b) (obtained by student number two, who's origin differs from mine by b). This means that P(x+c+d) must be identical to P(x+c) or the solution is an invalid solution (clearly c can be set to -a and d to a-b).

It seems to me that all this shows is there is no such thing as an absolute position in space (which truth is actually a tautology). All positions are measured relative to some arbitrary (assumed) coordinate axes. Your conclusion that P(x+c+d) = P(x+c) is based on an argument with an invalid inference (the inference confuses two different and arbitrary coordinate axes, one x-axis defined by you and one x-axis defined by the student, and assumes they refer to one and the same axis), thus the argument is unsound.

Best Regards

 

[Canute]

I think that very much depends upon your definition of "understand" and that is another issue which could require a lifetime to resolve.

Yes. But this comment applies equally to a mathematical understanding. Nobody has yet shown that mathematics provides the best way to understand the universe, or even that it is possible to understand it in this way. But this is an irrelevant issue here I think.

No, I don't think so. As I said, I define "An explanation" to be a method of obtaining expectations from given known information. A theory seems to qualify as such a thing as it provides one's expectations; however, the common concept of a description seems to be little more than a list of information: i.e., a way of representing something you think you know ("given known information").

That's fine. I will treat an explanation and a theory as the same thing. (However, I'll only do this here, because to me they are not necessarily the same thing.)

A "description of what you expect" seems to me to be quite similar to "predicting what you expect". The only real difference between the two concepts seems to me to be the issue of solidarity. "Predicting what you expect" seems to imply a static assertion whereas the idea of a "description of what you expect" implies a more dynamic assertion: i.e., your expectations can be seen as changing from moment to moment.

Ok. I'll take expectation and prediction as equivalent.

Except for the mathematics presented (which I regard as a mechanism for communication established by others having nothing else to do with my presentation) C represents everything known which is absolutely true. D represents everything one thinks is true which may not be true. C + D represents everything thought to be true. As such, they would seem to include any axioms presumed to be valid. They are part of your explanation are they not?

Fine. I'll assume C + D = axiom-set.

As I have said many times, there exists no way of separating C from C + D other than its failure to be yielded by the explanation:

Here I strongly disagree. However, I don't think this disagreement matters here, not yet anyway.

i.e., things which are eliminated via invalidity of expectations are certainly members of D and never members of C. The new explanation must continue to explain all of C.

OK.

The fact that Solipsism can not be invalidated is no more than the fact that one cannot prove C does not vanish; however, it is just as true to state that you cannot prove C vanishes so, a rational statement of the circumstance needs to include both possibilities. That is exactly why the set C is included.

If you are saying that C cannot include the truth or falsity of solipsism then I agree, It seems a very good point imo. (Although there are in fact three possibilites for solipsism, true, false and neither).

Now, from my perspective, your confusion arises from your attempt to understand without understanding mathematics. Sans mathematics, your logic can carry you no farther than a few meager steps.

No, this is not the case. It is not the mathematics that is confusing, it's the issues. Mathematics is an example of formal reasoning, not the only way of doing it. But again, this is a side issue.

You need to look at what I wrote to moving finger as to the difference between "logical thought" and what I like to call "squirrel thought". "Squirrel thought" (analogous to intuition or Zen) provides one with rational steps when the information relevant to the step is too complex to be processed logically (which is the most common situation one runs into).

Sorry, but this remark is based on complete misunderstanding of Zen etc. But yet again, the issue is not important here.

The fact that a set of axioms are false is contained in the set of axioms!

Oh yes.

The philosophical concept of "understanding the universe" is unachievable in the absence of mathematics

In your opinion.

I don't think anyone here has any real concept of the complexity achievable from very simple propositions via what is commonly referred to as "emergent" phenomena.

Except you, presumably. My feeling is that emergent phenomena are only complex if one does not understand the simple proposition from which they emerge. But again, I'm quibbling, this seems irrelevant to your mathematics so I'll back off.

I'm ok to move on. Shall I post the next essay?

(I get the impression that your proof is of the fact that the mathematical scheme of physics does not refer beyond itself and is thus tautological. Is this roughly it? If not just say no, I'll correct my impression as we go).

regards
Canute

 

[moving finger]

As moving finger has stated many times, one cannot make any deductions without making some assumptions.

It probably doesn't matter here but I think there are exceptional cases in which this statement is not true

Could you give us examples of these exceptional cases (apart from cases of tautology/analytic truths)?

Best Regards

 

[Doctordick]

That was rather unsubtle of you, Dr Dick. That’s not normally like you, is it?

Well, sometimes it is. I will admit that I am an opinionated old man and I sometimes get a little short with people who can't comprehend an alternate perspective on things; particularly when those people have sufficient education that one would expect a little more from them. One of my favorite quotes (it fact, it is framed over my desk) is: "Knowledge is Power" (in large capital letters) and then, is small letters, "and the single most popular abuse of that power is to use it to hide stupidity". Another framed quote I have consists of the three lines, "You can fool some of the people all the time and (new line) you can fool all of the people some of the time (new line) but you can't fool all of the people all of the time" with a red line through the third line and the comment "that requirement is never necessary!"

In general, I tend to rub authorities the wrong way. I believe I am personally responsible for the authorities on this forum closing down the category thread "theory development". The people in charge actually used to refer to it as the "nuts are us!" forum (they closed it to outside posting and started using it as a place to move "crank" posts then finally moved it to the archives). That is where I first got the idea of writing that paper "A Universal Analytical Model of Explanation Itself". Take a look at the thread I started Aug 15, 04: "Exactly what is theory all about?"

Then it follows that your statement “the future is completely unknown” is false. I can justifiably believe on July 4th that the statement “the sun rises on July 5th” is a true statement, and indeed “the sun rises on July 5th” may be a true statement, in which case by definition (the definition you accept) I know on July 4th that “the sun rises on July 5th”. Hence, the future is not completely unknown.

Ah, you and I are talking about two entirely different things here (again, problems with the vague nature of English). I thought you were referring to the definition of C+D not to my definition of time. My definition of time is simply that the past is what you know and the future is what you don't know (defined in terms of C). That has nothing to do with "justification". The only way which C differs from D is that C will absolutely never turn out to be wrong (see my comment to Canute on Solipsism). Again these are analytical truths, not hypothetical axioms. I don't think you can prove "absolutely" that the sun will rise in the future; there are lots and lots of scenarios (all quite possible circumstances) which would result in that statement being false.

Your latter statement “if it is impossible to arrive at the perfect explanation, we will fail to find one” is an analytic truth, but this is NOT the same as “we must have the perfect explanation at the outset”.

Well, as I remember, I never said the second. All I said is that I was looking for a route to it.

In other words, “having an imperfect explanation to start with” is compatible with “arriving at the perfect explanation in the end”. But “arriving at the perfect explanation in the end” does not entail “having a perfect explanation to start with”.

So what! I don't comprehend your complaint.

Thus imho your (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”.

First, I should comment that I didn't write that. It's Paul's attempt to explain what I am doing and he seems to be a better communicator than I so I don't generally try to change his presentations. But, what is important to me is to get straight to the most important issues. I think you are merely bringing up the way "rules of thumb" are generally acquired: the issue of obtaining useful results applicable to a given circumstance. I am interested in cutting to the meat of the problem and not really concerned with the "guess and by golly" aspects of the common course. They can be seen as ways of cataloging what we have come to think we know.

... but our journey towards that goal will entail working with imperfect explanations on the way.

Then you don't agree that analysis of where we want to go is a worthwhile endeavor?

Hence my point that we must first make assumptions before we can arrive at any meaningful understanding or meaningful explanation.

Now that is where I would like to go. The problem is that I suspect you and I have quite a different concept of the word "meaningful". Again, I think the most worthwhile thing I might do is present that geometrical proof I commented about earlier; however, to do so will take me a little time and I am kind of busy with other things at the moment.

Your conclusion that P(x+c+d) = P(x+c) is based on an argument with an invalid inference (the inference confuses two different and arbitrary coordinate axes, one x-axis defined by you and one x-axis defined by the student, and assumes they refer to one and the same axis), thus the argument is unsound.

No, I think you have missed the point entirely. The point is that they must refer to an axis before they can answer the question. This is an assumption which must be made prior to solving the problem and the solution of the problem cannot depend upon that assumption a subtly different fact. You might take a quick look at another post I made a year ago on the same subject (a post to one "saviormachine". Perhaps you might get a little better comprehension of what I am talking about.

Yes. But this comment applies equally to a mathematical understanding. Nobody has yet shown that mathematics provides the best way to understand the universe, or even that it is possible to understand it in this way.

But at least I can expect better understanding of what I say than I can if I use English.

That's fine. I will treat an explanation and a theory as the same thing. (However, I'll only do this here, because to me they are not necessarily the same thing.)

As you already know, I complain almost daily on the vagueness of the English language so I won't argue with you; however, I am curious as to what you think the difference is.

Fine. I'll assume C + D = axiom-set.

Now here I have to disagree with you. C+D being "everything you think you know" certainly cannot be constrained to an "axiom-set" as the concept is simply too constrained to express "everything you think you know" (unless you are a very strange individual).

As I have said many times, there exists no way of separating C from C + D other than its failure to be yielded by the explanation:

Here I strongly disagree. However, I don't think this disagreement matters here, not yet anyway.

No, I think it is a very serious issue. It appears to me that you do not understand the nature of the sets C and D. All I am doing here is separating "what is absolutely true" from what you think is true which is only a requirement of your explanation. Unless you can show me a way of proving every thing you think you know is either "absolutely true" or "absolutely not true" (which, by the way, would be a proof that Solipsism is false) there is no way of separating C from C+ D.

Sorry, but this remark is based on complete misunderstanding of Zen etc.

Then just take "Zen" out of the list. I am trying to point out the difference between logic and the other way we come to think we know things.

The philosophical concept of "understanding the universe" is unachievable in the absence of mathematics

In your opinion.

Certainly; and, as I said to moving finger, I am an opinionated old man.

My feeling is that emergent phenomena are only complex if one does not understand the simple proposition from which they emerge.

I really will have to set up that geometric proof.

I'm ok to move on. Shall I post the next essay?

Sure, why not?

Have fun – Dick

 

[Paul Martin]

Oops! Hi Dick,

You were a little too hasty.

Thus imho your (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”

First, I should comment that I didn't write that. It's Paul's attempt to explain what I am doing and he seems to be a better communicator than I so I don't generally try to change his presentations.

MF was referring to point (4) in

The Starting Point of "The Foundations of Reality"

by: Richard D. Stafford, Ph.D.

1) We know what we know whatever that might be! Of significance is the fact that it is all in the past and that the future is completely unknown!

2) We want to understand what we know! That means we are looking for an explanation of what we know. An explanation can be thought of as a collection of ideas which, taken as a whole will make describing what we know as easy as possible. Such a collection of ideas is called a mental model of reality.

3) A useable mental model of reality must be self consistent as, if it is not, it will not serve its purpose. It may give a different answer to the same question depending on the attack taken.

4) Finally, the explanation can not change as more information is added. That is, the "model" must be valid, no matter what the future consists of.

My entire presentation is based on those simple four ideas and it will "explain" any conceivable reality.

which was written by you and unchanged by me. On my website I identified which of the five attempts were written by me and which by you. You helped me edit and change mine, but I didn't change yours at all.

Warm regards,

Paul

 

[Canute]

As you already know, I complain almost daily on the vagueness of the English language so I won't argue with you; however, I am curious as to what you think the difference is.

I expect this is an irrelevant issue, but what I meant was that a theory would be based on one or more assumptions, whereas an explanation may not be. But we can forget this, I'm going with your definitions.

Now here I have to disagree with you. C+D being "everything you think you know" certainly cannot be constrained to an "axiom-set" as the concept is simply too constrained to express "everything you think you know" (unless you are a very strange individual).

Ok. But if ones explanation is derived from C and D then would these not constitute ones axioms?

No, I think it is a very serious issue. It appears to me that you do not understand the nature of the sets C and D. All I am doing here is separating "what is absolutely true" from what you think is true which is only a requirement of your explanation. Unless you can show me a way of proving every thing you think you know is either "absolutely true" or "absolutely not true" (which, by the way, would be a proof that Solipsism is false) there is no way of separating C from C+ D.

If your requirement is that C be demonstrable truths or falsities then I agree. But knowledge is not usually defined in this way. As it is not possible to demonstrate that a proposition is absolutely true or false it seemed to me that by your definition C & D may as well be the same set.

 

[Eric England]

"The vagueness of the English language" might be contingent upon the words one chooses to use, based on the "attack" one chooses to take.

If my memory serves me, it was John Archibald Wheeler who said "a complete theory might boil down to understanding the English language". (paraphrase)

 

[Doctordick]

You were a little too hasty.

Sorry Paul, if you say I said exactly that then I must have as I certainly wouldn't argue with it. My comment to moving finger was more to the point that the quote is on your website and not subject to my editing (I didn't realize it was a direct quote). Nonetheless, I will comment to moving finger as to exactly why that is stated the way it is.

"4) Finally, the explanation can not change as more information is added. That is, the "model" must be valid, no matter what the future consists of."

If that fact is not true, then we have failed to find a perfect explanation; it's as simple as that!

I expect this is an irrelevant issue, but what I meant was that a theory would be based on one or more assumptions, whereas an explanation may not be. But we can forget this, I'm going with your definitions.

The assumptions lie in D: i.e., my definition of "an explanation" includes the existence of assumptions. Again, one could admit the possibility that D could vanish (just as Solipsism presumes C vanishes) but, if D vanishes then only C remains and you are "all knowing": i.e., everything you think you know is absolutely true and nothing you will ever learn will violate your expectations: i.e., nothing will ever surprise you or change your opinions of anything. It seems to me that would be a "valid Religion": i.e., as unlikely as Solipsism.

Ok. But if ones explanation is derived from C and D then would these not constitute ones axioms?

I think you would have to define your concept of an "axiom" for me to understand what you are trying to say. If you want to define an axiom to be "everything which you believe to be true" then I would have to agree with you but I don't think that is the common concept of "an axiom".

If your requirement is that C be demonstrable truths or falsities then I agree. But knowledge is not usually defined in this way. As it is not possible to demonstrate that a proposition is absolutely true or false it seemed to me that by your definition C & D may as well be the same set.

First, I do not require that C be demonstrable truths or falsities: I simply define it to be that portion of "everything which you believe to be true" which is actually true; a subtly different thing. I do that for a reason which becomes very important down the line. Though you can not tell the difference between them they nonetheless obey a subtly different constraint. Since C constitutes what you actually know of the truth, all the elements of C must be available to your explanation and explained by that explanation. D, on the other hand, being a fictional construct (composed to make your explanation work) need not be so directly constrained: i.e., to have the existence of the elements of D implied by the explanation is sufficient.

Now I know you didn't understand that and I apologize. The issue is directly related to "Sub Problem number 1" in my presentation of http://home.jam.rr.com/dicksfiles/Explain/Explain.htm . The tau axis was introduced solely to make sure that a representation of the elements of the explanation as points on the x-axis would not limit expression of those elements. The elements of D need not be so constrained as they are fictitious constructs and need only serve the purpose of "making your explanation work". That difference has very important consequences when one goes to solve my fundamental equation; consequences having to do with evaluation of the impact of the Dirac delta function.

Have fun -- Dick

 

[moving finger]

Ah, you and I are talking about two entirely different things here (again, problems with the vague nature of English). I thought you were referring to the definition of C+D not to my definition of time. My definition of time is simply that the past is what you know and the future is what you don't know (defined in terms of C). That has nothing to do with "justification". The only way which C differs from D is that C will absolutely never turn out to be wrong (see my comment to Canute on Solipsism). Again these are analytical truths, not hypothetical axioms. I don't think you can prove "absolutely" that the sun will rise in the future; there are lots and lots of scenarios (all quite possible circumstances) which would result in that statement being false.

That is correct, I cannot prove absolutely that the sun will rise in the future. But knowledge is not about “absolute” certainty, is it? Even some of the things we think we know about the past may (or even do) turn out to be false (hence not knowledge after all). The belief that we possesses knowledge is a fallible belief, no matter whether that belief is about past or future events. Granted our inductive inferences about the past often tend to be more accurate than our inductive inferences about the future, but that’s as far as it goes. It does not follow from this that the future is “completely unknown” as you claim.

Are you now saying that you do not agree with the JTB definition of knowledge? If so, may I ask you to define just what you do mean by “knowledge”?

First, I should comment that I didn't write that.

I think Paul has answered this one for me.

Then you don't agree that analysis of where we want to go is a worthwhile endeavor?

Why would you think that? We seem to be talking past each other. I agree that knowing and analyzing where we (think) we want to go is “good” – but 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.

Now that is where I would like to go. The problem is that I suspect you and I have quite a different concept of the word "meaningful".

Indeed we might, because meaning is in the mind of the “meaner”. But explanation without a “meaner” is meaningless.

No, I think you have missed the point entirely. The point is that they must refer to an axis before they can answer the question. This is an assumption which must be made prior to solving the problem and the solution of the problem cannot depend upon that assumption a subtly different fact.

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.

Best Regards

 

[Canute]

"4) Finally, the explanation can not change as more information is added. That is, the "model" must be valid, no matter what the future consists of."

Agreed.

The assumptions lie in D: i.e., my definition of "an explanation" includes the existence of assumptions. Again, one could admit the possibility that D could vanish (just as Solipsism presumes C vanishes)

I would say that C cannot vanish, but that's another issue.

but, if D vanishes then only C remains and you are "all knowing": i.e., everything you think you know is absolutely true and nothing you will ever learn will violate your expectations: i.e., nothing will ever surprise you or change your opinions of anything.

I though C was 'what we know', are you saying it's 'everything that can be known'.

I think you would have to define your concept of an "axiom" for me to understand what you are trying to say. If you want to define an axiom to be "everything which you believe to be true" then I would have to agree with you but I don't think that is the common concept of "an axiom".

I may have muddled an issue here. My understanding of this is that C is what we know and D is what we assume. Then D would be the axioms/postulates on which our explanation rests. Is this what you mean?

First, I do not require that C be demonstrable truths or falsities: I simply define it to be that portion of "everything which you believe to be true" which is actually true; a subtly different thing.

Do you mean we know the truth/falsity of the propositions in C, or do you mean these are assumptions which we believe to be true and which happen to be true? The next comment suggests the latter.

Since C constitutes what you actually know of the truth, all the elements of C must be available to your explanation and explained by that explanation.

Ok. C contains only known facts.

D, on the other hand, being a fictional construct (composed to make your explanation work) need not be so directly constrained: i.e., to have the existence of the elements of D implied by the explanation is sufficient.

Got that.

I'll go get the next essay when I've a moment.

Canute

 

[Canute]

Dick

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.

An Abstract of "The Foundations of Reality"

If we look at the problem of understanding our universe, we realize that all we have to work with are sense impressions. As we know from familiar computer technology, all sense impressions, such as meter readings, sounds, images, verbal descriptions, etc. can all be represented by numbers. So the general problem of understanding our universe is the same as the general problem of understanding a big set of numbers. If we know nothing about these numbers, we can't say much about them specifically. But, as it turns out, we can discover some constraints on statistical patterns within supersets containing those numbers as a proper subset. Dick has discovered just such a constraint. 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. Dick then went on to solve his differential equation and discovered that the solutions matched familiar laws of physics that had been laboriously evolved by trial and error over the centuries in an attempt to find rules that match observed data. One philosophical implication of his discovery is that any universe which can be described, i.e. whose features can be communicated among people, can be interpreted in an entirely consistent manner which must conform to his equation, and thereby, must obey the laws of physics. God can do nothing to make that interpretation invalid.

 

[Eric England]

..."One philosophical implication of his discovery is that any universe which can be described, i.e. whose features can be communicated among people, can be interpreted in an entirely consistent manner which must conform to his equation, and thereby, must obey the laws of physics. God can do nothing to make that interpretation invalid."

Define God and God's relationship to the interpretation... please.

 

[Paul Martin]

Hi Eric,

..."One philosophical implication of his discovery is that any universe which can be described, i.e. whose features can be communicated among people, can be interpreted in an entirely consistent manner which must conform to his equation, and thereby, must obey the laws of physics. God can do nothing to make that interpretation invalid."

Define God and God's relationship to the interpretation... please.

Here you have quoted an example of where Dick edited and corrected an earlier attempt by me to articulate what he discovered. So I'll give you my understanding of what this means, and I'll let Dick further correct it if I get it wrong.

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. The interpretation mentioned is that of any human being, and is a particular explanation or theory of some particular phenomena. A "valid" interpretation would be one which makes accurate predictions. The laws of physics are one such interpretation, within certain limits of accuracy. There may be others. But in particular, 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. 'Communicable' means that the phenomena to be interpreted can all be represented by sets of numbers.

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.

I hope this helps, and I hope I haven't misrepresented Dick too badly.

Warm regards,

Paul

 

[Eric England]

Thanks Paul. Gives me something to work with. I will ponder this and respond in time.

 

[Eric England]

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.

 

[moving finger]

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

 

[Rade]

.. 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.

 

[Eric England]

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?

 

[Doctordick]

The belief that we possesses 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.

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".

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.

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".

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.

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.

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.

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.

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.

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.

... 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.

(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

 

[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?