Anybody interested in Dirac's equation?

[Doctordick]

It’s not what your equation says about reality that I wonder about. Clearly it can say nothing about reality as it was derived from symmetry constraints required by an explanation and then used to derive the fundamental equation.

Absolutely correct! It says nothing about reality and everything about your explanation.

The problem is that I can’t understand why it is that physicists arrived at the definitions that lead to the equations that you derive from the fundamental equation.

That is because you fail to start from the beginning. Sometime in your early life (and I am putting this all in terms of the current scientific explanation of reality; the accepted world-view) you began to comprehend that “things” existed and you began to define those “things” in terms of sounds and feelings that seemed to be related to them. The older you got the more complex your set of definitions became and the more things became familiar: i.e., your ability to generate expectations began to be a useful talent. Eventually, you went to school and began to learn things: definitions others had found convenient to explaining reality: i.e., analyzing more dependable expectations.

 

Why did physicists arrive at these definitions? Because they make estimating their expectations easier to explain. Sometimes whole fields of “defined concepts” are totally replaced with other defined concepts because the other ones seemed to work better (think of science vs astrology or, better yet, probability vs astrology; note that the stars and planets are little more than a big repetitive display and repetition is the real issue of expectations).

Would any tautology that could be arrived at from the fundamental equation have worked for what they were doing and they just happened to arrive at this one...

Mathematics is the very essence of tautological thinking as, in mathematics, absolutely everything follows from definition. As such it is a very valuable tool. It allows us to establish conclusions far beyond what can be reached via intuition (the raw power of simple feelings): i.e., what I am saying is that being a tautology is not equivalent to being “obvious” which is often the interpretation suggested by non-mathematicians. It was, nonetheless, the power of simple intuitive feelings which started mankind down this astonishing path. You might find it worthwile to read my opening post to this forum, Defining the nature of rational discussion!

But they do tell you already that it is always possible to interpret any valid explanation in terms of point particles moving in an [imath]x,y,z,\tau[/imath]-space.

I think both of you would benefit by taking another close look at my post about my simple geometric proof. If you presume each of the points being projected correspond to the position of each and every electron, proton and neutron in the universe then there exists an orientation of that figure which corresponds exactly to your impression of the universe at each and every time conceivable. Not only that, but the changes in the universe correspond directly to rotations of that figure.

 

That means that the exact structure which is you together with your current memories and thoughts is in that collection of orientations. It follows that you with your memories and thoughts a moment from now is another orientation of that figure. If you take that model as a correct representation of the universe, those two orientations differ from one another by a simple rotation. But let us look a little deeper into that representation. Suppose the universe is a totally random distribution of points (utterly no rules whatsoever). Any distribution can be seen as a specific orientation of that figure. Thus, in the set of all possible random distributions, the orientations which yield you together with your memories and thoughts exist.

 

Would not such an entity see the universe as a temporally evolving with continuity in his thoughts? The issue is that our universe, as we see it, can be built entirely from absolutely random information. That is why I keep commenting that explanations are actually nothing more or less than a powerful “data compression mechanism”.

It is as if you already had the definitions before the data itself, and once you get the data, you simply interpret it in terms of those pre-existing definitions.

It is entirely possible that your experiences with the universe have utterly no connection to my experiences. However, if you have an internally consistent explanation of the universe you think you know, I will identify your explanation to the universe I experience. What you have to understand is that my understanding of what you say is a solution of exactly the same problem: when I think I understand you it is because I have an internally consistent explanation of those sounds I hear or the things I see and that explanation must be internally consistent with the rest of my experiences: i.e., the whole thing, it the final analysis, has to obey my fundamental equation.

 

If we had a totally internally consistent interpretation of the sounds that birds make we could talk to birds. Not only that but we would think we understood them whether we did or not: i.e., our expectations of the related behavior would be exactly what the related behavior would appear to be. That is what a totally internally consistent interpretation means.

So, to answer to your question, you could say that it has been partially an accident that physicists made those definitions in conventional physics. I am saying "partially" because there are reasons why those definitions would be very useful features of a world view, but on the other hand it is always possible to come up with another set of definitions that is equally useful, or more useful for particular situations.

Back to talking to the birds ... . No matter what those definitions might be I could interpret our communications in terms of those definitions I have laid out in my deduction; collections of objects which, could move or be moved, and would obey the rules implied by Newtonian mechanics. Your explanations, if intelligible to me, would undoubtedly contain relationships which I could identify with the relationships I used in my world-view and I would interpret your explanations in terms of those definitions which I had built in my mind.

 

What I am getting at here is the fact that, if your explanation is internally consistent, it can be interpreted in terms of those very definitions I have laid out in my analysis of approximate solutions to the fundamental equation. The issue is, if a mapping exists between your explanations and my paradigm, do we really have different definitions? Isn't it just a different language?

Or two, we can look at it from the perspective that if we haven’t made any definitions than we are free to define an element in any way that we want and the definitions that we make will have there own required mapping of elements that results from using those definitions.

Back to what I said earlier; if you explain your world-view to me (using any definitions you wish) and your explanation is internally consistent, I can interpret that very explanation in terms of my defined relationships expressed in the fundamental equation. It is no more than a mapping problem.

Instead of saying "to explain a set of elements", it's better to say "to explain some information". Simply because "a set of elements" implies there are elements that have been defined, i.e. "a set of elements" is a characteristic of an explanation.

You are explaining your experiences as you see them in your world view. They may have absolutely nothing to do with my experiences or my explanations and yet I can interpret our communications in a manner which makes it look like we are talking about the same thing. That is why I keep harping on the fact that what we are talking about here is a data compression mechanism.

The [imath]x,y,z,\tau[/imath] coordinate system itself is "immaterial"; the "information to be explained" did not contain its definitions; we just made it up for convenience. That means, your expectations about the future of a particular element cannot be based on its position in the [imath]x,y,z,\tau[/imath]-space. Your expectations must be based on its position in relation to the rest of the defined universe.

As assembled in your world view!

 

Newton's fundamental law, “things at rest tend to stay at rest and things in motion tend to stay in motion” is actually a special case of the more general (and much simpler) purely inductive conclusion, “if something has been changing in a specific way up to now, it will most probably continue to change in the same manner in the future”. The value of my representation of that statement is that it actually has nothing to do with reality and everything to do with one's expectations.

I mean, focus onto the fact that the physics assumptions about what constitutes "a persistent object" are, after all, based on some sort of recurring familiarity to some information that we are interpreting according to our world view.

A perspective you intuitively arrived at probably before your first birthday.

 

Have fun – Dick

[Bombadil]

Let me know if that sounds like we are talking about the same issue. Also you might be interested to browse that thread backwards a bit as I feel there are parallels there with my previous post to this thread.

 

Well I think that we are talking about the same thing but I am also suggesting that prior to having some way of explaining something we have no way to map anything to a coordinate system because such a mapping must be part of an explanation and so there is no information to explain unless we already have a mapping for an explanation.

 

I have actually been following that thread as well and have noticed some similarities between it and what we are discussing.

 

Instead of saying "to explain a set of elements", it's better to say "to explain some information". Simply because "a set of elements" implies there are elements that have been defined, i.e. "a set of elements" is a characteristic of an explanation.

 

While I think that I can see what you are saying, hasn’t the idea of a set of elements been assumed so far in every derivation that has been done. For instance in the derivation of the Schrödinger equation it was assumed that a single element could be considered, in the derivation of the Lorenz transformation it was assumed that a set of elements existed that could be called a clock. And in this derivation it was assumed that two elements could be considered separately of the rest of the universe.

 

Basically I am saying that if we are going to say that we cannot split the data into sets, even if we can say nothing about what the sets are aren’t we back to that n-body problem again and even then at least one set exists and that is the set of all data that we are trying to explain. Even then we would still most likely consider the set of real and presumed elements even if we can’t tell them apart. Basically to me the word “set” says nothing about an explanation but rather it says something about what is being explained. And then it only says what elements we are explaining.

 

There's some information to be explained, and since nothing about the information is known, any explanation must operate via definitions that are based on familiarity to recurring patterns of some sort, with no actual knowledge about why those patterns are recurring. But any type of (semi)recurring activity will give the possibility to create valid definitions for (semi)predictably behaving persistent entities.

 

The thing here is that it says nothing about whether or not an explanation that uses some definitions might require as of yet unknown elements to exist in what is being explained. Take for instance the idea of a virtual particle . In particular the idea that if a virtual particle is observed then it can no longer be a virtual particle. The point being that it cannot be part of what is being explained until we have defined what is being explained in such a way that it becomes part of what is being explained. But after we do that can we really say that they are not part of what is being explained.

 

My understanding is that this thread has shown that such particles will have to be part of an explanation if we are going to use the definitions that lead to the Dirac equation. But would we accept an explanation that did not include them? Well, yes, I think so if it made the same predictions as one that did and those predictions where the ones that we where looking for. But are we only looking for those predictions because they are the same as the expectations that we have of our experiences? Simplicity doesn’t seem to be the issue here and accuracy seems to only be part of it. Efficiency seems to be the issue. But efficiency at doing what, seems to be a question of why we might choose some definition over another.

 

Putting this into consideration it seems that any element in an explanation may be defined in any way if we add presumed elements to the information being explained until such a definition satisfies what is being explained.

 

Would not such an entity see the universe as a temporally evolving with continuity in his thoughts? The issue is that our universe, as we see it, can be built entirely from absolutely random information. That is why I keep commenting that explanations are actually nothing more or less than a powerful “data compression mechanism”.

 

I still don’t really understand how this is a “data compression mechanism” as isn’t even this view of the universe defined by how that n dimensional object is oriented and how it is rotating? Unless the rotation of the object can be predicted from the projection. We still need to know how the projection is changing or how the n dimensional object is rotating if we are going to call this an explanation of the universe. The point being, I don’t see how any thing has been compressed unless you are suggesting that the definitions that we make define a particular orientation and rotation of that object and we just haven’t defined every orientation and possible rotation.

 

It is entirely possible that your experiences with the universe have utterly no connection to my experiences. However, if you have an internally consistent explanation of the universe you think you know, I will identify your explanation to the universe I experience. What you have to understand is that my understanding of what you say is a solution of exactly the same problem: when I think I understand you it is because I have an internally consistent explanation of those sounds I hear or the things I see and that explanation must be internally consistent with the rest of my experiences: i.e., the whole thing, it the final analysis, has to obey my fundamental equation.

 

But the explanation that you use must be based on a certain set of definitions, likewise I may use a totally different set of definitions to explain what we can agree is the same thing. So is there any reason to conclude that there is any type of mapping from your explanation to my explanation that will have an inverse. This seems equivalent to asking can I communicate my ideas to you and you communicate your ideas to me. Of course I think we can both agree that we can or we probably wouldn’t be trying, but do we have any defense for thinking that this is the case?

 

What I am getting at here is the fact that, if your explanation is internally consistent, it can be interpreted in terms of those very definitions I have laid out in my analysis of approximate solutions to the fundamental equation. The issue is, if a mapping exists between your explanations and my paradigm, do we really have different definitions? Isn't it just a different language?

 

Isn’t it different definitions? Isn’t this why something always seems to get lost or gained in translation? Aren’t we really saying that there exists a mapping from your explanation to my explanation that is invertible, and that we can both incorporate such a thing into our understanding of the universe? Isn’t this the very problem with communicating any idea to someone else. In particular, you must find a way to map some of our definitions to their explanation and likewise they must find a way to map some of their definitions to your explanation.

[Doctordick]

I still don’t really understand how this is a “data compression mechanism” as isn’t even this view of the universe defined by how that n dimensional object is oriented and how it is rotating?

You are confusing two very different things. My proof concerning the projection of a rotating n-dimensional solid onto a three dimensional space is a purely geometric proof: i.e., if the data is taken to be the (x,y,z,t) positions of n (an extremely large but still finite number) points, that same data can be represented by the projection of a rotating n-dimensional solid onto a three dimensional space. Now that isn't really a useful “data compression mechanism” as the actual amount of data (positions of n points in an n dimensional space) is much much larger than the simple display of n points in a three dimensional space; however, it is a conceptual compression of information. A rotating solid body is conceptually much simpler than n independent points moving around in a three dimensional space so, in one sense, it can be seen as a data compression mechanism.

 

It should be clear that the analogous mental image of a bunch of points (positions of named particles) obeying a set of physical laws together with an infinite background of defined virtual particles is a much more voluminous collection of data than is the simple statement that “any set of particles you can conceive of must obey a set of physical laws which can be written down in a library of physics”. So physics itself is a data compression mechanism in a conceptual sense, not in the sense of actual data.

 

My proof that, in the rest frame of the universe, the defined elements positions over time must obey my fundamental equation is a data compression mechanism in the same sense that the “library of physics” can be seen as a data compression mechanism. What you are missing is the fact that I can show that the n dimensional rotating solid is actually a solution to my fundamental equation. I don't think I have actually shown that proof to anyone as it is a somewhat ridiculous perspective and not exactly a trivial proof; however, it was my discovery of that solution which led me to work out that projection proof. The fundamental equation implied it had to true and I didn't initially believe it. Since that could easily have proved my deduction of that fundamental equation to be in error I examined the result carefully and discovered the geometric proof which, as I said, has profound consequences.

 

To make a story short, it appears to me that you are confusing these two very different proofs.

Unless the rotation of the object can be predicted from the projection. We still need to know how the projection is changing or how the n dimensional object is rotating if we are going to call this an explanation of the universe. The point being, I don’t see how any thing has been compressed unless you are suggesting that the definitions that we make define a particular orientation and rotation of that object and we just haven’t defined every orientation and possible rotation.

In a sense, you have touched upon exactly why the rotating n dimensional solid is a ridiculous perspective. The exact state of the universe (the positions of every point in the universe plus its rate of change of position) must be known in order to specify the orientation and rotation of that object and that is one hell of a lot more data than is in that “library of physics”. Again, it is a compression mechanism only in a conceptual sense. On the other hand, my fundamental equation is a real compression of the data in that “library of physics”.

But the explanation that you use must be based on a certain set of definitions, ...

My definitions (time, momentum, mass and even interaction potentials) are essentially labels of the various terms of my fundamental equation. The fundamental equation defines the relationships between these terms. If your explanation includes such relationships, I can relate them to my terms. That is exactly what I did in my deduction of Schrödinger's and Dirac's equations. In fact, that is why I gave those terms the specific labels I used; those English words are exactly the same English words used to refer to the pertinent relationships by the physics community.

...likewise I may use a totally different set of definitions to explain what we can agree is the same thing. So is there any reason to conclude that there is any type of mapping from your explanation to my explanation that will have an inverse. This seems equivalent to asking can I communicate my ideas to you and you communicate your ideas to me. Of course I think we can both agree that we can or we probably wouldn’t be trying, but do we have any defense for thinking that this is the case?

I have presented a proof that “any internally consistent explanation of anything” can be cast in a form which obeys my fundamental equation. That means that the implicit internal relationships and the implied elements behind that explanation must obey that equation. What you must not fail to include in your analysis of such issues is the fact that all communications include presumptions of facts not actually included in the details of the communication.

 

Essentially, I think you are presuming that the explanation which exists in your head (so to speak) can be accurately communicated. When you go to explain something to someone, they absolutely always make assumptions as to what is meant. These assumptions either lead to the same answers to questions or they don't. If they don't, further attempts to clarify will be made. Eventually communications will be broken off; either because the answers no longer appear to differ (and the people think they understand one another) or because the parties give up on their communication. What I am trying to point out is, even when they feel they agree, it is in fact that they are actually making a presumption that they understand one another. The fact of such presumptions shows up most often in translating between two languages. Subtle errors almost always arise in any complex representation; that is why living languages always include mixing of words. The people adapt words from the other language because they want to agree as to what they mean and what means is better than using the same word.

Isn’t this the very problem with communicating any idea to someone else. In particular, you must find a way to map some of our definitions to their explanation and likewise they must find a way to map some of their definitions to your explanation.

Yes, you are exactly right! That is the problem and, if the explanation is internally consistent there always exists an accurate translation (given the parties make the proper unexpressed assumptions). The real question is, is the explanation truly internally consistent? If it is, it can be expressed in terms of my equation. That makes translation a mere mapping problem; thus can we really say we are talking about different explanations or different definitions?

 

Have I made myself a little clearer?

 

Have fun -- Dick

[AnssiH]

I think both of you would benefit by taking another close look at my post about my simple geometric proof.

 

Had already forgotten that thread, and yeah doesn't look too hard, I think I'll just try and walk through that one too at some point.

 

Thus, in the set of all possible random distributions, the orientations which yield you together with your memories and thoughts exist.

 

Would not such an entity see the universe as a temporally evolving with continuity in his thoughts? The issue is that our universe, as we see it, can be built entirely from absolutely random information.

 

Ahha... Yeah, I must say, if I did not have the understanding of your treatment that I have thus far, it would have been almost impossible for me to understand what you are saying there. But right now it is not difficult for me to fathom that that should indeed be valid. But I need to walk through the little proof you've put up before I should say more.

 

What I am getting at here is the fact that, if your explanation is internally consistent, it can be interpreted in terms of those very definitions I have laid out in my analysis of approximate solutions to the fundamental equation. The issue is, if a mapping exists between your explanations and my paradigm, do we really have different definitions? Isn't it just a different language?

 

I know what you are saying, that's sort of the reason I call the human world-view "a semantical world-view". Meaning that there are many ways to transform a valid world view into a different but equally valid world view simply by accepting certain internally coherent changes to the definitions of your world view. I.e. different views would imply different ontological reality.

 

Your analysis of relativity is pretty obvious demonstration of that fact, if it isn't obvious already to people that such a thing can always be done. And I guess it isn't, judging by the amount of time some people spend in forums like these arguing over the correctness of their views, without understanding (or communicating) what other definitions have to be simply accepted on faith in specific forms for their argument to be valid.

 

Anyway, after all that, I think I'd still be prone to call them "different definitions", because I find it easy to communicate the matter that way. Like different QM interpretations, I'd consider each to be a different self-coherent set of definitions, but from the point of view of information-to-be-explained, only semantically different ways to produce the exact same expectations from the same exact same data.

 

But since I understand what you mean by your comment, that would be just arguing over semantics :) Hehe

 

Hey I think I've mentioned this before, but I just find it so hilarious; if you google "semantical worldview", the second result is to an old post of mine, which is touching the same subject as your post :confused:

 

Newton's fundamental law, “things at rest tend to stay at rest and things in motion tend to stay in motion” is actually a special case of the more general (and much simpler) purely inductive conclusion, “if something has been changing in a specific way up to now, it will most probably continue to change in the same manner in the future”. The value of my representation of that statement is that it actually has nothing to do with reality and everything to do with one's expectations.

 

Yup. Take notice of that Bombadil, that's why I've sometimes referred to this as an analysis about "data ordering mechanisms" (and why DD is calling it data compression mechanism), because it's about interpreting some features of some data in the terminology of newtonian mechanics. The point is that there is a translation from the "information to be explained" to the definitions of your worldview, and the "information to be explained" comes in very great volumes... ...but after the translation it should be expected to be in quite a bit more succint form (i.e. bunch of persistently existing entities etc).

 

-Anssi

[Doctordick]

But since I understand what you mean by your comment, that would be just arguing over semantics :D Hehe

Yeah, I went and read your post spotted by that google. It is astounding how similar our thoughts are. Thank you for existing even if you may be just a figment of my imagination. :)

 

Prometheuspan, you astound me. I don't very often place people on my “ignore” list and even then it is usually only after considerable irritation. You have a mere 23 posts and have already convinced me you should be ignored. That is quite an achievement. You are now on my official ignore list! :confused:

 

;)

 

Have fun -- Dick

[AnssiH]

Well I think that we are talking about the same thing but I am also suggesting that prior to having some way of explaining something we have no way to map anything to a coordinate system because such a mapping must be part of an explanation and so there is no information to explain unless we already have a mapping for an explanation.

 

It's of course true that there is no way to map the elements of an explanation without already having an explanation, but rather than saying "there is no information to explain unless we already have a mapping", we should more correctly say that we don't know anything about the nature or features of the "information-to-be-explained"... ...except that any valid world view must be based on finite amount of information.

 

I believe that is what you actually meant to say...

 

So, the symmetries that are discussed in terms of the [imath]x,y,z,\tau[/imath]-mapping, are present only after some features of the "information-to-be-explained" have become interpreted in terms of the defined elements of some valid explanation.

 

Obviously the analysis does not concern how exactly the mapping is done (how the information was explained). Of course, since it is not even possible to discuss the actual properties of the information-to-be-explained. That is why we are only concerned of the symmetries springing from the self-coherence of any valid explanation.

 

Instead of saying "to explain a set of elements", it's better to say "to explain some information". Simply because "a set of elements" implies there are elements that have been defined, i.e. "a set of elements" is a characteristic of an explanation.

While I think that I can see what you are saying, hasn’t the idea of a set of elements been assumed so far in every derivation that has been done.

 

Yes, any explanation operates in terms of a set of elements. I said what I said in that quote box, because it would be an error to imply that the information-to-be-explained is by itself also a set of elements. We have no way to discuss the actual properties of the information-to-be-explained; we would only be discussing the properties of some explanation (i.e. an interpretation of reality).

 

There's just one subtlety there, which is that any actual, valid explanation can only take into account a finite amount of information. I.e. any explanation must be based on a finite amount of information, which is what allows DD to refer to the "noumena" in terms of discrete data points. Whatever the information might be that is underlying a valid explanation, it can be represented by a set of discrete data points, in order to capture the fact that the amount of information is finite.

 

So in that context you can say that the information-to-be-explained can be considered as "a set of elements".

 

For instance in the derivation of the Schrödinger equation it was assumed that a single element could be considered

 

It was assumed that it is possible to generate such set of definitions, where the behaviour of some given element in some given situation is not dependent on the feedback from the rest of the universe.

 

I.e. that it is possible to generate a world view which allows one to predict the behaviour of some defined element without having to take into account the state of the rest of the (defined) universe.

 

Or another way to put it, since we know that this is the case with modern physics (that we have defined elements in a way that the feedback between the elements is as negligible as possible), it was analyzed what is an impact of such circumstance in terms of the fundamental symmetry equation.

 

in the derivation of the Lorenz transformation it was assumed that a set of elements existed that could be called a clock.

 

It is not assumed that such a set of elements "exists" in any actual sense; it was rather argued that such elements can always be defined, by stating that such and such circumstance inside a valid explanation would be taken to mean "a clock".

 

Once again the issue is in aligning the modern physics definitions with the analysis, in order to see the impact of the symmetry requirements. In that case, the impact was, lo and behold, relativistic time relationships.

 

Basically I am saying that if we are going to say that we cannot split the data into sets, even if we can say nothing about what the sets are aren’t we back to that n-body problem again and even then at least one set exists and that is the set of all data that we are trying to explain. Even then we would still most likely consider the set of real and presumed elements even if we can’t tell them apart.

 

I'm not sure I'm following what you are saying there, but perhaps it is helpful if I just remind you that the analysis is very much about pulling out the consequences of the symmetry requirements, and the point of it all is in explaining how certain features of modern physics are in fact consequences of having made some definitions that can always be made, and whatever then follows from the symmetry requirements.

 

Basically to me the word “set” says nothing about an explanation but rather it says something about what is being explained. And then it only says what elements we are explaining.

 

Well, if you are talking about the information that a world view is based on, then yes you can say "a set" I guess, meaning that an explanation only takes finite amount of information into account. But I can't be sure if that's what you meant. I hope this post has been helpful.

 

The thing here is that it says nothing about whether or not an explanation that uses some definitions might require as of yet unknown elements to exist in what is being explained. Take for instance the idea of a virtual particle . In particular the idea that if a virtual particle is observed then it can no longer be a virtual particle. The point being that it cannot be part of what is being explained until we have defined what is being explained in such a way that it becomes part of what is being explained.

 

Correct.

 

An explanation can contain defined elements that are entirely a feature of that explanation; their supposed existence being evident only by the fact that other definitions of the explanation requires their existence in order to be valid.

 

My understanding is that this thread has shown that such particles will have to be part of an explanation if we are going to use the definitions that lead to the Dirac equation. But would we accept an explanation that did not include them? Well, yes, I think so if it made the same predictions as one that did and those predictions where the ones that we where looking for.

 

Yes, of course other equally valid explanations can exist. The point with this thread is rather in looking at the role of the symmetry requirements in the specific definitions behind Dirac's Equation.

 

-Anssi

[Bombadil]

My proof that, in the rest frame of the universe, the defined elements positions over time must obey my fundamental equation is a data compression mechanism in the same sense that the “library of physics” can be seen as a data compression mechanism. What you are missing is the fact that I can show that the n dimensional rotating solid is actually a solution to my fundamental equation. I don't think I have actually shown that proof to anyone as it is a somewhat ridiculous perspective and not exactly a trivial proof; however, it was my discovery of that solution which led me to work out that projection proof. The fundamental equation implied it had to true and I didn't initially believe it. Since that could easily have proved my deduction of that fundamental equation to be in error I examined the result carefully and discovered the geometric proof which, as I said, has profound consequences.

 

That makes some sense from the prospective that a n dimensional rotating solid completely defines the way in which the projection will change, while if we tried to do this from the perspective of a collection of seemingly random points we would immediately have the problem of not having enough information to uniquely define how the location of the points is going to change.

 

But might not the prospective of a rotating n dimensional object supply us with an interesting mathematical prospective, as, if nothing else, it shows that the behavior of such a projection is still governed by no more then n orthogonal rotations of that n dimensional object.

 

Likewise the idea of obtaining expectations in the behavior of how an undefined collection of elements or information will change requires us to find a way in which to define a way that the set relates to itself and how such relations can be expected to change. As only internal effects can have any effect on the information. Or in other words a way of obtaining expectations about how the set will change in the future given some initial conditions. The idea that all of physics describes just such a method is conceptually a much more complicated prospective then the idea that any such method must simply satisfy the fundamental equation due to the amount of information that must be know in order to apply the resulting tools.

 

My definitions (time, momentum, mass and even interaction potentials) are essentially labels of the various terms of my fundamental equation. The fundamental equation defines the relationships between these terms. If your explanation includes such relationships, I can relate them to my terms. That is exactly what I did in my deduction of Schrödinger's and Dirac's equations. In fact, that is why I gave those terms the specific labels I used; those English words are exactly the same English words used to refer to the pertinent relationships by the physics community.

 

But, is there any reason that we should relate these terms in the same way even if we are trying to solve the same problem. So far I see no reason that we should and in fact there is no way to know if we have done such a thing unless there is some sort of uniqueness requirements to how an element may be defined. Which is set by the requirement of maintaining a self consistent explanation.

 

So can we define an object in an arbitrary way and still allow it to behave in any way or is the possible behavior of an element defined by how these term are related?

 

Essentially, I think you are presuming that the explanation which exists in your head (so to speak) can be accurately communicated. When you go to explain something to someone, they absolutely always make assumptions as to what is meant. These assumptions either lead to the same answers to questions or they don't. If they don't, further attempts to clarify will be made. Eventually communications will be broken off; either because the answers no longer appear to differ (and the people think they understand one another) or because the parties give up on their communication. What I am trying to point out is, even when they feel they agree, it is in fact that they are actually making a presumption that they understand one another. The fact of such presumptions shows up most often in translating between two languages. Subtle errors almost always arise in any complex representation; that is why living languages always include mixing of words. The people adapt words from the other language because they want to agree as to what they mean and what means is better than using the same word.

 

Isn’t this very much the same way that we conclude that we understand anything. That is we come up with a series of expectations about what is going to happen and then when our experiences of something are the same as our expectations we assume that we understand what happened and what will happen in the future.

[Doctordick]

That makes some sense from the prospective that a n dimensional rotating solid completely defines the way in which the projection will change, while if we tried to do this from the perspective of a collection of seemingly random points we would immediately have the problem of not having enough information to uniquely define how the location of the points is going to change.

Not really as the two perspectives are essentially equivalent. From the perspective of seemingly random points, we can simply see the distribution closest to the one just examined as the next picture (that would essentially give us the velocity of every element in the distribution). The rotation of an n dimensional solid would have to be quantized (angular momentum quantization is a pretty simple subject) and we would thus have to know the quantum state in every rotational mode. That is in fact exactly the same amount of information as is the position of every point.

But might not the prospective of a rotating n dimensional object supply us with an interesting mathematical prospective, as, if nothing else, it shows that the behavior of such a projection is still governed by no more then n orthogonal rotations of that n dimensional object.

Essentially the interactions in this paradigm are provided by the Dirac delta function terms. That amounts to a gas of point particles (it is only the uncertainty of the position of that point which allows the interaction. What I am trying to point out is that the two perspectives are essentially identical when it comes to the amount of data required to use either one.

Likewise the idea of obtaining expectations in the behavior of how an undefined collection of elements or information will change requires us to find a way in which to define a way that the set relates to itself and how such relations can be expected to change.

It seems to me that you are missing the fundamental issue here. Your “past” (what you know, at least with regard to your self defined world view) essentially constitutes a set of positions of those n points. From that point forward, obtaining [imath]\vec{\Psi}[/imath] is an interpolation problem. Conservation of momentum (which arises from the symmetry properties) determine the form of that function. New information (a measurement of some future result) results in a new collection of points and thus a new [imath]\vec{\Psi}[/imath]. In conventional quantum mechanics that process is called “collapse of the wave function”. In my paradigm it is simply, “new information means we have a new problem to solve” and the change in information is small compared to the information it takes to describe the past.

The real issue here is that the present looks a lot like the past. That is a consequence of the fact that most of the data your explanation is to explain doesn't change.

Maybe you do understand what I am talking about.

As only internal effects can have any effect on the information.

But here you seem to be talking about your explanation again not the underlying information.

But, is there any reason that we should relate these terms in the same way even if we are trying to solve the same problem. So far I see no reason that we should and in fact there is no way to know if we have done such a thing unless there is some sort of uniqueness requirements to how an element may be defined. Which is set by the requirement of maintaining a self consistent explanation.

I truly do not understand your confusion and can only conclude that you are really attempting to push my paradigm into the classical paradigm. That can only be done if the classical paradigm is internally consistent and that is a very difficult thing to prove. It is easy to prove my paradigm is internally consistent.

Isn’t this very much the same way that we conclude that we understand anything. That is we come up with a series of expectations about what is going to happen and then when our experiences of something are the same as our expectations we assume that we understand what happened and what will happen in the future.

Yes, and that is precisely why I see “explanations” as data compression mechanisms.

 

I really don't understand your confusion and can only presume it arises from your attempts to map the common paradigm into my paradigm. As I said, there is no guarantee that such a thing can be done unless the common paradigm you are using is totally internally consistent and I don't think you can prove that the common paradigm is absolutely flaw free: i.e., if you want to prove it is flaw free, you have to use my paradigm. :shrug:

 

Have fun -- Dick

[Bombadil]

Obviously the analysis does not concern how exactly the mapping is done (how the information was explained). Of course, since it is not even possible to discuss the actual properties of the information-to-be-explained. That is why we are only concerned of the symmetries springing from the self-coherence of any valid explanation.

 

Maybe we are talking about two separate mappings as what I am talking about is how a new element can be put into a coordinate system and so go from being completely undefined to being part of a coordinate system and become part of what is being explained by our explanation.

 

Or perhaps we are talking about the same thing here and you are referring to the symmetries that spring from the fact that we can only define an elements location in relation to the other elements that have already been defined.

 

I'm not sure I'm following what you are saying there, but perhaps it is helpful if I just remind you that the analysis is very much about pulling out the consequences of the symmetry requirements, and the point of it all is in explaining how certain features of modern physics are in fact consequences of having made some definitions that can always be made, and whatever then follows from the symmetry requirements.

 

Well if no part of the universe could be explained without considering every other thing in the universe then we can’t hardly say that it would look anything like modern physics with perhaps a few exceptions. Think of trying to define a clock inside of a star. Saying that there would be new challenges would likely be an understatement due to the number of interactions and the problems involved in defining an object. Of course everything so far would still be valid if you could define a clock and most of it if you could not define a clock but it would be difficult to apply in any way that we are used to applying it because of the number of interactions taking place.

 

Now if we are going to say that we can consider something other then the whole universe anything that we are going to consider can be considered a set of its own and any collection of such sets is also a set.

 

Well, if you are talking about the information that a world view is based on, then yes you can say "a set" I guess, meaning that an explanation only takes finite amount of information into account. But I can't be sure if that's what you meant. I hope this post has been helpful.

 

Well I would consider a set to be any collection of information or elements that has some particular property or characteristic that can be used to separate it out from the entire universe. This does not necessarily mean that it can be considered on its own.

 

Not really as the two perspectives are essentially equivalent. From the perspective of seemingly random points, we can simply see the distribution closest to the one just examined as the next picture (that would essentially give us the velocity of every element in the distribution). The rotation of an n dimensional solid would have to be quantized (angular momentum quantization is a pretty simple subject) and we would thus have to know the quantum state in every rotational mode. That is in fact exactly the same amount of information as is the position of every point.

 

But if we know the quantum state of every rotational mode haven’t we uniquely defined any future projection of that n dimensional solid while if we know the position of every point it can still change in any way in the future even if we have multiple such pictures so that we can define the speed of every element.

 

 

Originally Posted by Bombadil View Post

The real issue here is that the present looks a lot like the past. That is a consequence of the fact that most of the data your explanation is to explain doesn't change.

 

Maybe you do understand what I am talking about.

 

While I would have to agree with the quote in your post. it seems both to the point and eloquently put but I really don’t know where you quoted it from as I didn’t put it in my last post. If you are trying to put what I said into more eloquent wording that is kind of where I was heading although I wasn’t wording it quite the way you posted it and was having some difficulty finding the right way to word it.

 

But here you seem to be talking about your explanation again not the underlying information.

 

Well I may have had some bad wording there perhaps a better way to put it is, only what we know “our past” can have any effect on our expectations for the future.

 

I truly do not understand your confusion and can only conclude that you are really attempting to push my paradigm into the classical paradigm. That can only be done if the classical paradigm is internally consistent and that is a very difficult thing to prove. It is easy to prove my paradigm is internally consistent.

 

I’m not quite sure how to explain what I am trying to say and I suspect that it is a minor issue but I will try once more to describe it, then perhaps we would be best off not worrying about it at least for the time being.

 

In this thread you used the definition of a photon and electron that modern physics uses and found that two such element must satisfy the Dirac equation. But suppose that we wanted to know what kind of element would satisfy the Dirac equation. Clearly we have no means right now to know if two elements do except what you have referred to as the ‘by guess and by golly’ method but still suppose we wanted to know the consequences of two elements satisfying it. Is the derivation that you have done here sufficient to conclude that in your paradigm we must define the elements as they where in the opening post or is this still a open issue?

 

I’m starting to wonder if we would be better off coming back to these topics at a latter date? If you want to continue here I of course will continue as I think that there is still more here but I think that it is not what you where trying to get at with this thread and I suspect that these same issues will come up again so perhaps we would be better off continuing this discussion at a latter date and pursuing doctordick’s other thread “the final piece of the puzzle” that I see has been started.

[AnssiH]

Maybe we are talking about two separate mappings as what I am talking about is how a new element can be put into a coordinate system and so go from being completely undefined to being part of a coordinate system and become part of what is being explained by our explanation.

 

It's pointless to think about that issue. And also quite oxymoronic. There is no point in thinking about how some "undefined elements" correspond to some "defined elements", because we can't say anything about the underlying (undefined) information without using some definitions. That is the whole issue discussed by philosophers when they refer to "noumena" or "map-territory relationship", and that is exactly the problem that is completely side-stepped by this analysis, via focusing directly to the symmetry features that are common to ALL valid definitions.

 

It is a complete misnomer to even think about "a new undefined element". It's not like a point entity would just pop into existence, and then it would be placed somewhere into a coordinate system. There's no way to say what sorts of features of what sort of information are taken to correspond to "defined elements".

 

Like I tried to explain, it is a bit unfortunate that in this analysis, the "undefined reality" is referred to as a finite set of data because it can imply that an argument is being made about reality actually being a set of elements or something. The only reason that the undefined reality is referred to as a finite set is because any valid world view must be a function of a finite amount of information. A world view that is constructed according to an infinite amount of information is logically impossible, as its construction could never be completed.

 

In a nutshell, to understand the analysis, you don't need to understand how a world view picks up some features of some data and correlates them to defined entities. You just need to understand why those symmetries exist in the final results.

 

-Anssi

[Bombadil]

In a nutshell, to understand the analysis, you don't need to understand how a world view picks up some features of some data and correlates them to defined entities. You just need to understand why those symmetries exist in the final results.

 

Ok, so we have no concerns about how a new element might become part of what we know, that is how it is put into the x,[imath]\tau[/imath],t coordinate system. What is important is that anything can be represented by that coordinate system and that the definitions used in that coordinate system must obey those symmetries. The fundamental equation is then how we insure that we are looking at the consequences of those symmetries.

 

Now how I understand it, the idea that the explanation must be based on a finite amount of information is that if we considered an infinite amount of information to base our explanation on it would follow that the past would be infinite which we could never accomplish gathering. However, there may be an infinite number of elements in an explanation as there is no such constraint on presumed elements.

[AnssiH]

Ok, so we have no concerns about how a new element might become part of what we know, that is how it is put into the x,[imath]\tau[/imath],t coordinate system. What is important is that anything can be represented by that coordinate system and that the definitions used in that coordinate system must obey those symmetries. The fundamental equation is then how we insure that we are looking at the consequences of those symmetries.

 

Yes. If you look at the various derivations, they start with the fundamental equation, which is a algebraic expression of those symmetries. I.e. the results of those derivations are very much constrained by those symmetry requirements.

 

Now how I understand it, the idea that the explanation must be based on a finite amount of information is that if we considered an infinite amount of information to base our explanation on it would follow that the past would be infinite which we could never accomplish gathering. However, there may be an infinite number of elements in an explanation as there is no such constraint on presumed elements.

 

Exactly. An explanation cannot be a product of an infinite amount of information. But nothing's stopping an explanation to suppose the existence of a various infinities.

 

-Anssi

[Doctordick]

Bombadil, I think you are looking at this thing from the wrong direction.

But if we can tell that some elements in our explanation are invalid then we know that there are possible explanations that won’t require these elements.

Yes and no! Yes, in that the “what is” is “what is” explanation fits any circumstance. Not a very useful explanation, but one that is guaranteed to fit in absolutely any circumstance. Unless you find another explanation, there is no way to guarantee one exists! My equation defines what expectations are consistent with the knowledge your explanation is built upon, not what will actually happen.

 

You seem to keep thinking that my work provides some way of finding explanations. That it does not do. All it does is put certain very specific constraints on that explanation but those constraints in no way violate the “what is” is “what is” explanation. Essentially, my fundamental equation makes utterly no constraints on what is possible and, as such, there are still an infinite number of explanations which fit the given data perfectly. It is worthless when viewed as a method of explaining things; its value resides entirely in the ability to outlaw specific explanations. If an explanation violates that equation, it is wrong.

The problem is that I can’t understand why it is that physicists arrived at the definitions that lead to the equations that you derive from the fundamental equation.

Because those definitions worked; they provided an easy way to bring a lifetime of experience to bear on a single problem! Life has been working on understanding its environment for millions upon millions of years; if the expectations of living things were wrong, they often died because of the error. That's a very powerful sorting mechanism. And even then it took a long time for a living organisms to come up with mathematics and logical decision making. You apparently want to know how such a thing can be accomplished in your lifetime. I suspect it can not.

 

That is not what I am doing. What I am doing is showing that explanations are no more than a convenient mechanism for predicting things based upon the similarity to something we have already seen -- a data compression mechanism. Very analogous to the Dewey decimal system for cataloging books.

 

I prove that my fundamental equation is mathematically true. But that has utterly nothing to do with reality. It has only to do with rationally estimating our expectations based upon the data available to us. So far as I can tell (as demonstrated in my various posts), if one restricts the circumstances to the events scientists define together with the presumptions they make, then their mathematical relationships turn out to be solutions to my equation. Thus the conclusion is that their relationships also have “utterly nothing to do with reality”: i.e., they are true by definition. Just as are the religious arguments used to explain life.

 

Physics is just a very complex data compression mechanism. That doesn't mean it isn't a useful thing! It very much helps us decide what to expect. By the way, religious arguments provide exactly the same benefit; the beliefs that society holds are a consequence of that societies survival and they thus become a mechanism to give us guidance on behavior presumed to yield success at survival.

 

Have fun -- Dick

[Bombadil]

You seem to keep thinking that my work provides some way of finding explanations. That it does not do. All it does is put certain very specific constraints on that explanation but those constraints in no way violate the “what is” is “what is” explanation. Essentially, my fundamental equation makes utterly no constraints on what is possible and, as such, there are still an infinite number of explanations which fit the given data perfectly. It is worthless when viewed as a method of explaining things; its value resides entirely in the ability to outlaw specific explanations. If an explanation violates that equation, it is wrong.

 

I really can’t see how we can conclude that an explanation from this perspective is wrong. Because if you are going to say that something is explained by an arbitrary set of equations, that is, we are saying nothing about what is being explained only that a particular set of equations is going to produce our expectations of it. Then there must exist a solution to the fundamental equation that can be interpreted in such a way that it gives the same expectations. If this is not true isn’t our only alternative that whatever is being explained cannot be described in the notation that you have derived. The point being that there is no way to say that an explanation is wrong, we can only say that an explanation is an interpretation of a solution to the fundamental equation and not an actual solution.

 

That is not what I am doing. What I am doing is showing that explanations are no more than a convenient mechanism for predicting things based upon the similarity to something we have already seen -- a data compression mechanism. Very analogous to the Dewey decimal system for cataloging books.

 

So, is the issue here that we have no way to know how much the present looks like the past. That is, the idea that the present looks like the past tells us that we can expect the same thing now as what happened in the past, but we have no way to tell what the differences between the past and the present might result in in the future. Or is this what the definitions that have been applied to the fundamental equation do? That is, they tell us how much the future will resemble the past.

[Doctordick]

If this is not true isn’t our only alternative that whatever is being explained cannot be described in the notation that you have derived.

That is exactly why I take such care to assure that absolutely any explanation of anything can be described in my notation. If you can come up with a construct which cannot be described by that notation then, by all means, point it out to me; however, I do not believe you can do so. At least, if you can, I know you cannot communicate your construct to me via the Internet. Furthermore, regarding the notation only (and having nothing to do with my proof), there is significant evidence that I am not alone.

 

IDMclean has been trying to get me to examine others work with the essential point, “I send you the articles I do because I want to make sure you're not re-inventing the wheel unnecessarily and to accelerate your work.” I disagree with him because he has not taken the trouble to carefully examine my proof, not because aspects of my work have not been done by others. My point being that no one has carried it to the deduction of my fundamental equation. I am confidently of the opinion that, if a reputable scientist had done so, the entire scientific community would certainly be aware of it as it applies to any logical construct.

 

For example, once upon a time, I was employed as an economist and, seeing me working on some of my derivations, another economist asked me what it had to do with economics. So I worked up a deduction of the general accepted laws of economics based upon my equation and gave it to him. It reproduced all the laws I was aware of with a few subtle corrections. He neither understood it nor believed it. I wish I had kept a copy as that was a long time ago and I only have a vague memory of the derivation. As I said before, one needs to know exactly what things are to be ignored (i.e., thought of as inconsequential in the theory being put forward) in order to make the appropriate approximations and I am no longer as competent in economics as I once was.

Except that what you term the "past" would be the symbols known in a sequence so far. His probability, what he calls "entropy", refers to the ability to predict the next symbol based on past symbols. In this manner, I believe you're working on the generalization of this problem.

 

Of interest and note for you, Shannon's information theory is related to statistical thermodynamics. It seems to me that while your methods and object of research may differ in the details, they seem to be similarly aimed at the same objective: a description of an explanation.

 

[math]\cdots[/math]

 

You're most assuredly not alone in your endeavors, and you're not the only or first person to struggle with this problem. Your statement about "No one else is..." should be qualified in my opinion "No one else in the physics, math, or philosophy world..." I assure you in the artificial intelligence, natural language processing, semiotic, simulation, automated theory generation and proof, modeling, and associated worlds, your problem is being worked on.

What Mclean seems to miss is that I am not working on anything and I have no “object of research”; except trying to communicate what I discovered forty years ago.

That is, they tell us how much the future will resemble the past.

Not exactly, what the equation tells you is that, if your representation is totally consistent with your past and your explanation produces expectation for every specific t consistent with those known facts (when given only the information prior to that specific t), then there is a [imath]\vec{\Psi}[/imath] solution to my equation which will provide exactly those same expectations. If that is a fact, tell me why you would not expect that solution to yield exactly the same expectations for the future as your explanation does?

 

As I said before, in “Laying out ...”

It is then clear, at this point, that the problem of finding [imath]\vec{\Psi}[/imath] is one of interpolation. We need to find a function which fits the known circumstances (known for specific t indices) and use that function to express the hypothetical probabilities for all circumstances outside those known circumstances. The problem confronting us becomes quite obvious here: any mathematician knows that there exists an infinite set of solutions even for the simplest of such problems. Since every such solution is a flaw free explanation of the known circumstances, a blind search for a solution from the given perspective is clearly a complete waste of time.

In fact, the simplest explanation of all is the ”what is” is “what is” explanation. It just isn't a very valuable explanation. (There is actually a long story showing that it is in fact one of the possible solutions to my equation; just not a very good one.)

 

Have fun -- Dick

[Bombadil]

There is one point that IDMclean makes that I wonder about in particular

 

You're most assuredly not alone in your endeavors, and you're not the only or first person to struggle with this problem. Your statement about "No one else is..." should be qualified in my opinion "No one else in the physics, math, or philosophy world..." I assure you in the artificial intelligence, natural language processing, semiotic, simulation, automated theory generation and proof, modeling, and associated worlds, your problem is being worked on.

 

Not because that I think any one has got any where near what you have found but rather that I wonder if physicists are the right group to focus attention on as, so far, most of what you have shown they think they already know and so will try to correct or understand the same way they understand physics. So perhaps other groups would be more prone to understanding it, on the other hand perhaps this is a consequence of finding people that have the mathematical ability to follow your derivation, or perhaps everyone with the ability has already had so much experience with physics that they don’t see anything new.

 

Anyway, just wondering if you have ever tried to communicate your ideas to someone that was well outside of the study of physics but not quite in the study of pure mathematics.

 

That is exactly why I take such care to assure that absolutely any explanation of anything can be described in my notation. If you can come up with a construct which cannot be described by that notation then, by all means, point it out to me; however, I do not believe you can do so. At least, if you can, I know you cannot communicate your construct to me via the Internet. Furthermore, regarding the notation only (and having nothing to do with my proof), there is significant evidence that I am not alone.

 

I assume that you are referring to the notation that you explain in the thread “Laying out the representation to be solved.”

 

Not exactly, what the equation tells you is that, if your representation is totally consistent with your past and your explanation produces expectation for every specific t consistent with those known facts (when given only the information prior to that specific t), then there is a [imath]\vec{\Psi}[/imath] solution to my equation which will provide exactly those same expectations. If that is a fact, tell me why you would not expect that solution to yield exactly the same expectations for the future as your explanation does?

 

You have defined the solution so that it gives the same expectations for the past as what our expectations must give to be consistent with the past so the only issue that I see is the question of if the expectations for information that we don’t yet know is the same. That is do we expect the same future as the solution. The problem that I see is that as soon as something becomes part of the past there exists a solution that gives that as an expectation so is there really any difference between saying that our solution must be consistent with our expectations and saying that the solution must only be consistent with our past, if we are asking if they give the same expectations. So I would answer yes and no, there is a solution that will be totally consistent with the past that will give the same expectations as our expectations, but I see no reason for this to be the only possible expectations for the future that a consistent solution can give.

 

It is then clear, at this point, that the problem of finding [imath]\vec{\Psi}[/imath] is one of interpolation. We need to find a function which fits the known circumstances (known for specific t indices) and use that function to express the hypothetical probabilities for all circumstances outside those known circumstances. The problem confronting us becomes quite obvious here: any mathematician knows that there exists an infinite set of solutions even for the simplest of such problems. Since every such solution is a flaw free explanation of the known circumstances, a blind search for a solution from the given perspective is clearly a complete waste of time.

 

That is, there is an infinite number of equations that can be made to give the same expectations for the past but the problem is that they may also be made to give any expectations for the future. One of the issues is that if [imath] \vec{\Psi}[/imath] can truly be used for any past then the expectations for the future is nothing more then an expansion of the past to include some particular expectation that has not yet been experienced.

 

In fact, the simplest explanation of all is the ”what is” is “what is” explanation. It just isn't a very valuable explanation. (There is actually a long story showing that it is in fact one of the possible solutions to my equation; just not a very good one.)

 

How I understand the ”what is” is “what is” explanation is, it is merely the act of making a list of the past in such a way that it may be compared to the present. If this is the case I really can’t see how we can make such a function sufficiently continue to satisfy the fundamental equation except for in a limiting case of a solution of the fundamental equation. It would of course need to satisfy all of the constraints used to derive the fundamental equation but I don’t see how it would satisfy the fundamental equation.

[Doctordick]

Hi Bombadil, I was perusing the forum this morning and discovered that I had somehow missed the above post from back in June. That probably has something to do with us visiting our granddaughter for her birthday in Denver. At any rate, I apologize.

 

There is one point that IDMclean makes that I wonder about in particular

 

You're most assuredly not alone in your endeavors, and you're not the only or first person to struggle with this problem. Your statement about "No one else is..." should be qualified in my opinion "No one else in the physics, math, or philosophy world..." I assure you in the artificial intelligence, natural language processing, semiotic, simulation, automated theory generation and proof, modeling, and associated worlds, your problem is being worked on.

Not because that I think any one has got any where near what you have found but rather that I wonder if physicists are the right group to focus attention on as, so far, most of what you have shown they think they already know and so will try to correct or understand the same way they understand physics.

There are actually two reasons why I focus on physics. First is the fact that I have been trained in physics and am considerably more versed in the subject than I am in any other subject (I do have a Ph.D. in physics). The second is that my fundamental equation applies only to totally internally consistent explanations and physics is a rare field in that it is very close to being internally consistent. (The only consistency error I have run into is the inconsistency between QM and GR.) Most other fields are quite full of inconsistencies and actually finding the proper definitions and assumptions to be used to obtain results which have been examined is quite difficult.

 

Almost thirty years ago I was asked by an economist, who saw me messing around with my equation, “what does that have to do with economics?” (I was taking a course in economics at the time.) So I worked up a set of solutions which identified certain solutions with some of the commonly accepted economic assertions and gave it to him. That was back when I was still young and bright (in my late forties). I wish now that I had kept a copy of that presentation as I find it difficult to reproduce now.

 

I assume that you are referring to the notation that you explain in the thread “Laying out the representation to be solved.”

Yes, you are right on the mark with that.

 

You have defined the solution so that it gives the same expectations for the past as what our expectations must give to be consistent with the past so the only issue that I see is the question of if the expectations for information that we don’t yet know is the same.

I suspect there is a subtle error in your interpretation of what I am saying. I defined the past as “what we know” thus, with regard to the past, we don't really have “expectations”; we have “what we know” and/or, “what we think we know”. Now an explanation or [math]\vec{\Psi}[/math] is to provide us with “expectations” for circumstances which we don't know. The issue that our past (what we know) provides the boundary conditions for that function. That the function provides the correct probabilities is only resolved when we determine if what we know is consistent with what that function would have yielded when designed to fit the boundary conditions which existed prior to knowing the circumstances constituteing the argument of [math]\vec{\Psi}[/math]: i.e., are the probabilities produced via the given proposed [math]\vec{\Psi}(t)[/math] consistent with what was actually observed at time t. Once we know what was observed, we have to set new boundary conditions and, likewise, a new [math]\vec{\Psi}[/math].

 

That is do we expect the same future as the solution. The problem that I see is that as soon as something becomes part of the past there exists a solution that gives that as an expectation so is there really any difference between saying that our solution must be consistent with our expectations and saying that the solution must only be consistent with our past, if we are asking if they give the same expectations.

Yes, there is indeed difference between the probabilities produced by [math]\vec{\Psi}[/math] and the probability distribution which constitutes the past. For example, a coin toss sequence (a specific past) yielding a hundred heads in a row is perfectly consistent with the explanation that the outcome of the coin toss is fifty-fifty; it is the sequence which has a low (but not zero) probability not the individual tosses. If you examine my opening post in “Laying out the representation to be solved”, you should understand that [math]\vec{\Psi}[/math] is representing a specific explanation, not an actual past.

 

So I would answer yes and no, there is a solution that will be totally consistent with the past that will give the same expectations as our expectations, but I see no reason for this to be the only possible expectations for the future that a consistent solution can give.

As I said in that post, it is quite obvious that, if the data upon which the explanation is finite and the possibilities for the future are infinite, there are an infinite number of explanations which are totally consistent with the past.

 

That is, there is an infinite number of equations that can be made to give the same expectations for the past but the problem is that they may also be made to give any expectations for the future. One of the issues is that if [math] \vec{\Psi}[/math] can truly be used for any past then the expectations for the future is nothing more then an expansion of the past to include some particular expectation that has not yet been experienced.

Change that “give the same expectations for the past” to “give expectations consistent with the past” and I would agree with you. There may be an infinite number of explanations, each corresponding to a specific but different [math]\vec{\Psi}[/math]; however, for any given explanation there is but one specific [math]\vec{\Psi}[/math] consistent with the associated boundary conditions for the specific "t" of interest.

 

How I understand the ”what is” is “what is” explanation is, it is merely the act of making a list of the past in such a way that it may be compared to the present. If this is the case I really can’t see how we can make such a function sufficiently continue to satisfy the fundamental equation except for in a limiting case of a solution of the fundamental equation. It would of course need to satisfy all of the constraints used to derive the fundamental equation but I don’t see how it would satisfy the fundamental equation.

 

It is just making a list of the past; “period”. In order to understand how to actually fabricate the [math]\vec{\Psi}[/math] corresponding to the “what is” is “what is” explanation, you need to implement the mathematical representation of “the rules” which I will lay out in a future post once I am convinced that the people who have interest in this this thing have essentially understood what I was trying to say it that “conservation of ignorance” post.

 

The issue is, exactly what are your expectations regarding the ”what is” is “what is” explanation. The answer to that question should be relatively obvious to you. If you actually feel the “what is” is “what is” explanation is consistent with your expectations (that is, if you are actually working with that explanation), then any circumstance in the future is just as probable as any other. That result would be, the probability of any specific circumstance would be the same as any other. [math]\vec{\Psi}(x_1,x_2,\cdots,x_n)=\; a\;constant\;=0[/math]. In order to present the fundamental equation representing that situation one need the related representation of the rules for that outcome.

 

Once we have a mathematical way of representing the rules inherent in a specific explanation we will have deduced the fundamental equation I have presented and specified exactly what the terms mean. That last step is essential to understanding the equation.

 

Finally, the “what is” is “what is” explanation is absolutely consistent with the past because any specific present (as seen from the past at that time t) is totally consistent with “it could be anything”: i.e., it is certainly a flaw-free explanation.

 

Again, I apologize for not answering this post three months ago.

 

Have fun -- Dick