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# "a Universal Representation Of Rules"

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Regardless of what some universe is like, your explanation about it (i.e. "what it looks like to you") is entirely dependent on an ability to represent valid expectations. That is, regardless of the actual structure of reality, all that your worldview can recognize - and ultimately label as some defined elements with some sort of expected behaviour - is something that can be in some sense recognized from some "information" as recurring "patterns" of some sort (with some valid probabilities).

The problem that I have with this is that what we call recurring patterns is part of the world view that we hold. If we where to hold a different world view we should expect to have different recurring patterns and if we where to view it with different recurring patterns we would expect to have a different world view.

The recurring patterns that we see seem to me to be just the definitions that we have placed on our perceptions. What is more, our world view is dependent on how we have come to expect our definitions to behave which is of course dependent on how we defined them in the first place. So that in a sense we are defining our would view by defining the recurring patters that we have in our world view.

The point being that the recurring patterns that you are talking about might be nothing more then the consequences of the expectations we have, and I see no reason to believe that all interpretations of our expectations need use such recurring patterns. Of course perhaps such a world view would be near useless since communication in such a world view would require that the whole of the context be used in any communication. Since what are words except recurring patterns that we have defined.

Perhaps I am getting overly concerned with the question of what happens when we no longer assume that the context has no effect on the recurring patterns that we use. But just look at Language, can you really give any one word a meaning on its own? How many words does it take to produce a context that is useful even with all of the things that you assume you know when using them?

Their validity requires that noumenaic reality is interpreted via using the necessary approximations. I would say that, for instance, defining elements in ways that they have a minimal feedback to the rest of the universe, is very crucial step. Without it, things could look very different. But such a solution would also be incredibly impractical.

This I think depends on what you mean by impractical, such a view might be different but if such a view is needed to understand some consequences of consistency then to ignore such a thing would be like ignoring the inconsistencies in physics. We can do it but doing so might be more like wishful thinking then actually expecting something to be useful.

Of course not! The possibility exists that modern physics could be wrong. And, in fact, I have pointed out a number of issues within modern physics are clearly wrong. Their definition of time, the idea that there exist five different forces unrelated to one another and the idea that the “Higgs” particle is necessary to have “mass”. In particular, the conflict between quantum mechanics and Einstein's GR is a clear instance of error.

The correctness or incorrectness of modern physics is not what I was referring to, of course this is a place of concern as if modern physics is not consistent then clearly there is little point in considering it as even an approximation as the results of doing so must also be inconsistent which must make the result inconsistent, but rather the question that I am asking is if there are other approximations that are not compatible with modern physics. That is do there exist situations that simply make no sense to talk about in physics but that we must include to have a full description of the behaver of all possible explanations.

And by wrong you do mean inconsistent in the way that they are used?

Just out of curiosity though what five forces are you referring to? I thought that physics considered there to be four, so I have to wonder was this just a mistype or are you counting them differently then most physicists?

No language uses elements for which the users have no use.

Perhaps but I tend to think that some elements become obsolete and are no longer used and are mostly forgotten or their meaning is changed, they are still part of the Laguange they are just not used and their meaning is no longer needed (in a sense they are useless), so they are likely to be forgotten or replaced with something new.

Kind of like linear A

But the question still seems to me to be if elements can exist that behave in any possible way not if such elements are needed since if they are not it seems that physics must be making an assumption that makes it no longer completely general (I am talking about consistency not usefulness). Unless we are discussing the correctness of physics to predict our observations now?

Well, any solution to the fundamental equation must essentially obey quantum mechanics as the relationships required by quantum mechanics are quite similar to those required by my equation. Oh, approximations must be made; but of what character are those approximations? They all amount to presuming that some portion of the context can be ignored and recognizing exactly what is being ignored. If we can't ignore any part of the context, we have to solve the whole problem in one fell swoop. And that simply will never be accomplished as it requires you to be all knowing. And, by the way, that explanation is well known: it is the “what is” is “what is” explanation.

I have a rather mixed view on this, on the one hand the point that I think you are trying to make is quite valid, there is no known way to solve the problem in one fell swoop and so any such solutions are not going to be found any time soon and it is quite likely that such solutions are not going to be of much use to us even if we had them due to their apparent complexity and need for context.

Actually though it seems that you may have suggested one such solution already in your simple geometric proof

On the the other hand it seems that just because we can't see how such a thing can be done or what possible use it would be if we could do it, seems like no reason not to ask the question of if we are ignoring things that can't be approximated if we don't include such things which is what I am really asking.

Yeah, a million years of “by guess and by golly” have managed to achieve usable results without every considering the logical consequences of their definitions. I'm impressed.

Acutely I was thinking that the same result has been obtained “by guess and by golly” of mathematicians and physicists as can be obtained by logical analysis. Or maybe this shouldn't be at all impressive, but rather it just shows that all of the behaviors of people and the way that we understand things really is nothing more then the representation of an other solution to the fundamental equation and so any thing that we try to use to represent something is just an other approximation to the fundamental equation.

In which case maybe we should really be asking questions about the implications of all of this to artificial intelligence as any possible intelligence must also be following the same rules for how it behaves.

In fact, you can not prove that your neighbor's concept of the universe bears any resemblance to yours. In learning his language, you have come up with a way identifying what he means by his words, gestures and signs (your context as you see it) in terms of your personal concept of the universe. Does the fact that the information you have received can be so interpreted prove that the underlying experiences are what you think they are? That they are is a presumption (perhaps a useful presumption but that doesn't mean you can prove it is true).

But what about the question of if we can both interpret the others expectations to be consistent with our world view? There is no doubt that we will both see a different context. This is just an obvious fact but what do we do with the context? Even if we had the same context why would we expect to be able to come to the same conclusions?

Of course there is still the other side of the coin too, there sure as well better be a mapping from my view of the universe and my language to his, if there is not then we are going to have an awful hard time trying to communicate with each other even if it is only our interpretation of communication.

It isn't “any possible solution” that we are interested in. We are interested in a solution which yields our personal experiences as having a non-zero probability.

This statement seems to pretty well sum up much of what you are saying, and that is that the interest is in solutions that can yield our expectations, and here I thought that what we were interested in was the consequences of internal consistency to how expectations must behave.

I have to wonder are you talking about physics now?

Try proving to me that your concept of the universe looks anything like mine while still allowing all possible meanings to the words, gestures and signs we use in communicating.

I can see at least part of your point here, if we are truly allowing any possible meaning of whatever means that we are trying to use to communicate then you might as well use linear A and I might as well use binary. Both are clearly a language capable of representing something and indeed anything if we just allow any possible meaning for the symbols used.

This really becomes a problem if we ask the question of if we can communicate, but first we need to decide what we mean by communicating, I would think that we are communicating if we agree that the information supplied by someone is consistent with the context that we place it in.

But the question still exist of if it is possible for us to communicate and what is needed for it to be possible.

If he removed the need for summation, why in the devil did he need the convention “of summation over upper and lower script”. The summations are still there just in a much shorter notation.

So where is the difficulty in representing the fundamental equation in such a notation?

With several equations, you need to find all possible solutions to all the equations and then find the solution set which solves both. That is a far more difficult task than solving one equation. Essentially I showed that a transformation existed which inevitably solved both equations (so long as one is operating in what is essentially a center of momentum frame of reference). The problem you propose to solve is more easily solved by solving my equation first and then transforming the solution to a frame of reference where the total momentum does not vanish. But what purpose do you propose for being able to generate that particular solution? It is no more than a restatement of the "center of momentum" solution.

But don't your alpha and beta operators have to form some kind of base for every possible solution to the fundamental equation? That is, in a sense you are forming some kind of space that you must use as a base for any possible solutions to the fundamental equation. That is, any solution to the fundamental equation is going to have alpha and beta operators as terms in it.

I don't have a problem with this in its self, the problem is that I don't know what kind of space you are forming with the alpha and beta operators, and so I don't know if it is forming a bases for all of the solutions to the original equations? And I don't understand how we can know that such terms would be in all of the solutions to the original equations.

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He has never actually proven this. In the OP, at best he shows that a solution [imath]\vec{\Psi}[/imath] to his FE complies with his initial constraints, but what he claims is the other way around:So,

What I have claimed is that, under my definition of an explanation, the representation I propose for what is being explained makes no presumptions as to what the explanation might be and furthermore m

Thanks Bombadil, I got your note.   At this point the answer to that question is a definite “no”. There is no such thing as “points of interest”. You are apparently missing the central issue of the

[...]

Just out of curiosity though what five forces are you referring to? I thought that physics considered there to be four, so I have to wonder was this just a mistype or are you counting them differently then most physicists?

[...]

In in addition to the four known fundamental forces, a fifth force has been postulated. Theories of gravity such as Brans-Dicke theory have a fifth force—possibly with infinite range, which would manifest itself in an effect called the Nordtvedt effect. Lunar Laser Ranging Experiments and long baseline interferometry have been used to search for the effect, i.e., the existence of the fifth force is testable.(Ephraim Fischbach, Daniel Sudarsky, Aaron Szafer, Carrick Talmadge, and S. H. Aronson, "Reanalysis of the Eötvös experiment", Physical Review Letters 56 3, 1986)

Another postulation of a fifth force arises in Kaluza-Klein theory, where the universe has extra dimensions, or in supergravity or string theory, called the Yukawa force. This is testable by experiments which search for a deviation from the inverse square law of gravity.

Quintessence is a hypothetical form of dark energy postulated as an explanation of observations of an accelerating universe. It has been proposed by some physicists to be a fifth fundamental force of nature.

See too Beyond the Standard Model.

CC

Edited by coldcreation
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The five forces I was referring to are: gravitational forces, electro-magnetic forces, nuclear strong forces, the nuclear weak force and the force attributable to Pauli exclusion. Most people tend to forget about Pauli exclusion when they speak of forces; but the physical consequences of Pauli exclusion can, in many circumstances, be seen as a pressure which implies a force. Consider a neutron star resisting collapse due to gravity.

I can see at least part of your point here, if we are truly allowing any possible meaning of whatever means that we are trying to use to communicate then you might as well use linear A and I might as well use binary. Both are clearly a language capable of representing something and indeed anything if we just allow any possible meaning for the symbols used.

The issue is somewhat deeper than implied by your comment.

You should try to understand my thread “Perhaps Something Easier To Understand”. The issue there is that there are four concepts essential to solving the problem of creating a “world view”. Those four concepts are somewhat exemplified via the English words “understanding”, “explanation”, “information” and “language”. It should be quite clear to you that “language” is absolutely central to even thinking about the other three. Thus it is that “language” is part of the solution and not part of the given information. (I will use quotes to indicate that I am referring only to the specific concepts I am discussing and not necessarily the ideas people commonly attribute to those four words as I have no interest in getting into additional concepts some people want to include .)

If you have found a solution, that solution includes the “language” necessary for you to think about the elements of interest to your solution. “Information” is what lies behind your explanation: i.e., what it is that you are “explaining” and “understanding” is exemplified by the ability to answer questions as to your explanations.

As you have commented, the only thing required of a language is that it be capable of representing the required information thus a representation via numerical labels is as useful as any other representation and I propose using $(x_1,x_2,\cdots,x_n)$. Since any question can be represented by a finite number of true/false questions, $P(x_1,x_2,\cdots,x_n)$ can be used to represent any “understanding”. The explanation provides the means by which those answers are to be determined.

A very simple thought experiment should be considered. If two different people who speak exactly the same language have discovered exactly the same “explanation” of exactly the same “information”, it follows that they have come upon exactly the same “understanding” of that information (that is, their “explanations” will yield exactly the same answers to all possible questions) and thus have discovered exactly the same collection of probabilities represented by $P(x_1,x_2,\cdots,x_n)$. What is important in this thought experiment is the fact that we have made no constraints whatsoever on the actual numerical labels used to represent the indicated “information”.

The above implies that we are free to use a different collection of numerical labels to represent that “information” being explained by the two individuals. That fact implies some curious constraints on the probability function as represented. So long as xi used to label a “language” element used by individual #1 corresponds to the same element referred to by the numerical label xi+q used by individual #2, the function “P” must yield an identical result. It follows that

$P(x_1+a,x_2+a,\cdots,x_n+a) \equiv P(x_1+b,x_2+b,\cdots,x_n{+b})$

as all a and b do is relabel the elements without changing the possible internal relationships in any way. Thus, if we define b=a+Δa, we can assert the following relationship to be absolutely required:

$\frac{P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a+\Delta a)-P(x_1+a,x_2+a,\cdots,x_n+a) }{\Delta a} \equiv 0.$

Note that the value of Δa is of utterly no consequence: the equation is valid for absolutely all “non zero values of Δa. That fact requires the that if one defines $z_i=x_i +a$, the following relationship must be true by the very definition of a derivative.

$\frac{d}{da}P(z_1,z_2,\cdots,z_n)\equiv 0$

since the definition of that very derivative is given by

$\lim_{\Delta a \to 0 }\frac{P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a+\Delta a)-P(x_1+a,x_2+a,\cdots,x_n+a) }{\Delta a} \equiv 0.$

Note that we must speak of the limit and not the actual value of Δa in the limit as division by zero is undefined. (The derivative is defined by the way the division approaches Δa=0 and not by the actual division in the limit.)

It is a trivial understanding of partial differentiation which leads to the conclusion that

$\sum_{i=1}^n \frac{\partial}{\partial z_i}P(z_1,z_2,\cdots,z_n) = 0$

is an absolutely required constraint on $P(x_1,x_2,\cdots,x_n)$. Note that z and x are no more than different names for the relevant numerical labels; it follows that

$\sum_{i=1}^n \frac{\partial}{\partial x_i}P(x_1,x_2,\cdots,x_n) = 0$

That is, any solution to the fundamental equation is going to have alpha and beta operators as terms in it.

No, alpha and beta operators fix certain required relationships internal to the solutions; they are not terms in the solutions. As such what is commonly referred to as spin phenomena can be seen as required context to certain possible approximations.

Actually though it seems that you may have suggested one such solution already in your simple geometric proof

If you understood mathematics, you would comprehend that the “simple geometric proof” is not actually a solutions but is rather nothing more than a recasting of the fundamental equation. In the notation of the Fundamental Equation, the universe is represented by a collection of points in a low dimensional Euclidean space. In the proof you refer to, it is simply recast in a collection of angular momentum states in an n dimensional space. The information required to specify exactly what the information being represented is the same.

Or maybe this shouldn't be at all impressive, but rather it just shows that all of the behaviors of people and the way that we understand things really is nothing more then the representation of an other solution to the fundamental equation and so any thing that we try to use to represent something is just an other approximation to the fundamental equation.

In which case maybe we should really be asking questions about the implications of all of this to artificial intelligence as any possible intelligence must also be following the same rules for how it behaves.

I agree 100%! I would love to talk about the implications of all this to someone competent in AI and the associated programming.

So where is the difficulty in representing the fundamental equation in such a notation?

His notation involves mathematical structures far more complex than any used in my representation. A particular complexity involves using a non Euclidean geometry. Most physicists fail to point out the fact that displaying information in a non Euclidean geometry requires presuming some internal relationship between the variables. If one is to make no assumptions as to internal relationships between variables, one must use a Euclidean geometry. In order to represent Einstein's GR theory in a Euclidean geometry, one needs to add additional dimensions (geometries within which his coordinates can curve). If you want to endure that complexity, you might as well work in his system. In my opinion it is a waste of time as his attack has serious problems which mine does not.

I don't have a problem with this in its self, the problem is that I don't know what kind of space you are forming with the alpha and beta operators, and so I don't know if it is forming a bases for all of the solutions to the original equations? And

Originally, in including all possibilities, I introduced the abstract space for $\Psi$. I pointed out that such an abstract real space can be recast as an abstract space of half the dimensions where the coordinates become complex. The alpha and beta operators introduce correlations within that original real space.

I don't understand how we can know that such terms would be in all of the solutions to the original equations.

We don't! There are clearly solutions which do not require “spinners”. What is more interesting here is that physicists, in analyzing the universe have found that quantum spin effects exist. Since my deduction is no more than the result of including “all possibilities”, it would be much more meaningful if solutions to my equation were found which had no representation in reality. That would be an experiment which would differentiate between “the universe we find ourselves in” and “all possible universes”. Barring such a discovery, all we know about the universe is that what we have observed (the context of our experiences) is fact: i.e., “what is” is “what is”.

Have fun -- Dick

Edited by Doctordick
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The problem that I have with this is that what we call recurring patterns is part of the world view that we hold. If we where to hold a different world view we should expect to have different recurring patterns and if we where to view it with different recurring patterns we would expect to have a different world view.

The recurring patterns that we see seem to me to be just the definitions that we have placed on our perceptions. What is more, our world view is dependent on how we have come to expect our definitions to behave which is of course dependent on how we defined them in the first place. So that in a sense we are defining our would view by defining the recurring patters that we have in our world view.

The point being that the recurring patterns that you are talking about might be nothing more then the consequences of the expectations we have, and I see no reason to believe that all interpretations of our expectations need use such recurring patterns.

I think you are thinking of this issue absolutely correctly. The patterns we consciouscly perceive are the results of some interpretation of something. What I was referring to was not something we are conscious of, it was just a reference to something underlying our world view. But before I clarify;

Of course perhaps such a world view would be near useless since communication in such a world view would require that the whole of the context be used in any communication. Since what are words except recurring patterns that we have defined.

Such a world view is exactly what all our world views are. It's not useless as long as they provide useful expectations. A communication between two human beings can be seen as two world views modeling each others, and the more equivalently they can model each each others (they don't have to be the same, they just have to be logically equivalent to appear the same to each others), the better they can communicate.

It's exactly the same issue as a world view modeling anything else out there; its ontological correctedness is not a measurable factor at all, thus the "chosen language" for representing all that information is not an issue, only the validity of the expectations are measured.

I'm sure you can recognize the issues this kind of communication raises; it is exactly what we call miscommunication and misunderstandings. The activity we are engaging right now is just another case of exactly that; my reference to the idea of "recurring patterns" can be seen as a reference to patterns we can consciously think of - which I believe your interpretation was - or it can be seen as reference to some noumena that inductive expectations can be based on.

To understand better how I meant my comment, think about it this way. If there is something "out there" that our world view is based on, then it's safe to say it is possible to generate valid (/useful) expectations for that something (we did it). At the get-go; in the absence of knowledge for what that something is, all our expectations are based on some induction. I don't want to say "inductive reasoning" because I don't want to give the idea that this is something we consciously do. This should be viewed as some kind of completely mechanical process.

So, that's just another way to say that all our ideas and concepts in our world view, can be traced down to some inductive results if you go deep enough. Which is just another way of saying that all our ideas are fundamentall based on some kind of familiarity to something. While, it is also true there is no way to actually refer to what that something is, all we can refer to is some particular language representation of that something, which is already a result of some chosen interpretation form (or chosen mental language). That is the core problem that DD often refers to as "the problem".

Perhaps I am getting overly concerned with the question of what happens when we no longer assume that the context has no effect on the recurring patterns that we use. But just look at Language, can you really give any one word a meaning on its own? How many words does it take to produce a context that is useful even with all of the things that you assume you know when using them?

The fact that you can see parallels between this and natural human languages is encouraging, because language is exactly what we are talking about even when we talk about fundamental physics. It is a particular language to express some inductive expectations. What in physics are commonly referred to as properties or features of nature, are more accurately features of that chosen language. Especially tracing the quantum mysteries to such and such properties of language should be an interesting topic for any physicist to think about.

This I think depends on what you mean by impractical, such a view might be different but if such a view is needed to understand some consequences of consistency then to ignore such a thing would be like ignoring the inconsistencies in physics. We can do it but doing so might be more like wishful thinking then actually expecting something to be useful.

I think much along the same lines, but also think about the consequences of our limitations related to analytical solutions to many-body problems, and the advantages of choosing to use as general solutions as possible. At the same time, if you look at this from the epistemological fundamentals' point of view, it's easy to see some parallels between fundamental particle physics, and something like weather forecasting.

-Anssi

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...So, that's just another way to say that all our ideas and concepts in our world view, can be traced down to some inductive results if you go deep enough. Which is just another way of saying that all our ideas are fundamentall based on some kind of familiarity to something. While, it is also true there is no way to actually refer to what that something is, all we can refer to is some particular language representation of that something, which is already a result of some chosen interpretation form (or chosen mental language). That is the core problem that DD often refers to as "the problem".

...

-Anssi

so given that dd's problem is a "something", this all amounts to mental masturbation in a massive bowl of word-salad. nicely done with the blue-cheese dressing fellas. :blahblahblah: anyone not impressed by this prodigious effort is indeed a numbskull. :hammer:

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so given that dd's problem is a "something", this all amounts to mental masturbation in a massive bowl of word-salad. nicely done with the blue-cheese dressing fellas. anyone not impressed by this prodigious effort is indeed a numbskull.

Actually, you are right on the money. What I have done is to deduce essentially all of modern physics without recourse to the first experiment. It turns out that "internal consistency" is the only constraint I have placed upon the deduction of my fundamental equation: i.e., it is valid for all possible "internally consistent" explanations of anything.

If you look at the "1.a." definition of “language” given by the “free dictionary by farlex” you will find the following: “Communication of thoughts and feelings through a system of arbitrary signals, such as voice sounds, gestures, or written symbols”.

All I am doing is showing that the freedom implied by that word "arbitrary" yields some very important symmetries ignored by everyone.

The fact that you feel it is an issue to be derided is a comment on your own mental inadequacies.

Have fun -- Dick

Edited by Doctordick
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...

The fact that you feel it is an issue to be derided is a comment on your own mental inadequacies.

Have fun -- Dick

and so the pot calls the kettle black.

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The five forces I was referring to are: gravitational forces, electro-magnetic forces, nuclear strong forces, the nuclear weak force and the force attributable to Pauli exclusion. Most people tend to forget about Pauli exclusion when they speak of forces; but the physical consequences of Pauli exclusion can, in many circumstances, be seen as a pressure which implies a force. Consider a neutron star resisting collapse due to gravity.
For anyone with interest, there is a nice discussion of whether or not the Pauli Exclusion Principle is a "force", or instead, a mathematical construct that is a priori to such concepts as force or pressure...see discussion here:

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• 3 months later...

You should try to understand my thread “Perhaps Something Easier To Understand”. The issue there is that there are four concepts essential to solving the problem of creating a “world view”. Those four concepts are somewhat exemplified via the English words “understanding”, “explanation”, “information” and “language”. It should be quite clear to you that “language” is absolutely central to even thinking about the other three. Thus it is that “language” is part of the solution and not part of the given information. (I will use quotes to indicate that I am referring only to the specific concepts I am discussing and not necessarily the ideas people commonly attribute to those four words as I have no interest in getting into additional concepts some people want to include .)

It seems that in that presentation you are not entirely clear as to what you mean by communication, at least you don't seem to give it a very definite definition and rather seem to assume that some one knows when communication is taking place. Actually it is hard to say just what definitions you are using as you don't seem to give any or how and where you do give them don't stand out vary well.

Actually if you don't mind some constructive criticism which I don't think you will, that whole presentation seems to be lacking in direction in the sense that if someone had no idea as to what it was about it would be very hard to tell what the point of it was, and even harder to understand what was accomplished.

A little closer to topic, Isn't the problem of creating a world view increased even further by the need of a way to represent the information. That is, in order for us to refer to something that we wish to explain we need a way to represent it. Such a thing will have to be a language, this results in the representation of the information also being part of the solution.

Further more it might be said that the world view that we have is just the language that we represent the information in that makes up our understanding of it. My point being, aren't the things that you are calling the “world view” “understanding” and our “explanation” all going to require a language to represent them in.

It seems that it is worth bringing up that it seems to me, while the language needed to represent the information must be part of the solution the actual representation of the language need not be part of the solution it need only be completely general in its ability to refer to something hence your use of $(x_1,x_2,\cdots,x_n)$.

As you have commented, the only thing required of a language is that it be capable of representing the required information thus a representation via numerical labels is as useful as any other representation and I propose using $(x_1,x_2,\cdots,x_n)$. Since any question can be represented by a finite number of true/false questions, $P(x_1,x_2,\cdots,x_n)$ can be used to represent any “understanding”. The explanation provides the means by which those answers are to be determined.

I see no problem with this, all that you have done is choose a representation for whatever language it is that will be used and that representation is $(x_1,x_2,\cdots,x_n)$, and a way to represent our expectations of the language in, that is $P(x_1,x_2,\cdots,x_n)$, and a language that will be used to represent the actual explanation with and that is mathematics.

No, alpha and beta operators fix certain required relationships internal to the solutions; they are not terms in the solutions. As such what is commonly referred to as spin phenomena can be seen as required context to certain possible approximations.

I am somewhat puzzled by your use of the word context here. Isn't context the other elements that must be included in the explanation for the use of some definition to make sense. If this is the case in what way are the alpha and beta operators forming part of the context, aren't they rather constraints on the mapping from the space that the information is defined in i.e. $(x_1,x_2,\cdots,x_n)$to that of the expectations $P(x_1,x_2,\cdots,x_n)$.

Originally, in including all possibilities, I introduced the abstract space for $\Psi$. I pointed out that such an abstract real space can be recast as an abstract space of half the dimensions where the coordinates become complex. The alpha and beta operators introduce correlations within that original real space.

This is somewhat puzzling you are trying to lay out the presentation so that nothing is assumed about the possible expectations so what “correlations within that original real space” are you talking about? And if they are there to fill in some gap that was left when we went from a real space to a complex space why wasn't the topic brought up at that time?

We don't! There are clearly solutions which do not require “spinners”. What is more interesting here is that physicists, in analyzing the universe have found that quantum spin effects exist. Since my deduction is no more than the result of including “all possibilities”, it would be much more meaningful if solutions to my equation were found which had no representation in reality. That would be an experiment which would differentiate between “the universe we find ourselves in” and “all possible universes”. Barring such a discovery, all we know about the universe is that what we have observed (the context of our experiences) is fact: i.e., “what is” is “what is”.

But isn't any solution derived forum the fundamental equation going to include spinners by the very nature of how the equation is defined? Although this says nothing about if such solutions would differ in any way from ones that might not use spinners if such exist.

Such a world view is exactly what all our world views are. It's not useless as long as they provide useful expectations. A communication between two human beings can be seen as two world views modeling each others, and the more equivalently they can model each each others (they don't have to be the same, they just have to be logically equivalent to appear the same to each others), the better they can communicate.

Might not this idea be a basis for AI, that is intelligence might be seen as something that models its soundings and itself. It seems to me that this might even be thought of as a definition of sorts for intelligence on some level. Or if not the foundation at least a starting point worth considering.

How ever you bring up another point that I think is an interesting question and that is when are two world views logically equivalent?

I'm sure you can recognize the issues this kind of communication raises; it is exactly what we call miscommunication and misunderstandings. The activity we are engaging right now is just another case of exactly that; my reference to the idea of "recurring patterns" can be seen as a reference to patterns we can consciously think of - which I believe your interpretation was - or it can be seen as reference to some noumena that inductive expectations can be based on.

I'm not sure as to what you mean by reference to some noumena but what I think that you are referring to is the idea that there are some patterns that actually exist. That is you are referring to patterns in whatever it is that is being explained prier to the defining of an explanation. If this is the case then I'm not quite sure as of why you would be using this reasoning, it is definitely possible but I see no reason to assume such patterns exist. It seems perfectly possible that no such patterns exist and that all of the pattern that must arise on some level are nothing more then a fundamental bases for our understanding, that is more fundamental then what we are explaining. That is, it is part of the language used.

That is patterns are part of the explanation, because of the use of a language, that must include such patterns as part of the definitions being used.

So, that's just another way to say that all our ideas and concepts in our world view, can be traced down to some inductive results if you go deep enough. Which is just another way of saying that all our ideas are fundamentall based on some kind of familiarity to something. While, it is also true there is no way to actually refer to what that something is, all we can refer to is some particular language representation of that something, which is already a result of some chosen interpretation form (or chosen mental language). That is the core problem that DD often refers to as "the problem".

I see two different ways of looking at this, one way seems to be what you are suggesting and that is that there is some fundamental pattern/patterns that exist and that we must find a language for, and that finding this language is the problem. This is not overly precise as we could say that the problem is finding a way to understand or obtain expectations about the language and this would I think be a better way to say it. Although perhaps it depends on just how we choose to define things.

Or we can look at the language as fundamental and say that all of the patterns that arise are a result of how we understand the language and there is no longer a reason to suggest that the patterns exist but rather the language is the result of representation using some language. Ether way the representation of the language and the process of understanding how to obtain expectations for the language seems to be the problem this includes ones expectations for all aspect of the language and is not necessarily referring to a mathematical process although it can easily be one or at least equivalent to one.

I think much along the same lines, but also think about the consequences of our limitations related to analytical solutions to many-body problems, and the advantages of choosing to use as general solutions as possible. At the same time, if you look at this from the epistemological fundamentals' point of view, it's easy to see some parallels between fundamental particle physics, and something like weather forecasting.

Or the idea of modeling the behaver of people on any scale. Or any one of many other problems.

But my first question is, is there some form of equivalences that should be given to explanations and secondly when are explanations equivalent.

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Actually it is hard to say just what definitions you are using as you don't seem to give any or how and where you do give them don't stand out vary well.

I don't worry about definitions which are unimportant to my presentation. In essence, when the issue is not critical to my analysis, I just ride with the ordinary intuitive meanings of common usage. The two words I see as absolutely critical to my deduction are “explanation” and “language”. “Understanding” and “communication” are of significance only with regard to the relationships between an explanation and a language: that “understanding” implies you can explain something and an “explanation” in the absence of “communication” is pretty meaningless. Finally, those concepts are all kind of meaningless in the absence of a “language”.

Actually if you don't mind some constructive criticism which I don't think you will, that whole presentation seems to be lacking in direction in the sense that if someone had no idea as to what it was about it would be very hard to tell what the point of it was, and even harder to understand what was accomplished.

The sole point is to represent the constraints on an “explanation” required by the definition of an "explanation" without making any assumptions whatsoever on what that explanation is.

I am somewhat puzzled by your use of the word context here. Isn't context the other elements that must be included in the explanation for the use of some definition to make sense. If this is the case in what way are the alpha and beta operators forming part of the context, aren't they rather constraints on the mapping from the space that the information is defined in i.e. $(x_1,x_2,\cdots,x_n)$to that of the expectations $P(x_1,x_2,\cdots,x_n)$.

I use the word “context” to refer to all the issues people like Rade and Qfwfq insist on omitting in their “counter examples”. Essentially, they are omitting scads and scads of possibilities by presuming their examples make no presumptions. If you go back to my original derivation, you will discover that I come up with several relatively independent constraints. I use those alpha and beta operators to combine those constraints into one mathematical equation. Essentially they bring the necessity of satisfying those several issues together. In the common usage of the word “context”, they are critical to including the entire “context” in one equation.

This is somewhat puzzling you are trying to lay out the presentation so that nothing is assumed about the possible expectations so what “correlations within that original real space” are you talking about?

The correlations required by those alpha and beta operators.

And if they are there to fill in some gap that was left when we went from a real space to a complex space why wasn't the topic brought up at that time?

I simply show that the required correlations are easily provided if the abstract real space of the representation $\vec{\Psi}$ is converted into an abstract complex space. (And those required correlations correspond exactly to what physicists call "spinners".)

But isn't any solution derived forum the fundamental equation going to include spinners by the very nature of how the equation is defined? Although this says nothing about if such solutions would differ in any way from ones that might not use spinners if such exist.

The explanation as to “how I tie my shoe laces” does not require we include spinners; however, that explanation certainly cannot be inconsistent with the mental picture of the universe within which those shoe laces exist (the context of the explanation) and “spinners” are clearly one way (actually a very convenient way) of expressing a very necessary correlation within that “universe” (the common meaning of the word “universe” is “everything”).

I will also comment that most all explanations of anything are usually expressed totally "out of context": i.e., the actual context is a presumed issue in any common English conversation. In essence, all kinds of alternate possibilities are omitted in most all conversations. If you include all possibilities in your presentation, the full explanation (including all context) will obey my fundamental equation. That is exactly what I have proved.

I will leave your comments to Anssi for Anssi to comment on (if he wishes).

But my first question is, is there some form of equivalences that should be given to explanations and secondly when are explanations equivalent.

I thought I made that clear. Two explanations are equivalent if they yield exactly the same $P(x_1,x_2,\cdots,x_n)$ for all possible circumstances $(x_1,x_2,\cdots,x_n)$. Note that I have omitted all hypothetical elements there.

Have fun -- Dick

Edited by Doctordick
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...$P(x_1,x_2,\cdots,x_n)$ can be used to represent any “understanding”....

I see no problem with this, all that you have done is choose a representation for whatever language it is that will be used and that representation is $(x_1,x_2,\cdots,x_n)$, and a way to represent our expectations of the language in, that is $P(x_1,x_2,\cdots,x_n)$, and a language that will be used to represent the actual explanation with and that is mathematics.

I included only the most important bit from DD's quote just to call your focus on it. It basically states that the validity of an explanation is measured by the validity of the expectations it generates. As long as your explanation of something generates demonstrably valid expectations, and your explanation is coherent with itself, you will say that you understand "the meaning of" that something.

If you now suppose that you understand what I am thinking about - you suppose you understand the meaning of the words and sentences you are reading - you are at all times verifying your supposed understanding against the statements I seem to be making. If I make statements you would expect me to make, you suppose you understand what I am thinking (regardless of if you agree with the statements or not). If I suddenly make a statement you would not expect me to make, that casts a doubt in your understanding of me. Until you can explain one way or another to yourself, why did I make that statement. Did you interpret it wrong? Did I make a typo? Have you been understanding me wrong the whole time?

That is exactly what we do at all times to all the data coming in through all our senses, starting from the noumenaic "information".

Might not this idea be a basis for AI, that is intelligence might be seen as something that models its soundings and itself. It seems to me that this might even be thought of as a definition of sorts for intelligence on some level. Or if not the foundation at least a starting point worth considering.

Yes it might be exactly that. Any behaviour we call "intelligent" is a result of having generated reasonable expectations from some data. Whether or not the "real meaning" of the data has been known, is not measurable. Keep your focus on the fact that, a generation of valid expectations is still the only measure of validity, and as such the only measure of "understanding".

Have you thought about what John Searle was arguing about with the Chinese Room? That a british man could converse with a chinese man in chinese - without understanding a word of chinese or what the conversation is about - if he was simply given good enough instructions regarding how to respond to anything the chinese man could say.

Searle then draws out the conclusion that a computer that fundamentally works via following mechanical instructions, cannot have an understanding of anything in a way that human beings have an understanding, regardless of how the systems are built. The mistake of that statement is that he assumes "understanding" entails naive realistic understanding, i.e. that the human being simply understands "the intented meaning" of some data.

Whether you are chinese or british, no one can ever explicitly explain to you the meaning of chinese, in chinese. Or english, or any other language. Just like no AI can "decode" the "intented meaning" of any kind of sensory data without already knowing what it means. In both of these paradoxes, the "intented meaning" is irrelevant. The only thing that can happen is that some data can be modelled in some form that allows the generation of valid expectations. If those expectations are found to be valid, and your model about the data is self-coherent, then your model is what you think the data "means." That is exactly what "understanding" is. A succesful behaviour of any intelligent "survival machine" is entirely and explicitly tied to that kind of "understanding".

And as a detriment to Searle's argument, it is possible to have mechanical rules that allow a generation of a meaningful predictive model of any type of data. That is what a truly intelligent AI system would be.

Furthermore, through the necessity of self-consistency within a model, and with the aid of few generally valid terminology choices, that model can be made to look exactly like modern physics. As you will find out if you walk through all DD's arguments.

How ever you bring up another point that I think is an interesting question and that is when are two world views logically equivalent?

Over and beyond being able to generate reasonable expectations about the communication between one another, you cannot tell if someone else's world view is logically equivalent to yours.

If you are considering two alternative world views by yourself, then they are logically equivalent if they generate equally valid expectations for all possible circumstances. That's just a definition, don't go asking how to practically test such a thing...

I'm not sure as to what you mean by reference to some noumena but what I think that you are referring to is the idea that there are some patterns that actually exist. That is you are referring to patterns in whatever it is that is being explained prier to the defining of an explanation.

No no, what I mean is exactly what noumenon was referring to when Kant came up with the concept. It's probably the most misunderstood concept in the world but, the only reason it exists is just to be able to refer to "whatever it is that our world views are modeling". Since you are raising this point, and your criticism is quite valid, I think you understand the issue, and I'll just explain what I think Kant meant by noumenon (and why I used that word).

Our understanding of something is always a result of us having modelled something into some particular form, and as such we cannot "understand" (or "see") any kind of true form of reality underneath our models. Whatever "form" we ever see or think about is a result of our categorization of some data in terms of our models, and the "raw and uncategorized" something is what is referred to as "noumena".

If you feel uneasy that there exists a word "noumenon" that refers to something that cannot be referred to, then I think you got the idea :) The word doesn't exists in order to refer to what noumenon is. It exists so that we can converse this topic in some form. Like Kant said;

"...though we cannot know these objects as things in themselves, we must yet be in a position at least to think them as things in themselves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears."

I.e. "knowing" what noumena are, is impossible but also irrelevant to our conversation.

I would also like to point out, that the very concept of "meaning" of some data, is central to the mechanism with which we generate predictions. It is common that people suppose that when we create a valid world view, we are figuring out what exists out there. That implies they think we are figuring out what our sensory data "truly" means. I on the other hand think the idea of some kind of cosmic meaning or cosmic structure that exists over and beyound us seeing something in some chosen terminology, is nothing but naive realism to the point of absurdity. I think there is no point in thinking that anything has got "meaning" outside of our prediction generation mechanisms placing meaning on things purely for prediction purposes.

Or we can look at the language as fundamental and say that all of the patterns that arise are a result of how we understand the language and there is no longer a reason to suggest that the patterns exist but rather the language is the result of representation using some language.

Yes, that statement meets my expectations as to what you would say if you do understand the issue :)

Ether way the representation of the language and the process of understanding how to obtain expectations for the language seems to be the problem this includes ones expectations for all aspect of the language and is not necessarily referring to a mathematical process although it can easily be one or at least equivalent to one.

I'm not sure what it means that generating a language or obtaining expectations is a mathematical process (or if that is at all what you were saying), but let it be said that the only reason there exists some mathematics in DD's communication is because it is easier to represent complex logical connections via mathematical concepts, rather than via english language.

We have no right to assume that any physical laws exist, or if they have

existed up to now, that they will continue to exist in a similar manner in

the future. -- Max Planck (1858-1947), German physicist.

Yes exactly, because all our defined laws are based on inductive reasoning. Not on knowledge about reality.

-Anssi

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• 2 weeks later...

I think that a misunderstanding has developed and I am hoping that I can at least find out if this is the case and maybe clear a few things up.

Firstly the nature of the misunderstanding is that in particular DocterDick you seem to be of the opinion that I am always wanting to derive new explanations and that I see your derivation as a means of deriving them.

This is not really the way that I see it although I am beginning to find out more about physics and am beginning to suspect that what I see as defining an explanation may differ considerably from what you would consider it to be and I would at least like to know if this is the case.

Anyhow, firstly I see two different perspectives when I think of an explanation. The first is that when we are talking about an explanation I most often think firstly of a very mathematically orientated structure kind of like talking about abstract mathematics or a vector space. In thinking of it in this way I think of the original constraints almost as a set of axioms at times. I think that this is perhaps too mathematically strict for how you see things and perhaps this is even one of the things you see wrong with how scientists do things. None the less at times this is how I look at it.

The second way that I think of an explanation is as the logical result of the need for a way of arriving at expectations. In this case the requirements of symmetry and the need for rules combined with the use of mathematics as a consistent language lead to the fundamental equation not as an abstract mathematical idea but from a precise use of logic.

What is important about this idea is that we no longer need to look at it as a mathematical idea but instead can look at it as the natural result of the need of obtaining expectations in a consistent way of anything and so results whenever changing behaver based on past experience exists.

What I think is the most important thing about your derivation comes from this view and that is that there are no assumptions hidden in what is being explained. And so no matter why or how expectations are obtained they must obey the same representation at least in some general case and since all that we are really interested in is the general case we can be sure that this is applicable in all cases.

This I think is closer to how you think of the fundamental equation. The advantage here is of course that looking at it this way we are no longer locked into using a set of assumptions to build off of and instead we are only looking for consistency.

Whenever I think of an explanation my first thought is normally of the first case and as a result when I think of different explanations I think of a possible solution of the fundamental equation and although it has not been proved I will admit there is probably a unique solution and so the only thing that I think of making explanations different is the initial conditions to the fundamental equation, as a result when I think of different explanations I think of different initial conditions. Even though the idea of initial conditions has never been brought up and at this point I don't expect them to be brought up or see need to bring such a thing up.

The point being that the only time that I really think of actual explanations is when we are applying initial conditions to a possible solution to the fundamental equation, and that is really not of interest as if we ever have such a solution the initial conditions will be nothing more then a mathematical extinction of it.

I use the word “context” to refer to all the issues people like Rade and Qfwfq insist on omitting in their “counter examples”. Essentially, they are omitting scads and scads of possibilities by presuming their examples make no presumptions. If you go back to my original derivation, you will discover that I come up with several relatively independent constraints. I use those alpha and beta operators to combine those constraints into one mathematical equation. Essentially they bring the necessity of satisfying those several issues together. In the common usage of the word “context”, they are critical to including the entire “context” in one equation.

So by context you are simply referring to the consequences of consistency in an explanation? If so this seems like a very strange definition of context. I have always thought that when you say context that you where referring to an idea that is almost exactly what I get when I ask Google for a definition of the word and that is

1. The circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed.

And it seems clear to me that in the setting of a truly general explanation this can be nothing other then the entire collection of possible other elements not being referenced.

I simply show that the required correlations are easily provided if the abstract real space of the representation $\vec{\Psi}$ is converted into an abstract complex space. (And those required correlations correspond exactly to what physicists call "spinners".)

Lets try and take a step back and try to see this in a slightly different way, you have derived your original constraints, now you know that if you can form a single equation out of them this will be easier to work with then working with your equations separately, you must have been at this point at some time.

Now how do you go from this point to your fundamental equation. Did you just borrow your alpha and beta operators from the physics that you where doing at the time and say I'll just use these so I can work with just one equation, and then just think it must look like this and write out the fundamental equation, and only then show that it will indeed satisfy the original constraints?

If so then the idea is really just a abstract mathematical idea and has no basis in the need for consistency?

Have you thought about what John Searle was arguing about with the Chinese Room? That a british man could converse with a chinese man in chinese - without understanding a word of chinese or what the conversation is about - if he was simply given good enough instructions regarding how to respond to anything the chinese man could say.

I have heard of it before but I haven't thought about it too much. The truth is that depending on how you define a rule, (by rule I think of a statement like if something is true then do one thing otherwise do something else, in other words it is deterministic based on the current state and the rules are fixed), I don't think that using this definition that he will be able to convince someone that he understands the conversation, at least not for long.

Before I continue I think I will point out that I think the biggest difference between our views on the problem is how we think of a rule or set of rules. You seem to be thinking of rules as any set of instructions that may be followed, I on the other hand think of a rule as defining the next state. In other word when I think of a rule I think of something in which it makes no difference in how something was arrived at it simply makes the next step and adds this to the last state or starts a whole new state. I think that this is very much the approach to modern AI at least as far as I can tell.

In which case I think that what really has to be done away with here is firstly the rules and then the dependence on the past, at least as far as the past being fixed.

Of course when we remove these ideas there might not be much left at least not by modern standards and so I think we need to change our approach, I would suggest replacing the current state with a consistent model that is not fixed, and the rules with expectations of this model.

Whether you are chinese or british, no one can ever explicitly explain to you the meaning of chinese, in chinese. Or english, or any other language. Just like no AI can "decode" the "intented meaning" of any kind of sensory data without already knowing what it means. In both of these paradoxes, the "intented meaning" is irrelevant. The only thing that can happen is that some data can be modelled in some form that allows the generation of valid expectations. If those expectations are found to be valid, and your model about the data is self-coherent, then your model is what you think the data "means." That is exactly what "understanding" is. A succesful behaviour of any intelligent "survival machine" is entirely and explicitly tied to that kind of "understanding".

You aren't trying to suggest that the meaning of Chinese can be explained to someone in some other language are you. I agree that there is no way to explain the meaning of Chinese to someone in Chinese but you can't expect someone to have the meaning of Chinese explained to him in some other language ether.

All that I think that you can do is try to set up a context that is consistent with something that an explanation already exists for and so a way of obtaining expectations already exists. That or you have to do it the hard way and find a new way of obtaining expectations that is consistent.

Other then that I think that I can agree with you except when you say “ If those expectations are found to be valid, and your model about the data is self-coherent” the first part of this suggests to me a useless idea, maybe I am just reading more into how you are saying this then you intend but to me if the expectations form a consistent model then the expectations are as valid as any other expectations whether or not they are the same or as useful for what you are calling a “survival machine” which I also think is a somewhat misconceived idea.

This is why I ask when are two explanations logically equivalent, I don't think that to be equivalent they need to produce the same expectations then they are the same to be logically equivalent. I think they need only be consistent with two sets of data that are comparable is some way, I just can't decide in what way they must be comparable.

And as a detriment to Searle's argument, it is possible to have mechanical rules that allow a generation of a meaningful predictive model of any type of data. That is what a truly intelligent AI system would be.

I think that maybe I can agree with you here and in fact I have from time to time come to a similar if not the same conclusion, but just to be sure let me put it a different way. The AI and the expectations are no longer two separate things, instead, what the expectations are, is the position that the AI is in. I hope that statement is understandably as I can't think of a more straight foreword way of putting it without a considerable amount of describing that seems off topic right know.

If you are considering two alternative world views by yourself, then they are logically equivalent if they generate equally valid expectations for all possible circumstances. That's just a definition, don't go asking how to practically test such a thing...

I will take this as a definition, but I still want to know the consequences of two such explanations and how they are related. I might note that one consequence of this has already been explored and is in fact an important step in deriving the fundamental equation, in fact it leads to the relation

$\sum_{i=1}^n \frac{\partial}{\partial x_i}P(x_1,x_2,\cdots,x_n) = 0$

just think about that for a second. No one would suggest that your explanations are not logically equivalent if they produce the same expectations in this case they are even the same, and then all that we have to do is say that the elements that our explanations are a function of are shift symmetric.

Our understanding of something is always a result of us having modelled something into some particular form, and as such we cannot "understand" (or "see") any kind of true form of reality underneath our models. Whatever "form" we ever see or think about is a result of our categorization of some data in terms of our models, and the "raw and uncategorized" something is what is referred to as "noumena".

OK I can see the need for a way of referring to such a thing, I also can see the futility in trying to talk about such a thing. There really is no reason to try and discuss such a thing as to suggest something about it is to suggest that there is some meaning in the absence of a context and consistency, as, if you refer to ether a context or a consistent model you are no longer referring to these “noumena”. You cant even refer to a representation as, as soon as you do - it is no longer a “noumena”

I'm not sure what it means that generating a language or obtaining expectations is a mathematical process (or if that is at all what you were saying), but let it be said that the only reason there exists some mathematics in DD's communication is because it is easier to represent complex logical connections via mathematical concepts, rather than via english language.

Only that it is possible to use a mathematical function to generate consistent expectations versus, say, making a machine that we use to try and model the system and obtain our expectations from how it works, say like a Differential analyzer.

My point being is that all that is really important is the use of consistency.

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Anyhow, firstly I see two different perspectives when I think of an explanation.

That is why I define exactly what I mean by an explanation. If you do not do that, you introduce all kinds of confusion.

What is important about this idea is that we no longer need to look at it as a mathematical idea but instead can look at it as the natural result ...

I have utterly no interest in mathematics except as an internally consistent logical structure. The following two quotes are things I have said elsewhere and are quite essential to understanding my approach.

I make much use of Mathematics without defense or argument. In essence, it is quite clear that mathematicians are very concerned with the exactness of their definitions and the self consistency of their mental structures. I suspect mathematics could probably be defined to be the invention and study of self consistent systems. At any rate, their concerns are exactly those which drive my work; I am merely attacking a slightly different problem. I hold that the reason mathematics is so important to science is that science is actually attempting to map reality (which is assumed to be self consistent) into a logical system. Mathematics is a logical system which is self consistent by construction. In accordance with this view, I will hold that the fundamental mathematical relations require no defense by me. I will leave that defense to others far more qualified than myself.

Fundamentally, what I will present is often referred to as a tautology: strictly, "a needless repetition of the same idea in a different word, phrase or sentence". It would indeed be needless repetition were everyone brilliant enough to see those consequences; however, any decent education in mathematics will assure one that the consequences of definition can easily far outstrip the capabilities of common intuition.

This I think is closer to how you think of the fundamental equation. The advantage here is of course that looking at it this way we are no longer locked into using a set of assumptions to build off of and instead we are only looking for consistency.

I am not “looking for consistency”! I am assuming that the great mathematicians are taking responsibility for that issue. I am looking for a way of viewing the underlying information in such a way that absolutely no possibility is omitted.

I will admit there is probably a unique solution and so the only thing that I think of making explanations different is the initial conditions ...

It is well known fact that equations of the form I end up with do not have unique solutions. The central issue here is, “are there any solutions whatsoever to my equation which can not be seen as representing circumstances which exist in reality?” If there are, that fact would tell us something about reality. By its very construction, my equation tells us absolutely nothing about reality. The fact that I deduce most all of fundamental physics to be approximate solutions to my equation says that physics apparently tells us nothing about reality either. It is no more than a self consistent tautological construct.

The “initial conditions” are part and parcel of the explanation, not the circumstances to be explained.

1. The circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed.

Yeah, that is pretty well exactly what I mean! It is “the rest of the universe”! Presumed to be either understood or unimportant in most all explanations of anything. In my analysis, that context must be a solution to my equation. Nothing is to be left out! In looking for solutions, the best one can do is point out exactly which terms are being neglected and the possible consequences of that neglect. That is exactly what I do when I show that all of modern physics flows from my equation.

Did you just borrow your alpha and beta operators from the physics that you where doing at the time and say I'll just use these so I can work with just one equation, and then just think it must look like this and write out the fundamental equation, and only then show that it will indeed satisfy the original constraints?

Mathematics is chock full of logical constructs with interesting consequences often found to be valuable. Things you would never even begin to be aware of if mathematicians had not thought them out.

If so then the idea is really just a abstract mathematical idea and has no basis in the need for consistency?

Consistency is the fundamental underlying basis of mathematics.

I will let Anssi answer your remaining comments. I think his understanding is quite to the point.

Have fun -- Dick

Edited by Doctordick
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I have heard of it before but I haven't thought about it too much. The truth is that depending on how you define a rule, (by rule I think of a statement like if something is true then do one thing otherwise do something else, in other words it is deterministic based on the current state and the rules are fixed), I don't think that using this definition that he will be able to convince someone that he understands the conversation, at least not for long.

That just concerns the practicality of such a setup. What Searle is trying to say is just that, in his opinion a computer program that follows some explicit rules to produce intelligent output from some input, cannot have human type of understanding of the meaning of the input, even if it can produce apparently intelligent output. Which in my mind reflects a false assumption regarding what exactly human type of understanding is, and a false assumption regarding what exactly AI is supposed to be.

I agree that there is no way to explain the meaning of Chinese to someone in Chinese but you can't expect someone to have the meaning of Chinese explained to him in some other language ether.

That is correct.

All that I think that you can do is try to set up a context that is consistent with something that an explanation already exists for and so a way of obtaining expectations already exists. That or you have to do it the hard way and find a new way of obtaining expectations that is consistent.

Now that sounds like you are thinking of exactly the issue I was hoping you would. When you say we need to "set up a context that is consistent with something that an explanation already exists for", you are referring to the fact that when we acquire an understanding of something, we have done so via our pre-existing explanation. This is true every time we try to understand something about reality in general, not just human languages.

But it can't be true when we first started to form an explanation about reality, because there is no pre-existing explanation to rely on. Still it is possible to form an explanation starting with nothing, as we all have done so. It simply means, nothing in our explanations is connected to any explicit knowledge about reality.

Think about that starting point of an explanation from a purely logical point of view. Let's say, from the point of view of an AI, that starts without knowing anything about the information is is supposed to form an understanding of. That means, without knowing anything about how its sensory data is supposed to be interpreted.

Regardless of the strategy of the system, even if it is just making blind guesses about the meaning of the data, how is it exactly that it knows it has made the correct guesses?

Other then that I think that I can agree with you except when you say “ If those expectations are found to be valid, and your model about the data is self-coherent” the first part of this suggests to me a useless idea, maybe I am just reading more into how you are saying this then you intend but to me if the expectations form a consistent model then the expectations are as valid as any other expectations

By "valid expectations" I simply mean "demonstrably valid", i.e. that they are found to be correct "after the fact". Of course different valid explanations can generate different but equally valid expectations, until you get to the point that you can measure which one was actually correct.

This is why I ask when are two explanations logically equivalent, I don't think that to be equivalent they need to produce the same expectations then they are the same to be logically equivalent. I think they need only be consistent with two sets of data that are comparable is some way, I just can't decide in what way they must be comparable.

Well when I'm talking about two equivalent explanations, I'm certainly talking about explanations for the exact same set of data. In particular, the explanation commonly called "the world view", which is the explanation encompassing all the data you've ever come across (in principle). Different explanations may have invented completely different symbolism to represent the same data, and through those explanations the same data looks completely different. But they may both provide the exact same rate of accuracy in terms of predictions they make.

I'm not sure what you are thinking of as the idea of equivalence between two different explanations explaining two different sets of data doesn't make sense to me...

I will take this as a definition, but I still want to know the consequences of two such explanations and how they are related.

It really is just another way of saying that there always are a number of different ways to represent the exact same thing. There exists different languages to express the same ideas, and there exists different collections of imaginary elements to represents same things and behaviours. Different quantum interpretations essentially are just wildly different ways to represent the same relationships. We find ourselves from that situation because we don't have any explicit information about the reality, and anyone who can represent those same fundamental relationships of QM in any self-coherent manner, cannot be shown to be more wrong or right than the others.

-Anssi

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• 1 month later...

I am not “looking for consistency”! I am assuming that the great mathematicians are taking responsibility for that issue. I am looking for a way of viewing the underlying information in such a way that absolutely no possibility is omitted.

So just what is the difference between saying this and saying absolutely every consistent system has a representation?

It is well known fact that equations of the form I end up with do not have unique solutions. The central issue here is, “are there any solutions whatsoever to my equation which can not be seen as representing circumstances which exist in reality?” If there are, that fact would tell us something about reality. By its very construction, my equation tells us absolutely nothing about reality. The fact that I deduce most all of fundamental physics to be approximate solutions to my equation says that physics apparently tells us nothing about reality either. It is no more than a self consistent tautological construct.

The “initial conditions” are part and parcel of the explanation, not the circumstances to be explained.

Asking if there are any solutions that can not be seen as representing circumstances in reality seems equivalent to asking one of two things.

The first being if there is some law of reality that prevents some arrangement of circumstances, on the other hand I think that it should be faced that some arrangements are just out right unlikely.

Or saying that there are two different and incompatible solutions to the fundamental equation that are both consistent with the same past. That is, the only defining characteristics of the two separate explanations is the expectations that they would imply. The lack of such a possibility is what I mean when I say are there unique solutions. Maybe this is just too abstract of an idea to try to communicate at this time.

That just concerns the practicality of such a setup. What Searle is trying to say is just that, in his opinion a computer program that follows some explicit rules to produce intelligent output from some input, cannot have human type of understanding of the meaning of the input, even if it can produce apparently intelligent output. Which in my mind reflects a false assumption regarding what exactly human type of understanding is, and a false assumption regarding what exactly AI is supposed to be.

I can see that you have a point here and I can't completely disagree with you but there is to me a second possibility of what he is suggesting and that is that no Turing machine can duplicate human understanding.

I'm not going to seriously suggest this one way or the other as it seems to me to be a very iffy subject made all the more so due to my not knowing enough about the topic to even guess at what Searle was thinking and I don't want to start suggesting things that seem to be dependent on definition so heavily.

Even if this were taken seriously though it is kind of a half hearted point as it is clearly possible to construct a program that can simulate human behaver and human understanding whatever it may be.

In truth I think I would be more interested in the response of an AI in some kind of Mirror test then the Chinese room but perhaps such a test is not suitable for any type of AI at present.

Now that sounds like you are thinking of exactly the issue I was hoping you would. When you say we need to "set up a context that is consistent with something that an explanation already exists for", you are referring to the fact that when we acquire an understanding of something, we have done so via our pre-existing explanation. This is true every time we try to understand something about reality in general, not just human languages.

While I agree that this is the case in many situations I also agree when you say

But it can't be true when we first started to form an explanation about reality, because there is no pre-existing explanation to rely on. Still it is possible to form an explanation starting with nothing, as we all have done so. It simply means, nothing in our explanations is connected to any explicit knowledge about reality.

But I also see no reason to assume that this can only happen once. I would rather say that our experiences appear to be so similar that there is seldom the apparent need to form new explanations to rely on.

Regardless of the strategy of the system, even if it is just making blind guesses about the meaning of the data, how is it exactly that it knows it has made the correct guesses?

This question is not entirely clear to me as, if I assume that what you mean by correct guesses is in the “noumena” sense of the word which I doubt that you mean, the idea of knowing when it has made a correct guess is simple it must be correct if it knows the something in the “noumena” sense but this seems unlikely to be what you mean, other wise I really don't know what you are asking as the correctness of a guess seems like a question of the consistency of the guess, so in this case I would say that it knows when it has made a correct guess when it is part of a consistent system, in which case, since it made the guess it must be part of a consistent system, as whatever made the guess can be explained in a consistent way.

So my answer to your question is very simple, since it is guesses about something that we are interested in every one must be correct even if they are completely random guesses.

My conclusion is that the question that you are really trying to ask is how can it know when it has made a useful guess. To which I would say that it knows when it is making useful guesses when they look like the past.

By "valid expectations" I simply mean "demonstrably valid", i.e. that they are found to be correct "after the fact". Of course different valid explanations can generate different but equally valid expectations, until you get to the point that you can measure which one was actually correct.

So you mean that it is later shown to be a inconsistent set of expectations? As if it was a consistent set of expectations there is always going to be a way that they can be consistently expanded to include new information, no matter what that information is.

If I take your question to mean anything else you seem to be seriously suggesting the need for a reality of some sort.

While I don't object to the idea of a reality we are trying to include every possibility and so I see no way to use the idea without assuming the rules of reality and if we do that it seems like we are no longer talking about forming an explanation but rather we are just using one that already exists.

I'm not sure what you are thinking of as the idea of equivalence between two different explanations explaining two different sets of data doesn't make sense to me...

OK this is where I want to be as mathematically correct as is possible, think of it like this

If we have some arbitrary representation of a set of data $(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t)$ and we ask the question, when is this equivalent to some other representation, to me what we are really asking is under what transformations are our expectations invariant. That is, what symmetry can our representation combined with our expectations of it have.

That is, given multiple representations and corresponding expectations, when will it make no difference to our world view which one we use. What I am thinking of here as our world view, is composed of this representation and our expectations of this information.

To be very particular I am thinking if we preform some transformation to our representation and we perform a corresponding transformation on our expectations, if our resulting expectations are still consistent then there seems to me to be no way of distinguishing the combination of expectations and representation.

I hope that makes sense if not I will have to try and come up with a more understandably way of putting it.

It really is just another way of saying that there always are a number of different ways to represent the exact same thing. There exists different languages to express the same ideas, and there exists different collections of imaginary elements to represents same things and behaviours. Different quantum interpretations essentially are just wildly different ways to represent the same relationships. We find ourselves from that situation because we don't have any explicit information about the reality, and anyone who can represent those same fundamental relationships of QM in any self-coherent manner, cannot be shown to be more wrong or right than the others.

This might sound like a backwards question and one that is just silly to ask but, how do we know that there is more then one way to represent the same thing? If we are saying that there is more then one representation of something then we must have something that is not changed by the two representations that leads us to believe that it is the same thing being represented.

If this was mathematics then I would say that we know that we are representing the same object when there is a mapping that is invertible and it preserves some property of interest. I still want to say this in this setting but if I do, what is being preserved and what is the mapping defined as. It seems to me that the world view is what should be preserved but exactly how to define it is not at all obvious to me.

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• 2 weeks later...

Hi again

It's difficult to wade through the ambiguities of language, especially since I was not following the exchange between you and DD too closely, but I'll give it a go anyway... Just be aware that, despite my best efforts, my language may be different from what you are using.

So just what is the difference between saying this and saying absolutely every consistent system has a representation?

Perhaps DD misunderstood what you meant, perhaps by "looking for consistency" you were making a reference to the fact that self-consistency is an important constraint in DD's analysis. DD's comment "viewing information in such a way that absolutely no possibility is omitted" is simply referring to the idea of laying down a general form of "self-consistent explanations" (i.e. the "fundamental equation"). If that makes sense to you, I think you are good to proceed.

I suppose you understand that a "general form" implies that the expectations regarding something are seen as a function of their entire context. Otherwise, it is not general.

The important thing is that we know the exact logical steps that need to be taken from the general form, to get to the exact terminology of modern physics., and none of the steps includes an assumption that modern physics is correct at the outset (as far as I can see). All the steps can be seen as statements about what type of terminology is acceptable as a part of an explanation, for us. For instance, in reality, everything may well have constant feedback with everything else. But it is not possible for us to mentally handle that kind of view of the universe. What is practical for us though establishing defined elements where the feedback between everything is as simple as possible.

There exists logical mechanisms that accomplish exactly that, and DD's derivations of modern physics is exactly a representation of those mechanisms.

What does that imply in your mind?

Asking if there are any solutions that can not be seen as representing circumstances in reality seems equivalent to asking one of two things.

The first being if there is some law of reality that prevents some arrangement of circumstances, on the other hand I think that it should be faced that some arrangements are just out right unlikely.

Or saying that there are two different and incompatible solutions to the fundamental equation that are both consistent with the same past. That is, the only defining characteristics of the two separate explanations is the expectations that they would imply. The lack of such a possibility is what I mean when I say are there unique solutions. Maybe this is just too abstract of an idea to try to communicate at this time.

I can't be confident about whether or not I understand what you mean, but it strikes me that you may be ignoring the fact that how a circumstance is being represented (and the associated laws) is entirely a function of the explanation being employed to interpret some raw information. That is to say that different solutions to the fundamental equation imply that different terminology is being employed to represent circumstances. The same data looks very different through different language interpretation. Even the dimensionality choices may well be different.

So in that sense there is no way to analyze "laws of reality", there are only ways to analyze the laws we are using as part of a particular explanation of reality, and when they prevent some arrangement of circumstances, we are really only talking about what is possible by our defined terminology.

It is entirely possible, and it is happening all the time, that the entirety of our past is explainable in multiple different ways. The bigger paradigm shifts you allow for yourself, the more avenues are open for you.

I can see that you have a point here and I can't completely disagree with you but there is to me a second possibility of what he is suggesting and that is that no Turing machine can duplicate human understanding.

I'm not going to seriously suggest this one way or the other as it seems to me to be a very iffy subject made all the more so due to my not knowing enough about the topic to even guess at what Searle was thinking and I don't want to start suggesting things that seem to be dependent on definition so heavily.

As far as I understand, yes, he is mostly thinking about Turing machines. But when you really get down into defining what constitutes a Turing machine, you end up into the same semantical tar pit where it could mean almost anything, that accomplishes any kind of logic in any sense. But yeah it's impossible to confidently even understand what he means when he says "understanding". I don't know if he is including the "hard problem" in there as well, and whether he is saying "cannot have understanding" or "cannot be proven to have understanding". There are probably a lot of people who find his argument emotionally meaningful, without really understanding what he might mean.

Even if this were taken seriously though it is kind of a half hearted point as it is clearly possible to construct a program that can simulate human behaver and human understanding whatever it may be.

In truth I think I would be more interested in the response of an AI in some kind of Mirror test then the Chinese room but perhaps such a test is not suitable for any type of AI at present.

Well it's kind of the same issue there... I mean, chinese room is not really a practical test at all, it's just a thought experiment. The mirror test would imply something about the concept of self (and thus awareness of self) that a system has established. But that is just a concept among concepts, when you really get down to it.

By the way, talk about the hard problem of consciousness, it is not very difficult to show that the very definition of "explanation of consciousness" is immediately outside of what we even mean by "explanation", and as such it's not much of a puzzle why the issue is so mystifying. To explain it with a single element, or to explain it with multiple elements, are both dissatisfying as an explanation for different, purely logical reasons. At the same time, the only reason we see and think about the world in terms of a collection of defined elements with supposed identities to them, is that it is necessary for expectations to become generated at all. But does me seeing the reality through this method, also make reality conform to my method? It requires little bit of thought to realize that any attempt to think about whether or not the above could be possible, is just yet another attempt to categorize things in terms of elements, and you can't actually "think about" other forms. Keeping that in mind, I cannot point out any reason why a semantical conceptualization of reality, where the concept of self exists, would not also produce a subjective experience. I can't point out a reason for it to exist, or not to exist. I just know mine does, in the circumstance that I recognize as I stated above.

Regardless of the strategy of the system, even if it is just making blind guesses about the meaning of the data, how is it exactly that it knows it has made the correct guesses?

This question is not entirely clear to me as, if I assume that what you mean by correct guesses is in the “noumena” sense of the word which I doubt that you mean, the idea of knowing when it has made a correct guess is simple it must be correct if it knows the something in the “noumena” sense but this seems unlikely to be what you mean, other wise I really don't know what you are asking as the correctness of a guess seems like a question of the consistency of the guess, so in this case I would say that it knows when it has made a correct guess when it is part of a consistent system, in which case, since it made the guess it must be part of a consistent system, as whatever made the guess can be explained in a consistent way.

So my answer to your question is very simple, since it is guesses about something that we are interested in every one must be correct even if they are completely random guesses.

My conclusion is that the question that you are really trying to ask is how can it know when it has made a useful guess. To which I would say that it knows when it is making useful guesses when they look like the past.

Well, what I was getting at was the usefulness of the guessess yes, and its only judge is in whether or not the guesses yield useful/sensical expectations for the future and meaningful interpretation of the rest of the data. It's like reading a book in foreign language. If you interpret something in ways that makes zero sense to you, you would be inclined to think that you may have misunderstood something about the language, until you strike upon an interpretation that makes sense. Or if you are a physicist, you are creating experiments with particular expectations about the outcome. If your expectations are not met at all, you would be inclined to think you may have misunderstood reality somehow.

So in the context of the chinese room, it should concern some general learning mechanism, and being general means it can learn to "understand" any data. And the only way to know whether or not so-called "understanding" has been established, is to check whether or not valid expectations are being generated. In this context, being able to predict the data, entails a succesfull terminology has been established, which implies the system thinks it understands the data, just like you think you understand this text.

So, if the explicit rules inside the chinese room were to merely concern the mechanisms behind generating a valid predictive world view (valid terminology), out of any data, and that type of learning system becomes able to converse in chinese, I would say it has then established exactly the same type of understanding of chinese, as a chinese person has, through completely mechanical means. Completely implicit undertanding, hinging on assumptions and evaluated validity of expectations. Entirely within the possibility space of a Turing machine.

So you mean that it is later shown to be a inconsistent set of expectations? As if it was a consistent set of expectations there is always going to be a way that they can be consistently expanded to include new information, no matter what that information is.

If I take your question to mean anything else you seem to be seriously suggesting the need for a reality of some sort.

While I don't object to the idea of a reality we are trying to include every possibility and so I see no way to use the idea without assuming the rules of reality and if we do that it seems like we are no longer talking about forming an explanation but rather we are just using one that already exists.

What I was referring to was exactly that same practical activity of checking our expectations as we do when we are reading a book, or performing a physics experiment. Often our expectations may be wrong due to subtle inconsistencies yes, but those are extremely hard to track in practice.

OK this is where I want to be as mathematically correct as is possible, think of it like this

If we have some arbitrary representation of a set of data $(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t)$ and we ask the question, when is this equivalent to some other representation, to me what we are really asking is under what transformations are our expectations invariant. That is, what symmetry can our representation combined with our expectations of it have.

That is, given multiple representations and corresponding expectations, when will it make no difference to our world view which one we use. What I am thinking of here as our world view, is composed of this representation and our expectations of this information.

To be very particular I am thinking if we preform some transformation to our representation and we perform a corresponding transformation on our expectations, if our resulting expectations are still consistent then there seems to me to be no way of distinguishing the combination of expectations and representation.

I hope that makes sense if not I will have to try and come up with a more understandably way of putting it.

Well that sounds about right. It's what we've been referring to as two equally valid explanations. Assuming the underlying data is the same, but being represented differently by two different explanations.

That's why it confused me when you said "two explanations, explaining two different sets of data", I suppose by "different set of data" you meant two different representations of something.

This might sound like a backwards question and one that is just silly to ask but, how do we know that there is more then one way to represent the same thing? If we are saying that there is more then one representation of something then we must have something that is not changed by the two representations that leads us to believe that it is the same thing being represented.

If this was mathematics then I would say that we know that we are representing the same object when there is a mapping that is invertible and it preserves some property of interest. I still want to say this in this setting but if I do, what is being preserved and what is the mapping defined as. It seems to me that the world view is what should be preserved but exactly how to define it is not at all obvious to me.

Yeah it's a bit of a semantical issue regarding what is exactly considered to be "the same" or not. Fundamentally, I would say we know there are multiple explanations to any data as long as the amount of data is finite, and we know the amount of data being considered for any explanation, must always be finite.

And if two different explanations produce the observable expectations at the same rate of validity, then their equivalence or difference is entirely up to semantics. If they produce different observable expectations for some circumstances not yet checked, then I think it's easier to make the case about them being different.

-Anssi

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• 3 weeks later...

Well guys, I am finally back from our Christmas Holiday in Denver.

... I think that it should be faced that some arrangements are just out right unlikely.

That essentially presumes an understanding of reality. It should be clear to you that if you take that position as an initial position, you are merely throwing out millions upon millions of alternate possibilities.

The lack of such a possibility is what I mean when I say are there unique solutions. Maybe this is just too abstract of an idea to try to communicate at this time.

It's not abstract at all – you are merely throwing out solutions without cause! (You are presuming you know things you clearly do not know... the correct assumptions for example.)

...no Turing machine can duplicate human understanding.

Another comment which certainly can not be proved.

In truth I think I would be more interested in the response of an AI in some kind of Mirror test then the Chinese room but perhaps such a test is not suitable for any type of AI at present.

Please explain what you mean by a “mirror test”.

But I also see no reason to assume that this can only happen once. I would rather say that our experiences appear to be so similar that there is seldom the apparent need to form new explanations to rely on.

That is the essential conclusion I have laid out. In a nutshell, if any explanation is internally self consistent, the elements upon which that explanation must be built must satisfy my fundamental equation. What you apparently miss is the fact that your interpretation of an explanation (your understanding of the language being used to communicate that explanation) is, hopefully, an internally self consistent system.

Thus the elements you think are attached to the verbal representations being used are those which are consistent with your understanding. Thus it is that any internally self consistent explanation will appear to be quite unique and agreement quite easy to explain (even when the actual elements being discussed, the so called “noumena”, may be actually wildly different). Actually, that is a rather trivial issue: since you have no way of knowing what the noumena actually refer to, only the required historic relationships your explanations use to define the elements being referred to is of any significance.

To which I would say that it knows when it is making useful guesses when they look like the past.

That the elements by which it is described (the language names given to the elements) correspond to a solution to my fundamental equation!!! And that includes the definition of “t” regarding those elements.

This might sound like a backwards question and one that is just silly to ask but, how do we know that there is more then one way to represent the same thing?

That is a silly question. Human being communicate via some 2,000 different languages. It follows that most things have some 2,000 different ways to represent most everything! Most translators presume they are representing the same thing; however, that can often be an invalid presumption.

That one understands a specific language is itself an assumption: that is why living languages change subtly in every generation. Children assume they understand the language they grow up with. They are often wrong.

I agree with Anssi on everything he says; although that is based on the assumption that I my interpretation of what he is saying is in alignment with his interpretation.

If I take your question to mean anything else you seem to be seriously suggesting the need for a reality of some sort.

While I don't object to the idea of a reality we are trying to include every possibility and so I see no way to use the idea without assuming the rules of reality and if we do that it seems like we are no longer talking about forming an explanation but rather we are just using one that already exists.

Nowhere in my presentation am I "forming an explanation"; I am expressing a required fundamental constraint on all possible valid explanation (my fundamental equation). What is astounding (from my perspective) is that the need to satisfy that equation seems to reproduce all of the common relationships supposedly required by modern physics. The only conclusion is that no information whatsoever is required to reproduce modern physics: i.e., our mental picture of reality could not possibly be otherwise and still be self consistent.

It seems to me that the world view is what should be preserved but exactly how to define it is not at all obvious to me.

If you can perceive (or come up with) an interpretation of my communications consistent with your world view, you will perceive that world view to be preserved. Belief in that preservation is an assumption as there exists no way to guarantee they are actually the same (As Anssi says, it amounts to a finite amount of data). Down the road, it is always possible that some important difference will arise. My point is that satisfying my fundamental equation is an absolute necessity.

Find some solution to my equation which contradicts observation and that would tell us something about reality. Something consistent with my fundamental equation which is not consistent with reality!

Have fun -- Dick

Edited by Doctordick

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