"a Universal Representation Of Rules"

[Qfwfq]

Why do you accept as a truth statement the above interpretation used by DD without doing your homework ? Please post the publication by Einstein, with page number, where he defined time using the two different definitions of time exactly as worded above.

It's more subtle than that. While Einstein's wording wasn't as sloppy as given above, his discussion of the notion of time did involve two aspects which aren't to be regarded as two separate definitions of it.

 

It is essential to have some contraption in which a sequence of events occurs, which (are considered to) have a reasonably predictable duration in between them. It also requires the possibility of observing these events i. e. relating them to other events by simulaneity, which is definable for events at a same location.

 

This does not mean the notion of time is defined only by simultaneity, any more than it could be usefully defined only by having a clock somewhere in the universe with no chance of relating its reading to other events.

[Rade]

While Einstein's wording wasn't as sloppy as given above, his discussion of the notion of time did involve two aspects which aren't to be regarded as two separate definitions of it.

Yes, this was my point, what you said in bold. I agree with you that both DD and AnissH error when they claim that Einstein published two separate definitions of time (the sloppy versions). Einstein had a single (non sloppy) definition of time (in his 1905 paper), which has two aspects to it (1) simultaneity of events and (2) synchronized clocks. Thank you for clarifying the situation.

 

Now, in defense of DD, he also presents a "proof" that he claims derives SR and GR of Einstein that also uses a single definition of time. His definition of time is the difference between what is known in the human mind (past) from what is not known (future) and the the neural simultaneous translation between the two events (present). My objective was not to falsify this definition of DD, but to clarify the false claim made about Einstein concerning his single definition of time. DD separates the two aspects of time that Einstein unites, but they both have but a single "definition of time". If this is not correct, please let me know.

[Rade]

I think what AnssiH and DD refer to is the (1) notion of simultaneity based on Einstein's definition, and (2) the actual reading of clocks (the notion of time at different locations).

Yes, clearly, but where they error, as explained in above post by Qfwfq, is that they make the false claim that your (1) and (2) are two separate "definitions" of time made by Einstein, which they are not. Einstein had but a single definition of time, in his interpretation of his equations, which is found in his 1905 publication.

[AnssiH]

Not quite. I said “non-zero” for the probability of the known circumstances for a very real but subtle fact apparently ignored by most everyone. Just because a certain circumstance is a member of the set of known circumstances does not mean that the probability of obtaining (or seeing or being aware of or whatever ...) that circumstance is one. All you really know is that, if it is part of the collection of known circumstances, the probability of it occurring is non-zero. In fact, the “what is” is “what is” is a valid explanation of anything. As I said, that explanation is directly represented by [math]\vec{\Psi}=0[/math].

 

Hmmm, right, this is a somewhat difficult issue to handle in the communication of this whole analysis, because at least I have tried to make sure that I view the collection referred to as "the past", as whatever it is that stands behind an explanation. I.e., whatever it was that was actually taken into account in the formuation of the explanation. But do I read you right that your comment refers to the fact that the past is also expressed in the terminology of an explanation, and in that sense the existence of some circumstance is also a function of the correctedness of that explanation, and subject to whatever assumptions make up that explanation?

 

-Anssi

[AnssiH]

AnssiH. Einstein would never add the word "value" after the word "same" in any attempt to define time in the way you claim.

 

You misunderstood what I said by some margin :)

 

If you look at space time as a representation of some dynamics, i.e. some entities doing whatever it is they do, there are also interaction events expressed in that space time; points where some elements interact. I.e., some elements come in contact with each others. When I said "defining time as being at the same value when interactions between entities occur", I was referring to the fact that a space time representation does represent interaction between events, and that representation very much has to do with seeing where those world lines come together spatially and temporally. Or another way to say it, establishing when two elements are at the same place, at the same time.

 

In any analysis of any dynamics between two or more elements, where those dynamics are expressed via relativistic time definitions, there exists the idea that at some points in space and time the elements interact, and as a different concept, the definition of time measurement.

 

And don't worry, I do understand relativistic definitions and how Einstein meant them. Like I said, whatever consequences this issue leads into, are not in any sense of the word "obvious". The issues arise very deep inside the definitions of QM and/or GR. That also means, that if those issues were to be recognized exactly, they could probably be fixed by some adjustments to those definitions. Or, alternatively, it is possible to view time exclusively as the concept that is related to interactions between elements, and view clocks as devices that measure something quite different.

 

In terms of DD's notation, a clock would by its very definition be just a device that measures [imath]\tau[/imath] displacement. If you examine his derivation of special relativity, it should be easy to see that it represents special relativistic relationships exactly. Any deviations from the modern physics definitions occur much later down the road.

 

-Anssi

[Bombadil]

I had a subtle difficulty in my mind having to do with loss of information in representing circumstances, and the idea that the information behind so-called "momentum" would have to be embedded into a circumstance (as per your definition of "circumstance") was an attempt to resolve that difficulty. But I have to re-think this from the perspective that you are using to actually defend the constraint.

 

AnssiH I suspect and I may be wrong, but I think that the actual value of such things as “momentum” “mass” and “energy” are part of the initial conditions needed for [math]\vec{\Psi}[/math] something that so far has received no attention. I suspect partly because there is no interest in solving the fundamental equation. I guess this would make them part of your explanation and not have anything to do with what is being represented. Unlike the need to conserve them being a consequence of the representation.

 

Of course, every actual explanation (in order to be valid: i.e., not disprovable by experiment) must also be consistent with a very similar constraint: the presumed known data must be consistent with what is known. You need to comprehend that this constraint is quite different from what my constraint expresses.

 

Are we still only interested in if a [math] \vec{\Psi} [/math] exists for every possible set of elements forming a past?

 

I am still wanting to assert that a [math] \vec{\Psi} [/math] exists for every consistent explanation. I can agree that a [math] \vec{\Psi} [/math] exists that is following the exchange symmetry rules that you present, and that it is valid in that there is no way to disprove it since it is completely consistent with the past. But I am not so sure that any consistent explanation has such a representation. But then, this isn't what you are assorting is it? You are asserting that a [math] \vec{\Psi} [/math] exists for any possible past and how it is interpreted as an explanation or in fact what [math] \vec{\Psi} [/math] is, is really of no interest.

 

As I have proved elsewhere, any function can be represented as a sum of symmetric and antisymmetric function so nothing has been ignored.

 

At what point do we start using both parts of the function. I've been under the impression that you want to use antisymmetric functions for valid elements and so remove any symmetric properties from valid elements.

 

That is if we start with [math] \vec{\Psi} [/math] and want to use it to represent a valid element we then take the antisymmetric part with all other elements. That is we take [math] \vec{\Psi} [/math] and perform the transformation

 

[math] F(x,y)=\frac{f(x,y)-f(y,x)}{2} [/math]

 

for every other elements this is then what we would use.

 

If on the other hand it was an invalid element that we were interested in we would take the antisymmetric part as above for all other elements. We would then take the symmetric part when exchanged with other invalid elements by using

 

[math] G(x,y)=\frac{f(x,y)+f(y,x)}{2} [/math]

 

we would then add these two functions to form the function of interest which is just the original function. We now have a function in which a valid element can not be in the same location as any other element and invalid elements can occupy the same location as other invalid elements.

 

I am of the opinion that you have fallen into exactly the same mental trap that has apparently confused everyone except Anssi. You are presuming that what I am presenting is a theory of some sort. It isn't! It is exactly what I have been representing it to be from the first day: a representation of the constraints implied by the definition of an explanation and nothing more.

 

I suspect that perhaps you don't understand the issue that I am having with what you have done as a final step it may also be that you are doing something slightly different then what I have been thinking that you where doing, so let me try and point out just what I am talking about.

 

Every time that I have seen you show that any solution to your fundamental equation will satisfy the constraints that you have derived you do so by starting out at the fundamental equation and then showing that you can derive each of the constraints from it.

 

To me this asserts that if we where looking at a solution to the fundamental equation then we are looking at a solution that will satisfy the constraints that you have defined from your definition of an explanation. However if we where looking at a solution to the equations

 

[math] \sum^n_{i=1}\vec{\nabla}_i\vec{\Psi}(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t) = i\vec{k}\vec{\Psi}(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t) [/math]

[math] \frac{\partial}{\partial t}\vec{\Psi}(x_1,x_2,\cdots,x_n,t)=iq\vec{\Psi}(x_1,x_2,\cdots,x_n,t). [/math]

and

[math] \sum_{i\neq j} \delta(\vec{x}_i-\vec{x}_j) = 0. [/math]

 

it has not yet been shown that we are looking at a solution to the fundamental equation. Actually I am beginning to wonder if you ever meant to assert that it was, rather you are asserting that there exists a solution to the fundamental equation that is consistent with any possible past. That is, you are assorting the statement “there exists an [math] \vec{\Psi} [/math] consistent with the past that also satisfies the fundamental equation”.

[Doctordick]

Bombadil, once again, I think your problems stem from misunderstandings of certain subtle aspects of the representation. For that reason, I will answer your comments out of the order with which you present them.
 

If on the other hand it was an invalid element that we were interested in we would take the antisymmetric part as above for all other elements. We would then take the symmetric part when exchanged with other invalid elements by using

[math] G(x,y)=\frac{f(x,y)+f(y,x)}{2} [/math]

we would then add these two functions to form the function of interest which is just the original function.

 

The first thing which comes to mind here is that there are absolutely no “invalid” elements under consideration in any of my arguments. You are confusing “invalid” with “hypothetical”. Those are two rather different concepts. I use the word “invalid” to refer to an explanation which is inconsistent with the known information. One could call the element causing that inconsistency an invalid element but the issue is really of no significance since I have no interest in invalid explanations. A hypothetical element is one which is not required except through the assumption that the explanation is correct; “correct” means that the explanation will remain valid forever and no experiment will ever be performed which can invalidate that explanation.

It should be quite clear to you that absolutely any element can be hypothetical and that there exists no way to guarantee any explanation is “correct” (and so far as simple explanations go, it is always possible that one is misinterpreting the explanation: i.e., they are not talking about what you think they are talking about, ergo Qfwfq's main problem).
 

I reckon this doesn't make them universal unless you allow re-labellings which are so arbitrary that the whole thing makes no sense.

 

I have no idea as to where Qfwfq got the idea that “making sense to Qfwfq” was one of the requirements of my abstract definition of an explanation. Apparently under his meager understanding of abstract concepts all possible explanations are required to make sense to him to qualify as an explanation. Under Qfwfq's “universal interpretation” of my definition, Einstein's theory of General Relativity cannot qualify as an explanation unless it makes sense to a two year old. It does not appear that thinking in the abstract is one of Qfwfq's strong suits.

But back to Bombadil's post:

The sole purpose for which antisymmetric functions was introduced was to insure that non-hypothetical elements would not vanish from the representation when the numerical label referencing that element appeared more than once (the hypothetical tau axis was introduced in order to maintain the universality of the representation when the numerical labels “x” were represented as points on a line). It should be clear to you that the representation of those labels as points on a line cannot possibly be a universal representation without appending that extra dimension. Furthermore, I can conceive of no way of maintaining that separation (for those “non-hypothetical elements) all the way to infinity except via the antisymmetric representation. The whole issue here is to maintain the universality of the representation.

As I have commented a number of times, every element in any explanation could possibly be hypothetical (that is essentially the founding issue of “solipsism” and there exists no proof that solipsism is false). However, if we want to maintain the universality of the representation, we cannot presume solipsism is correct: i.e., we must include the possibility that some of those elements being explained are real elements of the universe. If they are truly real, then we cannot allow them to vanish in our representation of the known data; it is this fact alone which requires that hypothetical tau axis. Without that axis such elements simply cannot be represented as points on line.

Now, regarding the hypothetical elements; since they are not part of the truly known information, they can come and go anyway the explanation wishes them to come and go. There is no true data to be lost so they can have the same “x” (or x,tau) numerical label anytime the explanation wants them to. Thus it is that hypothetical elements can be represented by either symmetric or antisymmetric functions (which one is preferred is totally a consequence of the specific explanation being represented). And, once again, in order to maintain universality of the representation, we need to include all possibilities.

That brings up another point perhaps overlooked by you. If there is no reason to prevent two specific “x” numerical labels from being the same (we are then speaking of hypothetical elements), then the function representing the explanation need not be antisymmetric with respect to the exchange of those two arguments. That brings up an issue I suspect you have overlooked. Being antisymmetric with respect to exchange is a characteristic of the pairs of numerical labels “x”, specific arguments of the function [math]\vec{\Psi}[/math], not an overall characteristic of the function itself.

Secondly, that pair need only be antisymmetric when both elements being referred to are “real”. Thus it is that this characteristic of being “real” and/or not “hypothetical” can be attached to the individual elements themselves. Hypothetical elements and “real” elements can also have exactly the same numerical labels; being antisymmetric with respect to exchange with the other “real” elements is what is critical. However, we need to be careful here. Just because we find a mathematical function [math]\vec{\Psi}[/math] (an apparently valid explanation) which requires some element to be antisymmetric with respect to exchange with some other element, we cannot presume that either of those elements are “real”.

To make a long story short, any function may be divided into two different kinds of functions via the procedures I pointed out to you:

[math]
F(x,y)=\frac{f(x,y)-f(y,x)}{2}
[/math]

 

forcing the function to be antisymmetric under exchange of these two elements and

 

[math]
G(x,y)=\frac{f(x,y)+f(y,x)}{2}
[/math]

 

forcing the function to be symmetric under exchange of those two elements.

And your problem revolves around, what about element pairs where this symmetry is insignificant. That is very simple to handle. Since antisymmetric with respect to exchange requires both elements to be “real”, the problem you pose applies only to “hypothetical” elements. Since the only time that this issue arises is when the two labels are exactly the same, the function [math]\vec{\Psi}[/math] can be represented with two different pairs of arguments, one set for a boson representation (symmetry) and one set for a Fermi representation (anti-symmetry). Remember, these elements are, by definition, hypothetical and the correct function could very well be the sum of one which has been made antisymmetric under the above procedure and the other which has been made symmetric via the other procedure. Since they are “hypothetical” (and thus not part of the “real” information to be explained) seeing them as a sum of two different elements is no problem the number of hypothetical elements is an open issue and the number required are whatever it takes to get the probability yielded by the explanation. Remember what we are interested in representing are the explanations. The only requirement I place on them is that they be “valid”: i.e., they do not contradict themselves.

The final result of this analysis is the fact that all elements may be divided into two categories without in any way excluding any specific function: i.e., any probability distribution can be represented. Exclusion of a specific function is only accomplished via validity problems.
 

I am still wanting to assert that a [math] \vec{\Psi} [/math] exists for every consistent explanation. I can agree that a [math] \vec{\Psi} [/math] exists that is following the exchange symmetry rules that you present, and that it is valid in that there is no way to disprove it since it is completely consistent with the past. But I am not so sure that any consistent explanation has such a representation. But then, this isn't what you are asserting is it? You are asserting that a [math] \vec{\Psi} [/math] exists for any possible past and how it is interpreted as an explanation or in fact what [math] \vec{\Psi} [/math] is, is really of no interest.

 

Again, you are missing a subtle point. First, all explanations yield some information on one's expectations. Often times, explanations can be sloppy and thus may not explicitly yield a specific result for some circumstance but that is not a serious issue since “some number between zero and one” is sufficient to satisfy the requirement of validity. The underlying “what is” is “what is” explanation (which is guaranteed to be valid by virtue of it's nature) can handle any those sloppy circumstances not considered within the "formal" (think of as "incomplete") explanations. (This issue essentially has to do with the compartmentalization common to most human explanations.) Thus it is that every explanation yields some sort of probability for every circumstance and therefore the explanation defines the result to be achieved by [math]\vec{\Psi}[/math] and that means [math]\vec{\Psi}[/math] corresponding to that explanation is defined. If a specific function is defined for every explanation then there exists a one to one mapping between the two.

Validity has to do with agreeing with the “known” information to be explained. But the known information is a finite set of ??? (whatever they happen to be). What I have shown is that it is always possible to force an explanation to yield non-zero results for any specific desired antisymmetric elements (real elements) via the introduction of hypothetical elements. The relationship

[math]
\sum_{i\neq j} \delta(\vec{x}_i-\vec{x}_j) = 0.
[/math]

 

can be used to enforce that explicit constraint for all “real” elements and, since the underlying information to be explained is the “real” entities, that constraint is perfectly universal.
 

AnssiH I suspect and I may be wrong, but I think that the actual value of such things as “momentum” “mass” and “energy” are part of the initial conditions needed for [math]\vec{\Psi}[/math] something that so far has received no attention.

 

No, they are nothing more than names for specific terms in the fundamental equation. Because of the structure of the fundamental equation, the total sum of those terms become “conserved” quantities. Seeing them as defined with regard to individual elements is nothing more than a consequence of the structure of the fundamental equation.
 

Are we still only interested in if a [math] \vec{\Psi} [/math] exists for every possible set of elements forming a past?

 

That depends on what definition of “the past” you choose to use. If you are using my definition, the past is nothing more than the “known information”. The set of elements is that set of elements required by the explanation thus, if the representation is to be “universal” the representation must be capable of representing every possible “finite” set of such elements: i.e., it must be possible to represent them via circumstances which are collections of numerical labels, labeling the undefined references the explanation uses.

The past is an aspect of your explanation (the circumstances defined by your explanation which are to yield a non-zero probability) not an aspect of what is being explained. Nonetheless, we have no interest in an explanation which is inconsistent with its own representation of the past. That would be an invalid explanation. In essence, the past, constitutes boundary conditions on the specific proposed [math]\vec{\Psi}[/math] which is to yield the same expectations as the represented explanation. There is another point embedded in that observation which must be kept in mind: validity only requires a non-zero probability for known circumstances. An actual specific probability is a consequence of the explanation: i.e., the actual mathematical function representing that explanation in my abstract representation.
 

Every time that I have seen you show that any solution to your fundamental equation will satisfy the constraints that you have derived you do so by starting out at the fundamental equation and then showing that you can derive each of the constraints from it.

 

I don't think your representation of the situation is exactly correct. There is one very important aspect of that demonstration which you seem to neglect. What I show is that (via those anti-commuting operators which I define) any solution to my fundamental equation is also a solution to the three equations put forward as the necessary constraints on [math]\vec{\Psi}[/math]. It is not actually a general solution to those constraints but rather a very specific solution to the general problem. Any solution to my fundamental equation is a solution to those three equations only if the constants “k” and “q” (summed over the entire universe) vanish. (That makes the fundamental equation zero plus zero equals zero; a rather simple identity.) But the interesting point is that symmetry considerations imply that, given a solution which yields zero for those “conserved” quantities, it is quite easy to transform that solution to one that yields any value for those “conserved” quantities which may be desired.

In essence, that means that my fundamental equation is only valid in a universe where the total momentum of the universe vanishes (somewhat analogous to a center of mass system). The “energy” term can also be transformed to any value but the arguments are a little more complex. (A shift of energy level is a mathematical symmetry embedded in the original representation.)
 

That is, you are assorting the statement “there exists an [math] \vec{\Psi} [/math] consistent with the past that also satisfies the fundamental equation”.

 

I would rather say that there exist an infinite number of functions [math]\vec{\Psi}[/math] which are consistent with the past and satisfy the fundamental equation. The constraint imposed by the past only reflects a finite number of defined circumstances but there exist an infinite number of functions [math]\vec{\Psi}[/math] which will match those circumstances and yet each yield a different value for some circumstances outside those specific circumstances.

What I find interesting is the fact that the fundamental equation yields exactly the same statistical results accepted by those people who accept quantum mechanics as the “correct” explanation of reality. The critical issue here is that my construct is totally tautological and has absolutely nothing to do with reality and yet yields very close to exactly the same answers they obtain experimentally (totally within their expressed error limits). The philosophic question embedded in that result is, exactly what does that say about the fundamental presumed foundations standing behind their answers? Are those presumptions necessary or not?

My position is that their "foundations" are as necessary to their results as was Ptolemy's epicycles to the accurate predictions of the apparent motion of the stars and planets.
 

The Ptolemaic model accounted for the apparent motions of the planets in a very direct way, by assuming that each planet moved on a small sphere or circle, called an epicycle, that moved on a larger sphere or circle, called a deferent. The stars, it was assumed, moved on a celestial sphere around the outside of the planetary spheres.

[math]\cdots[/math] the Ptolemaic model was not seriously challenged for over 1,300 years.

I suppose I should not expect serious examination of my work for at least another thousand years.

Have fun -- Dick

 

Edited May 27, 2014 by Doctordick

[Qfwfq]

I have no idea as to where Qfwfq got the idea that “making sense to Qfwfq” was one of the requirements of my abstract definition of an explanation.

You totally missed my point there.

 

Also Dick, I've already told you to avoid saying things about me which are not true. :naughty:

[Bombadil]

The sole purpose for which antisymmetric functions was introduced was to insure that non-hypothetical elements would not vanish from the representation when the numerical label referencing that element appeared more than once (the hypothetical tau axis was introduced in order to maintain the universality of the representation when the numerical labels “x” were represented as points on a line). It should be clear to you that the representation of those labels as points on a line cannot possibly be a universal representation without appending that extra dimension. Furthermore, I can conceive of no way of maintaining that separation (for those “non-hypothetical elements) all the way to infinity except via the antisymmetric representation. The whole issue here is to maintain the universality of the representation.

 

That is without that extra dimension there would be no way of telling two elements apart. This extra dimension is part of the representation not part of the explanation. All that it supplies is a means by which elements can be represented to be different even if they are given the same x label. So it could be said to be hypothetical and not real, however it is required by the representation.

 

This issue becomes a bigger problem when we consider the possibility of expanding the representation out to an infinity number of elements since we may now have to represent things like a continuous set of elements and we can no longer add elements one at a time to insure that no two elements are at the same location. The representation is at this point not able to represent such things and still guarantee that no two elements will always be represented differently. Two elements may be given the same label and in the infinite limit we have no way to check and see if they were.

 

The antisymmetry will solve this problem in that it means that no two real elements can have a [math] \vec{\Psi} [/math] that would allow them to be in the same location, but is it really part of the representation isn't it part of [math] \vec{\Psi} [/math]?

 

And your problem revolves around, what about element pairs where this symmetry is insignificant. That is very simple to handle. Since antisymmetric with respect to exchange requires both elements to be “real”, the problem you pose applies only to “hypothetical” elements. Since the only time that this issue arises is when the two labels are exactly the same, the function [math]\vec{\Psi}[/math] can be represented with two different pairs of arguments, one set for a boson representation (symmetry) and one set for a Fermi representation (anti-symmetry). Remember, these elements are, by definition, hypothetical and the correct function could very well be the sum of one which has been made antisymmetric under the above procedure and the other which has been made symmetric via the other procedure. Since they are “hypothetical” (and thus not part of the “real” information to be explained) seeing them as a sum of two different elements is no problem the number of hypothetical elements is an open issue and the number required are whatever it takes to get the probability yielded by the explanation. Remember what we are interested in representing are the explanations. The only requirement I place on them is that they be “valid”: i.e., they do not contradict themselves.

 

So that if some element happens to be behaving like a symmetric element sometimes and an antisymmetric element at others it can simply be seen as a combination of symmetric and antisymmetric elements or as a hypothetical element that is symmetric to some elements. Since we can add any hypothetical elements that we choose to modify the expectations that will be arrived at. Furthermore more since the hypothetical elements are only added to satisfy the expectations there is no reason that the explanation can't allow a real and hypothetical element to have the same x label as long as the real element never vanishes from the representation and never has the same x label as some other real element.

 

Validity has to do with agreeing with the “known” information to be explained. But the known information is a finite set of ??? (whatever they happen to be). What I have shown is that it is always possible to force an explanation to yield non-zero results for any specific desired antisymmetric elements (real elements) via the introduction of hypothetical elements. The relationship

 

[math]

\sum_{i\neq j} \delta(\vec{x}_i-\vec{x}_j) = 0.

[/math]

can be used to enforce that explicit constraint for all “real” elements and, since the underlying information to be explained is the “real” entities, that constraint is perfectly universal.

 

But if we are truly going to consider our representation to be universal then don't we need to consider that no-matter how much information we have there is always the possibility that new information will become available in the future that will invalidate the current explanation and so we must be able to expand the known information to infinity? So don't we need to be able to include every possible future information that may become available? This seems to imply to me that any possible set of expectations must be included in the set of possible explanations, or do all that we really need, is as you seem to be implying, that it is possible to have a nonzero probability for any possible hypothesized future. By which I only mean that we have no way of knowing what the future will be and so any predictions is nothing but a hypothetical construct and we need only allow any such construct.

 

The past is an aspect of your explanation (the circumstances defined by your explanation which are to yield a non-zero probability) not an aspect of what is being explained. Nonetheless, we have no interest in an explanation which is inconsistent with its own representation of the past. That would be an invalid explanation. In essence, the past, constitutes boundary conditions on the specific proposed [math]\vec{\Psi}[/math] which is to yield the same expectations as the represented explanation. There is another point embedded in that observation which must be kept in mind: validity only requires a non-zero probability for known circumstances. An actual specific probability is a consequence of the explanation: i.e., the actual mathematical function representing that explanation in my abstract representation.

 

Maybe this is starting to go off topic but, isn't the past somewhat more then just a boundary condition as there is no one variable that can be seen as constant for the past, that is there is no variable that we can see as it being the boundary of but rather the past is a set of information that our explanation must be consistent with.

 

In essence, that means that my fundamental equation is only valid in a universe where the total momentum of the universe vanishes (somewhat analogous to a center of mass system). The “energy” term can also be transformed to any value but the arguments are a little more complex. (A shift of energy level is a mathematical symmetry embedded in the original representation.)

 

Are you suggesting that the momentum is something other then just a mathematical symmetry embedded in the original representation?

 

I would rather say that there exist an infinite number of functions [math]\vec{\Psi}[/math] which are consistent with the past and satisfy the fundamental equation. The constraint imposed by the past only reflects a finite number of defined circumstances but there exist an infinite number of functions [math]\vec{\Psi}[/math] which will match those circumstances and yet each yield a different value for some circumstances outside those specific circumstances.

 

But this kind of bypasses the original question. That is, if we have a function that satisfies the original constraints on an explanation can we transform it into a solution to the fundamental equation or at the very least a function that satisfies the fundamental equation with the possible addition of terms representing the change in energy mass and momentum that were allowed in the original constraints? Or are there functions that exist that would satisfy the original constraints but not have a corresponding solution to the fundamental equation?

[Doctordick]

That is without that extra dimension there would be no way of telling two elements apart.

 

I think you have a rather erroneous perspective of this issue. “Telling two elements apart” is no real issue here; if they are the same, they are the same so there is no need to tell them apart (we are talking about “numerical labels). The issue is, “how many are there”. If the representation of the information is a collection of numbers and one wishes to “represent” that information as points on a line, one has a serious problem with that “representation” (points on a line) when two numerical labels are the same. When viewed as “points on a line” the existence of two or more occurrences of the specific numerical label is lost.

 

This extra dimension is part of the representation not part of the explanation. All that it supplies is a means by which elements can be represented to be different even if they are given the same x label. So it could be said to be hypothetical and not real, however it is required by the representation.

 

It is the phrase, “telling two elements apart” which bothers me. You appear to understand the issue here.

 

This issue becomes a bigger problem when we consider the possibility of expanding the representation out to an infinity number of elements since we may now have to represent things like a continuous set of elements and we can no longer add elements one at a time to insure that no two elements are at the same location. The representation is at this point not able to represent such things and still guarantee that no two elements will always be represented differently. Two elements may be given the same label and in the infinite limit we have no way to check and see if they were.

 

I wouldn't say it becomes a bigger problem, but rather that it becomes a sticky problem in the infinite limit. You are correct, carried to infinity, continuity becomes a difficulty. Taken one step at a time the original process is always possible (the point where it fails can not be specified); however, it can not be done with an infinite collection of information. What is important is that anti-symmetry of the representative functions [math]\vec{\Psi}[/math] can handle the problem without complications. Essentially we are using what physicists call the “Pauli exclusion principal” to guarantee that the separation proceeds all the way to infinity. It is a convenient consequence of anti-symmetry attributed to Dr. Pauli.

 

The anti-symmetry will solve this problem in that it means that no two real elements can have a [math] \vec{\Psi} [/math] that would allow them to be in the same location, but is it really part of the representation isn't it part of [math] \vec{\Psi} [/math]?

 

Again I think you are making a subtle assumption here that is totally unwarranted. Your use of the word “real” bothers me. As you use it, it implies you know what is and what is not real. That is a major assumption which simply cannot be defended. If it could be defended, you could prove Solipsism is either true or false; and most intelligent scientists would agree that Solipsism can not be proved false nor can it be proved true. The “truth” of the data standing behind an explanation (what is being explained) is really of no consequence here. I am only concerned with representing the explanation, no matter what that explanation might be.

 

When I use the term “real” I mean an element which is required by every possible explanation which could ever exist. This is certainly not an identifiable characteristic of any element of an explanation; however, we must include such a possibility in our analysis.

 

Once one establishes what data must be explained, that is the data which must be explained. Its truth is not an issue under discussion. The only issue of concern is that the explanation does indeed yield the data to be explained as occurring with a non-zero probability (as reckoned by that explanation: i.e., the boundary conditions which I call validity) and that the explanation does not contradict itself (does not give different results for the same question). An important issue here is that some explanations (most in fact) do not actually give answers to all possible questions. In my representation, that situation is represented by [math]\vec{\Psi}[/math] not being known for some circumstance [math](x_1,x_2,\cdots,x_n,t)[/math].

 

Now that is a case worth thinking about. I started this whole thing by wanting to find out the constraints implied by the definition of an explanation. When I proposed representing every possible explanation by a mathematical function (not the converse)

[math]\vec{\Psi}(x_1,x_2,\cdots,x_n,t)[/math]

 

how does that representation handle questions not actually answered by a specific explanation? The answer is actually quite straight forward. If the explanation being represented does not actually yield answers to some questions, then the function [math]\vec{\Psi}^\dagger\cdot\vec{\Psi}[/math] must be integrated over all possibilities not specifically answered (the correct answer could be any internally consistent possibility). It is only after that integration is completed that we get the answers provided by the explanation. This brings up an interesting conundrum.

 

If this result only yields the answers provided by the explanation only after that integration takes place, the possibility exists that more than one function exists which represents the explanation supposedly being represented. Well I have taken a very specific stance with respect to that problem. If more than one function yields the same answers as the explanation (after the indicated integration has been done) then I take the position that it is possible that answers to questions not expressed by the explanation (its incompleteness) may come up in the future which might separate out those different functions: i.e., such events might separate the situation into separate explanations.

 

What is important about that shift in perspective is that it takes into account the fact that one may misunderstand or misinterpret an explanation. In such a case, [math]\vec{\Psi}[/math] separates into two different functions: i.e., the change in required integrations become significant. These integration can be seen as approximations being presumed by the explanation as presented: i.e., the explanation being represented is actually a number of explanations, each implementing significant presumptions.

 

By this mechanism, the universal generality of the representation is maintained even when the circumstances are seen as points in a multidimensional space. In addition, just because an element is hypothetical (necessary to the explanation), it is possible that the explanation may presume distinct specific numeric labels. For example, though a photon may be required to be hypothetical in my representation, the explanation being represented may require specific locations for that photon (all possibilities are equally acceptable by that explanation).

 

... So that if some element happens to be behaving like a symmetric element sometimes and an antisymmetric element at others it can simply be seen as a combination of symmetric and antisymmetric elements or as a hypothetical element that is symmetric to some elements.

 

I think you have the cart on the wrong side of the horse here. It is the explanation which yields the answers to you questions. If your explanation requires a symmetric function in some relationships and anti-symmetric functions in others then it requires elements numerically labeled to reflect that issue. Your perspective presumes that every possible function corresponds to a known explanation. That is a rather undefendable assumption.

 

Since we can add any hypothetical elements that we choose to modify the expectations that will be arrived at. Furthermore more since the hypothetical elements are only added to satisfy the expectations there is no reason that the explanation can't allow a real and hypothetical element to have the same x label as long as the real element never vanishes from the representation and never has the same x label as some other real element.

 

Again, the use of that term “real” with a connotation not intended by me. There is nothing in my presentation which requires “non-hypothetical” entities to fail to vanish. The fundamental equation does require overall conservation of energy and all components of momentum but that does not require any hypothetical elements (represented by symmetric or anti-symmetric relationships) not to vanish.

 

By which I only mean that we have no way of knowing what the future will be and so any predictions is nothing but a hypothetical construct and we need only allow any such construct.

 

I would say that is about right.

 

Maybe this is starting to go off topic but, isn't the past somewhat more then just a boundary condition as there is no one variable that can be seen as constant for the past, that is there is no variable that we can see as it being the boundary of but rather the past is a set of information that our explanation must be consistent with.

 

What you seem to miss is that satisfying the past set of information is the boundary condition. Functions of many variables are quite complex structures. Consider fitting a curve to a set of known data points. Those known data points are the boundary conditions the function is required to satisfy. I should point out that fitting a straight line to a set of data essentially makes the assumption that the data is uncertain and that the correct value of the specific points is only approximately given by the data.

 

Are you suggesting that the momentum is something other then just a mathematical symmetry embedded in the original representation?

 

No, I am not. My original deduction deduced that

[math]

\sum^n_{i=1} \frac{\partial}{\partial x_i}\vec{\Psi}(x_1,x_2,\cdots,x_n,t)=ik\vec{\Psi}(x_1,x_2,\cdots,x_n,t)

[/math]

and

[math]

\frac{\partial}{\partial t}\vec{\Psi}(x_1,x_2,\cdots,x_n,t)=iq\vec{\Psi}(x_1,x_2,\cdots,x_n,t).

[/math]

 

Had to be required by the symmetry properties of the referenced numerical labels(an arbitrary number can added to every numerical label used to represent the specific elements presumed by the explanation). Those constants (k and q) must be a part of the explanation (they cannot be changed by that renumbering procedure). However, as differential operations, those constants constraints can be changed via a mathematical procedure normally referred to as a Fourier transformation, without making any change in the underlying characteristics of the resultant solution (the transformation is reversible so the original function can always be recovered). In a sense, the constants (k and q) are totally arbitrary and can be anything one wishes without changing the fundamental information embedded in the function [math]\vec{\Psi}[/math]; however, the actual form of the function [math]\vec{\Psi}[/math] does indeed change.

 

My fundamental equation is not totally general in the sense that these constants are arbitrary. However, every solution of my equation is a solution to the above equations where the constants k and q are zero. Thus it is no more than a Fourier transformation of solutions to the above equations.

 

Or are there functions that exist that would satisfy the original constraints but not have a corresponding solution to the fundamental equation?

 

Yes, they certainly exist; however, there exists a Fourier transform which will transform them into a solution of the fundamental equation.

 

Have fun -- Dick

Edited May 28, 2014 by Doctordick

[Bombadil]

I think you have a rather erroneous perspective of this issue. “Telling two elements apart” is no real issue here; if they are the same, they are the same so there is no need to tell them apart (we are talking about “numerical labels). The issue is, “how many are there”. If the representation of the information is a collection of numbers and one wishes to “represent” that information as points on a line, one has a serious problem with that “representation” (points on a line) when two numerical labels are the same. When viewed as “points on a line” the existence of two or more occurrences of the specific numerical label is lost.

 

Perhaps I had a bad choice of wording, I was referring to the representation of multiple elements and it was perhaps a bad choice to use the word element when what I was referring to was the representation of the elements, a different issue. The elements themselves pose no problems, it is the representation in which we must be able to distinguish between multiple occurrences of the same x label or more precisely we must allow a means by which a distinction of the same labels may exist. That is when the same x label is given more then once there must exist a way of assigning the labels to a representation of different elements.

 

Talking about distinguishing between the elements themselves actually makes no sense since we don't even know what it is that we are talking about. All that we have is a representation of it.

 

Again I think you are making a subtle assumption here that is totally unwarranted. Your use of the word “real” bothers me. As you use it, it implies you know what is and what is not real. That is a major assumption which simply cannot be defended. If it could be defended, you could prove Solipsism is either true or false; and most intelligent scientists would agree that Solipsism can not be proved false nor can it be proved true. The “truth” of the data standing behind an explanation (what is being explained) is really of no consequence here. I am only concerned with representing the explanation, no matter what that explanation might be.

 

The whole issue of calling elements real and hypothetical at times bothers me and more often I start thinking of them as elements that have a symmetric exchange for hypothetical and an antisymmetric exchange for real elements, which is bound to lead to miscommunication and is incorrect.

 

The problem is of course that real elements must be included in every possible explanation of something (of course we don't know what we are explaining we just know that this label must be part of the representation) and the hypothetical elements are added so that the explanation is consistent with the past.

 

But how do we know that an element won't have to be represented in such a way that it will vanish from the representation at some point. Such an element would have to be a hypothetical element by your definition but you have not shown that an explanation won't have to include such elements since we really don't know what we are explaining.

 

You seem to be bypassing this question by saying that to ask this question we would be assuming that we know the explanation, but at the same time you seem to be saying that the symmetries are part of the representation which I still don't understand it seems to me that they are part of the explanation.

 

This all seems to mean that the use of ether term is prone to confusion. Of course the solution to this is just stick to the definitions that have been being used and try not to confuse them. But the problem is that some sets of elements contain both real and hypothetical elements but are hard to refer to without using terms that imply that something else is being talked about, for instance the set of all elements that are symmetric with respect to exchange. Of course we could use the physics names for these elements but with how that has gone in the past we are libel to trade one problem for another.

 

If this result only yields the answers provided by the explanation only after that integration takes place, the possibility exists that more than one function exists which represents the explanation supposedly being represented. Well I have taken a very specific stance with respect to that problem. If more than one function yields the same answers as the explanation (after the indicated integration has been done) then I take the position that it is possible that answers to questions not expressed by the explanation (its incompleteness) may come up in the future which might separate out those different functions: i.e., such events might separate the situation into separate explanations.

 

Are you suggesting that the boundary value problem that is made up of the past needs to only be approximated by an integration over segments of [math] \vec{\Psi} [/math] that we correspond to the past, which makes up the boundary value problem?

 

I think you have the cart on the wrong side of the horse here. It is the explanation which yields the answers to you questions. If your explanation requires a symmetric function in some relationships and anti-symmetric functions in others then it requires elements numerically labeled to reflect that issue. Your perspective presumes that every possible function corresponds to a known explanation. That is a rather undefendable assumption.

 

I'm not sure that I understand what you mean by a known explanation. Certainly if we had a function that satisfies the constraints on your definition of an explanation then it would make sense to call that a known explanation. And I'm not suggesting that there exist a unique function for each possible past, so perhaps it is that I may be assuming continuity to the information being represented which requires a particular form of the function of interest that you are saying is impossible. All that I am trying to do is understand how you have added these symmetries and not made some behaviors of functions impossible.

 

Again, the use of that term “real” with a connotation not intended by me. There is nothing in my presentation which requires “non-hypothetical” entities to fail to vanish. The fundamental equation does require overall conservation of energy and all components of momentum but that does not require any hypothetical elements (represented by symmetric or anti-symmetric relationships) not to vanish.

 

Are you suggesting that an element with an anti-symmetric exchange symmetry can vanish from the representation? I thought that it was specifically designed so that this couldn't happen?

 

What you seem to miss is that satisfying the past set of information is the boundary condition. Functions of many variables are quite complex structures. Consider fitting a curve to a set of known data points. Those known data points are the boundary conditions the function is required to satisfy. I should point out that fitting a straight line to a set of data essentially makes the assumption that the data is uncertain and that the correct value of the specific points is only approximately given by the data.

 

 

This all seems like a new idea to me, all of the differential equations that I have encountered that are solved are solved for, as an example the case of a time Dependant differential equation, for the case t=0 where F(x,t) is the solution and F(x,0) = f(x) is then the solution to the boundary value problem where f(x) is the boundary condition you seem to be setting [math]F(x_i,t_i)=f(x_i,t_i)[/math] where [math](x_i,t_i)[/math] is a finite set which represents the past. Not quite what I think of when you say boundary value problem.

 

Yes, they certainly exist; however, there exists a Fourier transform which will transform them into a solution of the fundamental equation.

 

Then can we derive the fundamental equation from your constraints rather then show that the constraints are satisfied by a solution to the fundamental equation? Is how you are showing it really how you originally came up with the fundamental equation? What is really concerning me is that I don't see an inverse to any of your operators that don't set something else to zero which is not encouraging when you are showing that your fundamental equation is universal. At the very least have you found the transformation that maps a solution to the original constraints into a solution to the fundamental equation?

[AnssiH]

The whole issue of calling elements real and hypothetical at times bothers me and more often I start thinking of them as elements that have a symmetric exchange for hypothetical and an antisymmetric exchange for real elements, which is bound to lead to miscommunication and is incorrect.

 

The problem is of course that real elements must be included in every possible explanation of something (of course we don't know what we are explaining we just know that this label must be part of the representation) and the hypothetical elements are added so that the explanation is consistent with the past.

 

But how do we know that an element won't have to be represented in such a way that it will vanish from the representation at some point. Such an element would have to be a hypothetical element by your definition but you have not shown that an explanation won't have to include such elements since we really don't know what we are explaining.

 

You seem to be bypassing this question by saying that to ask this question we would be assuming that we know the explanation, but at the same time you seem to be saying that the symmetries are part of the representation which I still don't understand it seems to me that they are part of the explanation.

 

This all seems to mean that the use of ether term is prone to confusion. Of course the solution to this is just stick to the definitions that have been being used and try not to confuse them. But the problem is that some sets of elements contain both real and hypothetical elements but are hard to refer to without using terms that imply that something else is being talked about, for instance the set of all elements that are symmetric with respect to exchange. Of course we could use the physics names for these elements but with how that has gone in the past we are libel to trade one problem for another.

 

I read this exchange in the past few posts and clearly there is a big ambiguity problem in the presentation, in terms of what is meant by "hypothetical elements" and "real/non-hypothetical elements". I think it should be communicated in different manner.

 

This is a good example of what I meant in the other thread about this being a delicate topic. It's just impossible to know what someone means by "real" and "hypothetical" because in slightly different contexts within this presentation, those words may easily refer to entirely different ideas. One significant idea is that all defined elements of any world view are hypothetical in ontological sense. This is implied often in the communication because it is important fact to keep in mind. And then the same word is used in this context in different manner, so now it's hard to figure out whether or not anything is understood as intented.

 

This issue can be viewed and communicated from many different perspectives, so may I suggest a perspective that I think captures the significant issue in less ambiguous manner.

 

View the information-to-be-explained as a collection of undefined events, and view an explanation as a way to label those events into a collection of defined elements.

 

A defined element typically consists of a large collection of undefined events; we typically take the same defined element to exist in the consecutive circumstances, even though the underlying events are not in any sense "the same events".

 

The labeling connects some collection of undefined events with some defined elements, yielding the idea of a world line (trajectory) of the element in [imath]x,\tau,t[/imath] space.

 

Even when an explanation has defined that element with the assumption that it follows its world line in a continuous manner, we can still express the epistemological constraint "no two defined elements can be in the same observable state simultaneously" via requiring anti-symmetry under exchange between such elements.

 

That kind of element is what DD was calling "real/non-hypothetical", even though ontologically it is entirely hypothetical; other equally valid explanations might not label the events in similar manner. Let me call them A-elements ("Anti-symmetric under exchange"-elements)

 

Now you might ask, what about those defined elements that are in modern physics defined in such manner, that a number of elements can be in the same state simultaneously. Such as "photons".

 

Note that they are never in the same observable state simultaneously. They are simply elements, whose definitions particularly requires they are taken to pass the same states along their trajectories (in terms of quantum mechanical statistics). We only observe those elements via some observable states associated with A-elements implying that they are there, via us interpreting the circumstance that way, as per our explanation.

 

So in that sense they are supporting elements to our explanation. Perhaps call them S-elements, for "symmetric under exchange"? Or "Support elements" :)

 

May I also note that this may not be the most trivial issue once you really dig deep into it. I think if you understand the above, you are good to continue. It is much easier to really think about this issue once you have walked through the deductions to modern physics.

 

-Anssi

[Doctordick]

Hi Bombadil,

I am sorry about my slow response and the length of this post. I wanted to be very careful as to what I said and it has become quite clear that confusion is the word of the day. Most of your comments are somewhat astray of what I intended and I think the underlying issues are in deep need of clarification. Modest and Qfwfq have made their misinterpretation of my work a bit clearer to me recently and I suspect some of your problems stem from exactly the same distorted perspective they have become attached to. The central problem behind that distorted perspective is pretty well brought out with the following post by modest.
 

And the claims of DD and Anssi are that any message can be cracked with a certain form of representation/explanation of the data while at the same time making no assumptions regarding the message. This is unreasonable.

 

The problem here is that Modest is making a subtle but unwarranted assumption. He is clearly presuming that my proof concerns “cracking a message” where the "sender" is reality and the "receiver" is the mind; a somewhat paraphrased generality of his comment (essentially expressed by Qfwfq in a private message). I suspect this is the pivotal source of their inability to understand what I am saying. I comment about it here because I suspect you have a tendency to fall into exactly the same intellectual hole.

The issue of my proof is, what are the constraints implied by the definition of “an explanation” and nothing else. That has to be approached as an absolutely universal issue. Making any attempt to clarify the definition of “an explanation” beyond the issue of answering questions is to place additional constraints on what is being talked about (which, by the way, is exactly what Rade always wants to do). Apparently everyone is driven to see my intention as divining a means of discovering explanations which it most definitely is not. I have a strong suspicion that you are also trying to see my proof as a method of discovering explanations.

Please take a look at my November 23 post to Rade. You should make a good attempt to understand exactly why I made that post as it displays exactly the misunderstood central issue of my proof. That central issue is the question as to exactly what absolutely universal constraints are implied by the definition of an explanation. As far as I am concerned, the fact that it provides answers to questions regarding things to be explained is the only absolutely universal assertion one can make about explanations. If anyone has any serious arguments that there exist any other absolutely universal assertions, please put them forward together with any deduction of interest they might bring forth.

I have held that mathematics is the invention and study of self consistent systems and an explanation which is not self consistent creates a great many logical difficulties. For that reason, I do not concern myself with inconsistent explanations (though the world of Man certainly contains many). It is the quality of being internally consistent which allows those answers to be represented by specific non-zero probability for specific circumstances [math](x_1,x_2,\cdots,x_n,t)[/math]: i.e., internal consistency means that, no matter how a question is approached by the logic of the explanation, the same answer is reached. This means that the answer is the significant issue here, not the logic required to achieve that answer.

As a pure aside having absolutely nothing to do with my proof, it is interesting to note the impact that last sentence has on Searle's Chinese room. If understanding is being able to map your solution to explaining some circumstances into another's solution then understanding is a mapping problem having nothing to do with the supposed logic of the solution. It is rather obvious that Searle's (and Chalmers') faith in “the mind as a consciousness entity” is an ontological belief essentially analogous to belief in God: an unnecessary presumption (a fictitious element only required if their explanations are correct). For those who think what I have just said is doubtful, please consider the fact that what I am really saying is quite simple. All I am doing is asserting that there might exist other explanations. That is the very essence of the “universality” of my presentation.

But back to my post:

The significance of that last comment is that we can simply step across the issue of the logic of the explanation. That is a very important issue because, if we are required to understand the logic of an explanation, it is impossible to even discuss the subject in an absolutely universal mode. No matter how much we know, there may be things we don't know. Nonetheless we do know that the answers to questions provided by an explanation are a function of the circumstances the explanation explains: i.e., that probability can be represented by [math]P(x_1,x_2,\cdots, x_n,t)[/math] a purely mathematical expression.

I have a habit of presenting the answers arising from an explanation as representable via a collection of true false questions (which seems to me to be a rather simple obvious truth); but that view is not really necessary; the answer to any question can be seen as a circumstance in itself: i.e., representable by [math](x_1,x_2,\cdots, x_n,t)[/math]. Which yields the probability as a measure of the acceptance of that specific answer: i.e., most of the complaints people come up with are involved with peripheral issues of no importance to my work. The only important fact in all of this is the fact that epistemology is, by this representation, reduced to a mathematics problem. Ontology has become an absent issue. This is a fact that only Anssi seems to truly comprehend.

The question being discussed by me is then, what can one say about that function without placing any additional constraints on that function. The fundamental issue is that we can modify that function or our representation of it in any way we choose so long as the modification itself introduces no additional constraints on the possible probabilities being represented.

The differential relationships I develop are a pure consequence of the fact that the actual numerical labels used to reference the elements of the explanation are totally immaterial to the problem. They clearly must hold because, for any specific explanation, expressing all relevant circumstances via references to the elements of that explanation cannot change in any way when the specific labeling is changed. I know that fact seems bothersome to most everyone but it really isn't difficult to understand once you understand my proof.

But, in the meantime, back to your post.
 

That is when the same x label is given more then once there must exist a way of assigning the labels to a representation of different elements.

 

No, that is not true. You simply have the problem totally backwards. The issue here is that the numerical labels refer to elements required by the explanation being represented. They are assigned only if a specific explanation is being represented and I have utterly no interest in how those labels are assigned; I am merely concerned with the fact that it is possible to assign them. The existence of computer facilitated communication pretty well assures the fact that any message is representable via numerical labels. Go back to the Chinese room problem.

The only fact of significance here is the possibility of circumstances containing multiple references to the same elements. The issue has to do with mapping the representation into a new representation as points on a line. I suspect you are failing to comprehend that mathematics is itself an epistemological structure based on ontological elements. Of course, the ontological elements of mathematics are entirely figments of your imagination (required by the explanations of those internally consistent systems) but they are, nonetheless, important aspects of mathematics.

As I have said many times, I accept mathematics as a supposed valid collection of internally self consistent systems. That does not mean that I am guaranteeing the correctness of those systems but rather that I leave the problem to others. I use mathematics because it is the most universally understood collection of internally self consistent structures available. As such, it should be clear that any truly self consistent system can theoretically be mapped into a mathematical structure as that is essentially the very definition of mathematics.
 

Talking about distinguishing between the elements themselves actually makes no sense since we don't even know what it is that we are talking about. All that we have is a representation of it.

 

But, you must keep in mind the fact that whenever we have a specific explanation, we know what we are talking about; however, so long as we are being absolutely universal, that issue simply cannot arise in the discussion of possibilities. On the other hand, we still need ontological elements in order to use mathematics. A numerical label constitutes a mathematical ontological element (normally called a number). We are simply working with a one to one mapping of the ontological elements of the explanation into the ontological elements of mathematics called numbers. Since the intention is to remain absolutely universal we cannot constrain these elements to any ontological elements specific to any given explanation other than the mathematical structure being used in the representation; to do so would destroy the universality of the representation.

So, the question arises, exactly what are we doing when we go to represent these numerical labels as points on a line. Points on a line are another fictitious ontological concept central to mathematics (the central ontological elements of geometry, another supposed self consistent structure). The problem is that although there may be a one to one mapping of numbers to points on a line, there is not a one to one mapping of collections of numbers to points on a line. It is possible that the collection may contain multiple occurrences of some specific numbers. If that circumstance occurs, the mapping will fail as a point on a line cannot represent such multiple occurrences.

The fictitious tau axis was introduced to alleviate that problem. I say “alleviate” because it doesn't really solve the problem. One still has that same serious mapping problem. We are now talking about a point in a plane and we still have the problem that, though there is a one to one mapping of number pairs to a plane, there is no one to one mapping of collections of number pairs, (x,tau), to points in a plane. The possible existence of multiple occurrences can still be lost in the representation.

What is important at this point is that the introduction of fictitious elements in no way constrains the universality of the representation. Actually, in a sense, it adds to that universality in that it allows an explanation to contain elements which are not part of what is actually being explained (exactly what I call “fictitious” elements).

If I have a specified circumstance to represent and I add an additional fictitious element, that act in no way constrains what can be represented. In fact, what it does is expand the field of what can be represented beyond what is actually to be explained (fictitious elements are, in fact, elements of the explanation). A little thought should convince you that explanations are, in general, ripe with fictitious elements (note that I define elements as fictitious if you cannot prove they are necessary without assuming the explanation is correct.) A good example is God in any religious argument. Even religionists admit the fact that the existence of God must be taken on faith and cannot be proved by any physical experiment.

Photons fall into exactly the same category, their existence must be taken on faith and cannot be proved by any physical experiment without presuming their existence: i.e., presuming electromagnetic theory is correct. This presumption is exactly equivalent to Ptolemy's presumption of the physical existence of the celestial spheres, a presumption Newton later showed to be completely unnecessary.

I brought that issue up because of your problem,
 

The whole issue of calling elements real and hypothetical at times bothers me and more often I start thinking of them as elements that have a symmetric exchange for hypothetical and an antisymmetric exchange for real elements, which is bound to lead to miscommunication and is incorrect.

 

This real and hypothetical division arises only because of the fact that most all explanations contain what I call fictitious elements (elements which are required only if one believes the explanation is correct). What is real and what is hypothetical must be seen as a totally open issue. If that issue is not kept open, Solipsism is removed as a possibility and the representation is no longer universal as it is a well known fact that proving Solipsism is invalid is impossible (invalidity of Solipsism is a faith issue). On the other hand, the possibility that some elements are in fact not fictitious and are required whether the explanation is correct or not must also be handled (if the issue is not handled, the representation is not universal).
 

The problem is of course that real elements must be included in every possible explanation of something ...

 

And again, you make a statement that you cannot prove (note the above).
 

(of course we don't know what we are explaining we just know that this label must be part of the representation) and the hypothetical elements are added so that the explanation is consistent with the past.

 

Once again, incorrect! Hypothetical elements are added in order to facilitate all possible explanations. In order to allow all possible probability functions, [math]P(x_1,x_2,\cdots, x_n,t)[/math], consistent with what is being explained: i.e., to keep the representation absolutely universal.
 

But how do we know that an element won't have to be represented in such a way that it will vanish from the representation at some point. Such an element would have to be a hypothetical element by your definition but you have not shown that an explanation won't have to include such elements since we really don't know what we are explaining.

 

And once again you make a totally false statement. Nowhere does my attack require any element to be in every circumstance. The only deduced requirement at this point (deduced directly from the symmetry issues in the mapping procedure itself) are the differential relationships on [math]\vec{\Psi}[/math]:

[math]
\sum_{i=1}^n \left\{\frac{\partial}{\partial x_i}\hat{x}+ \frac{\partial}{\partial \tau_i}\hat{\tau}\right\}\vec{\Psi} \equiv \sum_{i=1}^n\vec{\nabla}_i\vec{\Psi}=\left(\sqrt{-1}\right)\vec{k}\vec{\Psi}
[/math]

and

[math]
\frac{\partial}{\partial t}\vec{\Psi} =\left(\sqrt{-1}\right)\mu\vec{\Psi}.
[/math]

 

You seem to be bypassing this question by saying that to ask this question we would be assuming that we know the explanation, but at the same time you seem to be saying that the symmetries are part of the representation which I still don't understand it seems to me that they are part of the explanation.

 

As I said, the symmetries arise from the mapping issue. If one examines the representation of two absolutely identical explanations they must yield absolutely identical probabilities for all representations of identical circumstances but that does not require the numerical labels be identical. Following the consequences of adding a constant to every numerical label in one of those representations leads directly to the necessary validity of those differential relationships. It follows that those differential relationships must be universal consequences of the fact that such a mapping is possible.

It is also possible to make a replacement of every individual label with an alternate label. So long as every appearance of a given specific label in one explanation appears as that alternate label in the same circumstance being represented in the other representation of that explanation; if the explanations are identical, the probabilities for the circumstances must be identical. This leads to some interesting universal consequences which can only be understood with a clear understanding of that “simple geometric proof” I laid out back in 2006.

For the moment, it is more important to follow the derivation of my fundamental equation.
 

But the problem is that some sets of elements contain both real and hypothetical elements but are hard to refer to without using terms that imply that something else is being talked about, for instance the set of all elements that are symmetric with respect to exchange.

 

As I have already said, the division into real and hypothetical elements is entirely in your mind and has utterly no impact upon how they are handled except for one simple but very important factor. The explanation must yield non-zero probabilities for all “real” elements contained in each and every known circumstance including differentiating between those circumstances with different numbers of the same elements. These are specific elements (or labels) that must absolutely be represented in chosen representation (as points in that x,tau plane). The mapping from a collection of numbers must map one for one into points on the plane.

That result can be achieved by requiring [math]\vec{\Psi}[/math] to be anti-symmetric with respect to label exchange with regard to all elements required to be real. That anti-symmetry results in what is called Pauli exclusion. If the value of function changes sign when two specific arguments are exchanged (the definition of “anti-symmetry) then it must vanish when the arguments are identical as zero is the only number equal to its own negative. This is nothing more than a specific requirement demanded by the need to be an absolutely universal representation.

This result can be achieved by requiring “real” elements to be represented by functions which are anti-symmetric with respect to exchange of the numeric labels of those “real” elements. The converse of that requirement is not a requirement; just because [math]\vec{\Psi}[/math] is anti-symmetric with respect to exchange of two arguments does not mean that the elements represented by those labels are real. Allowing [math]\vec{\Psi}[/math] to be anti-symmetric with respect to exchange of some arguments simply allows the possibility of “real” elements.

As I told you once before, any function may be represented by a sum of anti-symmetric and symmetric components so no functions [math]\vec{\Psi}[/math] have been eliminated. [math]\vec{\Psi}[/math] is still open to any function yielding non-zero probabilities for the circumstances to be explained (except for the differential relationships implied by the mapping freedom).
 

Of course we could use the physics names for these elements but with how that has gone in the past we are libel to trade one problem for another.

 

Now here is where I get the impression that you think my fundamental equation is offered as a mechanism for uncovering explanations, which appears to be the central issue creating that distorted perspective everyone is so fond of. That is not what I am doing. What I am doing is creating an absolutely universal mathematical representation of any possible explanation. Every conceivable explanation is clearly representable in my notation.

In order to defend that last statement, let me point out a very simple problem representable in that notation. First of all, it should be quite obvious that the set of numerical labels x_i can be divided into three separate sets: x_i, y_i and z_i (the freedom to add hypothetical elements allows every conceivable circumstance to be seen as a function of such triplets). Each of those can be seen as an independent coordinate. That plus the fictitious tau and t coordinates yield a five dimensional Euclidean geometry. Quantization of momentum in the tau direction (and seeing that component as mass) makes the uncertainty in tau infinite thus totally projecting out the tau axis. We are then left with a representation which is essentially requires the known elements (the supposed real elements) to be seen as points in a three dimensional space who's position may change with time (it does not have to change).

That should convince you that the representation is quite open. In fact, every point going to make up the earth and every structure built upon the earth could be so represented in one such representation. That includes the Library of Congress, every university in the world together with every paper in existence; and can actually include every individual on earth together with their actions (and all the stars and planets in the heavens). So, it is clearly possible to embed in the representation every explanation mankind has ever written down and saved (they are in those papers).

It follows that there is no explanation in the representation itself. What is interesting is that the ontological elements of the mathematical representation (the points going to make up this picture) must approximately obey a set of equations almost exactly the standard relationships accepted by modern physics. And that result is dependent upon no experiment whatsoever. There is no need for physical existence of the celestial spheres; the moon is just falling.
 

Are you suggesting that the boundary value problem that is made up of the past needs to only be approximated by an integration over segments of [math] \vec{\Psi} [/math] that we correspond to the past, which makes up the boundary value problem?

 

Boy you sure do miss some important issues. The integration being referred to is the mathematical procedure required to include an estimate of the probability of all circumstances not explicitly defined by the enumerated list of circumstances to be explained. That is what Qfwfq is leaving out in every one of his supposed examples: i.e., he and everyone else is presuming the consequences of those issues can be ignored; they are presuming the old compartmentalization normally used in almost all arguments is a valid assertion and not an assumption.
 

I'm not sure that I understand what you mean by a known explanation. Certainly if we had a function that satisfies the constraints on your definition of an explanation then it would make sense to call that a known explanation.

 

No it is not. You are confusing what is being represented with the representation. The difference should be clear to you from the above.
 

All that I am trying to do is understand how you have added these symmetries and not made some behaviors of functions impossible.

 

The symmetries are a consequence of the representation (the mapping of the explanation from one form to another) and all it tells you are how the explanation will fill in between the known circumstances if it is internally consistent.
 

Are you suggesting that an element with an anti-symmetric exchange symmetry can vanish from the representation? I thought that it was specifically designed so that this couldn't happen?

 

Once again, you are mixing two very different issues. If an element to be represented vanishes, it better vanish in the representation (otherwise the representation is wrong). On the other hand, if an element to be represented vanishes because of a flaw in the representation, that means the representation is inadequate to its job. Anti-symmetry was introduced to avoid the second problem: representing multiple occurrences of the same element in a circumstance (representing a collection of numbers as a collection of points).
 

Not quite what I think of when you say boundary value problem.

 

You are thinking in terms of functions of one variable. Partial differential equations are quite different. The partial differential is defined to be the standard differential under the assumption that all the other variables are constants. That means that you have a great number of boundary conditions to establish the specific function: one boundary condition for every set of such “constants”. Fitting a set of points in a plot becomes such a boundary condition.
 

At the very least have you found the transformation that maps a solution to the original constraints into a solution to the fundamental equation?

 

Yes; it is actually quite trivial. You need to understand Fourier transforms. As I said long ago, if you really want to understand this stuff you need some serious professional education. More than I can present on this forum. Actually, the transformation required to show that the two solutions are equivalent is the double transform of a Fourier transform together with a related inverse transform. Such a double transformation can produce a solution for the following differential equation from a given solution with a different value of [math]\vec{k}[/math]. It follows that a specific value of [math]\vec{k}[/math] is immaterial to the solution of a differential equation such as:

[math]
\sum_{i=1}^n\vec{\nabla}_i\vec{\Psi}=\left(\sqrt{-1}\right)\vec{k}\vec{\Psi}
[/math]

 

The procedure is closely related to the mathematical problem of converting center of mass solutions to general solutions in physics problems and any educated physicist would be quite familiar with the process. It is closely related to the “shift property” referred to in equation #55 of the above reference.

As I said earlier, mathematics has its own ontology. Positions in a geometry (points) are an ontological element. My representation transforms into a representation where the only ontological elements are points in a geometry. The fact that such a transformation is possible brings out an interesting and little appreciated fact. In our mental picture of reality, we presume points in a geometry (where things are) are significant ontological elements; however, we also tend to presume that there are other significant ontological elements to consider.

But if we look at the issue carefully, it becomes quite obvious that everyone of those other ontological elements are defined in terms of peripheral circumstances. For example, consider an electron going from point a to point b. How do you know it is an electron? Well, the answer is, because of the surrounding peripheral circumstances leading up to that event. The problem is that any careful examination of those peripheral circumstances (element by element) result in the same question with the same answer. The result is, the ontological element “position” is the only element absolutely required.

That fact reduces the whole problem of explaining the universe to two issues; conservation of momentum (a well known constraint on reality required by the physical symmetry of the universe),

[math]
\sum_{i=1}^n\vec{\nabla}_i\vec{\Psi}=\sqrt{-1}\vec{k}\vec{\Psi},
[/math]

 

and my interaction term:

[math]
\sum_{i \neq j} \delta(\vec{x}_i-\vec{x}_j) = 0
[/math]

 

for hypothetically real elements which is clearly true because we can always add hypothetical elements (anti-symmetric under exchange) sufficient to exactly eliminate any circumstances which are not acceptable as possible real circumstances underlying our explanation. Omitting some of those elements merely adds to the uncertainty of the acceptable circumstances.

My result is entirely consistent with experimental modern physics in every way except for Einstein's explanation of general relativity which is well known to conflict with quantum mechanics. In my picture there is no conflict with general relativity.

A second problem with a conflict between quantum mechanics and relativity is also trivially solved. That is, collapse of the wave function. Modern Physics considers collapse of the wave function to be a real physical phenomena whereas my presentation holds that problem to be an absolutely different issue. The wave function yields our expectations, not reality, and when any new data is obtained our expectations must simply be recalculated (what we expect changes in order to be consistent with what we already know). The whole purpose of the index "t" is to divide what is known into changes in our knowledge (the present was defined to be the boundary between the past, what is known, and the future, what is not known). A recalculation of our expectations must be accomplished at every such boundary. Thus it is that it appears that the “what is” is “what is” is the only required explanation of the universe. Our expectations at every moment need only be consistent with what we have experienced up to that moment and that is the only constraint on any explanation.

The moon is just falling!

Have fun – Dick

Edited May 28, 2014 by Doctordick

[Qfwfq]

The problem here is that Modest is making a subtle but unwarranted assumption. He is clearly presuming that my proof concerns “cracking a message” where the "sender" is reality and the "receiver" is the mind; a somewhat paraphrased generality of his comment (essentially expressed by Qfwfq in a private message). I suspect this is the pivotal source of their inability to understand what I am saying.

Really, Dick. I have discussed these things inside out with Anssi as well as having read all your discussions about how we make sense of the world and comparing it to Plato's cave. I understand that your supposed proof is, itself, an abstraction and you mean it to apply to anything. But, whenever somebody dares to mention some of these possible things, you assume they have no idea what your talking about. You simply don't get the point of what folks are saying. :doh:

[Rade]

Making any attempt to clarify the definition of “an explanation” beyond the issue of answering questions is to place additional constraints on what is being talked about (which, by the way, is exactly what Rade always wants to do).

False. What Rade wants to do is to have you stop changing your definition of an explanation each time someone explains to you a problem with that definition you present.

 

That central issue is the question as to exactly what absolutely universal constraints are implied by the definition of an explanation.

Yes' date=' a very important issue, so how about you let us know exactly what absolutely universal constraints are implied by YOUR DEFINITION OF AN EXPLANATION. And, why do you add so many constraints to begin your proof presentation ? Please justify each one at a time, perhaps we can remove some of the constraints you have added and improve your presentation from the begin.

 

As far as I am concerned, the fact that it provides answers to questions regarding things to be explained is the only absolutely universal assertion one can make about explanations.

False. Many if not most explanations do not provide acceptable answers to both the person asking for an explanation and the person providing the explanation.

 

I have held that mathematics is the invention and study of self consistent systems and an explanation which is not self consistent creates a great many logical difficulties.

Many explanations are given on purpose not to be self consistent and their use is very logical. You have invented a very narrow and non universal world view of what an explanation means' date=' how it is defined.

 

I do not concern myself with inconsistent explanations (though the world of Man certainly contains many).

Well then, your proof cannot be universal because by your own words it concerns but one small sub-set of explanations, those that can be summed as A = A type explanation.

 

It is the quality of being internally consistent which allows those answers to be represented by specific non-zero probability for specific circumstances [math](x_1' date='x_2,\cdots,x_n,t)[/math']: i.e., internal consistency means that, no matter how a question is approached by the logic of the explanation, the same answer is reached. This means that the answer is the significant issue here, not the logic required to achieve that answer.

False. The answer to any question given as an explanation (thus explanation itself as a procedure) is useless unless it is based on use of logic (rational thinking) to arrive at the answer.

 

...faith in “the mind as a consciousness entity” is an ontological belief essentially analogous to belief in God: an unnecessary presumption (a fictitious element only required if their explanations are correct).

False. This view is is not "an ontological belief". Go back and reread the reference.

 

The significance of that last comment is that we can simply step across the issue of the logic of the explanation. That is a very important issue because' date=' if we are required to understand the logic of an explanation, it is impossible to even discuss the subject in an [b']absolutely universal[/b] mode.

False. The logic of the explanation is what makes the explanation "an explanation". You are always required to make a reasonable and rational attempt to understand the logic of an explanation given to you, and you are required to use logic to make an explanation to another.

 

No matter how much we know' date=' there may be things we don't know.[/quote']What a strange use of the English language. What do you mean there "may" be things we don't know ? Are you not clear on this point ?

 

Nonetheless we do know that the answers to questions provided by an explanation are a function of the circumstances the explanation explains

False. You can never say you "know this" for any answer provided to questions as a possible explanation. The answer given may on purpose be 100% a function of some circumstance completely unrelated to the circumstance the explanation explains' date=' and such an answer can be logically given and for good reason.

 

that probability can be represented by [math]P(x_1,x_2,\cdots, x_n,t)[/math] a purely mathematical expression.

Sure, but one of many other ways the probability can be presented.

 

The only important fact in all of this is the fact that epistemology is' date=' by this representation, reduced to a mathematics problem. Ontology has become an absent issue. This is a fact that only Anssi seems to truly comprehend.[/quote']Ontology is NEVER absent in any attempt to discuss epistemology. This is a fact that only you seem to not truly comprehend.

 

The question being discussed by me is then' date=' what can one say about that function without placing any additional constraints on that function.[/quote']Sure, but you have by your own words already placed so many constraints on that function, why in the world would anyone want to consider placing yet additional constraints ? You have already placed all the constraints needed well before you even begin your "question being discussed".

 

No' date=' that is not true. You simply have the problem totally backwards.[/quote']NO, it is you that have the problem totally backward as we can read from these two contradictory statements you made in a matter of a few sentences.

 

So, first you made the claim about role of ontology and mathematics:

 

epistemology is' date=' by this representation, [b']reduced to a mathematics problem. Ontology has become an absent issue[/b].

 

Then you make this contradictory claim which completely negates the logic of your "proof presentation".

 

I suspect you are failing to comprehend that mathematics is itself an epistemological structure based on ontological elements.

 

But' date=' you must keep in mind [b']the fact[/b] that whenever we have a specific explanation, we know what we are talking about

There is no such "FACT" concerning a "specific explanation", never has been, never will be. It is clearly observed by the specific explanation in your recent post suggesting you do not know what you are talking about on many issues, and that you did not know that you were making contradictory claims concerning relationship of mathematics and ontology.

[modest]

The problem here is that Modest is making a subtle but unwarranted assumption. He is clearly presuming that my proof concerns “cracking a message” where the "sender" is reality and the "receiver" is the mind; a somewhat paraphrased generality of his comment...

That's nothing like the problem.

 

Your tendency to imply an unintended meaning from a single word is a problem that impedes the progress of the conversation. You take a word (or example or analogy) and find from it a manufactured implication which confirms your suspicion that the person is misinterpreting what you're saying.

 

Another example. I onetime used the word "between", saying "well... if you define the present as the boundary between past and future..." Your reaction was to say:

 

I seriously doubt that I used the word "between" but perhaps I did; I do get sloppy sometimes. The real problem here is that you have not defined what you (or Rade) mean by the word “between”.

 

-http://scienceforums.com/topic/16156-what-is-spacetime-really/page__view__findpost__p__242896

 

Yet, in your last post which I just read and quoted you have:

 

...the present was defined to be the boundary between the past, what is known, and the future, what is not known...

So clearly the use of the word "between" isn't a problem. The use of "cracked" isn't a problem either. There is no reason to derail the progress of discussion based on these things.

 

Please just consider that you might do what I'm saying and it might not be helpful.

[Rade]

That's nothing like the problem. Your tendency to imply an unintended meaning from a single word is a problem that impedes the progress of the conversation. You take a word (or example or analogy) and find from it a manufactured implication which confirms your suspicion that the person is misinterpreting what you're saying.

Hello. I agree with your analysis of the method of dialog used by DD on this forum..in all his many thread posts.

 

Consider the example you provide that DD demand that you and I present a "definition of between" before we are worthy of questioning his proof presentation:

 

QUOTE of DD: I seriously doubt that I used the word "between" but perhaps I did; I do get sloppy sometimes. The real problem here is that you have not defined what you (or Rade) mean by the word “between”.

 

Yet' date=' on another thread, when on another thread I requested that DD provide his own list of definitions for the concepts he uses, he replied that it was unnecessary for him to provide such a list for his proof presentation. In fact, he specially stated that there is no need to worry about definitions in general or of specific concepts such as "between"....so we read his wisdom on the value of definitions for his proof presentation...

 

Quote of DD: definitions are used to establish the ontology necessary to understand whatever is intended in the communication which uses whatever it is that is being defined. You are concentrating on that issue (the issue of definitions) when it actually has nothing to do with what I am talking about. You need to be able to think the situation out in the abstract without worrying about definitions.

 

So, definitions are a one-way argument street for DD. He is allowed to make comments about his proof presentation "without worrying about definitions", but, when anyone else makes a comment, well, they better have definitions at hand for all the terms they use.

 

Another example:

 

QUOTE of DD: I have made no attempt to define "definition" as I regard the issue as totally immaterial.

I rest my case.

 

==

Edit: I will also make the claim that the reason DD refuses to define the word "between" as used in his definition of "time" is because to do so would make his definition of "time" null and void, thus his entire proof presentation falls apart from the get-go, from his lack of clear understanding of how the concept "between" is critical to the concept of "time". But, perhaps I error, perhaps DD does in fact have a definition of "between" that is consistent with his concept of how the "present" relates to the "past" and "future". Because the concept of "time" used by DD has nothing at all to do with how Einstein defined time, it makes sense that DD would conclude that his proof presentation does not agree with GR Theory of Einstein.