What can we know of reality?

[Doctordick]

While I can see that a formal education in theoretical physics has some advantages for the time binging I’m going to continue doing it as I have been.

I suspect you misunderstood my “word of mouth” comment. Many times, in both lectures and one on one conversations, professors will elaborate on the subject with a few personal, somewhat non-technical comments, on how issues came to be seen the way they are seen. The background of thought behind physics is an issue almost too large to be set down in a lifetime and little issues you won't find in any book can be very enlightening. Buffy has often tried to push me into making such “examples”; I resisted because my original thoughts were often totally unsupportable associations which I am afraid could detract attention from the proofs and be used as “solid evidence” that I am a nut and that the proofs need not be examined.

 

None the less, a formal education is a very valuable experience which you should make every effort to obtain. Symmetry is very much such an issue; I would not refer to the formal presentations as particularly enlightening. Of course, my take on symmetry (developed out of “word of mouth” comments by professors) is quite alien from from most all formal presentations. If you haven't yet, I would suggest you read the following three posts: my comments on symmetry, selfAdjoints response and my response to selfAdjoint.

Then for now should the right side of the fundamental equation be thoughts of as ...

Somehow I suspect a little confusion about my statement still exists here.

 

The relationship being imposed by shift symmetry in the index t (which I have decided to defined to be “time” as it is there to handle “change in what we know” which, to me, is the very essence of the concept time) is,

[math] \frac{\partial}{\partial t}\vec{\Psi}=0 [/math]

 

The central issue of my generalization to

[math] \frac{\partial}{\partial t}\vec{\psi}=-im\vec{\psi}, [/math]

 

has to do with algebraic manipulation convenient to solving differential equations. That is to say, if I have a solution to the first equation above, I know that [imath]\vec{\psi}=e^{-imt}\vec{\Psi}[/imath] is a solution to the second. In exactly the same vein, if I happen to have a solution to the second equation, I immediately have a solution to the first: [imath]\vec{\Psi}=e^{imt}\vec{\psi}[/imath]. If you read John Baez's web site, you should come to understand that these transformations relate to “conserved quantities” embedded in the representations implied by the associated differential equations. The m in the above equation is closely related to conservation of energy in Schroedinger's representation of quantum mechanics where different values for m essentially amount to changing the zero point reference for that conserved quantity. I believe this will all become clear as I develop the solutions to my fundamental equation.

I had started to notice that this seemed to be the effect although when the second equals sine is put in there I’m not quite sure how it remains equal.

(I presume you mean “the second equal sign” there.) That also will become clear as I roll out the solutions. How it remains equal is central to the solution. The fact that it must remain equal is essentially a statement that a conserved quantity related directly to that differential must exist.

Hello, sorry it took me a while to reply again, just being a bit busy until the end of february at least.

Don't worry about it. When we got back from Denver, we ended up with more visitors here than we have had in the last thirteen years. Thirteen years ago, the whole house was occupied by guests; the back room being chock full of brides maids in sleeping bags. For last week, my wife and I were far too busy to even think about looking at the internet. But everyone is gone now. Ah, peace and quite is wonderful; especially for an old man.

Some things that have puzzled me little bit were actually mentioned in the posts to Bombadil and Qdwdq. I see

*** [imath]\vec{\psi}[/imath] and [imath]\vec{\Psi}[/imath] and [imath]\vec{\phi}[/imath] ***

all being used to refer to the same function, at least that's what it looks like to me. Is there a reason there's a slightly different symbol used from time to time, or was it just to make the explanation little bit clearer?

Some of it is probably just my sloppiness but most of it should be related to nearby differential equations with slightly different structures (see my comment to Bombadil above).

If I've understood it correctly, the left sides of those equations are essentially identical?

Not exactly; that is why psi is capitalized in one and not in the other (the functions are solutions to slightly different differential equations).

And the reason for allowing the [imath]-iKvec(psi)[/imath] was - I believe - for mathematical convenience?

The answer is yes if you mean mathematical convenience in solving the differential equation. Note that K here is an arbitrary constant and that, with regard to the solutions of the differential equation, K=0 encompasses the solution to [imath]\frac{\partial}{\partial t}\vec{\Psi}=0 [/imath].

My understanding becomes very much superficial when it comes to your explanation of the deduction with [imath]e^{-frac{i K}{n}(x_1+x_2+cdots+x_n)}[/imath], and similarly in post #83 the explanation with [imath]vec{phi}=e^{iK_x * ( x_1+x_2+cdots+x_n)}e^{iK_tau * (tau_1+tau_2+cdots+tau_n)}e^{imt}vec{psi}[/imath]

The central issue there is that [imath]e^{-A}e^A=1[/imath]. The complex conjugate of [imath]\vec{\phi}[/imath] is found by changing the sign of the imaginary parts (those parts multiplied by i). Thus it is that the resultant probabilities are not affected by these terms (there will be two multiplicative exponential terms with opposite signs yielding a net effect of “unity”). As Qfwfq has commented, such terms only yield phase changes (in the complex space representation of [imath]\vec{\psi}[/imath]). For the moment, you can look at these things as conveniences in algebraic representations of solutions to a differential equation.

 

In the final analysis, we are concerned with the magnitude of the vector [imath]\vec{\psi}[/imath] (the probabilities are defined to be given by that normalized magnitude) and complex numbers simply allow specification of a particular kind of change in that abstract vector convenient to examining certain changes. Remember, any complex number can be represented as a position in a two dimensional space; what Qfwfq and I are calling a “phase shift” is no more than a rotation in that two dimensional space which yields no change in the magnitude of the abstract vector. The whole thing is no more than a mathematical operation which yields changes convenient to our analysis. For the moment, I think we can let the thing go; hopefully the issues will become clearer later.

And still related to that, it would be interesting to hear how that sort of differential expression is used in conservation of momentum in quantum mechanics?

In Schroedinger's expression of quantum mechanics, momentum of an object represented by a given wave function is defined to be given by some constants times [imath]\frac{\partial}{\partial x}\Psi(x)[/imath] or rather, the expectation of the momentum is given by [imath]\Psi^*(x) \frac{\partial}{\partial x}\Psi(x)[/imath] integrated over all x. In quantum mechanics, this relationship is essentially established by postulated axiom. If that definition is taken as a true expression of the classical idea of momentum, then the many body equation

[math]\sum_i \frac{\partial}{\partial x_i}\Psi(x_1,x_2,\cdots,x_n, t) =0[/math]

 

is no more than a statement that the sum of the momentum of all the bodies involved is zero (and that would be in the “rest position of the center of mass” of the system). Of course, the coordinate system of interest might not be in the “rest position of the center of mass” and, in that case, the sum would not be zero but it would still be constant (i.e., momentum is conserved); however, I have not yet defined either the “rest position of the center of mass” or momentum so the issue is yet mute (I have made utterly no connection with reality, other than “time” as a change in what we know, and everything I have presented is pure mathematical tautology).

Perhaps it would be useful to say that in this presentation the probability function is not allowed to depend on the specific labels, and that requirement is being justified by the fact that the labeling procedure cannot add any additional information on the noumena no matter how it is performed.

My point is that, if that probability function is dependent upon the specific labels attached to those noumena then we need a method of determining that specific attachment. Now the common answer is certainly, ”when you get the proper probabilities, you know you have attached the labels properly”. That answer is most certainly an erroneous statement as I have demonstrated a specific procedure for developing exactly the correct probabilities for any specific labeling (so long as the number of elements is finite): the ”what is”, is “what is” tabular function, augmented by specific “invalid” noumena. It follows that the specific labeling simply can't be an issue; just as the specific language within which our solution is presented cannot be a requirement of the solution.

A small side question...would it not be correct to hold true in all cases that: to explain an outcome of a real event [E] you must always define the real cause(s) of [E] ?

Absolutely! That is what explanations are all about: explanations are mechanisms which supply causes. The phrase “explain an outcome” presumes the outcome is related to that “real event” and the relation itself is a fundamental part of the explanation.

Thus, because all explanation of any type requires definition of at least some type, can we not hold true that it is impossible for such a phenomenon as "undefined explanation" of reality ?

But every explanation requires its own definitions; thus my question would be exactly what do you propose for a collection of definitions applicable to all possible explanations? I have given one: I have defined time to be an index on changes in the information upon which the explanation is based and I have a couple of other definitions which I will put forth as I solve that differential equation, all of which I claim are applicable to all possible explanations. Are you intending to propose some definitions?

 

I think we are getting very close to being concerned with looking at solutions to my equation; but, before we can go there, there are a couple subtle issues which must be raised and taken care of. Again, the equation to be solved is

[math]\left\{\sum_i \vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\Psi} = K\frac{\partial}{\partial t}\vec{\Psi}.[/math]

 

Anssi, you should take careful note that, if a given [imath]\vec{\Psi}[/imath] is a solution to that equation then so is [imath]A\vec{\Psi}[/imath] for any arbitrary value of A. The constant A can be directly factored from the differential equation. This fact goes directly to the issue of normalization.

 

Furthermore, please note that the fourth underlying constraint was

[math]\sum_i \frac{\partial}{\partial t}\vec{\Psi}=0[/math]

 

(deduced from the shift symmetry in t) which I have already discussed, superficially, in my earlier post. I might further comment that, as the equation is a linear first order equation, the full general solution is a sum over all possible solutions of the form

[math]\sqrt{A}e^{-imt}[/math].

 

I say my discussion was superficial because, it turns out that the actual solution is not the central issue. We are essentially speaking of a differential equation of many (and when I say many, I mean many; perhaps on the order of [imath]10^{20}[/imath] or more variables) and finding solutions depend very much on reordering the terms in those sums.

 

Meanwhile, there are some subtle issues to be discussed here. All of my proofs depended very much on the finite nature of that collection of variables. I hope no one minds my referring to those reference indices as variables as they certainly merge over into variables as the [imath](x,\tau, t)[/imath] space used to reference them becomes continuous and we take the limits on to infinity (that limit being necessary to obtaining the differential representation).

 

The first difficulty which occurs is the definition of normalization. Normalization was supposedly achieved by summing over all possibilities for the proposed [imath]\vec{\Psi}[/imath] associated with a given t and setting the amplitude (that A in the equation above for example) such that the sum is one. It should be clear to everyone here that, if the number of possibilities goes to infinity, the final value for A must go to exactly zero. The fact that it goes to exactly zero and not just some very small number is the problem introduced by continuity.

 

Actually, normalization is no real difficulty as, if the number of possibilities is infinite, one isn't concerned about a single possibility anyway (that obviously has to be zero). Rather, one is concerned about the expectation of certain finite array of possibilities as compared to an alternate collection. In such a case, our sums over those collections go into integrals over some continuous range and we are concerned with the ratios between those integrals: i.e. normalization is not required at all in order to view the results as probabilistic in nature and that is the central issue of laying out expectations consistent with an explanation. All that is important here is that [imath]\vec{\Psi}[/imath] can be seen as yielding the appropriate distribution of expectations and normalization isn't really a serious issue at all.

 

However, the result is a little more serious when it comes to our third constraint:

[math]F\vec{\Psi}=\sum_{i\neq j}\delta(x_i-x_j)\delta(\tau_i-\tau_j)\vec{\Psi}=0.[/math]

 

That constraint was introduced as a mechanism which required that no two indices to be the same; however, if [imath]\vec{\Psi}[/imath] becomes exactly zero (not just extremely small) that expression ceases to enforce such a constraint. Since [imath]\vec{\Psi}[/imath] vanishes even when the argument represents a valid possibility, the above equation allows the sum over Dirac delta functions to go to infinity for those valid possibilities. This fact essentially removes the constraint which was supposedly being enforced. Note that the expression itself still remains a true expression so there is no reason to remove it from the differential equation, it is just no longer appears to be sufficient to accomplish that original goal of constraining our numerical indices to our valid knowledge.

 

This issue becomes quite subtle as continuity certainly cannot be a characteristic of the actual numeric indices and thus becomes an unexaminable consequence of the continuity hypothesis. As such, I will hold that it is what might be called a virtual phenomena which cannot be detected: i.e., it is an unprovable consequence of the explanation and does not bear upon actual reality (the valid ontological elements). However, it has some very serious consequences when it comes to assigning numeric reference labels to those valid noumena. The tau, admittedly invalid ontological information, axis was introduced for the sole purpose of allowing multiple occurrences of valid ontological elements in a possible explanation to be represented by points in our [imath](x,\tau,t)[/imath] space. You should comprehend that, without tau, identical x indices (which might be required by some specific explanation) would reduce to a representation by one point and the fact of multiple occurrences would be lost in the representation: i.e., the representation consisting of points in the x tau t space fails to correctly represent the known information. Continuity of the tau dimension has clearly defeated that essential purpose of tau. Somehow we must assure that such a circumstance can not occur.

 

Essentially, we must come up with an additional constraint which will maintain all valid ontological elements as different points in that [imath](x,\tau,t)[/imath] space. It is interesting to note that the real burden here is to constrain the valid ontological elements. Constraining the invalid ontological elements is not actually required by any of the proofs I have given and it can be argued that leaving them unconstrained might even be a more accurate representation of “all possible explanations” then constraining them. In actual fact, we really should not limit possibilities unless those limits are expressly required by the proofs.

 

But back to the valid ontological elements. In this case, the constraint that every valid ontological element must map to a specific point in [imath](x,\tau,t)[/imath] space is central to the proofs I have presented. With regard to that issue, a mechanism capable of accomplishing that result is available to us. That mechanism is commonly referred to as “Pauli exclusion”. There exists another symmetry which we need to discuss called “exchange symmetry”. By exactly the same arguments which implied shift symmetry, we can deduce that exchange symmetry must be applicable to our representation: i.e., if we were to exchange any two numerical indices in our ”what is”, is “what is” representation of what we know (that would be labels of elements defined by an explanation), the expectations yielded by that explanation can not change. It turns out that there are two orthogonal types of exchange symmetry, one leading to Bose Einstein statistics and one leading to Fermi statistics.

 

Suppose we find a solution to my fundamental equation, [imath]\vec{\Psi}[/imath], which fails to display exchange symmetry: i.e., the function changes when two representative points (x tau arguments) are exchanged. It should be clear to the reader that exactly the same [imath]\vec{\Psi}[/imath] will solve that equation if any two points specified by given arguments ( [imath](x.\tau)_q[/imath] and [imath](x.\tau)_p[/imath]) are exchanged. (the equation doesn't care which is which as they all appear in a symmetric manner). Since we are dealing with a first order linear differential equation (only first order derivatives appear) we can be assured that any sum of solutions is also a solution. If we construct the collection of all possible exchanges and add them all together the result will still be a solution to the differential equation and will now be symmetric under all possible exchanges (any exchange of arguments is exactly equivalent to simply exchanging the specific terms in that sum which represent that exchange). This solution will be consistent with Bose Einstein statistics.

 

The procedure which yields a solution consistent with Fermi statistics is a little more complex to describe. If we begin with a specific solution [imath]\vec{\Psi}[/imath] and exchange two x tau points and then subtract that second function from the first, we still have a solution to the equation. If we then take that function and exchange a different pair and subtract that result from the result of the first step we again will have a solution to the equation. If we continue that process until all possible pairs have been exchanged, we again end up with a function where any exchange will yield back the same function but with a subtle difference: in this second case the function is antisymmetric: i.e., an exchange of any two points will yield a change in sign.

 

Finally, the exchange properties of [imath]\vec{\Psi}[/imath] need not be entirely symmetric or entirely asymmetric. The points referred to by the indices may be divided into two sets: one set symmetric under exchange and one set asymmetric under exchange. The antisymmetric case has a very interesting property. If [imath]\vec{\Psi}[/imath] is antisymmetric under exchange of a specific pair of arguments [imath](x.\tau)_q[/imath] and [imath](x.\tau)_p[/imath], [imath]\vec{\Psi}[/imath] must change sign under that exchange (that is the definition of the asymmetric case). Suppose the two points are exactly the same (the x, tau indices representing the two different ontological elements are exactly the same)? In such a case, exchanging the arguments is totally immaterial (if x and y are exactly the same number, f(x,y)=f(y,x)) and yet the function must change sign. There exists but one number which equals the negative of itself and that number is zero. Two different elements simply cannot be represented by the same point, the probability is zero even before normalization. Two identical Fermions can not be in exactly the same position at exactly the same time.

 

Now this exchange issue was introduced here because my proof required no two valid noumena could be represented by the same point in that x tau space. Essentially the exchange symmetry can be seen as arising from the fact that these noumena are indistinguishable from one another. Since I have defined reality to be a collection of valid noumena, one could certainly interpret this circumstance as equivalent to defining reality to be a collection of indistinguishable “particles” moving in an x tau space (t being the parameter defining that motion); however, I would very much caution the use of the word “particle” (as the idea of a particle carries a lot of inductive baggage which really doesn't belong here; we are speaking of numerical indices with no evidence that two such identification at a different time are related). Furthermore, I am sure that the idea of “indistinguishable” noumena will raise a lot of objection; however, I challenge anyone to come up with a mechanism for distinguishing noumena in the absence of an explanation.

 

For Buffy and her interest in examples: at this point, my fundamental equation can be seen as analogous to a wave equation, a Schroedinger representation of a universe of massless infinitesimal dust motes (those dust motes being a collection of Fermions and Bosons) interacting via no interaction other than a contact interaction (that interaction being an infinite repulsion with a range of zero). The propagation of the probabilities (our expectations) is defined by that wave equation. The alpha operators attached to each index could be seen as spin operators; however, that would take a bit of a stretch in one's imagination as they don't quite follow the entire spin thesis. Nevertheless the fundamental equation can certainly be seen as a Schroedinger type representation of a many body problem constituting the entire universe and, at the same time, it can be seen as a mathematical representation of any conceivable circumstance (any collection of known data at all).

 

At any moment of the past, the shape of that wave represented by [imath]\vec{\Psi}[/imath] can be seen as defined by our knowledge of that moment: i.e., the square of the magnitude of [imath]\vec{\Psi}[/imath] providing us with an estimate of the probability that distribution of indices corresponds to our knowledge. Shift symmetry together with exchange symmetry yields a definition of how that wave will propagate between “observations”: i.e., additional information concerning unobserved behavior consistent with those symmetries. It should be clear that such a paradigm is entirely consistent with any possibilities as, the past (what we know) defines the shape of the function and the continuous nature of the solution disallows no possibility for any future event; one merely restarts the propagation when any new information is obtained. It makes no predictions not required by the associated symmetries and is thus entirely general, the paradigm itself being perfectly consistent with the known past.

 

Once we settle the issues in this post, I will present my method of solving that equation.

 

Have fun -- Dick

[AnssiH]

can we not hold true that it is impossible for such a phenomenon as "undefined explanation" of reality ?

 

Correct. We cannot conceive any type of reality without some definitions (of entities). That's what Kant was on about regarding noumena (=undefined reality) vs. phenomena (=reality the way we defined it and consequently conceive it in our minds)

 

You are probably asking this because Doctordic has been so insistent on "not defining anything" and yet talking about explanations. It is a tricky thing to balance yourself between these semantical issues here and it can definitely become somewhat confusing to follow.

 

So, yes, if you have an explanation, you also have a worldview (set of defined entities) with which that explanation is understood. In Doctordick's terms, you have that "right hand table" (that you filled according to your definitions) in which your "probability function" and "explanations" operate.

 

The definition of "x,tau,t"-table itself is such that it should allow for any sort of worldview to be mapped to it.

 

That "undefined table" (in your left hand) can be thought of as hypothetical in that we cannot see any sort of "correct mapping" to it (IOW its content has not been defined by us). It can be thought of as the noumena; raw unexplained data according to which we come to build a set of self-coherent definitions. When we have made some assumptions and come up with definitions, we could fill the table in the right hand "according to our definitions" (or one might say, according to our beliefs).

 

The only reason the idea of the "right hand table" (or noumena) is invoked, is to refer to the fact that even though our definitions of reality are not the reality itself, there does exist an undefined reality (just we cannot "think about it as it is" because our thoughts are "made of" the definitions we made). Or the way Kant puts it: "...though we cannot know these objects as things in themselves, we must yet be in a position at least to think them as things in themselves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears."

 

Now, some of those definitions we made, we can also readily recognize as mere assumptions, but some assumptions are embedded so deep into our worldviews that they seem like fundamental parts of reality (when in fact they are merely fundamental parts of our own worldviews).

 

And indeed, usually groundbreaking advances in scientific models are cases of someone letting go of some assumption that so far seemed to be very much immutable facts of reality, and defining it (and associated things) differently (rather obvious example would be relativity of simultaneity).

 

When you look at our worldview as an "x,tau,t"-table, it is probably easier to see, that given any finite "left hand table", an infinite number of valid "right hand tables" can be built (with different assumptions). Many of them would look radically different from each others, and they would only be consistent with themselves (and the left hand table), but not with each others.

 

It is easy to get stuck inside your own worldview and not see all the possibilities open to you if you did let go of all unnecessary assumptions, and instead only cling onto relationships that must exist in all valid worldviews as a consequence of their self-coherence. And so the focus of Doctordick's treatment is not in any specific right hand table, but in the constraints that any self-coherent worldview must obey.

 

Does that seem to make sense?

[Rade]

...Two identical Fermions can not be in exactly the same position at exactly the same time...

Thank you for your reply, it leads to another question about your comment above. I can see how your tau axis is needed for valid ontological elements (VOEs) that would be like "Fermions", since they cannot be in same position at exactly same time and so they must in your equation--but--why would you need a tau axis for VOEs that would be like "Bosons", since by definition, many bosons can be in same position at exactly the same time ? I'm sure you are not saying that your equation does not apply to bosons as VOEs given the vast number of bosons in existence (since you mention Bose-Einstein statistics that apply to bosons), but I just cannot see how the tau axis is needed if bosons are present in your right hand as VOEs--seems to me that the tau axis not a good idea for bosons in your equation, since we do not want them to be separate but lumped together. I'm sure I am missing something important.

...I have defined time to be an index on changes in the information upon which the explanation is based...

So, by this are you saying that "time" is a type of number, the number of VOEs that are counted between two "moments" (in this case, the information change in VOEs from moment A to moment :naughty:, in the same way that time is a type of number that measures changes in motion of physical matter ? If so, then you appear to equate relationship of time to motion of matter (change in position) in same way as relation of time to motion in information content (change in constraint on variety) --is this correct understanding ?

[Rade]

Correct. We cannot conceive any type of reality without some definitions (of entities). That's what Kant was on about regarding noumena (=undefined reality) vs. phenomena (=reality the way we defined it and consequently conceive it in our minds). You are probably asking this because Doctordic has been so insistent on "not defining anything" and yet talking about explanations. It is a tricky thing to balance yourself between these semantical issues here and it can definitely become somewhat confusing to follow.

Yes, this was the motivation for my question. For me, the left hand table = the ontological given, reality in of itself, it is what we perceive without subjective bias as a set of information. Humans can never "add" definitions to the left hand table--impossible by definition. Think of a radio, and you throw things at the radio, and some things bounce off, some break it, others enter (as waves) and become transformed into music. For me, all these things that come at the radio are "in the left hand", they are not defined a priori. Next, for me, the right hand table = our placement of definitions on the set of information in the left hand table. We do this via process of concept formation--that is, we "define" a "concept", a concept without definition is a contradiction of terms. So, back to radio, if brain is like radio, we can only "define" those undefined perceptions that enter, and definition then is a type of "transformation", a change in information such that it goes from a state of undefined to defined, and we can only explain what we can define (that is, those ontological things that bounce off or break our brain are outside explanation). Reality then (for me) is the dialectic merging of the two hands. Thus, for me, reality is neither (1) in itself in the left hand}--the set of valid ontological elements, nor (2) as defined by reason in righthand{. For me, reality is {existence defined}--the two hands merged together to form one. Where Kant errors (IMO), is that he forms a dualistic view (either-or), his noumena vs phenomena--this is what I do not agree with--I reject this aspect of Kant philosophy, for me, ALL IS DIALECTIC.

 

Since it does not appear this is what you are talking about, I think we have a fundamental different view of the relationship of ontology to epistemology to explanation, but perhaps I just do not understand what you are saying. Let me know where you disagree with what I claim above, that seems like a good place to continue discussion.

 

edit: As pointed out by DoctorDick in a future post--I have reversed his use of the concepts of right hand vs left hand. So I have edited the two terms in red--now all I claim conforms to the handedness concept being discussed on this thread.

[Doctordick]

I can see how your tau axis is needed for valid ontological elements (VOEs) that would be like "Fermions", since they cannot be in same position at exactly same time and so they must in your equation--but--why would you need a tau axis for VOEs that would be like "Bosons", since by definition, many bosons can be in same position at exactly the same time ?

You clearly do not understand what I am saying as you are, in your post, referring to a specific explanation of reality here: i.e., your personal world view as to what is and is not real. As Anssi says, “It is easy to get stuck inside your own worldview and not see all the possibilities”. You are obviously presuming your world view is correct. Prove that bosons exist without using any theoretical constructs or ideas.

I'm sure I am missing something important.

Yes you are!

For me, the right hand table = the ontological given, reality in of itself, it is what we perceive without subjective bias as a set of information.

Wrong! It has been made quite clear that the right hand table is to represent your explanation of the ontological given information; the left hand constitutes the actual ontological given, the undefined noumena your explanation is trying to explain.

Humans can never "add" definitions to the right hand table--impossible by definition.

So where do you think definitions come from if they don't come from humans?

ALL IS DIALECTIC.

Glad to hear you understand everything. I presume you believe Peter Abelard had it all figured out in 1122 when he published his outline of dialectical reasoning.:confused:

 

Anssi, your post was excellent; however, I don't think Rade can be reached. Thanks for trying anyway.

 

Have fun -- Dick

[Bombadil]

I suspect you misunderstood my “word of mouth” comment. Many times, in both lectures and one on one conversations, professors will elaborate on the subject with a few personal, somewhat non-technical comments, on how issues came to be seen the way they are seen. The background of thought behind physics is an issue almost too large to be set down in a lifetime and little issues you won't find in any book can be very enlightening. Buffy has often tried to push me into making such “examples”; I resisted because my original thoughts were often totally unsupportable associations which I am afraid could detract attention from the proofs and be used as “solid evidence” that I am a nut and that the proofs need not be examined.

 

Yes I did misunderstand your comment but I think that I understand what you are saying now.

 

The central issue of my generalization to

 

frac{partial}{partial t}vec{psi}=-imvec{psi},

 

has to do with algebraic manipulation convenient to solving differential equations. That is to say, if I have a solution to the first equation above, I know that vec{psi}=e^{-imt}vec{Psi} is a solution to the second. In exactly the same vein, if I happen to have a solution to the second equation, I immediately have a solution to the first: vec{Psi}=e^{imt}vec{psi}. If you read John Baez's web site, you should come to understand that these transformations relate to “conserved quantities” embedded in the representations implied by the associated differential equations. The m in the above equation is closely related to conservation of energy in Schroedinger's representation of quantum mechanics where different values for m essentially amount to changing the zero point reference for that conserved quantity. I believe this will all become clear as I develop the solutions to my fundamental equation.

 

Ok, I understand how if we have a solution to one of these equations we can easily get one to the other one but I don’t understand how the m corresponds to a conserved quantity.

In your equation is there just a conserved quantity due to symmetry, (which the way I understand it is a requirement of symmetry) or is there something else that is being conserved?

 

Actually, normalization is no real difficulty as, if the number of possibilities is infinite, one isn't concerned about a single possibility anyway (that obviously has to be zero). Rather, one is concerned about the expectation of certain finite array of possibilities as compared to an alternate collection. In such a case, our sums over those collections go into integrals over some continuous range and we are concerned with the ratios between those integrals: i.e. normalization is not required at all in order to view the results as probabilistic in nature and that is the central issue of laying out expectations consistent with an explanation. All that is important here is that vec{Psi} can be seen as yielding the appropriate distribution of expectations and normalization isn't really a serious issue at all.

 

To do this do we just integrate over all values of the function [imath]\vec{\Psi}[/imath] taken in what ever interval we are interested in and then divide it by the integral of [imath]\vec{\Psi}[/imath] taken over all possible elements of the explanation? If so how do we integrate over the possible values of the function [imath]\vec{\Psi}[/imath].

 

That constraint was introduced as a mechanism which required that no two indices to be the same; however, if vec{Psi} becomes exactly zero (not just extremely small) that expression ceases to enforce such a constraint. Since vec{Psi} vanishes even when the argument represents a valid possibility, the above equation allows the sum over Dirac delta functions to go to infinity for those valid possibilities. This fact essentially removes the constraint which was supposedly being enforced. Note that the expression itself still remains a true expression so there is no reason to remove it from the differential equation, it is just no longer appears to be sufficient to accomplish that original goal of constraining our numerical indices to our valid knowledge.

 

If the function [imath]\vec{\Psi}[/imath] becomes zero for all possible elements won’t we just get zero when we integrate it?

I thought that if [imath]\vec{\Psi}[/imath] was equal to zero that element was not a valid possibility and so was not in that explanation. If the function can in fact equal zero for a possible element of the explanation how can we tell if it is an element of the explanation or if it has got a probability of zero for being in the explanation and so can’t be in the explanation?

 

Essentially, we must come up with an additional constraint which will maintain all valid ontological elements as different points in that (x,tau,t) space. It is interesting to note that the real burden here is to constrain the valid ontological elements. Constraining the invalid ontological elements is not actually required by any of the proofs I have given and it can be argued that leaving them unconstrained might even be a more accurate representation of “all possible explanations” then constraining them. In actual fact, we really should not limit possibilities unless those limits are expressly required by the proofs.

 

How can the invalid ontological elements not also satisfy the same requirements that the valid ontological elements satisfy? They are both part of the same explanation and we can’t tell the difference between the valid and invalid so how can we know that they do or don’t satisfy the same requirements? Wouldn’t this create a way of telling them apart which we decided was not possible? Do we just say that they don’t have to because we can’t prove that they do?

 

This issue becomes quite subtle as continuity certainly cannot be a characteristic of the actual numeric indices and thus becomes an unexaminable consequence of the continuity hypothesis. As such, I will hold that it is what might be called a virtual phenomena which cannot be detected: i.e., it is an unprovable consequence of the explanation an does not bear upon actual reality (the valid ontological elements). However, it has some very serious consequences when it comes to assigning numeric reference labels to those valid noumena. The tau, admittedly invalid ontological information, axis was introduced for the sole purpose of allowing multiple occurrences of valid ontological elements in a possible explanation to be represented by points in our (x,tau,t) space. You should comprehend that, without tau, identical x indices (which might be required by some specific explanation) would reduce to a representation by one point and the fact of multiple occurrences would be lost in the representation: i.e., the representation consisting of points in the x tau t space fails to correctly represent the known information. Continuity of the tau dimension has clearly defeated that essential purpose of tau. Somehow we must assure that such a circumstance can not occur.

 

I don’t understand why continuity can’t be a characteristic of the numerical indices. Didn’t we assume continuity when we found the constraints from shift symmetry, or at least a limit that was equivalent to continuity? And isn’t this just a property of the coordinate system that you set up for the elements and has no effect on the explanation except making it continuous?

 

Then this is something that we can nether prove one way or the other, that is we can’t show that two elements are the same while at the same time we cant prove that they are different?

 

Then any solution to the equation must satisfy Bose Einstein statistics so if an element also satisfies Fermi statistics it must be equal to the negative of it’s self which makes the only possible value zero.

 

Now this exchange issue was introduced here because my proof required no two valid noumena could be represented by the same point in that x tau space. Essentially the exchange symmetry can be seen as arising from the fact that these noumena are indistinguishable from one another. Since I have defined reality to be a collection of valid noumena, one could certainly interpret this circumstance as equivalent to defining reality to be a collection of indistinguishable “particles” moving in an x tau space (t being the parameter defining that motion); however, I would very much caution the use of the word “particle” (as the idea of a particle carries a lot of inductive baggage which really doesn't belong here; we are speaking of numerical indices with no evidence that two such identification at a different time are related). Furthermore, I am sure that the idea of “indistinguishable” noumena will raise a lot of objection; however, I challenge anyone to come up with a mechanism for distinguishing noumena in the absence of an explanation.

 

Then a noumena is just a valid ontological element?

 

Does this also mean that all possible elements in the explanation must be in it since we can’t tell them apart? We can’t say that some elements aren’t in it without a way of telling what element it is that we are leaving out of the explanation.

 

I don’t see how this allows us to stop two elements from being in the same location. How is it that these symmetries are used? You seem to be giving it with out giving any way of insuring that the equation or the elements satisfy it, Unless you are saying to have the solution for the equation for every possible location of each element and then add them together, which will give us a new solution to the equation.

 

This is leading me to the question, what symmetries must an equation satisfy in order for any value of the variables to be a possible value without changing the value of it? This question doesn’t seem to be important right know but it seems that it may be later.

[Rade]

...Prove that bosons exist without using any theoretical constructs or ideas...

No, I rather that first you prove that Fermions exist without using any theoretical constructs or ideas, for the simple reason that I mentioned Bosons as reaction to your first use of Fermions to support your use of tau. Once we have your proof then it will be easy to derive existence of Bosons.

Wrong ! It has been made quite clear that the right hand table is to represent your explanation of the ontological given information; the left hand constitutes the actual ontological given, the undefined noumena your explanation is trying to explain.

Yes, you are correct, my error--I reversed the two, so we agree 100% :Glasses:

...Glad to hear you understand everything. I presume you believe Peter Abelard had it all figured out in 1122 when he published his outline of dialectical reasoning...

But what exactly do you mean by "understand everything"--how is this possible ? I am not aware that I made this claim. And, by the way, not good to presume too much, can lead to false claims such as you present here.

[Rade]

To summarize this thread topic, which is somewhat long now, there are only two correct answers to the OP question...what can we know of reality (call it K):

 

1. The facts of reality via perceptual observation

2. The facts of reality via a process of reason derived from (1)

 

Thus the equation: K = dialectic superposition of 1 + 2.

 

I think the thread closed now ?

[AnssiH]

Sorry it is taking me a while to reply Doctordick. I just had time to ready your post #171 yesterday, and it seems interesting. More meat to the bones I thought. But I need to have proper time to really think about it, and then I'll also have more questions.

 

In the meantime;

 

Yes, this was the motivation for my question. For me, the left hand table = the ontological given, reality in of itself, it is what we perceive without subjective bias as a set of information. Humans can never "add" definitions to the left hand table--impossible by definition. Think of a radio, and you throw things at the radio, and some things bounce off, some break it, others enter (as waves) and become transformed into music. For me, all these things that come at the radio are "in the left hand", they are not defined a priori. Next, for me, the right hand table = our placement of definitions on the set of information in the left hand table. We do this via process of concept formation--that is, we "define" a "concept", a concept without definition is a contradiction of terms. So, back to radio, if brain is like radio, we can only "define" those undefined perceptions that enter, and definition then is a type of "transformation", a change in information such that it goes from a state of undefined to defined, and we can only explain what we can define (that is, those ontological things that bounce off or break our brain are outside explanation). Reality then (for me) is the dialectic merging of the two hands. Thus, for me, reality is neither (1) in itself in the left hand}--the set of valid ontological elements, nor (2) as defined by reason in righthand{. For me, reality is {existence defined}--the two hands merged together to form one. Where Kant errors (IMO), is that he forms a dualistic view (either-or), his noumena vs phenomena--this is what I do not agree with--I reject this aspect of Kant philosophy, for me, ALL IS DIALECTIC.

 

When you say, that reality is "existence defined", are you assuming that reality simply does not exist until it has been defined by a human being?

 

Did you read this part of my post:

The only reason the idea of the "right hand table" (or noumena) is invoked, is to refer to the fact that even though our definitions of reality are not the reality itself, there does exist an undefined reality (just we cannot "think about it as it is" because our thoughts are "made of" the definitions we made). Or the way Kant puts it: "...though we cannot know these objects as things in themselves, we must yet be in a position at least to think them as things in themselves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears."

 

It is one thing to understand your perception of reality is not exactly how reality exists in a naive realistic sense, and another thing to reject the whole existence of the "undefined reality" altogether. (btw, I don't know why you see the concept of "noumena" as "either-or" dualism)

 

OR, does your ample usage of "for me" mean, that you believe reality itself exists without human definitions, but in your philosophy you don't see any practical use for the concept of noumena because they cannot be understood by themselves anyway?

 

If that is the case, please note that it is a useful concept; it is useful for this very discussion! :) Perhaps the confusion lies in how the reality is referred to as a set of "valid elements" when there's no reason to see reality itself as elements at all? If so, please note that this treatment is not out to find out "the true nature of reality" but necessary constraints to OUR views of reality. You seem to understand that in OUR view of reality it is necessary to see reality as a set of elements, and if there is any valid way (predictionwise) to break reality into elements, then the treatment is useful. I think it is safe to say that such validity can be reached; we all can make useful predictions with our worldviews.

 

But if you just flat out refuse to use the concept, for the simple reason that your personal philosophy has not deemed it practical, then I'm afraid you will not be able to pick up anything from this discussion. (but it is not very smart to voice your dialectic view and declare the thread moot)

 

Additionally, your last post implies you think there are perceptions first, and worldview built out of them. Think about that for a while. Does reality exist the way we comprehend it? What is a perception that is not comprehended as anything at all? Just like you noted, a concept without definitions is a contradiction of terms, so is a perception without definitions, as a perception has to be understood as something before it is a perception. (Note that even when we semantically say we "do not understand what we are seeing", we still understand we are seeing "something" and can comprehend many features of our perceptions, because we have some set of definitions in our worldview describing those features!)

 

-Anssi

[Doctordick]

Thank you for your note Anssi. Though there may be some very serious questions in your mind, I am convinced you at least see the purpose of my approach. In many respects, your knowledge of mathematics is too limited to pick up on possible flaws in my deductions; that is something Qfwfq or Buffy might be better at accomplishing but they are much more concerned with the outcome than how I get there. Though there are some serious flaws in my presentation (Bambadil has brought up one) I don't think any of them pose any serious threat to my deductions. Perhaps the time to discuss my mode of solving that differential equation has arrived. If you think you are ready to look at that algebra, let me know and I will post the opening move in my approach.

 

Meanwhile, I need to answer Bombadil's post:

Ok, I understand how if we have a solution to one of these equations we can easily get one to the other one but I don’t understand how the m corresponds to a conserved quantity.

If [imath]\frac{\partial}{\partial t}\vec{\Psi}(x,t)=m\vec{\Psi}(x,t)[/imath] then it is quite clear that the operator [imath]\frac{\partial}{\partial t}[/imath] can always be replaced with “m” no matter what value of t is being examined (so long as you are using the correct [imath]\vec{\Psi}[/imath]). This implies that the specific solution being examined defines a value which is conserved for all time: i.e., that number “m”. Likewise, if [imath]\frac{\partial}{\partial x}\vec{\Psi}(x,t)=K\vec{\Psi}(x,t)[/imath] then the operator [imath]\frac{\partial}{\partial x}[/imath] can be replaced by the number “K” no matter what value of x is being examined. Now, when the differential equation relates a large number of variables, such as [imath]\sum_i\frac{\partial}{\partial x_i}\vec{\Psi}(x_1,x_2,\cdots,x_n,t)=K\vec{\Psi}(x_1,x_2,\cdots,x_n,t)[/imath] this does not mean that the individual operators, [imath]\frac{\partial}{\partial x_i}[/imath] can be replaced with a constant but it does imply that the sum can be so replaced (so long as we are dealing with the correct solution to that specific differential equation).

In your equation is there just a conserved quantity due to symmetry, (which the way I understand it is a requirement of symmetry) or is there something else that is being conserved?

Symmetry always requires some kind of conserved quantity. The symmetry can always be seen as a lack of information of some kind. If one can express a specific solution given that lack of information, say “x” when the origin of the coordinate system is unknown, then there must exist a method of transforming all those possible solutions for “x” (each one being referenced to some specific origin) into one another. If you follow my mathematics and the logic behind them, see this post, then it becomes quite clear that these symmetries can be related to differential operators when we extend the analysis to the realm of continuity.

To do this do we just integrate over all values of the function [imath]vec{Psi}[/imath] taken in whatever interval we are interested in and then divide it by the integral of [imath]vec{Psi}[/imath] taken over all possible elements of the explanation? If so how do we integrate over the possible values of the function [imath]vec{Psi}[/imath].

Not quite. You should rephrase this as, “to do this do we just integrate over all values of the function [imath]\vec{\Psi}[/imath] taken in whatever interval we are interested in and then divide it by the integral of [imath]\vec{\Psi}[/imath] taken over a second interval we are interested in (which could of course be “all possible values”) then the ratio is the probability of one interval compared to the second. The issue here being that actual “normalization” need not be accomplished (nor is it explicitly required to ever integrate over the entire range). The point being that being able to interpret the result as a measure of expectations is the only significant issue.

If the function [imath]vec{Psi}[/imath] becomes zero for all possible elements won’t we just get zero when we integrate it?

My apology; the problem here is the slight (but very important) shift in meaning of the expression, [imath]\vec{\Psi}[/imath], upon transition from a discrete distribution to a continuous distribution. If [imath]\vec{\Psi}[/imath] is to be the function who's squared magnitude is to give the probability of the express arguments of that function then the value of [imath]\vec{\Psi}[/imath] certainly goes to zero; however, it is the normal procedure to transform over to probability density at that point: i.e., when one goes over to continuity, the function who's squared magnitude is to give the probability of the express arguments of that function is written [imath]\vec{\Psi}(x)dx[/imath] or for many variables [imath]\vec{\Psi}(x_1,x_2,\cdots,x_n) dV_n[/imath]. Please forgive an old man for his sloppy presentation.

 

Actually, the transformation from representation of probability to probability density can be accomplished while the possibilities are still discrete. If the discrete set of possibilities are laid out on the x axis and a definition of covered range is created (suppose from the halfway point between the adjacent discrete possibilities) and the magnitude of the vector [imath]\vec{\Psi}[/imath] is divided by the square root of that distance, the resultant vector can be seen as a generator of probability “density”. Of course, the probability is then given by the square of the vector magnitude times that distance. As one goes over to continuity, the distance defining that density goes over to zero but the density itself can remain finite. This whole thing has to do with converting sums over to integrals and that “dV” term always present in the integral. It is such a common mental transformation that it is easy to forget we are doing it. Sorry about it very much.

I thought that if [imath]vec{Psi}[/imath] was equal to zero that element was not a valid possibility and so was not in that explanation. If the function can in fact equal zero for a possible element of the explanation how can we tell if it is an element of the explanation or if it has got a probability of zero for being in the explanation and so can’t be in the explanation?

This is purely a consequence of continuity itself. If the discrete set of possibilities goes over to a continuous set, the number of possibilities goes over to infinity. In such a case, the probability of any given specific case has to go to zero. That is the exact reason that we want to deal with the density instead.

How can the invalid ontological elements not also satisfy the same requirements that the valid ontological elements satisfy? They are both part of the same explanation and we can’t tell the difference between the valid and invalid so how can we know that they do or don’t satisfy the same requirements? Wouldn’t this create a way of telling them apart which we decided was not possible? Do we just say that they don’t have to because we can’t prove that they do?

This issue is a very subtle issue and must be examined carefully. First of all, this is not the first time I have introduced something specifically defined to be “invalid”. When I introduced the tau axis it was introduced as a specifically invalid construct. Did that create a way of telling the difference between “valid” and “invalid” indices? I say that it did not. It is still very possible that my explanation contains invalid x indices: i.e., ontological elements or noumena we presume are valid which are not.

 

Likewise, the requirement that [imath]\vec{\Psi}[/imath] be antisymmetric with respect to exchange for all valid ontological elements does not suffice to tell the difference between “valid” and “invalid” ontological elements. It is entirely possible that our explanation might require some “invalid” ontological elements to also be antisymmetric with respect to exchange. Consider the possibility of solipsism: that would be the circumstance if all ontological elements were invalid. You have to remember here that I introduced the antisymmetric requirement for “valid” ontological elements for the sole purpose of maintaining individual representation of these ontological elements so that no possible explanation would fail to include their existence. This is a pure requirement of those “valid” ontological elements and not at all a requirement of the invalid ontological elements (they can easily vanish with a new and different explanation). That is the rational behind my comment to Rade that he cannot prove that bosons exist without using any theoretical constructs or ideas.

 

As an aside, I will comment that, once tau has been introduced (as a mechanism to preserve the individuality of valid ontological elements) to fail to include it in representations of “invalid” ontological elements would require me to present a method of determining whether or not a given element were valid or invalid. It is the fact that such a method cannot exist which is the driving issue here. If I know that I personally have created an element for the sole sake of creating an explanation, I can be quite confident it isn't a “valid” ontological element under my definition (it's a theoretical entity) but it must still obey the rules laid out in that explanation. As I say, these are subtle issues here. In the paradigm I am laying out, “valid” ontological elements must be represented by antisymmetric [imath]\vec{\Psi}[/imath] for a very specific reason. Just as one could say that “valid” ontological elements must be part of reality whereas “invalid” elements need not be; that statement does not require we be able to tell the difference but it certainly requires that all “valid” ontological element be included in every flaw-free explanation. Essentially, being real can have real consequences; the issue being that those consequences can not be used to tell “valid” and “invalid” ontological elements apart.

I don’t understand why continuity can’t be a characteristic of the numerical indices. Didn’t we assume continuity when we found the constraints from shift symmetry, or at least a limit that was equivalent to continuity? And isn’t this just a property of the coordinate system that you set up for the elements and has no effect on the explanation except making it continuous?

The fundamental issue is that a realistic portrayal of the circumstances cannot include an infinite amount of information. If you go back and look at my outline of the circumstances and the solution I proposed, it is very dependent upon the finite nature of the information available. Though finite, the size of that information is not bounded. If follows that my arguments are still valid when the quantity of information to be explained becomes incomprehensibly large. It is only natural that, in such a circumstance, one look at the situation in the limit where the quantity becomes infinite even though, by the very definition of infinity, that limit can never be reached. What I was trying to point out is that subtle problems arise when one actually goes to infinity, though actual failure of the argument is not really there because, in reality, infinite information can never be obtained.

 

If you have the time, it might benefit your comprehension of what I am doing to review a few posts I have made earlier. If it is too much, don't worry about it.

 

1. The fundamental issue of ontology and the introduction of time as the single most basic epistemological concept.

2. A rather clear exposition of the issue of “change” and the need for the concept, “time” in any explanation of reality.

3. My original reference to Kant pointing out the necessity of handling ontological elements as unknowns.

4. The only solution is to develop a rational way of referring to a ontology which is all encompassing and thus requires no “speculative edifice”.

5. Laying out the problem of explaining a set of valid ontological elements without defining them.

6. A clear statement of a simplified problem analogous to the one we need to solve. Opening description of the general problem.

7. Initial introduction to the ”what is”, is “what is” table (in this case, containing only valid ontological elements).

8. The issue of seeing “our expectation” as a mathematical function of a specific “present” plus my introduction of symmetry to Anssi.

9. The fundamental reason for introduction of the tau axis explained clearly.

10. Comparison between what I am doing and the “Dewey Decimal System”. Just an orientating post easily worth reading.

11. The use of “invalid” ontological elements for the purpose of solving the problem posed by trying to explain a set of valid ontological elements.

 

Then this is something that we can nether prove one way or the other, that is we can’t show that two elements are the same while at the same time we cant prove that they are different?

When we actually let the number of possibilities go to infinity and include all possibilities, we run into the circumstance where the difference between two indices can go to zero. Now, if we have two indices who differ by exactly zero, is it not true that they are the same? If they are the same then the two points which were to represent different noumena become a single point and the purpose for which the tau axis was created is no longer effective. I got around this difficulty by requiring [imath]\vec{\Psi}[/imath] to be asymmetric with respect to exchange; by driving the probability density to exactly zero, this will guarantee the difficulty never arises.

Then any solution to the equation must satisfy Bose Einstein statistics so if an element also satisfies Fermi statistics it must be equal to the negative of it’s self which makes the only possible value zero.

If we have any valid solution to the equation, we can always create a solution which is either symmetric or antisymmetric under exchange (I gave you the mechanical procedure for constructing that solution). This divides the possible solutions into two sets which mutually exclude one another. The symmetric solution will obey Bose-Einstein statistics and the antisymmetric solution will obey Fermi statistics. The two solutions portray very different circumstances leading to, in common physics jargon, Bosons and Fermions (an issue Rade brought up).

 

What is important here is that I have brought up this exchange symmetry issue for the specific purpose of guaranteeing two “valid” ontological elements will not end up being represented by a single point in my x, tau space. There is a lot more to the conventional physics picture of Fermions and Bosons than the simple fact of symmetry or antisymmetry of the wave function; there are, for example, issues having to do with spin which is certainly not yet a defined issue in the paradigm I am presenting.

Then a noumena is just a valid ontological element?

I don't know; I don't believe the issue has been defined. Note that in the quote you bring up, I refer to “valid” noumena and one could presume that, if the adjective is necessary, the mind of the writer includes the idea of “invalid” noumena. In my head, I use the word “noumena” as referring to an ontological element behind the explanation and it might or might not be valid. Perhaps Anssi could tell us how he thinks the term should be used; I could be persuaded either way.

Does this also mean that all possible elements in the explanation must be in it since we can’t tell them apart? We can’t say that some elements aren’t in it without a way of telling what element it is that we are leaving out of the explanation.

I do not understand the question here. The function [imath]\vec{\Psi}[/imath] by definition tells us the expectations produced by a specific particular flaw-free explanation for the set of ontological elements referred to by the indices [imath]x_i[/imath]. If there is one not in there, it fails its definition as the expectation for that element can not be obtained.

I don’t see how this allows us to stop two elements from being in the same location. How is it that these symmetries are used? You seem to be giving it with out giving any way of insuring that the equation or the elements satisfy it, Unless you are saying to have the solution for the equation for every possible location of each element and then add them together, which will give us a new solution to the equation.

I hope my earlier comments clear this up. If not make your question as clear as you can and I will try to answer it again.

This is leading me to the question, what symmetries must an equation satisfy in order for any value of the variables to be a possible value without changing the value of it?

Without changing the value of what? Sorry but this question is not clear to me at all. Perhaps you can make it a little clearer.

... I mentioned Bosons as reaction to your first use of Fermions to support your use of tau.

I did not use Fermions to support my introduction of tau. I used asymmetry under exchange to guarantee that no two “valid” ontological elements would have to map to the same point; quite a different issue.

Once we have your proof then it will be easy to derive existence of Bosons.

The impossibility of proving solipsism false guarantees you can not prove either the existence of Fermions or Bosons.

Yes, you are correct, my error--I reversed the two, so we agree 100% :surprise:

You did a lot worse than that. I doubt you and I posses 100% agreement about anything.

But what exactly do you mean by "understand everything"--how is this possible ?

If you believe that “ALL IS DIALECTIC” and you also believe you understand “DIALECTIC” that means you think understand everything! How else can your assertion be taken?

 

Have fun -- Dick

[Rade]

..When you say, that reality is "existence defined", are you assuming that reality simply does not exist until it has been defined by a human being?

No. This is the false position of the logical positivist. Let me try this way to explain. Let Existence = undefined reality. Then by definition "defined reality" does not Exist. Reality is then, for humans, "existence (undefined reality) defined".

 

..It is one thing to understand your perception of reality is not exactly how reality exists in a naive realistic sense, and another thing to reject the whole existence of the "undefined reality" altogether. (btw, I don't know why you see the concept of "noumena" as "either-or" dualism)

But, I do not reject "undefined reality"--it is in fact the only thing that Exists. It is Kant that uses noumena vs phenomena as either-or, this is what I reject.

 

OR, does your ample usage of "for me" mean, that you believe reality itself exists without human definitions, but in your philosophy you don't see any practical use for the concept of noumena because they cannot be understood by themselves anyway?

In my philosophy existence exists without human definition as "undefined reality". I do see practical use of noumena as the "set of ontological elements", but not all of them (recall from the radio analogy--many noumena never become reality for humans). Noumena have practical use as soon as they are transformed into "existence defined", not before--thus, you are correct in that I do not hold a priori all noumena as potentially useful.

 

.. this treatment is not out to find out "the true nature of reality" but necessary constraints to OUR views of reality...

As I said above, one constraint is that not all 100 % of noumena are practical. And, is not "the true nature of reality" a necessary constraint to our view of reality ?

 

(but it is not very smart to voice your dialectic view and declare the thread moot)

Sorry, the good doctor has a way of bringing out the worst in me--but I do believe the dialectic view is correct answer to OP.

 

Additionally, your last post implies you think there are perceptions first, and worldview built out of them. Think about that for a while. Does reality exist the way we comprehend it? What is a perception that is not comprehended as anything at all? Just like you noted, a concept without definitions is a contradiction of terms, so is a perception without definitions, as a perception has to be understood as something before it is a perception. (Note that even when we semantically say we "do not understand what we are seeing", we still understand we are seeing "something" and can comprehend many features of our perceptions, because we have some set of definitions in our worldview describing those features!)

No, it is not necessary to "define" or "understand" a perception. A perception is a group of sensations AUTOMATICALLY retained and integrated by the brain of animals. All animals with brains can perceive entities--however, counter to your claim, what they can not do is perform the abstract process of taking those perceptions and forming abstract concepts and then putting definitions on those concepts to allow understanding. All definitions have ultimate origin in perception, even those within imagination. Understanding is never a priori to perception--this is the false position (imo) of priority of consciousness over existence.

[AnssiH]

It is Kant that uses noumena vs phenomena as either-or, this is what I reject.

 

I don't know where you got that idea. If it was something I said unclearly, I apologize. Kant's idea of "noumena" is - seems to me - exactly the same as what you refer to as "undefined reality". i.e. When we refer to some phenomenon, that is essentially "noumena having been defined as something".

 

If that's so, then it seems like the only confusion is that you assume we are talking about how reality is ontologically, when the discussion is about what can we know about our views of (any sort of) ontological reality. I.e. the discussion is very much about what can be considered given in any semantical (or "dialectical") view of reality. I.e:

 

Perhaps the confusion lies in how the reality is referred to as a set of "valid elements" when there's no reason to see reality itself as elements at all? If so, please note that this treatment is not out to find out "the true nature of reality" but necessary constraints to OUR views of reality. You seem to understand that in OUR view of reality it is necessary to see reality as a set of elements, and if there is any valid way (predictionwise) to break reality into elements, then the treatment is useful.

 

From what I gathered regarding the Bose Einstein statistics & Fermi statistics, that just seems like one rather concrete example; If you don't have the information to recognize the specific identity of some elements (that is, elements that you defined semantically, or can I say "dialectically"), i.e. there exists "exchange symmetry" in the available raw data, then those statistics can be used to describe that reality. At least that is what the implication seems to be to me, Doctordick might have a different view.

 

Instead you took all that as if Doctordick was trying to prove the actual ontological existence of Fermions?

 

No, it is not necessary to "define" or "understand" a perception. A perception is a group of sensations AUTOMATICALLY retained and integrated by the brain of animals.

 

Oh it's automatical, that's nice. And all this time I thought it is a rather complex process to interpret sensory data.

 

Seriously though, did you really think that I claimed that all perception requires conscious mental effort?

 

When you "perceive an entity", is that not an entity that you have defined in your worldview? When you perceive any feature at all, is that not a feature that has a definition in your worldview? Do you realize how many definitions/assumptions are required before ANY "spatial/temporal pattern" inside a cortex can be seen as carrying any meaning at all? Sure it does not require conscious mental effort from your part, so what? And btw, it makes absolutely no difference whether some of those definitions have come to exist due to biological evolution already (I suspect very few have for humans; that is why it takes so long for us to do anything sensible at all after we are born), and some due to an organism building a worldview.

 

All definitions have ultimate origin in perception, even those within imagination. Understanding is never a priori to perception--this is the false position (imo) of priority of consciousness over existence.

 

I haven't said anything about consciousness or conscious efforts of understanding something. I am talking about any process in which understanding (=our ability to predict) any facet of reality comes to be.

 

From a pattern recognition standpoint, "a perception" is by definition a case of having interpreted some "features" of the raw sensory data as "X" (where X is an entity or feature that has been defined in your worldview); that also means that there must exist some tiny bit of a worldview in order to have any perception. On the other hand, you cannot build a worldview without perceiving something first. Yes? No?

 

That is exactly the problem that Doctordick often refers to as the problem that most people don't even recognize as a problem. And the solution is, in a nutshell, that "sensory interpretation is a free parameter of one's worldview". It means that the worldview can be built out of the sensory data, even when its meaning is initially completely unknown. If you don't think that is possible, then please realize that that problem - regarding the interpretation of raw data to come up with "perceptions" - is actually completely analogous to how children learn to interpret sound patterns as language, even when they don't know any language when they are born.

 

In a simplest form, you could think of it as making assumptions, and when those assumptions yield sensical interpretation of the raw data, stick with them. A worldview that is built like that only needs to be self-coherent, and it needs to be able to yield meaningful interpretation of the data. It doesn't need to be ontologically correct (and as you already seem to understand know, it never is)

 

That a worldview can be built out of initially unknown (or meaningless) data is actually a quite convenient turn of events, because it offers a solution to another perplexing problem of AI; human semantics. There will always exist many valid ways to interpret the same raw data (i.e. you could build many different but equally useful worldviews), and if you think about this a bit, you end up with exactly that; semantics.

 

Unfortunately, it appears that most people never seriously think about this issue, and rather just tacitly assume "perception comes first", and by doing that they just cling onto naive realism without realizing it.

 

And I didn't say anything about consciousness because consciousness itself is something that hinges entirely upon however you happent to define it (and associated parts of your worldview). What I can say is that once again there are those tacit "naive realistic" views that prevent people from seeing all the available possibilites regarding their own ontological identity; there is absolutely no reason to attach any ontological identity on "self", even though we do so in our worldviews, and even though we have memories about past, since we can explain our memories as a specific configuration of "brain" that always exists in "present".

 

If you don't understand what I'm talking about above - and if you can't figure out what Doctordick's treatment is even about - then with all due respect, I'm afraid there's no sense to continue this discussion with you.

 

EDIT: Some clarifications, wrote the post little bit hastily, hope it's not too confusing.

 

-Anssi

[AnssiH]

Thank you for your note Anssi. Though there may be some very serious questions in your mind, I am convinced you at least see the purpose of my approach. In many respects, your knowledge of mathematics is too limited to pick up on possible flaws in my deductions; that is something Qfwfq or Buffy might be better at accomplishing but they are much more concerned with the outcome than how I get there. Though there are some serious flaws in my presentation (Bambadil has brought up one) I don't think any of them pose any serious threat to my deductions. Perhaps the time to discuss my mode of solving that differential equation has arrived. If you think you are ready to look at that algebra, let me know and I will post the opening move in my approach.

 

I wrote a reply to you in the beginning of my last post but now it's not there, and I don't know what happened to it as I wrote the whole thing in a bit of a hurry ;)

 

Anyway, what I said was just that yes, I definitely see the purpose of your approach, and don't get me wrong, I just want to spend some time to really understand what you are saying, and it's a time consuming process when you are referring to many concepts that I just don't happen to be too fluent with. It takes time to think things through.

 

I think I understand why you were referring to Bose-Einstein statistics, and Fermi statistics; Just another specific ignorance that allows us to use those descriptions for nature. Is that the way you view it?

 

If you want, you can start the discussion of solving the differential equation, but I think I will be replying to that older post first as soon as I have enough time to really look at it properly.

 

btw, I believe the difficulty with Rade is essentially just that he is missing the topic due to some terminology differences. He keeps saying there is no understanding of reality without definitions for its features (I guess the human definitions & noumena put together is what he refers to as "dialectic union"), and when he says "everything is dialectic", he essentially just means "every and any kind of view of reality that we can conceive is one part noumena and one part definitions, put together". Of course, fair enough so far, but unfortunately he assumes the topic refers to actual ontological reality as oppose to its descriptions, and if I've figured his mind right, then in his terminology, this topic could be described as 'what logical constraints always apply to the "human definition" part of that "dialectic union"'... Goddamn semantics, huh? :)

 

But I could be reading him wrong, in which case I don't think there's reason to argue about his views in this thread, too much noise.

 

-Anssi

[Rade]

..btw, I believe the difficulty with Rade is essentially just that he is missing the topic due to some terminology differences. He keeps saying there is no understanding of reality without definitions for its features (I guess the human definitions & noumena put together is what he refers to as "dialectic union"), and when he says "everything is dialectic", he essentially just means "every and any kind of view of reality that we can conceive is one part noumena and one part definitions, put together". Of course, fair enough so far, but unfortunately he assumes the topic refers to actual ontological reality as oppose to its descriptions...

So, AnssiH, you are a good mind reader, what you claim in red above is true. But, as to the last part of your statement, I did not assume that the OP topic, which is:

What can we know of reality?

refers only to "the description of ontological reality", as opposed to "actual ontological reality"--but apparently this is what you and Doctordick assume, so please do carry on with your dialog to support this assumption. Thank you for the clarity of your replies to me.

[AnssiH]

I did not assume that the OP topic, which is:

What can we know of reality?

refers only to "the description of ontological reality", as opposed to "actual ontological reality"

 

Well it is pretty much refers to the "descriptions of ontological reality", because "what can we know of reality" pretty much boils down to what characteristics can we consider as necessary to any valid worldview. Certainly the title can be confusing as it is, depending on how one interprets it. It would probably be better understood as "what can we know about valid worldviews".

 

Thinking back to this thread, perhaps it's easy for you to appreciate this perspective; We are ignorant about many aspects of the actual ontological nature of reality, and what Doctordick is discussing about is that certain cases of ignorance forces certain symmetries / characteristics to our worldviews.

 

Doctordick, would you think that's an okay way to phrase it?

 

-Anssi

[HydrogenBond]

Science is still pushing forward trying to get a clearer picture of reality. Based on the existing perception of reality, if it was already reality, there would be no need for any further push in science. But since there is a push, many scientists don't believe this is the final understanding. So if we use this soon to be replaced current understanding as the basis for our current perception of reality one is, by default, out of touch with the reality of the future which is closer to reality. It is only a short term perception of what we would like to call reality, so we can pretend before it changes.

 

This brings up the reason for this. All perception comes from the brain. Not just the conscious mind but also the unconscious mind. For example, the terror threat, from a rational level is a small under equipped army by any standards. Yet the perception is some super power ready to take over the world. At the rational or conscious level it doesn't stack up, but at the unconscious level, the fear is strong enough that most people forget about the rational. The reality of the situation does not equal the perception of reality created. But most people can't see the difference.

 

The question becomes, how well do people know the tool, i.e., brain-mind, that is responsible for blending rational and irrational reality together? If one is not sure how the mechanism of the unconscious works, one can't be sure what they think is reality is not cross contaminated with something in the imagination. It sort of like the chemist who knows how the run a GC but not how it works. He can analyze the output data but can't separate any noise coming from instrument problems. But if he knows the instrument and realizes there is a leak, then there is a different reality.

 

That is one of the problems with theoretical science. Many are pushing the limits of perception to the extreme without having to know how the neural instrument works. How much of extreme theory is mostly imaginary or due to problems or noise coming from the instrument itself? Maybe we need to require those who push the neural mechanism to the limits of human perception have a full understanding of how the mind works, so they can better filter out noise that might distort their perception of reality. Or we can do it backwards. We will no longer require any scientists know how their instruments and tools work. This shouldn't affect things any more than not knowing how the mind works when we use that tool for reality.

[Bombadil]

The procedure which yields a solution consistent with Fermi statistics is a little more complex to describe. If we begin with a specific solution vec{Psi} and exchange two x tau points and then subtract that second function from the first, we still have a solution to the equation. If we then take that function and exchange a different pair and subtract that result from the result of the first step we again will have a solution to the equation. If we continue that process until all possible pairs have been exchanged, we again end up with a function where any exchange will yield back the same function but with a subtle difference: in this second case the function is antisymmetric: i.e., an exchange of any two points will yield a change in sign.

Then is this something that we have to do to make the function antisymmetric?

Does this also mean that all possible elements in the explanation must be in it since we can’t tell them apart? We can’t say that some elements aren’t in it without a way of telling what element it is that we are leaving out of the explanation.

I do not understand the question here. The function vec{Psi} by definition tells us the expectations produced by a specific particular flaw-free explanation for the set of ontological elements referred to by the indices x_i. If there is one not in there, it fails its definition as the expectation for that element can not be obtained.

What I’m trying to ask is this, suppose we made an explanation based on a set of elements that we know were not all valid. Now while there is no way to tell if an element is valid it seems that it is possible to tell if an element can’t be valid for instance if an element is not antisymmetric it can’t be valid although it seems that there is no way to tell which element is not valid, so it seems that all elements must be antisymmetric. What I’m asking is, in the absence of an explanation is there any way to leave out the invalid elements? I see no way that we can, due to the fact that in the absence of an explanation there is no difference between the two sets and so not only is there no way to tell valid from invalid if there was there would be no way to leave invalid elements out of the explanation. This seems to suggest to me that all elements in an explanation must appear valid although it seems we had already agreed on this earlier.

Quote:

This is leading me to the question, what symmetries must an equation satisfy in order for any value of the variables to be a possible value without changing the value of it?

Without changing the value of what? Sorry but this question is not clear to me at all. Perhaps you can make it a little clearer.

I wasn’t very clear there, for a example I will use the function [imath]\vec{\Psi}[/imath] we know that we are ignorant of the coordinates of the elements in [imath]\vec{\Psi}[/imath] now I know this leads to shift symmetry and now exchange symmetry but it seems to me that this is insufficient to lead back to being ignorant of all coordinates of the elements in [imath]\vec{\Psi}[/imath]. What I’m wondering is just what are we saying when we say that we can label the elements in any way without changing the solution?