What can we know of reality?

[AnssiH]

Originally Posted by Qfwfq

Well, I suppose I didn't word my post very well and you misunderstood it.
i should have said which are the arbitrary labels, not what. In the spy's case there are some non-arbitrary numbers and I don't see what the arbitrary labels would be. I don't see what you would map those numbers on to and I don't know what the table would be. I'm therefore unable to deduce the validity of your constraints.

The "arbitrary labels" are referring to names that you give to the components of reality that you have tacked with identity (look at my previous post). In Doctordick's treatment the names are just numbers. I.e. a guard could be a number 5, a spy could be a number 3, etc... They are arbitrary because guard could be any number and it would not have an effect on the predictions of the worldview.

This can be a confusing example because the guards also happen to be shouting "numbers" at each others. The numbers that the guards shout at each others need to be understood as elements in the worldview as well and in this treatment they could be labeled with any number. A shouted word "thirteen" could be labeled as "7856" or whatever. The only reason it would have a label is so that its existence can be marked down into the x,tau,t-space.

If that was confusing, please ignore it and let me explain this properly I think I know what you are asking about as I tried to take the same route to figure out what the "x,tau,t"-table is for when Doctordick first mentioned it to me. I.e. I tried to figure out how would some simple system be described by it.

Unfortunately that is going besides the point. The point is precisely that there is NO "one and only" correct way to map some physical system onto that table.

Let's say you map a dual slit experiment onto it, then each different ontological interpretation would map different ontological elements to exist at different certain moment. That is to say, two different people with different worldviews could produce completely different looking tables when describing the same system. The tables might look like they have absolutely nothing in common. It would look like completely different entities would be moving through time in different tables. (Remember, they have merely marked down what entities (that they defined) exist at specific moments)

Case example: I think a particularly interesting case is Milo Wolff's attempt to model reality by having defined everything in terms of "spherical standing waves" that are like "ripples of space" (i.e. here space is defined as something that can have 3 dimensional "ripples"). I don't know if that's valid, the point is simply that any physical system mapped through that worldview (where the waves or the standing waves have identity) would look quite a bit different from one where elementary particles move around (relativistically or otherwise).

Now the point is that whatever that table might look like, it will have certain properties if it is self-coherent. For example that shift symmetry regarding the probability function arises from the fact that the labels we assigned to the features (that we defined) were completely arbitrary to begin with and cannot affect the behaviour of the probability function (whatever it might be). In common terms, our predictions of reality would be the same even if we called apples oranges and vice versa, or if we perceived red as blue and vice versa.

The "x,tau,t"-table will NOT be able to tell you which of all possible models is somehow "correct one". The purpose is to investigate the common properties of all valid models.

-Anssi

[Doctordick]

Originally Posted by Qfwfq

Well, I suppose I didn't word my post very well and you misunderstood it.
i should have said which are the arbitrary labels, not what. In the spy's case there are some non-arbitrary numbers and I don't see what the arbitrary labels would be. I don't see what you would map those numbers on to and I don't know what the table would be. I'm therefore unable to deduce the validity of your constraints.

There is no such thing as a non-arbitrary label. Labels are what the “person who is trying to understand” uses to identify or refer to specific patterns he or she has identified (or decided are significant). They are a consequence of some epistemological construct he believes necessary to solving the problem. When you say, “in the spy's case there are some non-arbitrary numbers” you are in fact saying, “there is additional information here which is not being taken into account” (the meaning of the word spy, the meaning of the utterance your refer to as “13”, etc.). If that is indeed the case, then it is necessary (if you want to communicate the information the epistemological construct is based upon) that you provide that additional information. When you go to do that, the symbols you use can be arbitrarily labeled.

Otherwise, your description of the problem is biased by your assumption that some epistemological construct (in this case, I would suspect your presumption that your world view and the expression of the problem in English) is a valid basis within which to consider the puzzle. That epistemological construct may very well be a flaw-free construct but I have no interest in the constraints presumed by some successful epistemological construct; my interest is the constraints required by ALL flaw-free epistemological constructs.

And Anssi, you are, as usual, dead on with your interpretation of the situation. Thanks for the help; I hope it does some good.

Have fun -- Dick

PS This is an addition which occurred to me upon rereading this post. Perhaps it will never be read but I will add it anyway (with a reference to it later). Qfwfq is overlooking the fact that I have said many times that “an interpretation exists” which conforms to my equation. He apparently wants a solution, not an interpretation of a solution: if he were to give me a solution (complete enough that I could reason out his expectations in detail from it) then, with sufficient time, I could present him with a which would yield those expectations (i.e., an interpretation of his solution which satisfied my equation). All I have to do is write a computer program which yields those expectation (if his explanation is sufficient to reason out his every expectation) and then set down the output of that computer program for every possible set of inputs (that would be a table representation of . Exactly what numerical label I attach to each input (the address where that variable is to be stored is immaterial: i.e., consider the inputs to be the information bits themselves).

Please let me know if this act violates any rules of the forum. If it does, I apologize. -- Dick

[Kriminal99]

Originally Posted by AnssiH

(btw, this is relevant also to your example about babies learning language.

On to your response to QFQW...

You cannot suppose the baby just knows what constitutes a "word" or that there even are such things as "words". That is part of your worldview)

So I hope this clears up what I mean by us deciding what constitutes an object. For more philosophical aspects of this, take a look at "Ontological perspective" and "Epistemological perspective" at post #34. (really take a look, I spent a lot of time on that one

....

The question is now, is there something that is common to each and every possible (valid) worldview. By valid I mean they do not contain self-conflict. So, how do we express the constraints that arise from the simple fact that each worldview, whatever it may be, needs to be internally coherent. If it contains self-conflict, it cannot be a good description of reality can it?

Now we are moving closer to where Qwfwq is already standing (I think). Onto the next post ->

-Anssi

I am not sure if you were agreeing with my example or proposing there was a problem with it. Just in case, in that example the baby doesn't need to know what a word means. All that matters is that the word is being uttered at the same time as the object is being seen. This is why the & sign was used to denote a coincidental connection.

It doesn't have meaning until they start to be repeatedly heard at the same time as they see the object or chain of events. Thus an idea of an object is just a collection of related perceptions, with no special status attributed to any one of those perceptions based on what sense they came from or anything else. This simple system explains why no arcane understanding of time/space is needed to begin defining the world around them. Everything is just defined in terms of each other, which of course makes perfect sense considering that:

1) There is no end to a chain of explanations of "why", so a better instinctual understanding would require infinite brain mass to support...

2) Neural networks seem to indicate that things work this way

This approach doesn't really require the assumptions you mention in the other post you referenced. It is simply recognizing coincidences. Once we are old enough to question these coincidences by realizing our parents could have called those things something different, we also realize that they "make the interpretation of the consequent patterns meaningful" enough that it is pointless to change them.

On to your response to QFQW and DD's post...

I don't think the problem is explaining that every world view needs to be internally coherent. Everyone knows that, they just don't know how or care to know how to test it.

People are not by nature rational beings. They are after animal related goals and too much reasoning doesn't seem to allow them to reach those goals. What we need to do is create an enviornment that forces people to accept rationality to achieve their animal goals. That is basically what is behind people like you and me.

Originally Posted by Doctordick

Otherwise, your description of the problem is biased by your assumption that some epistemological construct (in this case, I would suspect your presumption that your world view and the expression of the problem in English) is a valid basis within which to consider the puzzle. That epistemological construct may very well be a flaw-free construct but I have no interest in the constraints presumed by some successful epistemological construct; my interest is the constraints required by ALL flaw-free epistemological constructs.

So given that a person cares about doing so, how would they do this?

Everyone involuntarily uses the same basic system to understand their surroundings up to a certain point, and they always use this system to some degree.

Because of this, the same rules are necessary for everyone.

Completeness is not one of those rules. You can never achieve it. However you should always look for more information than you currently have, especially if you think it might have relevance to the integrity of your belief set.

No logical contradictions obviously is one of those rules. However, we cannot perceive infinite logical consequences of any given claim. Thus I propose several "efficiency" rules to best allow us to use what little resources we have.

Cut anything from definitions of words other than the context the word is meant to refer to. Then determining logical consequences simply becomes math, instead of dealing with a pile of spaghetti that you have to untangle. And then you can actually see logical contradictions. An important part of this is cutting out metaphorical definitions of words.

If anything unnecessary cannot be removed (such as the label), then be aware that infinite other labels could be used without affecting the core beliefs.

[Qfwfq]

Originally Posted by AnssiH

The "arbitrary labels" are referring to names that you give to the components of reality that you have tacked with identity (look at my previous post).

Which is the semiotic issue, and my choice of example had more to do with this than you might have imagined. But I still can't figure out what help the x, , t table is. I'm now unsure if only the x'es are labels, as I thought, or all three groups of variables.

Originally Posted by AnssiH

The point is precisely that there is NO "one and only" correct way to map some physical system onto that table.

I wasn't asking for the one and only way, I was asking for some indication of how the the things can be organized into tables in a way that actually reflects what is to be explained and a justification of the constraints.

Originally Posted by AnssiH

The "x,tau,t"-table will NOT be able to tell you which of all possible models is somehow "correct one". The purpose is to investigate the common properties of all valid models.

Obviously, and I'm trying to justify the constraints.

[Buffy]

Dick,

Thanks for the extended explanation. I'm going to try to stick to something simple to focus on that still gets at the core of my lack of clarity about what you are doing:

Originally Posted by Doctordick

Now, the important thing in all this is that the given known information is actually the things being labeled, not the labels themselves.

Got that. Meta versus meta-meta versus meta-meta-meta is not problem for me. I've had it from philosophy to math to computer science and I'm really good at it! I'm meta-gal!

But:

Originally Posted by Doctordick

Since it can be represented as a mathematical function of those numerical labels, we know certain symmetries must exist in that representation. In particular we know shift symmetry must be a property of the representation.

WHY?

This is why I thought your example of non-associative algebras was so useful! I can come up with lots of excuses as to why those mathematical functions should show no shift symmetry whatsoever!

From my point of view so far, this is an unjustified assumption, that makes agreeing on your formula in the abstract impossible without further explanation as to why this restriction would hold.

As I think both Q and I are trying to do, it seems that a better understanding of the justification--indeed *mapping* even if it is one or two meta levels above a concrete example--is necessary before justifying such a restriction can be seen as valid.

A side note: I can definitely see how this can degrade into the "'what is' is 'what is'" argument, but I appreciate and *agree* with you that its not really relevant, nor is it "preposterous." On the other hand, I think its evidence that there is something missing in your math here, because it may be the case that that conclusion is only showing an incompleteness in the mapping: much like quantum mechanics shows "illogical" or "inconclusive" "infinities" when applied to gravity. The conclusions drawn may or may not be wrong, but the math is inadequate to justify those conclusions.

I'm fond of noting that the list of logicians who have seriously proposed formal systems that turned out to be inconsistent reads like an honor roll: Frege, Church, Curry, Quine, Rosser,
Buffy

[AnssiH]

Originally Posted by Kriminal99

I am not sure if you were agreeing with my example or proposing there was a problem with it.

There was not enough information for me to say if there's a problem or not (presumably your idea has got more details to it than were voiced)

I was just trying to steer the conversation from an AI model more towards the original subject.

Thus an idea of an object is just a collection of related perceptions, with no special status attributed to any one of those perceptions based on what sense they came from or anything else. This simple system explains why no arcane understanding of time/space is needed to begin defining the world around them. Everything is just defined in terms of each other

Yes, everything is defined in terms of each others [in self-coherent manner]. That is the crux of what I was calling "semantical worldview".

So it seems we agree, and I suppose the only thing you have reservations of is whether all that math is how we build our worldviews. I'm fairly sure it is not I should have stressed before that Doctordick is not exactly proposing that this is how we do our worldviews. Rather this should be viewed as a fairly high-level analysis about our worldviews. What consequences there are as a result of that analysis, is a different matter. (Certainly it could lead to methods for building self-coherent predictive models out of completely unknown information, and those methods could be completely different from how brain does it...)

-Anssi

[AnssiH]

Originally Posted by Qfwfq

Which is the semiotic issue, and my choice of example had more to do with this than you might have imagined. But I still can't figure out what help the x, , t table is. I'm now unsure if only the x'es are labels, as I thought, or all three groups of variables.

I can't remember where there would be a good succinct post defining these so;

Let's say you were to map down a worldview where reality is identified as bunch of electrons and protons, then electrons would get different X label than protons. Let's say electrons are "1" and protons are "2" on the X-axis.

If a certain moment consisted of three electrons and four protons (according to that worldview), you'd need to mark down three 1's and four 2's -> to do that you need the tau axis.

So to answer your question, different sorts of elements are labeled with different X (what is different sort depends on your worldview), and each individual element would be labeled with (x, ).

The beforementioned "moment" could look like this:
(1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (2,4)

Or obviously you can conceive it as points on an x,tau -plane

I'm sure you can figure out that the t is there so we can index different "moments", i.e. multiple x,tau -planes. (Doctordick calls them "presents")

And I'm sure you realize immediately that it's not quite that simple; typically worldviews have some definition for "space" too so the mapping needs to contain that specific definition as well one way or another.

I actually asked about this in the PF forums (post#422) but it got drowned between other issues, so Doctordick needs to clarify on that. (Let's say one's interpretation of a situation is that "an electron is bouncing between two protons in an euclidean space"; how would that be mapped, as an example).

-Anssi

[Doctordick]

Originally Posted by Qfwfq

But I still can't figure out what help the x, tau, t table is. I'm now unsure if only the x'es are labels, as I thought, or all three groups of variables.

The table is no more than a tabular representation of exactly the same data displayed as points in the abstract Euclidean space. The actual points in the space are nothing more than a way of representing the references specific to some epistemological construct. Any collection of references to the ontological elements underlying a specific epistemological construct can be displayed in such a structure. Think of it as a collection of references defining the language used to describe one's epistemological solution: i.e., used to display the basic data sufficient to decipher the solution you have in mind.

Originally Posted by Qfwfq

I was asking for some indication of how the the things can be organized into tables in a way that actually reflects what is to be explained and a justification of the constraints.

It just takes a lot of data and each element of that data can be referred to by any label you wish to use as figuring out the meaning of the labels is a very real part of figuring out the epistemological solution you have in mind. For example, (and Buffy, here is another example) consider your problem of the spy and the code with the guards only, instead of giving it to me, give it to a two day old infant. What response would you expect?

Certainly that infant has the innate ability to understand what you are talking about. The problem is that it would take you maybe ten to twenty years to provide him with sufficient data to decipher exactly what the question was. Now, your presentation of that data, had it been carefully documented could be labeled with arbitrary labels. When his actions eventually became consistent with your expectations (i.e., what you would expect of someone who understood what you were talking about) you would come to believe he understood you. Then, and only then, could you talk about the issues you want to talk about. The issue here is that your concern is only meaningful within a rather complex specific epistemological construct.

Originally Posted by Qfwfq

Obviously, and I'm trying to justify the constraints.

Then you are looking in all the wrong places for that justification. The justification is not to be found in any epistemological construct as it lies not in the epistemological construct but rather is a consequence of the fundamental symmetries of the references system used to express that epistemological construct. Those constraints are a direct consequence of the embedded symmetry of that arbitrary reference system and have absolutely nothing to do with any specific table related to reality.

We have a subtly significant structure here. The epistemological construct is a function of the ontological elements themselves, not the actual numerical references chosen to display them in the table. Yet, independent of how those numerical labels are created, if the epistemological construct may be deduced from the ontological elements themselves, it can be deduced from that collection of numerical labels. The constraints I am referring to are a consequence of the symmetry necessarily embedded in that representation no matter how that representation is created.

By the way, as another example for Buffy, in attaching reference indices to data, consider the following hypothetical situation. We have a flaw-free epistemological solution to archeology: i.e., it is perfectly consistent with all the data available to us. Under that solution, fire was not used by humans prior to 65,000 years ago (I just pulled that out of my hat so don't quibble with its accuracy). An archaeologist digging at a site already definitely dated as being prior to 75,000 years ago discovers a charcoal bed together with chewed bones and other indications of human habitation. This is new information: i.e., by my definition of time we are talking about the future (i.e., a "new" present). Relative to the epistemological construct he was working with, this is a future event: i.e., his finding this stuff occurred in the future, not in the past of his epistemological construct; however, in order to maintain the overall structure of his epistemological construct, he will probably assign a t index of this bed of charcoal to somewhere in the vicinity of -75,000 years.

What is significant here is that the division between past and future (a specific “present”) contains this new information; his assignment of this information to -75,000 years in his table is an assumption and not exactly an objective representation of his experiences. He has eliminated the possibility that the charcoal bed came into existence the moment he uncovered it. Note that I am not saying his assumption is wrong, I am merely saying that it is an assumption; the real question being “what other assumptions is he inadvertently making?” It is certainly true that the assignment for t may nevertheless lead to a new flaw-free epistemological construct but that is not the issue under discussion. The issue here is that, in the absence of an epistemological solution, those reference indices are open undefined numerical labels.

Originally Posted by Buffy

This is why I thought your example of non-associative algebras was so useful! I can come up with lots of excuses as to why those mathematical functions should show no shift symmetry whatsoever!

Again, you are scumming to the overwhelming urge to look at epistemological constructs. The issue here is the embedded symmetries in the reference system used to express the information on which those epistemological constructs are built.

Certainly you will accept the fact that one can use numerical labels to refer to the specific elements of that information. If you had that entire collection of references, including the time index which yields changes in that collection, it is quite clear that patterns would occur (that's pure finite numerology). If your explanation (your epistemological construct) is actually no more than a data compression mechanism (which it certainly must be since the collection of numerical labels, in the absence of an epistemological construct, cannot possibly contain any information themselves) then it is quite reasonable to presume that such data compression mechanisms are feasible.

So, start with a set of such numerical labels (that hypothetical ”what is”, is “what is” table and nothing more) and create an epistemological construct which yields a flaw-free explanation of your experiences (recreates the table). Now you have solved the problem; you have explained your experiences! Now take that original table and add the number a to every element. In what way have you changed the problem confronting you? That is called shift symmetry. You cannot remove that symmetry from the problem and it follows that the symmetry must be likewise embedded in the solution.

Thanks for trying Anssi but I suspect your presentation will sway few.

Have fun -- Dick

[Qfwfq]

Actually Dick, I found Anssi's presentation quite clarifying. Considering it with his remark:

Originally Posted by AnssiH

And I'm sure you realize immediately that it's not quite that simple; typically worldviews have some definition for "space" too so the mapping needs to contain that specific definition as well one way or another.

I actually asked about this in the PF forums (post#422) but it got drowned between other issues, so Doctordick needs to clarify on that. (Let's say one's interpretation of a situation is that "an electron is bouncing between two protons in an euclidean space"; how would that be mapped, as an example).

it seems that the "what is, is what is" table begins to look a bit like Fock space. Since he found no answer to his query as of post#422 in the PF forums, I'll say to his benefit that it is defined in any good book of field theory. The most pedestrian treatment is perhaps the one in Schweber's book, of which I believe this should be a recent edition and it seems an accessible price too, especially for us € folks these days. It does suppose quite a bit of calculus, linear algebra and stuff to be familiar, but I wouldn't be surprised if Anssi could follow the overall line of reasoning concerning his query.

It didn't really take all that much after all, to give me a useful bit of insight.

[Doctordick]

Hi Anssi,

I am answering your note here because I think the issue is being confused by everyone. Qfwfq keeps telling me he knows what I am talking about and then immediately goes off in a direction having absolutely nothing to do with the issue of interest. Everyone seems to have this terrible compulsion to get into epistemological issues and avoid thinking about the representational issue central to the discussion. Even you, who manage to see the central issue so clearly, are easily drawn into off the wall discussions involving specific epistemological constructs.

Originally Posted by Anssi

I've thought about Buffy asking about the shift symmetry, and I suppose what she's thinking of is that if you have a x,tau,t-table where, let's say on the X-axis "2" is usually followed by "3" (on the next t), and "3" is usually followed by "1", and you had a probability function that told you this, then after shifting the labels, that same probability function would yield wrong probability as it would tell you "3" is usually followed by "4" (instead of "2"), for example.

So the missing bit was that the probability function itself was not seen as a function of the *patterns* on the table, but as a function of specific indices. After all, if you've mapped a specific table, it should be possible to have a flaw free probability function (in that it works for all the past) that works with that specific table but cannot cope with a shift in the labels since it happens to rely on specific labels instead of specific patterns.

Is that right? It is in fact an (so far unvoiced) requirement that the probability function we are talking about relies on patterns instead of specific labels?

What you are presenting is a specific epistemological construct. You are clearly trying to comprehend how that specific construct is to be seen as a ”what is”, is “what is” table. Understanding how a specific epistemological construct is to be represented in a ”what is”, is “what is” table is exactly the same problem as trying to understand a language or reality itself (that understanding requires a specific epistemological construct which itself needs to be understood). I am simply not concerned with how that all is to be achieved. The only issue of interest to me is that it can be done! That is to say, any explanation of anything must be expressed via a collection of ontological elements. What ever specific epistemological construct you have developed, your understanding of it is based on a collection of ontological elements to which you can refer. My ”what is”, is “what is” table is nothing more or less than an abstract representation of that collection; or rather, an abstract representation of references to that collection. The issue is very very simple: the symbols being used to refer to those ontological elements cannot possibly be of any significance at all as the nature of the reference symbols themselves constitute a totally free arena. That, and that alone, is the central issue of my presentation.

Now, the mathematical issue is a another thing. You must understand that , when seen as a function of, say, (i.e., say we are concerned with the probability of being “6.254” for example) then it should be obvious that the correct answer depends upon what all those other references are. That is to say, can represent an entirely different probability distribution for each and every possible collection of those (n-1) other references (think, “how do you know the difference between an electron and a bug?). To hold that the epistemological construct cannot depend on patterns in the collection of symbols is simply not correct. All that shift symmetry requires is that if all the indices happen to be incremented by the same factor, we must get back to exactly the probability distribution we had before they were all incremented because we have altered no patterns. If does not satisfy such a constraint then those numerical references simply cannot be arbitrary and just where the devil are we supposed to acquire the information as to what symbol is to be used? The real issue here is that the possibilities are so wide open that discussing the possibilities is a complete and utter waste of time. All that is really important, as far as this discussion is concerned is ”those symbols have to be absolutely arbitrary!”

Originally Posted by AnssiH

I actually asked about this in the PF forums (post#422) but it got drowned between other issues, so Doctordick needs to clarify on that. (Let's say one's interpretation of a situation is that "an electron is bouncing between two protons in an euclidean space"; how would that be mapped, as an example).

I couldn't care less. Again, the possible ways of expressing such information is such a wide open issue that the mechanics of a specific example is a worthless endeavor; particularly in view of the fact that the representation must include ALL significant information including the order with which it came to be known.

Originally Posted by Qfwfq

Actually Dick, I found Anssi's presentation quite clarifying. Considering it with his remark:it seems that the "what is, is what is" table begins to look a bit like Fock space.

Off we go again. You have brought up “Fock space” at least three times already. Can't you comprehend that the idea of “Fock space” is an epistemological construct? See Slowikowski's outline of his course.

Originally Posted by Slowikowski

The origin of the Fock space concept lies in physics.

This implies we need to understand physics (an epistemological construct).

Originally Posted by Slowikowski

A construction made by the Russian physicist Fock in 1932 suggested the way of passing from states of single objects to states of collections of these objects.

Now we have to define “states” and “objects” and “collections”.

Originally Posted by Slowikowski

Actually, it gave an abstract formulation of Hermite expansion ...

And “Hermite expansion” yet.
In order to talk about “Fock space” you need to define a whole slew of things. Why do you find it so impossible to simply consider the issue of “an undefined ontology” referred to by some set of references as the fundamental basis of any explanation.

Originally Posted by Qfwfq

It does suppose quite a bit of calculus, linear algebra and stuff to be familiar, but I wouldn't be surprised if Anssi could follow the overall line of reasoning concerning his query.

Yeah, I am sure he could but, as far as I am concerned, the whole issue is outside what I am trying to present. What I want to do is make sure that anything I use is well defined and that the use of it makes no assumptions whatsoever about what the final solution will be: i.e., the necessity of maintaining absolute generality.

To date, I have put forth but one serious definition: that would be “time” which is defined to be no more than a parameter which establishes a change in information available standing behind the thing to be explained. Yes, I do hold that my definition is the fundamental issue behind the common concept of “time” but that isn't really an issue here at all. In order for it to be an issue, you would have to have an epistemological construct (a world-view) in mind and any such constraint is unacceptable. The real issue is the arbitrariness of the reference system itself. To deny that “shift symmetry” exists within a field of arbitrary numerical references is to totally overlook the arbitrary nature of that reference system itself. If you ignore that, you are ignoring the single most important fact behind all your ideas.

Originally Posted by Qfwfq

It didn't really take all that much after all, to give me a useful bit of insight.

I would really like to know what that insight could be. As far as I can comprehend your reactions, it seems to have very little to do with what I am talking about.

So you see “Fock space” as a representation which seems somewhat consistent with what I am doing. As time goes on, if we ever get to looking at solutions to my fundamental equation, more and more things of modern physics will show up as quite analogous to what I am doing; but, in every case, whatever it is, I will provide exact definitions which make absolutely no assumptions about the final solution to be achieved: i.e., I will keep the whole thing completely general right down to the last step. The issue of absolute generality is the single most important issue in this presentation and anytime a short cut of any kind is attempted, the whole conclusion of the work is made null and void. Any and all short cuts are essentially equivalent to making unwarranted assumptions.

At the moment, only two issues are under discussion. First there is the existence of shift symmetry within the arbitrary numerical reference system I have defined and the fact that the symmetry requires the differential consequences I lay out as basic constraints. Those constraints must apply to any epistemological structure based on any collection of such references. And second, there is the issue of “invalid” ontological elements created to constrain the “valid” ontological elements to what they are to be (i.e., consistent with the past). What is important here is that the “invalid” ontological elements need not be consistent with the past; they need only be consistent with the world view imposed by whatever epistemological construct lies behind your explanation of your world-view.

The only point of significance here is, “Does my fundamental equation indeed enforce the constraints I have proved to be required by the numerical reference system I have defined?” Your inability to understand how to represent your epistemological constructs (or any epistemological construct) in such a reference system is of utterly no importance as such a representation requires a complete understanding of that epistemological construct in all of its far flung glory including each and every detail upon which it is based; a mental construct far beyond our mundane comprehension. Worrying about such issues is beyond useless. If you want to understand what I am talking about, you have to keep your eye on the undefined ontological elements the appearance of which I have defined to be “what is to be explained”. Start defining them and you are off subject!

Looking for a response -- Dick