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An explanation of what I am talking about.


Doctordick
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The following comment in the “Deriving Schrödinger's Equation from my Fundamental Equation” leads me to post this alternate thread.

Perhaps it is helpful to point out here also that those symmetry constraints "on all flaw free explanations" are springing from the fact that the explicit meaning of the "data to be explained", is fundamentally unknown.
It appears to me that a little clarification on what I am doing would be worthwhile.

 

Perhaps it would be useful for me to point out exactly what I am talking about in my overall presentation: i.e., what we are working with and where we are going. When I was a student (some half a century ago) I was made aware of the power of symmetry arguments. As one professor once told me, “symmetry arguments are the most powerful arguments which can be made as they are the only arguments which can produce iron clad relationships out of total ignorance.”

My original purpose was to create a useful mental model of any explanation of any information so that I could comprehend exactly what could be deduced from the simple notion of internal consistency and symmetry principals. This thought resulted in what I call, “A Universal Analytical Model of Explanation Itself”, a paper within which I the development of what I call my “fundamental equation”. It is very important that the reader realize that there is utterly no content in that equation. It is no more than a exercise displaying the tautological consequences of the definitions brought forth in that paper.

 

1. [imath]x_i[/imath] is defined to be a numerical label for a specific undefined ontological element used in that explanation.

2. Time (as an index) is defined via the following: the past is the information being explained; the present (indexed by [imath]t_k[/imath]) is a change in that information. [imath]t_k[/imath] refers to a specific set of ontological elements [imath]x_i[/imath].

3. A Euclidean geometric space is defined as a mechanism to display the [imath]x_i[/imath] belonging to [imath]t_k[/imath] of interest.

4. [imath]\tau_i[/imath] is defined to be a numerical label attached to [imath]x_i[/imath] in order to assure identification of multiple occurences of a specific [imath]x_i[/imath]. The addition of [imath]\tau_i[/imath] adds a third orthogonal axis to the Euclidean display.

5. The explanation is defined to be a method of obtaining our expectations for a given collection of indices [imath](x_i,\tau_i)[/imath]

specified by a specific [imath]t_k[/imath]. The probability is a number and the arguments are numbers, thus the result can be expressed as a mathematical relationship: [imath]P=\vec{\Psi}^{\dagger}(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t)\cdot\vec{\Psi}(\vec{x}_1,\vec{x}_2,\cdots,\vec{x}_n,t)[/imath]. If we have an explanation, we know P and likewise, a [imath]\vec{\Psi}[/imath] (a method of obtaining that probability) must exist.

 

6., 7. and 8. These five definitions plus symmetry principals together with the undefined nature of those ontological elements are sufficient to deduce the validity of my fundamental equation. Three more definitions are then introduced as specific components of that fundamental equation: those would be energy, momentum and mass.

 

Thus I end up with eight defined concepts together with a tautological relationship between those concepts; mere self consistent consequences of those definitions. By showing that Schrödinger's equation is an approximation to my equation, I show that my construct (which is constrained in no way) requires all the ontological elements standing behind any explanation to obey classical mechanics in the classical limit. It follows that classical mechanics itself must be a tautology: i.e., classical mechanics must be true by definition.

 

I have shown that any proposed algorithm capable of answering meaningful questions about reality within my entirely general model must obey a rather simple equation. I have further shown that my model corresponds to the common picture of reality in sufficient detail to map ordinary anthropomorphic experience directly into my model: i.e., classical mechanics.

 

In effect, I have shown that all conceivable universes may be seen as a three dimensional space occupied by objects which are required by definition to obey classical mechanics in the classical limit. This can be taken in two different ways: one can see the result as demonstrating that our classical view of the universe (a three dimensional space occupied by objects which obey classical mechanics) is entirely general and capable of representing any conceivable universe or one can view my results as demonstrating the fact that classical mechanics is true by definition and that no classical experiment tells us anything about the universe except perhaps that our definitions are self consistent.

 

With regard to the second viewpoint, if one takes the position that the job of a research scientist is to search out the rules which separate the "true" universe from all possible universes, then no classical experiment can provide any guidance on the subject whatsoever. Classical mechanics is itself a tautology.

 

That is the central result of my presentation at this point. If you care to follow me further down this path, I will show you that the same is true of most all of modern physics.

 

Have fun -- Dick

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Thus I end up with eight defined concepts together with a tautological relationship between those concepts; mere self consistent consequences of those definitions. By showing that Schrödinger's equation is an approximation to my equation, I show that my construct (which is constrained in no way) requires all the ontological elements standing behind any explanation to obey classical mechanics in the classical limit. It follows that classical mechanics itself must be a tautology: i.e., classical mechanics must be true by definition.

 

I still don’t know if it is a good approximation or not, but I suspect that it is a useful approximation in that it tells us something about how all explanations behave, that is they behave approximately like classical mechanics in what you are referring to as the classical limit. But I suspect that a satisfactory answer for me will only come with a better understanding of the fundamental equation and a better understanding of the Schrödinger equation. The latter of which is well outside of our interest here, especially since I am not yet sure what I would consider a good approximation.

 

I have shown that any proposed algorithm capable of answering meaningful questions about reality within my entirely general model must obey a rather simple equation. I have further shown that my model corresponds to the common picture of reality in sufficient detail to map ordinary anthropomorphic experience directly into my model: i.e., classical mechanics.

 

I am wondering at this point if you have also shown that anything that can be mapped into your model is equivalent to a classical mechanics model or are there other models that would be based on your model, that is based on the fundamental equation? I am not asking what such models would be used for or even what might be different about them or how they would be derived, but rather just do they exist?

 

I suspect that this question has a rather straight forward answer and I would be able to answer it if I knew more about the Schrödinger equation, and that the answer may be outside of the topic under discussion.

 

With regard to the second viewpoint, if one takes the position that the job of a research scientist is to search out the rules which separate the "true" universe from all possible universes, then no classical experiment can provide any guidance on the subject whatsoever. Classical mechanics is itself a tautology.

 

I’m not quite sure where you draw the line. At what point do we go from looking at every possible explanation to looking at some particular explanation or explanations? I suspect that it is when we start defining elements or give values to anything in the fundamental equation, or is it when we put forward the idea that we can tell two elements apart? I suspect that these are all equivalent.

 

With regard to the latter I suspect that this is one thing that I keep forgetting, in particular that we can’t tell the difference between one element and any other element until we already have defined an explanation so any question of how an element behaves is of no interest because quite simply it is all part of the assumptions that we make to form a world view.

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My original purpose was to create a useful mental model of any explanation of any information so that I could comprehend exactly what could be deduced from the simple notion of internal consistency and symmetry principals. This thought resulted in what I call, “A Universal Analytical Model of Explanation Itself”, a paper within which I the development of what I call my “fundamental equation”.

In your email to me, you suggested I post questions about this paper on this forum. (If I should use a different thread, let me know.)

 

When you introduce A, B and C, you say "B(tk) is a finite unordered collection of elements of A." But there is a point in the paper where you start using Bk instead of B(tk), which I like because it emphasizes that there is no implied ordering of the sets in B. (This is defined by the t introduced by C.)

 

Would it be correct to only use Bk in the earlier references also, instead of B(tk)?

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I still don’t know if it is a good approximation or not, but I suspect that it is a useful approximation in that it tells us something about how all explanations behave, that is they behave approximately like classical mechanics in what you are referring to as the classical limit.
No, you are way ahead of the curve here. I am not talking about how all explanations behave. I am talking about how all ontological elements upon which those explanations depend behave; a seriously different issue. You are trying to function way out in that “all encompassing flaw-free explanation” without understanding what you are talking about. What I will end up proving is that the underlying ontological elements lying behind any explanation of anything are the physical elements commonly thought of as the underlying ontological elements of physics. It is an absolute proof that the correct answer to the question ”Can Everything be Reduced to Pure Physics? is Yes? But you will have to follow the argument to its conclusion in order to comprehend that answer. There are deeper consequences to that result than even the physicists can comprehend and that issue goes very much to your second question. (Reading the first and final page of that thread might be a very worthwhile endeavor!)
I am wondering at this point if you have also shown that anything that can be mapped into your model is equivalent to a classical mechanics model or are there other models that would be based on your model, that is based on the fundamental equation? I am not asking what such models would be used for or even what might be different about them or how they would be derived, but rather just do they exist?
They exist, but only in your head.
I’m not quite sure where you draw the line. At what point do we go from looking at every possible explanation to looking at some particular explanation or explanations?
Essentially we do not and that is also an issue to be discussed later.
I suspect that it is when we start defining elements or give values to anything in the fundamental equation, or is it when we put forward the idea that we can tell two elements apart? I suspect that these are all equivalent.
The moment you begin talking about “an explanation” you are, in a very real way, fundamentally outside the issue under discussion here.
With regard to the latter I suspect that this is one thing that I keep forgetting, in particular that we can’t tell the difference between one element and any other element until we already have defined an explanation so any question of how an element behaves is of no interest because quite simply it is all part of the assumptions that we make to form a world view.
What is truly interesting here is that “fundamental modern physics” is exactly isomorphic to my fundamental equation. A rather unexpected result with deep and profound consequences.

 

 

Hi jeft0, it is nice to see a post from you.

In your email to me, you suggested I post questions about this paper on this forum. (If I should use a different thread, let me know.)
There seems to be no strong response to this thread so it seems to be as reasonable as any other.
When you introduce A, B and C, you say "B(tk) is a finite unordered collection of elements of A." But there is a point in the paper where you start using Bk instead of B(tk), which I like because it emphasizes that there is no implied ordering of the sets in B. (This is defined by the t introduced by C.)

 

Would it be correct to only use Bk in the earlier references also, instead of B(tk)?

Sure, if you feel that makes more sense then I will go along with it. :eek2:

 

Somehow, if I were doing it again, it seems to me that identifying A with “undefined ontological elements” would be a plus if it were done in a way which didn't confuse the masses. :)

 

Have fun -- Dick

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Sure, if you feel that makes more sense then I will go along with it. :)

 

Somehow, if I were doing it again, it seems to me that identifying A with “undefined ontological elements” would be a plus if it were done in a way which didn't confuse the masses. :phones:

 

I'm not at the point yet where I could be confused by what the terms are identified with. :) I'm just trying to make sure I follow the equations. (I think I have enough math background to do this and I'll try to not get sidetracked by interpretations.)

 

Another basic question: I may be tempted to say that the type of element in the set Bk is a pair of real numbers, but I suspect I would be wrong (even though the paper uses phrases like "all [math](x,\tau)_k[/math] elements in Bk"). Rather, I must resist the temptation to identify what the elements of the set Bk actually are by giving them a mathematical type - we don't assume we can know this. Instead, we are simply giving each a label which is mapped to a point [math](x,\tau)[/math]. The set of [math](x,\tau)[/math] is not Bk but is simply a set of points from the x, [math]\tau[/math] plane. (And, in the equations, we are not working directly with elements of B.)

 

Am I on the right track?

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No, you are way ahead of the curve here. I am not talking about how all explanations behave. I am talking about how all ontological elements upon which those explanations depend behave; a seriously different issue. You are trying to function way out in that “all encompassing flaw-free explanation” without understanding what you are talking about. What I will end up proving is that the underlying ontological elements lying behind any explanation of anything are the physical elements commonly thought of as the underlying ontological elements of physics. It is an absolute proof that the correct answer to the question ”Can Everything be Reduced to Pure Physics? is Yes? But you will have to follow the argument to its conclusion in order to comprehend that answer. There are deeper consequences to that result than even the physicists can comprehend and that issue goes very much to your second question. (Reading the first and final page of that thread might be a very worthwhile endeavor!)

 

Ok so all that you have done is show that any particular element will behave according to the Schrödinger equation and while you have defined the form of V(x) the actual value of V(x) is defined by the remainder of the universe.

 

I read the first and final page of that thread it seems to me that the main reason that any one thought that everything can’t be reduced to pure physics is that they are only interested in what can be predicted. It may be the case that such predictions aren’t possible due to never knowing what elements aren’t known or possible to an extent but quite impractical due to the complexity of the problem. But if all that is of interest is explaining what we already know then obviously a function exists that will explain the data. The question of if the data will continue to match such a function is only of interest if it is predicting things that we want to know about.

 

What is truly interesting here is that “fundamental modern physics” is exactly isomorphic to my fundamental equation. A rather unexpected result with deep and profound consequences.

 

How I am understanding this right now, is that the Schrödinger equation tells us something about the elements in any explanation but it tells us nothing about the actual explanations in that even though the Schrödinger equation approximates Newtonian mechanics it doesn’t tell us anything more, because Newtonian mechanics is just a more particular explanation that is derived from quantum mechanics as a result of the Schrödinger equation.

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Hi Jeff,

 

Sorry I have been slow to answer. We have been out of town and out of touch with the internet for this last week.

I'm not at the point yet where I could be confused by what the terms are identified with. :) I'm just trying to make sure I follow the equations. (I think I have enough math background to do this and I'll try to not get sidetracked by interpretations.)
That is probably good.
Another basic question: I may be tempted to say that the type of element in the set Bk is a pair of real numbers, but I suspect I would be wrong (even though the paper uses phrases like "all [math](x,\tau)_k[/math] elements in Bk").
No you would be correct. Both x and tau are no more than numerical labels: i.e., stand-ins for actual labels used in the explanation being represented by the function [imath]\vec{\Psi}(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n\cdots,t_k)[/imath], which generates the probability of Bk. It is when the “model” proposes to denote the information represented by the total set of labels going into making up Bk as points on the x axis that the need to introduce tau arises and that is an issue you need to understand. Thus the model becomes a set of points in an [imath](x,\tau,t)[/imath] Euclidean space.
Rather, I must resist the temptation to identify what the elements of the set Bk actually are by giving them a mathematical type - we don't assume we can know this. Instead, we are simply giving each a label which is mapped to a point [math](x,\tau)[/math]. The set of [math](x,\tau)[/math] is not Bk but is simply a set of points from the x, [math]\tau[/math] plane. (And, in the equations, we are not working directly with elements of B.)
In a sense we are. We just do not have that representation expressed in what is called “English” (or any other language for that matter); nonetheless, what we have (once we actually have a specific Bk assembled via that third coordinate tk) is exactly the same information we would have in an explanation expressed in a language.

 

It is very convenient to think of the information available to us as expressed in an unknown language. Each fundamental element of that language is a single specific label and every “communicated message” is essentially a specific Bk. All we have to do is translate that language into the one we prefer (English for this forum). In this picture, do you not find the fact that everyone sees “reality” as an assemblage of physical elements in a Euclidean space changing position (moving about) as time changes a rather interesting thing?

Am I on the right track?
I presume you are but I am not in your head so I do not know for sure.

 

Now to Bombadil's post.

Ok so all that you have done is show that any particular element will behave according to the Schrödinger equation and while you have defined the form of V(x) the actual value of V(x) is defined by the remainder of the universe.
That does not really capture the essence of what I have proved. I have shown that “every” specific element in any conceivable universe (when represented as a set of points in a Euclidean space) will behave in accordance with Schrödinger's equation and that there always exists (for every such element) a Schrödinger potential V(x) (defined by the rest of the universe) which will yield exactly that observed motion.

 

By the way, dimensionality of that picture is another issue we have not yet gotten to and perhaps now is the time to discuss that issue. I think I will open another thread concerning the most probable reason we see the universe as having three dimensions. In my head, that is an issue worth some serious thought.

I read the first and final page of that thread it seems to me that the main reason that any one thought that everything can’t be reduced to pure physics is that they are only interested in what can be predicted. It may be the case that such predictions aren’t possible due to never knowing what elements aren’t known or possible to an extent but quite impractical due to the complexity of the problem. But if all that is of interest is explaining what we already know then obviously a function exists that will explain the data. The question of if the data will continue to match such a function is only of interest if it is predicting things that we want to know about.
I would put a slightly different twist on the question. If our interest is in explaining “what we know” and “what we know” is continually changing, what we should be interested in would be the simplest way of obtaining a new solution consistent with the “new” entirety of “what we know”: i.e., the simplest way in which those “ontological labels” could be changed such that “all the data known” is still explained. That brings up the issue that “changing labels” are themselves a interesting aspect of our explanations and right there we have some strong interest in how those points might move in that hypothetical space.
How I am understanding this right now, is that the Schrödinger equation tells us something about the elements in any explanation but it tells us nothing about the actual explanations in that even though the Schrödinger equation approximates Newtonian mechanics it doesn’t tell us anything more, because Newtonian mechanics is just a more particular explanation that is derived from quantum mechanics as a result of the Schrödinger equation.
Well now, I don't really feel that “it tells us nothing about the actual explanations”. First of all, Newtonian mechanics is not exactly “a more particular explanation that is derived from quantum mechanics”. Long before Newton lived, most everyone saw the world as a collection of “things” distributed in a three dimensional Euclidean space. The positions of these things, for the most part, were fixed and only people and animals (plus waves and winds attributed to gods, entities quite similar to people) moved or caused movement. Newton came up with some very powerful mathematical relationships lying behind motion. His discoveries were called “Newtonian mechanics” and were not at all an explanation derived from quantum mechanics.

 

In fact, the origin of quantum mechanics lies in the mathematical relationships implied by Newtonian mechanics. The beginnings of quantum mechanics came about through examination of methods of solving the differential equations arising in Newtonian mechanics. That alone is a long story far beyond this forum. Newtonian mechanics was a very powerful invention for explaining a lot of phenomena central to common reality and quantum mechanics was a major advance on that power. What is important about the transformation to quantum mechanics is the fact that, given quantum mechanics as correct, all of Newtonian mechanics can be shown to be an approximation to gross quantum mechanical solutions. Likewise what I have begun to show (and I will show much more) is that quantum mechanics is an approximation to gross solutions to my fundamental equation. And, since my equation and the mental picture behind that equation is no more than a tautological explanation of any body of unknown information, it implies that the common “physics” explanation of any phenomena lies (at least as a gross approximation) is fundamental to any explanation of anything.

 

In other words, modern physics (or at least a rather simple variation of that picture) lies as a basis behind any explanation of anything. If any ontological elements behind your explanation of anything cannot be reduced objects explainable by my equations (which can essentially be called “valid modern physics”) then your explanations are flawed or inconsistent in some way.

 

Have fun -- Dick

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I would put a slightly different twist on the question. If our interest is in explaining “what we know” and “what we know” is continually changing, what we should be interested in would be the simplest way of obtaining a new solution consistent with the “new” entirety of “what we know”: i.e., the simplest way in which those “ontological labels” could be changed such that “all the data known” is still explained. That brings up the issue that “changing labels” are themselves a interesting aspect of our explanations and right there we have some strong interest in how those points might move in that hypothetical space.

 

Would I be correct in saying that changing labels is what would be interpreted as movement or is movement more closely related to the mass, energy, and momentum of the element of interest? Of course any such movement can only be defined in comparison to the remainder of the universe so that it is just part of V(X).

 

In other words, modern physics (or at least a rather simple variation of that picture) lies as a basis behind any explanation of anything. If any ontological elements behind your explanation of anything cannot be reduced objects explainable by my equations (which can essentially be called “valid modern physics”) then your explanations are flawed or inconsistent in some way.

 

How I am understanding this, it is also true though that there exists an explanation that can explain any behavior of a collection of objects no matter how they behave. So that it is always possible to reduce any behavior to one described by “valid modern physics”.

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Would I be correct in saying that changing labels is what would be interpreted as movement or is movement more closely related to the mass, energy, and momentum of the element of interest?
No such thing as “motion” actually exists in the data being explained (the past is a static structure). Movement is an aspect of your explanation which allows different possible labels to refer to the same defined entity as time changes: i.e., a numerical index on the x axis in the present (a change in the known past) is taken to refer to the same entity at a different position in that “past” (what was known prior to the addition of the present). The explanation of course sees the past as a collection of “presents” made up of the same entities.
Of course any such movement can only be defined in comparison to the remainder of the universe so that it is just part of V(X).
This is a bit twisted. V(x) is the source of the “force” (force is something which changes momentum: i.e., changes the value of the partial with respect to x) which changes the momentum of the entity described by x. It is the measure of things like position and time which are a function of the remainder of the universe. The form of V(x) is also a consequence of the rest of the universe.
How I am understanding this, it is also true though that there exists an explanation that can explain any behavior of a collection of objects no matter how they behave. So that it is always possible to reduce any behavior to one described by “valid modern physics”.
Yes! But that requires “valid” modern physics. At the moment there are a few problems with modern physics which need to be fixed and I will show you these problems down the road.

 

Have fun -- Dick

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No such thing as “motion” actually exists in the data being explained (the past is a static structure). Movement is an aspect of your explanation which allows different possible labels to refer to the same defined entity as time changes: i.e., a numerical index on the x axis in the present (a change in the known past) is taken to refer to the same entity at a different position in that “past” (what was known prior to the addition of the present). The explanation of course sees the past as a collection of “presents” made up of the same entities.

 

When describing [math]\Psi[/math], you say it is a function of a "set of elements", e.g. [math]\vec \Psi(x_1, x_2, ..., x_n, t)[/math]. The use of the term "set" implies that there is no order to the elements. But if we want to say [math]\Psi[/math] is a function of a set of elements, we would write [math]\Psi(\{x_1, x_2, ..., x_n\}, t)[/math], where [math]\{x_1, x_2, ..., x_n\}[/math] is standard set notation. However, you don't do this, and I think for good reason because it is not a "set of elements", it is a "vector of elements", where the order as listed in the vector matters.

 

Is it fair to say that there is some extra information encoded in the fact that that you use a vector [math]\vec \Psi(x_1, x_2, ..., x_n, t)[/math] and not a set [math]\Psi(\{x_1, x_2, ..., x_n\}, t)[/math], where the position in the vector from one t to the next matters (to associate it with the same entity for different t)? It seems this is the way to make sense of your quote above. (I'm trying not to get hung up on your repeated use of the word "set" by assuming it always means "an unordered collection of elements with no duplicates".)

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When describing [math]\Psi[/math], you say it is a function of a "set of elements", e.g. [math]\vec \Psi(x_1, x_2, ..., x_n, t)[/math]. The use of the term "set" implies that there is no order to the elements.
The problem here is that my background is in physics (and that would be physics forty years ago) and not mathematics. I am not very familiar with mathematical notation or definitions for such things as sets or set theory. My personal concept of a “set” would be little more than some sort of collection.
But if we want to say [math]\Psi[/math] is a function of a set of elements, we would write [math]\Psi(\{x_1, x_2, ..., x_n\}, t)[/math], where [math]\{x_1, x_2, ..., x_n\}[/math] is standard set notation. However, you don't do this, and I think for good reason because it is not a "set of elements", it is a "vector of elements", where the order as listed in the vector matters.
Not really. It is much more due to the fact that I have never had an expression such as [math]\{x_1, x_2, ..., x_n\}[/math] given the definition you assign to it. Concerning the significance of the order as listed in the vector, if you look at the paragraph immediately following equation 1.2 in the document I sent you, you will find the following:
Up until now I have not defined what I mean by a pattern. I have made it clear that we are dealing with a set of numbers. The subscripts in the above expressions normally would be taken to imply that we are concerned with an ordered set. I would like to specifically exclude order from consideration: i.e., all permutations of a set of numbers are considered to be the same pattern.
I know I have made this same comment somewhere on this forum but finding it seems to be a serious problem. I actually use the vector notation for the simple reason that it makes the notation short.
Is it fair to say that there is some extra information encoded in the fact that that you use a vector [math]\vec \Psi(x_1, x_2, ..., x_n, t)[/math] and not a set [math]\Psi(\{x_1, x_2, ..., x_n\}, t)[/math], where the position in the vector from one t to the next matters (to associate it with the same entity for different t)?
My analysis gives no specific identities; those identities are part and parcel of the explanations. Your concern with the issue reminds me of an event that took place my first year in graduate school. New students were required to do some historical experiment and report on it. I chose Thompson's measurement of e/m for the electron, essentially using equipment equivalent to what is shown here. One of my comments concerning the experiment was that I was making a presumption that the blue line in the container was a stream of electrons. No one seemed to comprehend what I was saying. The issue in my mind was that the identification as a collection of electrons was based upon a whole stream of assumptions not expressed correctly. Essentially, the fact that the line consisted of electrons was defined by the existence of all the peripheral stuff; outside the definition all one could really say was that an interaction of some sort had occurred. Back in 04 I tried to bring up this issue on physicsforums.com (see post 77 of the “Why you should like my perspective!” thread) where, near the end, I asked, “Seriously, how does one tell the difference between an electron and a Volkswagen?” I tried to explain my answer in post 81 of that same thread with an example but failed miserably. To quote myself, in that post, “The example is clearly silly but what it points out is that the identification of an event is a constraint on acceptable surrounding events.” an issue very important to a rational view of events. In the absence of a world-view (i.e., an explanation of “the past”) all events are just events and there is fundamentally utterly no difference between any of them.
It seems this is the way to make sense of your quote above. (I'm trying not to get hung up on your repeated use of the word "set" by assuming it always means "an unordered collection of elements with no duplicates".)
Now here I apparently do not use the word “set” correctly as I define B to be a collection of elements taken from A which I essentially do define as a set.

 

Essentially I have shifted away from that terminology to numerical labels of undefined ontological elements which, at the moment, seems to be much clearer to me. But I don't know; apparently nothing I say is very clear to those who read my stuff. Sorry about that!

 

Have fun -- Dick

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  • 8 months later...
Hi AnssiH

You refer to Dr D's "fundamental equation", and I note that in the "Dirac" thread he says:

There is no need whatsoever to justify my model as I have shown that it is entirely general: i.e., there exists no communicable explanation of anything which cannot be analyzed from the perspective of my model. I need not argue that my view is the only rational view; I need only show that it provides a useful foundation from which real observations may be analyzed with confidence.

 

[snip]

 

I have brought together, in one expression the entire realms of physics represented by Newtonian mechanics, quantum mechanics, electrodynamics and relativity (both special and general). And all this without postulating a theoretical relationship but rather by deduction from the simple limitations required by self consistency.

That is quite a claim, and might be considered hubris, unless, of course, it is true.

 

Now I may not be the most qualified person in the world to check for algebraic validity, but I have used very much time to walk through it very very very carefully, and as far as I can tell, it is absolutely true.

 

But I think you may have initially mis-interpreted the claim slightly. He is not talking about a specific world-model, but about the algebraic relationships referring to relationships in world-models. It is more a model of world-models, or a model of explanations, you might say.

 

Or in other words, it is of course important that the reader understands exactly what you were quick to point out;

 

Also, it sems to me that mathematics is entirely reality neutral. E.g. It is possible to model the universe with eleven dimensions (the M-theory), but that does not make it real. So I'm doubtful of his claim "There is no need whatsoever to justify my model", as I would suspect (not knowing anything about the equation itself) that it's relevance to reality cannot be presumed. Self consistency alone does not make something real.

 

That is exactly the case. There is no ontological information to be found from DD's "model", but there are some very interesting and somewhat surprising epistemological facts to be found, which say something about what is usually thought to be part of ontology.

 

Since there was some confusion about those words, let me just say that by "ontology" I mean "what reality is made of", and by "epistemology" I mean the "methods of knowing" about reality.

 

Are you aware of anywhere I can read an exposition of the "fundamental equation". I.e. Not just the mathematical equation itself, because that is likely to be meaningless to me, but an exposition of the meaning associated with the equation, and its derivation. I'd like to know how it brings together in one expression "the entire realms of physics represented by Newtonian mechanics, quantum mechanics, electrodynamics and relativity (both special and general)".

 

There's been a lot of discussion about the analysis in the forum, but it is little bit scattered and buried underneath a lot of noise. My latest attempt to collect things underneath hyperlinks is here:

 

http://hypography.com/forums/philosophy-science/11733-what-can-we-know-reality-37.html#post265994

Post #370

 

But since that is so scattered, I would imagine it can be somewhat confusing to try to pick up things, so I thought maybe I'll give you an overview of what is going on right here. This will be little bit of a hand-waving kind, but anything else would be far too lengthy for me to write right now.

 

First an overview of an overview.

 

We can view the analysis in two parts.

 

First part is the formulation of a differential equation ("fundamental equation"), which expresses the requirement that worldviews are self-coherent. The worldviews need not be ontologically true, but they must not contradict themselves. This analysis is exploiting the fact that the nature of reality is fundamentally unknown and the resulting definitions are statements about some fundamentally unknown circumstances (i.e. there exists a transformation from "unknown patterns" to "defined entities"). The symmetry arguments that will yield the fundamental equation are the consequences of that type of transformation.

 

Second part is a derivation of established physical definitions from those circumstances. The fact that we can do those derivations means that physics is not so much a statement about ontological reality, as it is a statement of useful data-ordering mechanisms. I.e. whatever reality is like, we come to interpret it in specific ways (think about the question of ontological identity of objects)

 

Then let me expand on that "first part".

 

The symmetry constraints (that are succintly expressed as a single "fundamental equation") exist as "aspects of your explanation that cannot affect the answers". They cannot affect the answer because they arise as necessary symmetries during the transformation process from "unknown patterns" to "set of persistent entities".

 

I'll start by dissecting what that means.

 

Open up the page:

User:UniversalExplanation - Wikipedia, the free encyclopedia

 

It contains the definitions for the framework in a very analytical manner. In brief terms, the definitions yield an [imath]x,\tau[/imath]-space, which can be used to describe any worldview. Essentially it plots down what defined entities are thought to exist at given moment "t". The function [imath]\Psi[/imath] represents the probability function which yields the correct probabilities for the future of those defined elements.

 

We do not know what that probability function is like, nor what elements have been defined by whatever worldview has been chosen to be mapped in these terms. But we do know, that as a result of that transformation process from "unknown patterns" to "defined entities" - if the worldview is without self-contradiction - there exists few symmetries to the behaviour of the probability function. I.e. we know that we can do certain changes to the plotting of the defined entities, and still quarantee that the probability function we had is still yielding the same probabilities from the same circumstances. (This is what my comment "things that aren't real cannot affect the answers" had to do with)

 

Under the title "The first important consequences of this model" you can find three symmetry constraints to the behaviour of the probability function [imath]\Psi[/imath]. Shift symmetry in x-axis, shift symmetry in [imath]\tau[/imath]-axis, and shift symmetry in t-parameter (time or "evolution parameter"). I.e. the whole plotted universe can be "shifted" to whichever direction in the [imath]x,\tau[/imath]-space, and the probability function is still valid.

 

Under the title "Adding one last component", he brings up a fourth constraint, which is simply "no two points can be the same" (as otherwise they'd basically be "two things that are the same thing" -> not valid definition)

 

The rest of the page, with the appendixes, is basically just the algebra putting together those 4 constraints into a single differential equation; the same equation you saw in the OP of Dirac's Equation thread:

 

[math]

\left\{\sum_i \vec{\alpha}_i \cdot \vec{\nabla}_i+\sum_{i \neq j}\beta_{ij}\delta(\vec{x}_i -\vec{x}_j)\right\}\vec{\Psi}(\vec{x}_1,\vec{x}_2,\cdots,t)=K\frac{\partial}{\partial t}\vec{\Psi}

[/math]

 

At this point, you can just take that as an expression of the differential constraint that any [imath]\Psi[/imath] must obey for its associated worldview to have collected the "unknown data patterns" into "defined entities" in a self-coherent and rational manner.

 

So we get to the expansion of the "second part", "derivation of established physical definitions".

 

First the Schrödinger's Equation:

http://hypography.com/forums/philosophy-science/15451-deriving-schroedingers-equation-my-fundamental-equation.html

 

Understanding that properly probably requires one to walk through the algebra, but you can perhaps get an idea if you just read it through and take the validity of the algebra on faith (I have walked through it and I am not aware of any more errors in it).

 

In english terms what he does there is, he modifies the differential expression from a form of referring to the entire universe, to a form of referring to a single element, assuming that the feedback from the rest of the universe is negligible (in other words, do the same assumptions as are done in conventional physics). And then he gives few simple definitions that co-incide by their behaviour exactly by the same definitions in conventional physics. If you look at the end of the post, you find the definitions for "Energy", "Momentum" and "Mass".

 

The form of the equation in the end of that post is exactly Schrödinger's Equation, and you need to think about how it was obtained here exactly. It is an approximation of the fundamental equation, given few specific definitions that can ALWAYS be given. I.e. Schrödinger's Equation is, in a very unobvious way, a statement of those original symmetry constraints to our explantion of reality. Not a constraint to the reality itself. <- And this is the first time that Bell experiments are explained in a very mundane fashion, at least mundane in my opinion.

 

Newtonian mechanics is an approximation to that via the conventional physics displaying that fact.

 

In Dirac's Equation thread, he is pulling out the relationships expressed by electrodynamics/quantum electrodynamics in much the same fashion.

http://hypography.com/forums/philosophy-science/20316-anybody-interested-diracs-equation.html#post273461

 

It is a derivation from the fundamental equation, doing the approximations that are done by physics, and giving definitions that can always be given.

 

General relativity I have not walked through yet, but special relativity is clear as a day to me:

http://hypography.com/forums/philosophy-science/18861-analytical-metaphysical-take-special-relativity.html

 

A lot of people have misinterpreted that as some sort of restatement of relativity because they have not know where the fundamental equation is coming from (or just plain have not payed attention), but it really isn't. It is a statement about why relativistic time relationships must be valid for a world model that obeys those symmetry statements. The investigation is still in the form of [imath]x,y,z,\tau[/imath]-space, but you must remember that is in itself an abstraction about worldviews.

 

I think you should read this (post #48):

http://hypography.com/forums/philosophy-science/18861-analytical-metaphysical-take-special-relativity-5.html#post271521

 

At any rate, it will be displayed that given the same definition for mass as was established as the conventional view in Schrödinger's Equation, you do not only get the mass - energy equivalence, but also the expectation that massive objects are "time dilated" in terms of "what they measure" in exactly special relativistic manner, because that is how the definitions made by your worldview must work together for it all to be self-coherent.

 

This same exact circumstance is actually in my opinion fairly visible in conventional view too, if you just know about the history of relativity, in terms of how it arose as a consequence of Maxwell's equations (specific definitions that can always be made, remember), and the desire to express those in coordinate invariant manner. The actual data patterns underneath are still unknown of nature of course, but relativistic time relationships must appear from the definitions we have already made.

 

Now if you read the OP of all those threads, you can see a lot more interesting subtleties arising from these circumstances.

 

And I hope this gives you some idea of how it all works.

 

-Anssi

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  • 2 weeks later...
Now if you read the OP of all those threads, you can see a lot more interesting subtleties arising from these circumstances. And I hope this gives you some idea of how it all works.

I must admit that I have not read all the references you gave. I came to the conclusion that I was wasting my time. Not because I doubt the validity of Doctordick's equation, but because I am largely indifferent to it.

 

Compare the following statement from the OP of this thread:

It is very important that the reader realize that there is utterly no content in that equation. It is no more than a exercise displaying the tautological consequences of the definitions brought forth in that paper.

and from his paper:

It should be clear that, in order to analyze an actual explanation (a process of no interest here)...

with the claim:

I show that my construct (which is constrained in no way) requires all the ontological elements standing behind any explanation to obey classical mechanics in the classical limit. It follows that classical mechanics itself must be a tautology: i.e., classical mechanics must be true by definition.

Classical mechanics, QM and relativity etc. all make claims about reality. Hence their truth is not simply a matter of definition, it depends upon how well they describe reality. So it seems clear that he is NOT claiming that the truth in such cases is a matter of definition only, but these words, to me, offer no other meaning.

 

Also, he says:

The rules are quite dependent upon what is presumed to exist and, likewise, what must exist is quite dependent upon what the rules are.

Note: He says "The rules are quite dependent upon what is presumed to exist", i.e.he is clearly discussing presumed existence. But he follows that with "what must exist is quite dependent upon what the rules are", which appears to be making a statement about reality. If he meant "what must be presumed to exist is quite dependent upon what the rules are", then, presumably, he would have said that. So we cannot take that as his meaning. He clearly is not talking about reality, but again these words, to me, offer no other meaning.

 

Lastly he says:

In doing so, I have accomplished two very significant things: first, I have deduced quantum mechanics from fundamental concepts...

Clearly he has not deduced anything of the sort! To claim that he has created a model in which any information can be put is very different from claiming that he has specifically deduced QM from fundamental concepts. Yet, again, these words, to me, offer no other meaning.

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It would help me at this point of the discussion if DoctorDick would please define what he believes the definition of the word "to know" is. For example, his concept of time is defined, in part, by this statement...."the past is what you know". But, I have no idea how he defines "to know", or "knowledge". What exactly is "known"--would it be his "ontological elements" ? Is he saying that in the past of each entity with potential for knowledge was a quantum type interaction with some specific "ontological element", and after this transformation "knowledge" was the result ? If so, then I would think the fundamental equation has much to say about both ontology and epistemology.

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What is important here is the realization that any explanation is actually a combination of two very different components. There are things presumed to exist (the set D) and the rules of the explanation (which is modeled in this presentation by the function). Since there exists absolutely no way of establishing whether or not a given piece of information is actually derived from C and not D, the B(tk) must itself be a combination. It follows that there is a trade off here. The rules are quite dependent upon what is presumed to exist and, likewise, what must exist is quite dependent upon what the rules are.

If we take his statement "what must exist is quite dependent upon what the rules are" to relate to information about reality, rather than reality itself, then Doctordick's model seems to boil down to a meta-statement about information which can be summarized as:

 

"All information can be described by what you already know, and a set of rules for predicting what you do not yet know."

 

Which is fine, but does not get us very far because he has cleverly defined those rules as part of the information to be modeled, rather than part of the model. Thus relieving himself of the onerous task of defining those rules. But without those rules, what do we have? What rules are there for defining rules, apart from saying that they are dependent upon your existing knowledge? Well, elsewhere he says they are probabilistic:

In order to complete the problem, it is necessary to model a general mechanism capable of yielding the probability of any specific set B(tk) derived from the elements of A. This general mechanism must transform the distribution of elements defined by B(tk), a set of points in a real (x,tau,t) space, into a probability, a real number bounded by zero and one.

So it appears that he is defining probabilities about knowledge, not knowledge itself. Hence the above meta-statement becomes:

 

"The probability that all information can be described by what you already know, and a set of rules for predicting what you do not yet know, can be described by the equation given."

 

If that is a correct analysis of the meaning of Doctordick's equation, then it seems to fall somewhat short of his claim:

I have established a fundamental means of communication as anything conceivable is representable as an object (a collection of information) in the x, tau, t space which is required to obey the above relations.

 

Of course, it is entirely possible that I have simply lost the plot.

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I must admit that I have not read all the references you gave. I came to the conclusion that I was wasting my time. Not because I doubt the validity of Doctordick's equation, but because I am largely indifferent to it.
You are clearly indifferent to it because what I am saying is, from your perspective, simply beyond belief and you can find no interpretation of my assertions consistent with your beliefs.
Compare the following statement ... with the claim:
The first quote is the statement that I am doing nothing except creating a tautological construct based upon some very simple definitions. The second is the assertion that the analysis I am proposing has utterly nothing to do with the explanation being analyzed: i.e., the analysis is absolutely general and applies to any explanation of anything (it is a tautological construct based upon those simple definitions). It follows that the actual explanation being analyzed is of no consequence: i.e., the conclusions are tautological and contain no information whatsoever.

 

The claim which seems to bother you is the claim that the fact that my tautology yields classical mechanics, quantum mechanics, relativity (both special and general) and electrodynamics implies that those fields are tautologies. It is clearly the idea that modern physics is a tautological construct is the issue you find impossible to believe.

Classical mechanics, QM and relativity etc. all make claims about reality. Hence their truth is not simply a matter of definition, it depends upon how well they describe reality.
That is what they would like you to believe when the real issue is that they have simply not examined the consequences of their definitions together with “internal self consistency”. As you say, “but these words, to me, offer no other meaning”: i.e., what I am saying is quite simply beyond your comprehension. Beyond your comprehension in exactly the way Galileo's assertions were beyond the comprehension of the medieval theological scholars who could not comprehend that their analyses based upon their belief in the existence of God could be in error.
It would help me at this point of the discussion if DoctorDick would please define what he believes the definition of the word "to know" is.
As you comment, I define "the past is what you know": i.e., the facts which stand behind your world view. The issue being that what those facts are is not the issue in my analysis; that is why I use simple numerical reference labels to talk about them. My deductions are true no matter what those things are (I presume you comprehend what a tautology is). The fundamental equation says absolutely nothing about ontology, the definition of the ontology is left as an entirely open issue (that is why I refer to the ontology via undefined numerical labels). You can not “define” those ontological elements without presuming some sort of explanation. ;)
If that is a correct analysis of the meaning of Doctordick's equation, then it seems to fall somewhat short of his claim: ...
My conclusions are derived via the requirement that the “explanation” (the probability of experiencing a specific set of “ontological” elements) must be in exact agreement with the past (the facts upon which that explanation is built) together with the inductive conclusion that the totality of the experience (as you include the future) must be as close to the same as possible (i.e., no "earth shaking changes" in your world view are to be expected). The issue there is that, if “earth shaking changes” are required by new information, there is something wrong with your explanation! :hihi:
Of course, it is entirely possible that I have simply lost the plot.
I don't think you ever had an inkling of the plot here. :)

 

Anssi, maybe you can make it clearer to jedaisoul.

 

Have fun -- Dick

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I don't think you ever had an inkling of the plot here. :hihi:

I disagree with that. I believe that I have both understood your claims, and exhibited my understanding of them. I just don't accept them.

 

Anssi, maybe you can make it clearer to jedaisoul.

I don't think that AnssiH can convince me that you have anything other than a probabilistic model about knowledge that lacks even the rules necessary to link existing knowledge to what is unknown. As such, it tells us absolutely nothing about reality. But thanks for your reply.

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