- #456
Siah
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Are 'moments' composed of time? If not, what are they composed of?Rade said:As I see it, "time" is defined by "moments", time is not composed of moments, thus "moments" are outside of time but are the bounds of time,
Are 'moments' composed of time? If not, what are they composed of?Rade said:As I see it, "time" is defined by "moments", time is not composed of moments, thus "moments" are outside of time but are the bounds of time,
NO, moments are not composed of time, moments are an "attribute" of time. An attribute is something that is not the entity itself, yet the entity and attribute are not two different things. A "moment" as an attribute of "time" is what can be separated only mentally from time--as opposed to a "part" which can be materially separated from the whole. It is not possible to have a concept of "moment" without a concept of "time", nor a concept of "time" without a concept of "moment". Moments are like electrons, they are "composed" of themselves. Moments, like all attributes of entities, are indivisible. Moments are the "now", the "present". Moments are the limit of the "past" and "future"--the "before" and "after". Moments are infinite in number.Siah said:Are 'moments' composed of time? If not, what are they composed of?
Rade said:NO, moments are not composed of time, moments are an "attribute" of time. An attribute is something that is not the entity itself, yet the entity and attribute are not two different things. A "moment" as an attribute of "time" is what can be separated only mentally from time--as opposed to a "part" which can be materially separated from the whole. It is not possible to have a concept of "moment" without a concept of "time", nor a concept of "time" without a concept of "moment". Moments are like electrons, they are "composed" of themselves. Moments, like all attributes of entities, are indivisible. Moments are the "now", the "present". Moments are the limit of the "past" and "future"--the "before" and "after". Moments are infinite in number.
Doctordick said:If by, “how we have chosen to describe reality thus far”, you mean your world view, then you understand exactly what I meant.
There are a few other minor details which will have to be cleared up sooner or later but for the moment, I would like to get over to that symmetry issue as I think you understand enough of my attack to understand it. At the moment, I have defined the knowledge on which any explanation must depend as equivalent to a set of points in an (x, tau, t) space: i.e., a collection of numbers associated with each t index which I have referred to as B(t). Any explanation can be seen as a function of those indices (the explanation yielding a specific expectation for that set of indices at time t. The output of that function is a probability and may be written
[tex]P(x_1,\tau_1,x_2,\tau_2,x_3,\tau_3,\cdots,x_n,\tau_n,t)[/tex]
Now, the thoughts we need to go through here are subtle and easy to confuse but I think you have the comprehension to follow them. Suppose someone discovers a flaw free solution to the problem represented by some given collection of ontological elements. That means that their solution assigns meanings to those indices used in P. But, if we want to understand his solution, we need enough information to deduce the meanings he has attached to those indices. It is our problem to uncover his solution from what we come to know of the patterns in his assignment of indices. The point being that the solution (which has to contain the definitions of the underlying ontological elements) arises from patterns in the assigned indices. And the end result is to yield a function of those indices which is the exact probability assigned to that particular collection implied by that explanation.
But the indices are mere labels for those ontological elements. If we were to create a new problem by merely adding a number a to every index, the problem is not really changed in any way. Exactly the same explanation can be deduced from that second set of indices and it follows directly that
[tex]P(x_1+a,\tau_1+a,x_2+a,\tau_2+a,x_3+a,\tau_3+a,\cdots,x_n+a,\tau_n+a,t)[/tex]
must yield exactly the same probability. That leads to a very interesting equation.
[tex]P(x_1+a,\tau_1+a,x_2+a,\tau_2+a,\cdots,x_n+a,\tau_n+a,t)-P(x_1+b,\tau_1+b,x_2+a,\tau_2+b,\cdots,x_n+b,\tau_n+b,t)=0[/tex]
Simple division by (a-b) and taking the limit as that difference goes to zero makes that equation identical to the definition of a derivative. It follows that all flaw free explanations must obey the equation.
[tex]\frac{d}{da}P(x_1+a,\tau_1+a,x_2+a,\tau_2+a,x_3+a,\tau_3+a,\cdots,x_n+a,\tau_n+a,t)=0[/tex]
Let me know if you have any problems with that.
Rade said:NO, moments are not composed of time, moments are an "attribute" of time. An attribute is something that is not the entity itself, yet the entity and attribute are not two different things. A "moment" as an attribute of "time" is what can be separated only mentally from time--as opposed to a "part" which can be materially separated from the whole. It is not possible to have a concept of "moment" without a concept of "time", nor a concept of "time" without a concept of "moment". Moments are like electrons, they are "composed" of themselves. Moments, like all attributes of entities, are indivisible. Moments are the "now", the "present". Moments are the limit of the "past" and "future"--the "before" and "after". Moments are infinite in number.
No, this is not how I see it. Moments do not have a "time-span"--moments are not divisible, thus no span concept exists for moments. To be "between" logically requires a concept of three. Suppose two moments (A) and (D) at the present, the now. "Time" (B ---> C) is that which is intermediate between the moments, time is neither within A nor D as the present, A and D are limits of time (B----> C). So you see the concept of three--this is what I mean when I say "time is intermediate between moments": (A) | (B ---> C) | (D).Siah said:I am trying to clarify this earlier statement:
"Time is that which is intermediate between moments"
You say 'moments are an "attribute" of time. As I understand it you are saying that moments have a time-span. Is this correct?
The equation is a direct consequence of “symmetry”. The addition of a to every term in a collection of reference numbers is essentially what is normally referred to as a “shift symmetry”. With regard to symmetry, I think I already gave you a link to a post I made to “saviormachine” a couple of years ago (post number 696 in the “Can everything be reduced to physics” thread.”) That post, selfAdjoint’s response to it (immediately below that one) and my response to selfAdjoint’s (post number 703) should be read very carefully before googling around. I will paste one quote which I think is the central issue here.AnssiH said:Well, how would you put it, what does this say about "symmetry"?
What I feel everyone seems to miss is the fact that there exists no proof which yields any information which is not embedded in the axioms on which the proof is based. In fact, that comment expresses the fundamental nature of a proof! In my opinion, the fundamental underpinning of Noether’s proof is the simple fact that any symmetry can be seen as equivalent to the definition of a specific differential: i.e., in a very real sense, Noether’s theorem is true by definition as are all proofs.Doctordick said:My interest concerns an aspect of symmetry very seldom brought to light. For the benefit of others, I will comment that the consequences of symmetry are fundamental to any study of mathematical physics. The relationship between symmetries and conserved quantities was laid out in detail through a theorem proved by http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Noether_Emmy.html sometime around 1915. The essence of the proof can be found on [URL='https://www.physicsforums.com/insights/author/john-baez/']John Baez's web site[/URL]. This is fundamental physics accepted by everyone. The problem is that very few students think about the underpinnings of the circumstance but rather just learn to use it.
Doctordick said:Our first grandchild (we thought we would never get one) will be one year old Sunday and she can sure wear out an old man. She’s not quite walking yet (not by herself anyway) and wants to walk everywhere holding on to your finger (which requires me to walk bent over).
Doctordick said:What I feel everyone seems to miss is the fact that there exists no proof which yields any information which is not embedded in the axioms on which the proof is based. In fact, that comment expresses the fundamental nature of a proof! In my opinion, the fundamental underpinning of Noether’s proof is the simple fact that any symmetry can be seen as equivalent to the definition of a specific differential
I was somewhat sloppy when I wrote my last post because the issue was to get you to think about the impact of shift symmetry in ontological labels. It is very interesting to note that x, tau and t are all totally independent collections of indices (the fact that we have laid them out as positions in a three dimensional Euclidean space says that shift symmetry is applicable to each dimension independently). In other words, that equation can actually be divided into three independent equations.
[tex]\frac{d}{da}P(x_1+a,\tau_1,x_2+a,\tau_2,x_3+a,\tau_3,\cdots,x_n+a,\tau_n,t)=0[/tex]
[tex]\frac{d}{da}P(x_1,\tau_1+a,x_2,\tau_2+a,x_3,\tau_3+a,\cdots,x_n,\tau_n+a,t)=0[/tex]
[tex]\frac{d}{da}P(x_1,\tau_1,x_2,\tau_2,x_3,\tau_3,\cdots,x_n,\tau_n,t+a)=0[/tex]
I think you should find that quite satisfactory.
The next step involves what is called “partial” differentiation. A partial differential is defined on functions of more than one variable (note that above we are looking at the probability as a function of one variable: i.e., only a is being presumed to change; all other variable being seen as a simple set of constants). When one has multiple variables, one can define a thing called the “partial” derivative. A partial derivative is the derivative with respect to one of those variables under the constraint that none of the other variables change (all other variables are presumed to be unchanging). Essentially, the equations above can be seen as partials with respect to a except for one fact: the probability P is not being expressed as a function of “a”. That is to say, “a” is not technically an argument of P.
On the other hand, the equation does say something about how the other arguments must change with respect to one another. In order to deduce the correct implied relationship, one needs to understand one simple property of partial derivatives. The property that I am referring to is often called “the chain rule of partial differentiation’. I googled “the definition of the chain rule of partial differentiation” and got a bunch of hits on “by use of the definition of the chain rule of partial differentiation …” which seems pretty worthless with regard to exactly what it is. If you know what it is, thank the lord.
Doctordick said:Paul gives case 1 as the problem of computing dz/dt when z is given as a function of x = g(t) and y =h(t) or, to put it exactly as he states it, Case 1: z=f(x,y), x=g(t), y=h(t) and compute dz/dt).
What we want to do is compute is dP/da, which we know must vanish, but is expressed in terms of the reference labels of our valid ontological elements. We have established that the probability of a specific set of labels is given by an expression of the form,
[tex]Probability= P(x_1,\tau_1,x_2,\tau_2,x_3,\tau_3,\cdots,x_n,\tau_n,t)[/tex]
or, just as reasonably
[tex]Probability= P(z_1,\tau_1,z_2,\tau_2,z_3,\tau_3,\cdots,z_n,\tau_n,t)[/tex]
where our shift symmetry has resulted in the fact that those arguments, when expressed as functions of x and a are given by
[tex]z_1=x_1+a, z_2=x_2+a, z_3=x_3+a,\cdots, z_n=x_n+a.[/tex]
With regard to our representation that dP/da vanishes, we can apply the example given by Paul,
[tex]\frac{dz}{dt}=\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dx}[/tex]
as, in our case, equivalent to
[tex]\frac{dP}{da}=\sum_{i=1}^{i=n}\frac{\partial P}{\partial z_i}\frac{dz_i}{da};[/tex]
however, in our case,
[tex]\frac{dz_1}{da}=\frac{dz_2}{da}=\frac{dz_3}{da}=\cdots=\frac{dz_n}{da}=1[/tex].
which yields the final result that
[tex]\frac{dP}{da}=\sum_{i=1}^{i=n}\frac{\partial}{\partial z_i}P = 0[/tex]
when the x arguments of P are symbolized by z. But z is just a letter used to represent those arguments; one can not change the truth of the equation by changing the name of the variable. This same argument can be applied to the other independent arguments of P, yielding, in place of the differential expressions in post 462, the following three differential constraints.
[tex]\sum_{i=0}^{i=n}\frac{\partial}{\partial x_i}P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=0[/tex]
[tex]\sum_{i=0}^{i=n}\frac{\partial}{\partial \tau_i}P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=0[/tex]
and
[tex]\frac{\partial}{\partial t}P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=0[/tex]
which has utterly no mention of the shift parameter a.
Don’t worry about it.AnssiH said:Sorry for being so slow to reply again.
In is interesting to note that this exchange concerns exactly what I am talking about: i.e., getting on the other side of that barrier. Tarika is using “%” for exactly the reason I am using numerical labels. The only reason I am using “numerical labels” is that there are a lot more of them then there are things like %, #, @, &, etc. Plus that, I have the advantage that there exists a world of internally self consistent defined operations on those numerical labels. That is, I don’t have to explain each and every manipulation I want to perform on the labels. (See Russell’s works on definition of mathematics.) You can google the phrase and get enough stuff to keep anyone busy for years. The only reason I bring it up is that he was very much interested in defining mathematics from “ground zero”. That is exactly the problem which constitutes the essential nature of the barrier being referred to above.Anssi said:Heh, isn't it interesting to try to force yourself through this barrier?
:) At least it gives us a better understanding about how there really is a barrier there, doesn't it?
Yeah, I knew that was going to be a problem; but I think we are beginning to clear up the true depth of the difficulty. I think we can handle it.AnssiH said:I am having a summer vacation and was away for couple of days, and on top of that it takes me a while to figure out all the math concepts since I need to study them before I understand what is being said :)
The capital sigma is used as a shorthand notation to represent a sum. The definitions of i given above and below the sigma tell you the starting value of i and the ending value of i. The term to be summed has an i reference in it which tells you how to construct the ith term in that sum. If you look at Paul’s example (for Case 1) you will see that the original function was a function of two variables and that his “total derivative”, dz/dt, is given by a sum of two terms: a partial with respect with each of those two variables times the “total derivative of each variable with respect to t. (“Total derivative” is the term used for what was originally defined to be “a derivative” so as to contrast it with the idea of a “partial derivative”). In our case, we have n arguments subject to our shift parameter "a" so our total derivative consists of a sum of n terms, one partial for each term in the function (times the respective total derivative).AnssiH said:Here I'm starting to have some troubles understanding what is being said. What is meant with [tex]\sum_{i=1}^{i=n}[/tex] ? Something about this applying to every entry in the table?
Our shift symmetry can be seen as a simple change in variables where each x has been replaced by a related z where each z has been defined by adding a to the respective x.AnssiH said:I understood we are using [tex]z_i[/tex] to express [tex]x_i+a[/tex], but I don't understand how [tex]\frac{dz_1}{da}=1[/tex]
Exactly right except for one thing. We haven’t proven dP/da = zero here; what we have done is shown how that result (as you say “established earlier”) is totally equivalent to the assertion that the sum over all partials with respect to each argument must vanish.AnssiH said:Hmmm, that final result [tex]\frac{dP}{da}= 0[/tex]
Isn't it the same as was established earlier already? I.e. changing "a" will not change the probability P?
This says that every ontological element (valid or invalid) associated with “that explanation” has associated with it, another thing (a consequence of symbolic shift symmetry). If we have the function for the probability relationships and the numerical labels, we can deduce a proper label (numerical label) to be assigned to that ontological element. What is interesting is the fact that the sum over all those “deduced proper labels” must be zero. We are talking about here is a conserved quantity; the sum over all of them is unchanging though the individual quantities associated with each ontological element might very well change.AnssiH said:Hmm, how should I read these expressions...? That the probability doesn't change when we change... what? I hope you (or anyone) can clear up the things I am not getting :)
Don’t worry, we’ve survived it. We will be heading home this weekend. That’s the great thing about being grandparents; you can always go home when the strain begins to show (and believe me, it's beginning to show; I am looking forward to our own schedule and our own home). You can’t do that with your own kids.AnssiH said:Heh, don't break your back :) I also became an uncle couple months back, plus my two other sisters are just about to multiply as well :)
Doctordick said:Regarding “they are % and % is not a thing.
In is interesting to note that this exchange concerns exactly what I am talking about: i.e., getting on the other side of that barrier. Tarika is using “%” for exactly the reason I am using numerical labels.
Doctordick said:Yeah, I knew that was going to be a problem; but I think we are beginning to clear up the true depth of the difficulty. I think we can handle it.
The capital sigma is used as a shorthand notation to represent a sum. The definitions of i given above and below the sigma tell you the starting value of i and the ending value of i. The term to be summed has an i reference in it which tells you how to construct the ith term in that sum. If you look at Paul’s example (for Case 1) you will see that the original function was a function of two variables and that his “total derivative”, dz/dt, is given by a sum of two terms: a partial with respect with each of those two variables times the “total derivative of each variable with respect to t. (“Total derivative” is the term used for what was originally defined to be “a derivative” so as to contrast it with the idea of a “partial derivative”). In our case, we have n arguments subject to our shift parameter "a" so our total derivative consists of a sum of n terms, one partial for each term in the function (times the respective total derivative).
This defined operation (the thing called the partial derivative with respect to the given argument multiplied by the common derivative of the same argument with respect to a) is to be performed for every numerical label in the collection of labels which constitute the arguments of that probability function (the mathematical function which is to yield the probability that the specific set of labels will be in the table). The n different results which are obtained by performing that specific mathematical operation which (if we happen to know what the function looks like, will yield a new function for each chosen i) are to be added together.
The requirement that the shift of "a" cannot yield any change in that resultant expression yields a rule which the probability function can not violate. Putting it simply, if we did indeed know exactly the correct function for n-1 of those arguments, we could use that differential relationship to tell us exactly the appropriate relationship for the missing argument. This is a simple consequence of “self consistency” of the explanation.
Our shift symmetry can be seen as a simple change in variables where each x has been replaced by a related z where each z has been defined by adding a to the respective x.
[tex]z_1=x_1+a, z_2=x_2+a, z_3=x_3+a,\cdots, z_n=x_n+a.[/tex]
In order to evaluate the sum expressing the total derivative of P with respect to a (the derivative which we deduced earlier must vanish) we need the total derivative of each z with respect to a. But each z is obtained from a by adding a to the appropriate x. This constraint (as a function of a) presumes there is no change in the base x (as it is a shift on all x’s). From this perspective, each z can be see as a constant x plus a; it follows that dx/da vanishs (x is not a function of a) and da/da is identically one by definition.
Exactly right except for one thing. We haven’t proven dP/da = zero here; what we have done is shown how that result (as you say “established earlier”) is totally equivalent to the assertion that the sum over all partials with respect to each argument must vanish.
We first proved that we could see any specific explanation of our “what is”, is “what is” table as a mathematical function which would yield the probability of seeing a specific entry in that table. Then we argued that shift symmetry required that the total derivative with respect to that shift to vanish. Now I have shown that that requirement is totally equivalent to requiring a specifically defined sum of partial derivatives of that probability function, with respect to those numerical labels (numerical labels which are defined by that explanation), to vanish.
This says that every ontological element (valid or invalid) associated with “that explanation” has associated with it, another thing (a consequence of symbolic shift symmetry). If we have the function for the probability relationships and the numerical labels, we can deduce a proper label (numerical label) to be assigned to that ontological element. What is interesting is the fact that the sum over all those “deduced proper labels” must be zero. We are talking about here is a conserved quantity; the sum over all of them is unchanging though the individual quantities associated with each ontological element might very well change.
What is somewhat more important is the fact that I have proved that such a function exists and that one achieves that function through the addition of “invalid ontological elements”. What you need to remember is that these “invalid ontological elements” are invalid, not because the yield incorrect answers regarding the information to be explained but rather because they are not actually among the ontological elements which constitute the information our explanation is to explain. They are instead, total figments of our imagination. That is to say that they are inventions; inventions created to provide us with the ability to say what can and can not be under the presumed rule our explanation implements (i.e., the rule being that F=0): i.e., they are ontological elements our explanation presumes exist. If our explanation is indeed flaw free, it will be totally consistent with the existence of these invalid ontological elements.Doctordick said:This means that the missing index can be seen as is a function of the other indices. Again, we may not know what that function is but we do know that the function must agree with our table. What this says is that there exists a mathematical function which will yield
[tex](x,\tau)_n(t) = f((x,\tau)_1, (x,\tau)_2, \cdots, (x.\tau)_{n-1},t)[/tex]
It follows that the function F defined by
[tex]F((x,\tau)_1,(x,\tau)_2, \cdots, (x,\tau)_n) = (x(t),\tau(t))_n - f((x,\tau)_1, (x,\tau)_2, \cdots, (x.\tau)_{n-1},t) = 0 [/tex]
is a statement of the general constraint which guarantees that the entries conform to the given table. That is to say, this procedure yields a result which guarantees that there exists a mathematical function, the roots of which are exactly the entries to our "what is", is "what is" table. Clearly, it would be nice to know the structure of that function.
Doctordick said:Thank you Anssi. This is the first time I have ever gotten anyone (other than Paul Martin, who is a personal friend) this far along in my arguments. Everyone else drops out long before we get to this point. We only have a small number of steps to complete my deduction. Remember post number 426 on this thread? It was there that I pointed out that there had to exist a set of invalid ontological elements which would guarantee that a function existed who's roots would yield that exactly that "what is", is "what is" table.
What is somewhat more important is the fact that I have proved that such a function exists and that one achieves that function through the addition of “invalid ontological elements”. What you need to remember is that these “invalid ontological elements” are invalid, not because the yield incorrect answers regarding the information to be explained but rather because they are not actually among the ontological elements which constitute the information our explanation is to explain. They are instead, total figments of our imagination. That is to say that they are inventions; inventions created to provide us with the ability to say what can and can not be under the presumed rule our explanation implements (i.e., the rule being that F=0): i.e., they are ontological elements our explanation presumes exist. If our explanation is indeed flaw free, it will be totally consistent with the existence of these invalid ontological elements.
What is really profound about this realization is the fact that it implies there exists a fundamental duality: the rule and what is presumed to exist are exchangeable concepts. That is to say, what the rule has to be is a function of what is presumed to exist: it is possible to exchange one for the other so long as one maintains some complex internal relationships. It turns out this is exactly the freedom which allows us construct a world view consistent with what we know; without this freedom the problem of “explaining the universe” could not be accomplished.
Another way to state the circumstance is to point out that the “explanation of reality” is actually a rather complex data compression mechanism. One's best bet for the future is very simply: one's best expectations are given by how much the surrounding circumstances resemble something already experienced.
But let's get back to this F=0 rule. There exists a rather simple function which can totally fulfill the need required here. That function is the Dirac delta function (google “Dirac delta function” for a good run down on its properties). The Dirac delta function is usually written as [itex]\delta(x)[/itex] and is defined to be exactly zero so long as x is not equal to zero; however, it also satisfies the relationship:
[tex]\int_{-\infty}^{+\infty}\delta(x)dx= 1. [/tex]
Clearly, since it is exactly zero everywhere except when x=0, it must be positive infinity at x=0. It is that property which makes it so valuable as a universal F=0 function. First, it is a very simple function and is quite well defined and well understood. Second, as it is only positive, the sum indicated below will be infinite if any two labels are identical (have exactly the same x, tau numerical label).
[tex]\sum_{i \neq j}\delta(x_i -x_j)\delta(\tau_i -\tau_j) = 0, [/tex]
It is thus a fact that the equation will constrain all labels to be different and any specific collection of labels can be reproduced by the simple act of adding “invalid ontological elements” until all the wrong answers are eliminated. Now that sounds like an insane suggestion; however, it's really not as insane as it sounds and it ends up yielding an extremely valuable representation which I will show to you in my next post (after I have read your response to this post).
Sorry I was so slow to respond but I needed time to decide exactly how I was going to present this last step as it clearly seems like an rather extreme move to make even if it is true.
Well, since it is pretty well based on what I am showing you right now, I think it will have to be put off until you understand the essence of this presentation.AnssiH said:Yeah, we have to discuss your ideas about practical AI at some point.
As I said, it's really not as insane as it sounds. Stop and think about vacuum polarization: i.e., the problems with conceiving of the vacuum as “absolutely empty” thing, impossible to interact with. The existence of a “pure” vacuum in the sense originally put forth by scientists seems very much to be in conflict with modern physics; if there is no such thing as an “empty spot” doesn't that imply every location is full of something? I only make that comment to point out that one cannot count the idea as insane if one has any faith in modern science. However, note that I use it as a collection of “invalid ontological elements” because of its ability to yield all possible observed results, not because modern science has come to the conclusion that it is correct (I like deduction, not induction). (By the way, that “observed result” would be any possible collection of ontological elements we need to explain: i.e., it's a very powerful tool.)AnssiH said:That sounds insane alright!
I further showed how viewing that probability as a square of some function (the vector dot product) provided a valuable consequence: i.e., I introduced a mechanism for guaranteeing that the constraints embodied in the concept of probability need no longer be extraneous constraints. Under my representation, they are instead embodied in the representation without constraining the remaining possibilities in any way! This is the central issue behind the representationDoctordick said:This same argument can be applied to the other independent arguments of P, yielding, in place of the differential expressions in post 462, the following three differential constraints.
[tex]\sum_{i=0}^{i=n}\frac{\partial}{\partial x_i}P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=0[/tex]
[tex]\sum_{i=0}^{i=n}\frac{\partial}{\partial \tau_i}P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=0[/tex]
and
[tex]\frac{\partial}{\partial t}P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=0[/tex]
which has utterly no mention of the shift parameter a.
Everybody is slow when they are not sure what should be done.AnssiH said:Good thing I'm not the only slow one here :)
Again you make it quite clear that you did not follow my presentation. My equation says absolutely nothing about reality. It speaks entirely to the problem of interpreting reality. My source data is taken to be explicitly uncorrelated in any manner (the ”what is”, is “what is” information table). What I show is that absolutely any flaw-free explanation of anything can, through the presumption of implied ontological elements (and there are presumptions made unconsciously in any attempt to understand anything), can always be interpreted in a manner such as it will obey my fundamental equation.Rade said:...represents the "implicate order" of Bohm, (e.g., the veiled underlying order that governs the universe) ?
Doctordick said:My equation says absolutely nothing about reality. It speaks entirely to the problem of interpreting reality
I am sorry I have upset you; that was not my intention. You simply have no idea of the difference between an explanation and the constraints on such; they are actually rather different concepts.Rade said:Good gravy--do you not see the contradiction of your words. You cannot on the one hand say that your equation "says nothing about reality" (absolutely even you say), and then on the other hand claim "it speaks to interpreting reality". Well good Dr. when you say you "interprete reality" you most clearly do say "some"thing" about reality.
I am very sorry I tried a civil attempt at communication with you, it is clear you have absolutely no idea what I was asking in my question about Bohm.
Doctordick said:At this point, there are three paths open to us. One, we could spend some time discussing anything underlying my deduction which seems shaky to you; two, I could show the details of those solutions I spoke of; or three, we could talk about the philosophical implications of my discovery.
Doctordick said:This means that the missing index can be seen as is a function of the other indices. Again, we may not know what that function is but we do know that the function must agree with our table. What this says is that there exists a mathematical function which will yield
[tex](x,\tau)_n(t) = f((x,\tau)_1, (x,\tau)_2, \cdots, (x.\tau)_{n-1},t)[/tex]
It follows that the function F defined by
[tex]F((x,\tau)_1,(x,\tau)_2, \cdots, (x,\tau)_n) = (x(t),\tau(t))_n - f((x,\tau)_1, (x,\tau)_2, \cdots, (x.\tau)_{n-1},t) = 0 [/tex]
is a statement of the general constraint which guarantees that the entries conform to the given table. That is to say, this procedure yields a result which guarantees that there exists a mathematical function, the roots of which are exactly the entries to our "what is", is "what is" table. Clearly, it would be nice to know the structure of that function.
Clearly, since it is exactly zero everywhere except when x=0, it must be positive infinity at x=0. It is that property which makes it so valuable as a universal F=0 function. First, it is a very simple function and is quite well defined and well understood. Second, as it is only positive, the sum indicated below will be infinite if any two labels are identical (have exactly the same x, tau numerical label).
[tex]\sum_{i \neq j}\delta(x_i -x_j)\delta(\tau_i -\tau_j) = 0, [/tex]
It is thus a fact that the equation will constrain all labels to be different and any specific collection of labels can be reproduced by the simple act of adding “invalid ontological elements” until all the wrong answers are eliminated.
As I said, it's really not as insane as it sounds. Stop and think about vacuum polarization: i.e., the problems with conceiving of the vacuum as “absolutely empty” thing, impossible to interact with. The existence of a “pure” vacuum in the sense originally put forth by scientists seems very much to be in conflict with modern physics; if there is no such thing as an “empty spot” doesn't that imply every location is full of something?
I further showed how viewing that probability as a square of some function (the vector dot product) provided a valuable consequence: i.e., I introduced a mechanism for guaranteeing that the constraints embodied in the concept of probability need no longer be extraneous constraints. Under my representation, they are instead embodied in the representation without constraining the remaining possibilities in any way! This is the central issue behind the representation
[tex]P(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)=\vec{\Psi}^{\dagger}(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)\cdot\vec{\Psi}(x_1,\tau_1,x_2,\tau_2,\cdots,x_n,\tau_n,t)dV[/tex]
Note that the "[itex]\dagger[/itex]” is there solely to bring the representation closer to the common Schrödinger representation of quantum mechanics: i.e., allowing the components of that indicated vector to be “complex” is essentially adding nothing which could not just as easily be represented by twice as many “real” components in the vector nature of [itex]\vec{\Psi}[/itex]. The fact that the number of components must be even is of no account at all when seen from the perspective of the availability of invalid ontological elements (if that really needs clarification, I will clarify it).
I think we need to go back to that post where I first began adding “invalid ontological elements”. The fact that we can add these invalid ontological elements gives us the power to organize or represent that ”what is”, is “what is” table in a form which allows for easy deduction. In that post, I said I wanted to add three different kinds of “invalid ontological elements”, each to serve a particular purpose. You need to understand exactly why those elements are being added and how the addition achieves the result desired.AnssiH said:Actually, let me get back to that older quote about recovering missing indices. I don't know if the answers are supposed to be obvious to me but they are not :) Hopefully you can pick up what am I missing.
One could continue the process of adding “invalid ontological elements” in order to define a function which would yield two missing indices but I see no purpose to such an extension. My purpose was to prove that one could always achieve a circumstance (by adding invalid ontological elements) such that the rule which determined what reference numbers existed in the ”what is”, is “what is” table consisted of “those entries are the roots of the function F”: i.e., the rule can be written asAnssiH said:Is this valid only when there is only 1 missing index, or is it valid for larger number of missing indices?
It says that the only acceptable reference numbers for the ”what is”, is “what is” table are roots of some function “F”. Or rather, that there always exists a collection of “invalid ontological elements” such that the rule as to what reference numbers can be seen in that table are given by the solutions to some equation expressed in the form F=0.AnssiH said:I took it on faith that the above expression "guarantees that there exists a mathematical function, the roots of which are exactly the entires...", but I don't fully grasp what that expression says.
In a sense you are right; but the issue is not really to test the function F as we do not have it. Before you can actually have that function, you have to have the solution to the problem. That is F can not be defined until the epistemological construct which explains that ”what is”, is “what is” table is known (it is that explanation which specifies those numerical references). What is important here is that, if I am given a set of “valid ontological elements” there always exists a set of “invalid ontological elements” which together with a rule F=0 will yield exactly those “valid ontological elements” (along with those presumed “invalid ontological elements”). That is, it is always possible to construct a flaw-free epistemological construct where the only rule is “F=0” and the entire problem is reduced to “what exists”. This is a much simpler problem than being confronted with two apparently different issues to solve: “What exists?” and “What are the rules?”.AnssiH said:The part that I thought I understood is that it would be possible to recover one missing index from a specific B, if we had a function that gave "0" with the input of the correct (full) set of indices of that B. So we could just test which index gave a 0. That was the idea with this?
You appear to understand what I am saying; however, it is possible that you are stepping off trying to construct a epistemological solution which conforms to the circumstance I have laid out. That, you shouldn't be trying to do. Remember, what I have laid out must be capable of representing all possible epistemological constructs. That is a pretty extensive field and it would be a mistake to presume that simple answers exist. I have proved that the procedure I described could be accomplished in principal since the number of elements being referred is finite; however, their number could easily exceed any mechanical equipment we might envisage to carry out such a procedure. I certainly have not proved any such thing could actually be done in one's life time; even with the simplest problem. All I have shown is that the process can be done “in principal”.AnssiH said:I suppose the expression essentially means we take a specific B, and its every X is compared with every other X and every tau is compared with every other tau. So that we'll see if any of them are the same. Or in other words, we are simply labeling every entry as unique?
First of all, the Dirac delta function does not make every single entry unique, all it does is yield an infinite result when any two are the same. It should be clear that, if there exists a finite set of “invalid ontological elements” which will make the rule “F=0” yield both the “valid ontological elements and those we added (providing us with that flaw-free epistemological solution), we can certainly add a bunch more without bothering that solution. All we need do is recognize them as “presumed” and not necessarily part of that valid ”what is”, is “what is” table.AnssiH said:I am missing, why do we need a dirac delta function to make every single entry unique?
That seems to me to be a pretty straight forward issue. The only real problem is that the number of references has now gone to infinity and we can no longer argue things from a “finite” perspective. That introduces some subtle problems which require additional mathematics to handle. Other than that, I think my statement is rather incontrovertible.Doctordick said:It is thus a fact that the equation will constrain all labels to be different and any specific collection of labels can be reproduced by the simple act of adding “invalid ontological elements” until all the wrong answers are eliminated.
Let me start with the relationship between Psi and our probability. The issue is the fact that probability is defined to be bounded by zero and one. As a function, that makes P a rather special function. Note that, in my presentation, I don't want to make any limitations on the possibilities at all. It follows that I need to work with a totally unconstrained function: i.e., the solution to our problem must be left to be ANYTHING. Now, “any mathematical function” is a pretty obvious entity: it's arguments are a collection of numbers and it's output is a collection of numbers. A “mathematical function” is a method from getting from the first to the second, “PERIOD”, no other constraints! If we are to include all possibilities, that is about all we can say about the solution to our problem, the possible epistemological construct.AnssiH said:Yeah I think some things need clarification at least. I don't know what the [itex]\dagger[/itex] means. I am not familiar with Schrödinger representation (as I am not familiar with mathematical representation of much of anything :)
If we go to representing the components of the vector function Psi as complex numbers, it is completely equivalent to using two components for each normally real component so, in a sense we are limiting our consideration to functions with a even number of components. This isn't really troublesome as, if the correct answer turns out to be a function with an odd number of components, it can just as well be seen as a function of an even number where one of the components is always zero. All this move really does is make the notation appear to be similar to Schrödinger's.AnssiH said:I may have forgotten something but, why does the number of components have to be even?
I have read the thread and their comments are pretty typical of physicists I have run across in the past. As far as interacting with professional physicists is concerned, I have done plenty of that in my life time. I have earned a Ph.D. in theoretical physics from a reputable university and had plenty of interactions with the academy during that period. At that time (the early sixties) the position of theoretical physicists was that the big problem was not understanding the universe (they already understood it all) the big problem was how to calculate solutions to their equations. As I have said somewhere else, Richard Feynman got a Nobel Prize for developing a notation for keeping track of terms in an expansion of an infinite series (which everyone believed to be correct ). To quote Caltech themselves, http://pr.caltech.edu/events/caltech_nobel/ And I do not intend any insult to Richard in any way. In fact, I talked to him in 86 and he said he would like to follow my thoughts as soon as he finished with that NASA accident (he was the chairman of the investigating committee). Next thing I heard, he had died of cancer (I finally get an intelligent educated person to talk to me and he ups an dies; just my luck).Rade said:In response to a comment you made in post # 478 above, I started a thread in quantum theory section of forum, and I see that you will have to provide clarification of your thoughts. I think this a good opportunity for you to interact with professional physicists about your philosophy here presented--see here if you have an interest:
At least he finds my rebellion “understandable” though he clearly does not think my thoughts are worth thinking about.jostpuur said:I'll put it this way: "Physicists are usually not interested in philosophy, they are interested in calculating." That is something that many will probably agree with, and if Doctordick is criticizing it, it is understandable, although I'm not convinced that he himself would be improving anything.
Yeah, sure they are interested; as long as it comes from a recognized authority and not a rebellious skeptic of their great accomplishments.country boy said:But every physicist I know is interested in the possibility that QM and other aspects of modern physics might be derivable from more fundamental, as yet unrecognized, principles.
Yeah, there is a lot of truth to that all right. When it comes to serious thought, most people have an intention span of about two minutes. They want “simple minded” answers to their questions, not simple answers. One should recognize that Newton's theories are quite simple but they are not at all “simple minded”. There is a great difference between “simple " and "simpleminded”.Hurkyl said:... you run the risk of losing some of your audience if they have to do a lot of theoretical work before they can actually compute anything.
That is a succinct statement of the academies position on the issue. As I have said many times, physicists say what I am doing is philosophy and they have no interest in it; philosophers say what I am doing is mathematics and they have no interest in it and mathematicians say what I am doing is physics and they have no interest in it. All I am looking for is people who are interested in thinking; a very rare breed indeed.Llewlyn said:Please note that all physics is put in axiomatic form.
Doctordick said:Tell your friends to start with post #211 on this thread
What I am saying is that understanding implies it is possible to predict expectations for information not known; the explanation constitutes a method which provides one with those rational expectations for unknown information consistent with what is known
The procedure we follow differs in one remarkable way from the manner that has in the past been followed in setting up physical theories. Normally one starts by establishing a mathematical formalism, setting up a set of equations, and then one tries to append an interpretation to it. This is a very difficult problem; historically it has affected not only statistics and statistical physics – what is the meaning of probabilities and of entropy – but also quantum theory – what is the meaning of wave functions and amplitudes. The issue of whether the proposed interpretation is unique, or even whether it is allowed, always remains a legitimate objection and a point of controversy.
Here we proceed in the opposite order, we first decide what we are talking about and what we want to accomplish, and only afterwards we design the ap- apropriate mathematical formalism. The advantage is that the issue of meaning never arises.
The Foundations of Physical Reality said:The issue of truth by definition rests on two very straight forward points:
(1.) we either agree on our definitions or communication is impossible and
(2.) no acceptable definition can contain internal contradictions.
The Foundations of Physical Reality said:Thus, the problem becomes one of constructing a rational model of a totally unknown universe given nothing but a totally undefined stream of data which has been transcribed by a totally undefined process.
The Foundations of Physical Reality said:As it is my intention to make no assumptions whatsoever, even the smallest assumption becomes a hole which could possibly sink the whole structure. As I do not claim perfection, errors certainly exist within this treatise. None the less, I claim the attack will be shown to be extremely powerful.
The Foundations of Physical Reality said:Thus, the problem becomes one of constructing a rational model of a totally unknown universe given nothing but a totally undefined stream of data which has been transcribed by a totally undefined process.
(Excuse me for correcting your spelling; it's sort of a compulsion ingrained by my father years ago.) You are clearly misinterpreting what I am doing. I made no claim to understanding how human beings unconsciously solve the problem; all I said is that they obviously solve it on a regular basis which implies it is a solvable problem. Thus the fact that I have solved the problem bears little impact on how the average person does so. In fact, there are a lot of points to persuade one to accept the fact that they certainly do not use my method. In particular, we have the fact that no one (to my knowledge) uses that equation I derived and, secondly, their solutions are often ripe with errors. But they certainly are “solutions”, and dammed good ones at that (almost everyone agrees with “what is real”).Fra said:How do you picture an observer being exposed to this data stream? What happens when the observers memory is full, and runs out of memory for your constructions?