Why you should like my perspective

[Doctordick]

For my lack of mathematical knowledge, I will still willing to respond to your math expressions.

The responses are rather worthless unless the purpose is to increase your mathematical knowledge!

1. The sum of all partial derivatives of a certain function with respect to 1-dim space is proportional to the imaginary part of this same function.

This is a mathematically meaningless statement. There is no such thing as a partial derivative with respect to a one dimensional space! Derivatives are taken with respect to variables and space is not a variable, it is range of variables defined by a coordinate system.

2. The sum of all partial derivatives of a certain function with respect to timelike independent variable is proportional to the imaginary part of this same function.

There is nothing in this derivation to suggest any relationship between $\tau_i$ and t. Furthermore, multiplying a function by i does not extract the imaginary part of that function (this comment goes to both comment #1, #2 and #3).

3. the partial with respect to time of this function is proportional to the imaginary part of same function.

Again, there is nothing in this derivation (except the use of the symbol t) which says t has any relation to time.

Now to say what I intended to do as far as the use of math is concerned are the following:

1. I am getting rid of all uses of derivative (partial or exact).

It would be much better if you would rather study the uses of these concepts.

These were partly Newton's doing. We are now beyond that.

If you are beyond that, then I take it to mean you have no interest in understanding mathematics.

The partial derivative is a way of dealing with continuous change of continuous functions such as a wave function. All wave functions depend on two keys properties, the wavelength and the frequency.

You display your ignorance of wave functions. Any competent physicist can show you wave functions which have neither a wavelength nor a frequency. These are properties of momentum quantized and energy quantized wave functions only.

The wavelength is a vector.

Wavelength is not a vector, it is a measure of the distance between repetitions of a specific phase of the wave function.

The frequency is a scalar and it is the inversely proportional of time. I have more to say here but will defer for the time being.

Frequency is not inversely proportional to time (of time is a meaningless phrase). I am sorry you have more to say as you have already said enough to stop a competent physicist from thinking listening to you will serve any purpose.

2. I am getting rid of the numeral "zero" in the math I'm using. I am using only Hadamard matrices with elements consist of 1 and -1.

And why should I concern myself with these "Hadamard" matrices?

3. There are functions that can only be added together. I call them Hamiltonian functions. To me, the true Hamiltonian is a function that gives the square of energy. Only Hamiltonian possesses a quantum.

The word "Hamiltonian" already has a very specific meaning derived from the work of that physicist. I would suggest you find yourself a new name for whatever it is that you want to talk about.

4. There are functions that can only be subtracted. I call them Lagrangian functions. These do not have a quantum.

You don't seem to have any comprehension of the meaning of the word "function". You need to study mathematics; please!

More to say on all of these working principles of my research.

Please don't say it to me. I hold it in the same category I would place someone if they told me the "working principles" of their research" was to smoke pot.

If you want to talk to me, you need to spend some effort learning mathematics. If you continue to post such drivel, you leave me no option but to ignore you.

Have fun -- Dick

 

[PFanalog57]

...appear to be jumping to #4 without even considering what comes before.

What are you trying to say here? Is this supposed to indicate to me that you understood what I wrote down? I have not mentioned a "spacetime manifold" and you have not defined what you mean by the term "spacetime manifold". I have not brought up or defined any concept referred to as "connected" nor have you! Just what does the symbol M^+ refer to and/or the symbol M^-.

It appears to me that you do not understand the difference between fact and theory.

[...]

In order to think about theories, you must first know and understand the facts.

Failure to understand this is exactly the reason the "Theory Development" forum is considered "crackpots are us" heaven.

You need to have an education as to what the facts are and popular generalizations of hard scientific results do not qualify as facts even if they are promulgated by recognized authorities!

Have fun but think about it -- Dick

"A little learning is a dangerous thing;Drink deep, or taste not the Pierian spring."

--Alexander Pope


I get the impression that you are hoping someone will find a flaw in your derivation?

 

[Antonio Lao]

Dick,

The velocity of a wave (EM waves) is the product of its wavelength and frequency. My question is what is the physical meaning when the frequency is exactly 1? 1 cycle per second. Does this mean that the period is 1? Does this wave move? It must! The wavelength is 186,000 miles. Can these waves of 1 frequency be added in phase to give infinite magnitude? Or added out of phase to give zero amplitude?

 

[PFanalog57]

Dr. D:
The experimenter will throw the clock across the room where upon it is smashed to smithereens.

Now, let us examine that experiment from a number of different frames of reference. I make the claim that all observers (totally independent of their frame of reference) will find the reading on that clock at the moment it leaves the experimenters hand will have a specific value. They will all agree as to what that reading was and the reading has absolutely nothing to do with their frame of reference.

I further make the claim that all observers will find the reading on that clock at the moment it is smashed to smithereens will also have a specific value. And once again, they will all agree as to what that reading was. Once again, that reading has absolutely nothing to do with their frame of reference.

In fact, they will all observe that clock to be a measuring device which starts with some reading and terminates with a second reading, having progressed through all the intermediate readings between the two. The only differences they will claim have to do with the coordinates describing the event in their personal frames of reference. In particular, the length of time required for the event to occur will vary from frame to frame. What is important here is that the reading on the clock has absolutely nothing to do with the "time" used in the description of the experiment in anyone's frame of reference!

That fact must be true as the functioning of the clock is determined by physical laws and those physical laws are (from the axioms of relativity itself) independent of your frame of reference! The functioning of that "ideal" clock cannot possibly be a function of your frame of reference!

The experimenter throws the clock across the room, and, when it is smashed, it has a specific reading. A ray of light travels from the clock to the experimenters with velocity c.

E <----- C

What the experimenters see will not be the actual time of the clock. It will be readings of a past moment. What the clock is actually doing from the various experimenter's frames of reference is uncertain.

Dr.D:
What are you trying to say here? Is this supposed to indicate to me that you understood what I wrote down? I have not mentioned a "spacetime manifold" and you have not defined what you mean by the term "spacetime manifold". I have not brought up or defined any concept referred to as "connected" nor have you! Just what does the symbol M^+ refer to and/or the symbol M^-.

An n-dimensional manifold is a topological space M equipped with charts mapped onto the real numbers , with smooth transition functions.
The manifold is simply connected if it consists of one piece and doesn't have any circle-shaped "holes" or "handles". For example, a doughnut is not simply connected, but a ball is simply connected. A circle is not simply connected but a disk and a line are.

Take the path integral over all metrics h on M. Stephen Hawking derived the wavefunction of the universe as a path integral, for the functions of classical configuration space: psi(q) = integral exp(-S(g)/hbar) dg

exp is the base of the natural logarithm "e" raised to a power. The power in this case, is the quantity -S(g)/hbar, where S(g) is the Einstein Hilbert action.

The Lagrangian, which is the difference of kinetic and potential
energies, has a formulation in general relativity:

Lagrangian = R vol

R is the Ricci scalar curvature of the metric g, derived by contracting the Ricci tensor and "vol" is the volume form associated to g. The Einstein Hilbert action then becomes:

S(g) = integral R vol

The surface of M can be divided into M^+ and M^-. The probability for the manifold to have a metric h, are the wave functions psi^+ and psi^- . Hawking says that if the two wave functions are equal the superscripts may be dropped.

 

[matt grime]

The first inconsistency in your theory is in the non-definition of the set A. You insist that there are no constraints on A (or B and C) yet that there must be an injection to the real numbers, thus A must have a cardinality less than or equal to the continuum. You also dont' define a proper probabilty measure, as it happens.

 

[Doctordick]

The experimenter throws the clock across the room, and, when it is smashed, it has a specific reading. A ray of light travels from the clock to the experimenters with velocity c.

E <----- C

What the experimenters see will not be the actual time of the clock. It will be readings of a past moment. What the clock is actually doing from the various experimenter's frames of reference is uncertain.

What the clock is doing as seen from the perspective of modern physics as it is taught is not ambiguous at all.

With regard to this and the rest of your post, from my perspective, you are freely mixing three completely different issues: 1) the clock issue which was nothing more than an attempt to show that the readings on a clock have nothing to do with the experimenters frame of reference; 2) Modern physics which has nothing to do with the derivation I am showing you; and 3) the central issue of this thread which has to do with a very specific mathematical deduction which you really haven't discussed at all.

The first inconsistency in your theory is in the non-definition of the set A. You insist that there are no constraints on A (or B and C) yet that there must be an injection to the real numbers, thus A must have a cardinality less than or equal to the continuum. You also dont' define a proper probabilty measure, as it happens.

My first and foremost complaint about your criticism is that I am not at all putting forward a theory of any kind. I am doing nothing except pointing out the fact that a very specific mathematical deduction exists. Oh yes, I do believe that the deduction has a great impact on our understanding of reality but that issue must be laid aside until you understand the deduction and its consequences.

That being said, let me respond to your express difficulties. I said that A was completely undefined. Are you saying that the statement that I can refer to an element of A implies A must have a cardinality less than or equal to the continuum? Not in any theory of sets I have seen! The only set which contains no elements which can be referred to contains no elements at all and the empty set is easily accommodated here.

I did not say there were no constraints on B and C. I made some very specific constraints on them: a specific set B is a finite collection of elements from A and C is a finite collection of sets B. Now, if you are referring to my solution to sub problem number 2, I will admit that the elements of A represented in C must have a cardinality less than or equal to the continuum but that cannot be taken to prove that there exists any specific element in A which cannot appear in C. That is the essense of the power of infinity. The problem was the issue of an existence of a C containing elements not in the basis on which our $\vec{\Psi}$ was built. No case involving a non-finite C is actually of any significance at all.

And yes, it is true that I do not define a proper probability measure at all. The definition is not necessary as I do not use it. I leave that issue entirely open except for one very specific fact: it is a number between zero and one (including the end points). Now, if you can define a "proper measure of probability" which cannot be represented by a number in that range, then it might be possible you have something to complain about. I would like to see your definition and a little evidence that it would be acceptable to the scientific community (I put that into prevent you from defining probability measure to be the number of fuzzy white balls in your pocket!).

Come on people, isn't there anybody out there who can come up with a serious criticism? If you can't than you should accept the derivation as valid or, at the vary least, be a little interested in the consequences.

Does anyone out there have any idea how to recover the constraints

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

from the final equation

$$\left\{\sum_i\vec{\alpha_i}\\,\dot\,\vec{\nabla_i}\,+\, \sum_{i\not=j}\beta_{ij}\delta(\vec{x_i}\,-{\vec{x_j}})\right\} \vec{\Psi}\,\,=\,\,K\frac{\partial}{\partial t}\vec{\Psi}\,= \,iKm\vec{\Psi}$$
​

under the constraints I placed on it?

It results in an interesting insight. I would explain it to you but I would really like to find someone who is capable of following the math presented here.

If you can't follow the math, I don't see what we are talking about-- Dick

 

[PFanalog57]

Does anyone out there have any idea how to recover the constraints

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

from the final equation

$$\left\{\sum_i\vec{\alpha_i}\\,\dot\,\vec{\nabla_i}\,+\, \sum_{i\not=j}\beta_{ij}\delta(\vec{x_i}\,-{\vec{x_j}})\right\} \vec{\Psi}\,\,=\,\,K\frac{\partial}{\partial t}\vec{\Psi}\,= \,iKm\vec{\Psi}$$
​

under the constraints I placed on it?

It results in an interesting insight. I would explain it to you but I would really like to find someone who is capable of following the math presented here.

Why is your approach better than Feynman's path integral?

 

[Doctordick]

Why is your approach better than Feynman's path integral?

My approach to what? You simply have no idea of what I am doing do you?

 

[PFanalog57]

My approach to what? You simply have no idea of what I am doing do you?

When one lobs a clock at the wall, it has a trajectory, with position and momentum along a path. Respectfully, I ask, are you describing trajectories & dynamics ...or not?

If not, then what predictions are to be made from it[your approach]?

What are "you" doing? ..."You" are summing partial derivatives.

 

[Doctordick]

When one lobs a clock at the wall, it has a trajectory, with position and momentum along a path. Respectfully, I ask, are you describing trajectories & dynamics ...or not?

As I have mentioned several times, the only purpose of that post was to make people think about the fact that the clock readings had absolutely nothing to do with the frame of reference: i.e., clocks do not measure time! I admit the approach was an absolute failure! That fact is so totaly blocked from your view that you cannot comprehend that there is a problem there.

If not, then what predictions are to be made from it[your approach]?

Common modern experimental physics!

What are "you" doing? ..."You" are summing partial derivatives.

Yes! But do you understand why? As I implied earlier, I have no idea as to how to reach you.

 

[PFanalog57]

As I have mentioned several times, the only purpose of that post was to make people think about the fact that the clock readings had absolutely nothing to do with the frame of reference: i.e., clocks do not measure time! I admit the approach was an absolute failure! That fact is so totaly blocked from your view that you cannot comprehend that there is a problem there.

There seems to be a failure to communicate then

Yes! But do you understand why? As I implied earlier, I have no idea as to how to reach you.

Doctor D, that probably means that you don't fully understand your own "approach".

If you can't explain something simply, you don't know enough about it.

You do not really understand something unless you can explain it to your grandmother.


It should be possible to explain the laws of physics to a barmaid.
---Einstein

 

[PFanalog57]

Dr. D, I completely agree with the following statements from your web page:

Dr. D:

To a certain extent we owe some of the confusion surrounding relativity to the scientists who, in the face of this problem, define "simultaneous" in a manner which they felt was the most obvious: they define it in a manner which is consistent with the standard Newtonian space time diagram. We can't really fault them as such an attack at least allows relativistic phenomena to reduce to the Newtonian result when the finite speed of light becomes inconsequential. However, they shortchange the customer when they hold that such is the only possible definition of "simultaneity".

This is obviously true, what are you trying to say then? that Euclidean and non-Euclidean geometries are two different, yet, equivalent ways of explaining nature?

http://www.cord.edu/dept/physics/credo/etrain.html

Special Relativity and Simultaneity

The special theory of relativity is based on two postulates:

1. No test of the laws of physics provides any way to distinguish one inertial reference frame from another. (Any frame moving at constant velocity is as good as any other as far as the laws of physics are concerned.)

2. The speed of light in a vacuum is a constant independent of the motion of the source or observer.

If we accept these two statements as true we must give up our ideas about the constancy of time and space as independent quantities. This is most obvious when looking at "simultaneous" events. In relativity theory the determination of simultaneity is frame dependent. In other words, two events that are simultaneous in one frame are not simultaneous in any other inertial frame.

 

[Doctordick]

Russell,

I have a solution to a mathematical equation with far reaching implications. I do not believe you have the wherewithal to follow the solution so there is no point to continuing this discourse. I have no disagreement with either of the quotes you choose to post above! They just have no bearing on understanding this thread! You clearly have no interest in what I am talking about at all. Now that doesn't bother me; you are in good company.

Have fun -- Dick

 

[PFanalog57]

Russell,

You clearly have no interest in what I am talking about at all. Now that doesn't bother me; you are in good company.

Have fun -- Dick

This is a false statement Dr. D.

 

[Doctordick]

This is a false statement Dr. D.

Then are you saying you can follow the mathematics of what I wrote? If so, then let's talk about exactly what the presumed constraints on the fundamental equation are. Once I am convinced you understand that, then we need to look at the solutions. But, until you understand the equation and its solutions, let's not talk about the implications.

Dick

 

[PFanalog57]

Then are you saying you can follow the mathematics of what I wrote? If so, then let's talk about exactly what the presumed constraints on the fundamental equation are. Once I am convinced you understand that, then we need to look at the solutions. But, until you understand the equation and its solutions, let's not talk about the implications.

Dick

If the tau dimension is interchangable with the other dimensions then symmetry holds, as explained previously by you Dr. D. So the terms in your constraint equation can be interchangable.



If the fundamental equation can represent/explain anything, it is analogous to the "wave function of the universe" proposed by Hartle and Hawking, derived from the Wheeler Dewitt equation/constraint:

H(psi) = 0

H is the "Hamiltonian" but its terms do not have the symmetry of your constraints equation since the tau axis of your equation is interchangable with the other dimensions.

If at the present time , I still do not "have a clue", I hope you will still show me a little mercy ...


Of course the symmetry means that everything reduces to a scalar.

Interesting...

 

[Doctordick]

If the tau dimension is interchangable with the other dimensions then symmetry holds, as explained previously by you Dr. D. So the terms in your constraint equation can be interchangeable.



If the fundamental equation can represent/explain anything, it is analogous to the "wave function of the universe" proposed by Hartle and Hawking, derived from the Wheeler Dewitt equation/constraint:

H(psi) = 0

H is the "Hamiltonian" but its terms do not have the symmetry of your constraints equation since the tau axis of your equation is interchangable with the other dimensions.

If at the present time , I still do not "have a clue", I hope you will still show me a little mercy ...

I think you are trying to jump ahead of the presentation and trying to interpret what I am saying in terms which you already understand without looking carefully at what I am doing. I am defining only five things. Five very simple concepts: A – what it is we wish to explain; C – what it is we have to go on; B – the things we will use to defend the accuracy of our expectations; $\vec{\Psi}$ the mathematical algorithm which will yield those expectation.

The only serious issue to consider at this point is, can C indeed be referenced by a set of numbers without imposing any constraint on what C actually is?

If it can be then what we are looking for is a mathematical algorithm which will convert B into the proper expectation. If it cannot be, then I have a major problem. All you need do to stop the proof is to show me a counter example: i.e., show me a set whose elements cannot be referred to. If they can be referred to than I can use the reference itself as a label.

If indeed what I am doing is analogous to what is being done in the references you give then I ask why they haven't worked out the consequences of their solution. I think you are confusing the issue of what I am doing with the consequences of what I am doing. Let's take what I am doing one step at a time and we will get to the consequences down the road.

Of course the symmetry means that everything reduces to a scalar.

Interesting...

Now here, I have no idea of what is going on in your mind. What could you possibly mean by "everything"? Certainly you can not be referring to A, B or C as I have done nothing which requires any of them to be a scalar. And if you are referring to $\vec{\Psi}$, that certainly is not a scalar as it is nothing but an absolutely unconstrained representation of a mathematical algorithm: some procedure which carries one set of numbers into another.

The only possibility which remains is that you think it implies my references to the elements of A are scalars. Sure they are; they are just references, nothing more than mere labels which are, at the moment, undefined!

Personally, I think your biggest problem is trying to read too much into what I am saying. Definition is the essence of communicating and one should be very careful that all definitions used are understood by all parties. At the moment, we have only five things defined (except for basic math itself which I am presuming is understood).

The first issue is, under the definitions I have given, is the fundamental equation a valid equation? Once we have established that, we can proceed to solve the equation. As I do that, I will, from time to time, define additional things. Exactly what is meant by those definitions will be clear when I present those definitions.

This is all just straight logic -- Dick

 

[PFanalog57]

The only serious issue to consider at this point is, can C indeed be referenced by a set of numbers without imposing any constraint on what C actually is?

An approximation of C is not necessarily, a limitation on C. An optimal definition?

There will always be unknowns... The only certainty is uncertainty.

 

[Doctordick]

Russell, I don't know how to reach you with my thoughts. Let me try with another tack!

I believe some things are true and you believe some things are true; but the things you believe to be true don't exactly all map into the things I believe to be true. I put forth that the real problem between us is that you want me to explain what you believe to be true: i.e., it's like asking one to prove the authorities are in error while assuming they are right, a very foolish proposition!

I am asking you to believe five very specific things which I believe are correct. I only continue this conversation because I believe that you also believe these specific things are correct. Clearly, if you do not believe they are correct then we have no basis for communication.

So let's look at exactly what I am asking you to believe:

1) I am asking you to believe that mathematics is a logical structure: i.e., that any results of any mathematical deduction are as true as is the start position of the deduction. If you don't believe in that then you don't believe in the validity of mathematical deduction.

2) That there exists something to explain which we do not understand! I call it A. If you don't believe in A then you have nothing which needs explanation.

3) That there exists some information about A which is available to us. I call it C. If you don't believe in C then you have nothing on which to build an explanation of A.

4) That there exists some part of C which we can use to evaluate our explanation. I call it B. If you don't believe in B then you have no way to defend an explanation of A.

5) That there exists a way to refer to significant aspects of A, B, and C. If you believe there exist aspects of the problem which cannot be referred to, then I hold that you believe you cannot think about the problem.

Now, which one of those beliefs do you think is false? These are the only beliefs I ask of you.

Believe me Russell, I am trying very hard to be clear!

An approximation of C is not necessarily, a limitation on C. An optimal definition?

All I require is that any significant aspect of C can be referred to! If it can be referred to, then I can use the referrence as a label. If I can label it, I can assign a number to it. If I can assign a number to it I can record it's existence as a point on the x axis. This is no more than a recording device to allow reference to that particular significant aspect without any idea of what it really is. The essense of abstract thought is being able to talk about things without knowing what they are.

Why do I need a limitation on C? or an optimal definition? I am solving an abstract problem and the solution must serve any definition of C as I have utterly no idea of what C actually is, and neither do you! That is the most central aspect of my presentation.

Looking forward to your response -- Dick

 

[PFanalog57]

Russell, I don't know how to reach you with my thoughts. So let's look at exactly what I am asking you to believe:

1) I am asking you to believe that mathematics is a logical structure: i.e., that any results of any mathematical deduction are as true as is the start position of the deduction. If you don't believe in that then you don't believe in the validity of mathematical deduction.

As long as you cannot prove both a statement and its negation, then the mathematical structure is logically consistent. I hope you understand also Dr. D.

2) That there exists something to explain which we do not understand! I call it A. If you don't believe in A then you have nothing which needs explanation.

Belief or non-belief is irrelevant, since unknowns definitely exist, independent of our belief.

3) That there exists some information about A which is available to us. I call it C. If you don't believe in C then you have nothing on which to build an explanation of A.

If the information is available to us then our non-belief is totally bogus.

4) That there exists some part of C which we can use to evaluate our explanation. I call it B. If you don't believe in B then you have no way to defend an explanation of A.

So B is a way to "test" the validity of our explanation for A, iff, my interpretation of the Dr. D explication of B, is correct...

5) That there exists a way to refer to significant aspects of A, B, and C. If you believe there exist aspects of the problem which cannot be referred to, then I hold that you believe you cannot think about the problem.

Logic is the final arbiter of truth Dr. D, not beliefs.

Now, which one of those beliefs do you think is false? These are the only beliefs I ask of you.

Ambiguity rears its ugly head once again Dr. D. Why are you saying that mathematical "definitions" are beliefs?

The essense of abstract thought is being able to talk about things without knowing what they are.

Of course, the essence of truth boils down to symbolic arrangements of identities. Symmetry forms the basis of truth.

Why do I need a limitation on C? or an optimal definition? I am solving an abstract problem and the solution must serve any definition of C as I have utterly no idea of what C actually is, and neither do you! That is the most central aspect of my presentation.

Looking forward to your response -- Dick

C is the information; A is the unknown; B is the way to validate expectations of A.

 

[geistkiesel]

Dr. D, I completely agree with the following statements from your web page:



This is obviously true, what are you trying to say then? that Euclidean and non-Euclidean geometries are two different, yet, equivalent ways of explaining nature?

[URL]http://www.cord.edu/dept/physics/credo/etrain.html[/urll]

Dr. D, I completely agree with the following statements from your web page:

To a certain extent we owe some of the confusion surrounding relativity to the scientists who, in the face of this problem, define "simultaneous" in a manner which they felt was the most obvious: they define it in a manner which is consistent with the standard Newtonian space time diagram. We can't really fault them as such an attack at least allows relativistic phenomena to reduce to the Newtonian result when the finite speed of light becomes inconsequential. However, they shortchange the customer when they hold that such is the only possible definition of "simultaneity".

This is obviously true, what are you trying to say then? that Euclidean and non-Euclidean geometries are two different, yet, equivalent ways of explaining nature?

http://www.cord.edu/dept/physics/credo/etrain.html

Special Relativity and Simultaneity

The special theory of relativity is based on two postulates:

1. No test of the laws of physics provides any way to distinguish one inertial reference frame from another. (Any frame moving at constant velocity is as good as any other as far as the laws of physics are concerned.)

2. The speed of light in a vacuum is a constant independent of the motion of the source or observer.

If we accept these two statements as true we must give up our ideas about the constancy of time and space as independent quantities. This is most obvious when looking at "simultaneous" events. In relativity theory the determination of simultaneity is frame dependent. In other words, two events that are simultaneous in one frame are not simultaneous in any other inertial frame.

I authored a thread regarding the usefulness of simultaneity postulate and offer a contination of the theme here.

I disagree with the statement that "two events that are simultaneous in one frame are not simultaneous in any other inertial frame." The moving train gedunken of Einstein, where O' moving through the midpoint M between light sources A and B, when the two the lights are pulsed simultaneously will be determined as simultaneous in the moving frame also.

Einstein’s original simultaneity experiment, “Relativity”, pages 25-27, has a moving observer, O’ moving toward a light source B, from a light source A, behind. As O’ passes, M at velocity v = 1 at t = t0 = 0, the midpoint between A and B in the stationary frame, the lights are pulsed on at A and B. Sometime t1 later, the light from B is recorded by O’ and at t2 later, the light from A is recorded.

This example is a definition of simultaneity, or the lack of, the simultaneous occurrence of events between inertial frames moving wrt each other.

A t0|→----------------------------------|--------------------------------------------←|t0 B

--------------------------| -t1-----------|t0→--------|t1------|t2-------------------------→

According to theoretical postulates, that O’ measures the light from A and B at different times, O’ must conclude the lights are pulsed on at different times as O’ has no way of knowing he is moving wrt the sources at A and B.

Is this the only valid interpretation?

First, O’ can conclude he does not know if he is moving or not. If he is moving wrt to the sources of the light then the different times of recording do not leave the simultaneity postulate as the only conclusion. Therefore, O’ makes an effort to determine any O' motion wrt to a stationary frame. When he records the pulse from B, he notes the wavelength and time of arrival. Sure enough, at t2 the light from A arrives. Immediately O’ notices the blue/red shift of the light pulses and concludes there is a possibility of the pulses measured with blue/red shifts are from sources with identical light characteristics, hence O’ determines v = 1. From the measured time between pulses, Δt ═ t2 – t1 = 1, he calculates the distance O’ traveled from the measured velocity, v = 1, as d’ = vΔt = 1.

Now O’ asks, if the pulses were simultaneous emitted in a stationary frame, where is t1 located wrt to the midpoint. Of course O’ is starting from an assumption he crossed M at t0 in the stationary O frame. This is just the first of many assumptions he can make.

O’ is moving at v ═ 1 for a time t1 when the pulse from B arrives at t1. The distance B-M = D = ct1 + t1 = t1(c + 1). During ∆t = 1 the light from A would travel from -t1 to t2 or a distance 2t1 + v∆t = 2t1 + 1 during ∆t = 1. This assumes the lights were pulsed simultaneously. So O’ waits and measures Δt = 1.

O’ having recorded the time for the arrival at t2, calculates backwards a distance dA = cΔt, and obtains the distance traveled by A from –t1 to t2. This distance is 2t1 + vΔt, or 2t1 + 1. This confirms the lucky guess. If O’ hadn’t passed the midpoint of A-B at to = 0, then the measured ∆t would be greater or less than 1 if the assumption that O’ was moving is correct.

Because he problem is framed as it is O’ correctly determines his relative motion and velocity and the fact that the pulses started at t0 in the stationary frame and the moving frame. Whatever the frame used, the result is the same. In other words O’ can make the calculations using a symbolic reasoning with the Δt and v measurements only. The measured Δt, the measured v gives the same result in analysis of the problem. The difference in numbers using the stationary frame numbers, as calculated by O, for instance, gives the same result. However, O has the advantage that he knows that O’ is the moving frame and that the conditions are as outlined in the definition of the problem. O’, knowledgeable in time dilation phenomena of clocks, does not fall into a dogmatic trap of assuming the relativity postulate of simultaneity without question.

The O’ observer, therefore determines the significant events as simultaneous, notwithstanding his measured values of t and v differ from those made by the stationary O observer.

 

[PFanalog57]

:zzz:

-----A'-----O'-----B'------>TRAIN

----A-----O------B----EMBANKEMENT

According to Einstein, two lightning flashes strike the ground at both points A and B simultaneously for the observer at O on the embankement, but not for the observer on moving train at O' , because the lightning flash at B will appear to the person on the train, to occur before the lightning flash at A, due to the train's forward motion.

 

[Doctordick]

Russell,

I have been slow to respond to your latest posts because I am seriously trying to understand exactly why you are baulking at the five issues I am trying to get you to accept. After considerable thought, I think I may understand what is bothering you.

Belief or non-belief is irrelevant, since unknowns definitely exist, independent of our belief.

Once again, you have made a statement which made me suspect that you were trying to muddy the issue through use of the ambiguity of the English language. I have no argument at all with what you are saying. What I find it to be is a misdirection of attention toward an issue which has no bearing at all on what I am trying to communicate; an issue which I had presumed we had no disagreement. My reactions to such things has, in the past, been to conclude that either there is something about what I am saying which you are missing or that or you are intentionally using misdirection of attention to prevent communication. You have continually assured me that you are only trying to clarify my position. I am going to continue to take you at your word.

Belief and/or non-belief is always an issue in any communication because people invariably believe they know what the words they are using mean. Very few people are aware of the shear volume of assumptions in that belief. That is, in fact, the first hurdle we have to get over. Once we can get the discussion into mathematics proper, communication should get much easier.

Assuming our only real problem is miscommunication, I suspect it may be due to your misinterpretation of what I am trying to do. One problem I have always had is the fact that everyone presumes I am trying to present a theory. I am not! I am trying to present a careful analysis of the problem of creating an explanation itself. That is the reason I have to move to the abstract.

Essentially, almost every complaint you have put forward could be categorized as an attempt to clarify my assumptions. That desire on your part is very understandable as all scientists are trained to be very careful about their assumptions. The real difficulty here is that I am doing the very best I can to make no assumptions at all and you find that approach very difficult to comprehend. That is exactly the reason why I cannot get the attention of any professional scientist. His mind is utterly closed to the idea that any success is to be found down that rabbit hole!

It is the assumption of the scientific community that absolutely nothing of consequence can be deduced from such an approach. As a result no one who has been trained in science has ever taken the trouble to look down that hole! I have looked and found astonishing consequences. Not a theory but fundamental constraints on theories themselves which yield far reaching consequences. It both closes and opens many doors in the realm of imaginative thought.

I have said, several times I think, that I want to show you a derivation of physics from first principals. In order to do that, I must first get across exactly what I mean by "first principals". That is what I have been attempting to do. In actual fact, the entire derivation is presented in messages #3 and #4 of this thread. Once you understand exactly what is being said there, the only problem which remains is to actually examine the solutions to that "fundamental equation".

All I really ask of you is that you accept, as first principals, the four things that derivation is based on. The word used for that acceptance is a rather mundane issue; whether it be "belief", "acceptance", "understanding" or whatever, the real issue is, will you work with it? The first thing is acceptance of mathematics as a good communication medium: i.e., that mathematical terms are well understood. From our current discussion, I don't think you have any real argument with that so, please, let's drop opposition to the suggestion that it is a fundamental first principal.

The other three issues are the definitions of A, B and C. I think you want these issues to be clarified when, in actual fact, clarifying them essentially amounts to making assumptions about them. If I make any assumptions, then I am limiting the applicability of my deductions and I have no wish to do so. In order for you to seriously argue with my deduction, you must show that some step in my deduction is not possible without clarifying what A, B and C stand for (beyond the definitions I have specified).

The final critical lynch pin in the deduction might be called a "labeling axiom". That would be the fact that I assume all significant issues represented by A, B or C can be referred to with labels. That it is not necessary to make any specification as to what these labels actually refer to beyond the fact that they are significant issues. The central issue of the deduction is that I can deal with all significant issues without knowing what they actually are.

If that is my intention, just exactly how do you expect me to explain to you what they are? I have identified the categories they refer to and the relationship between them: i.e., why I want to talk about three different aspects of explanation. Beyond that I cannot go.

1) A is what is to be explained!
2) C is what we have to work with!
3) B is a subset of C which we will use to test the validity of our model.

The first step is to accept the "first principals" as I have presented them. The second step is to understand, in detail, the derivation given in message #3 and #4: how it is a direct consequence of being able to label the significant elements of A, B, and C and nothing else.

Once you understand the necessity of the fundamental equation, then we can look at the solutions to that equation and learn a lot about what we can and cannot know.

Only with regard to clarifying your impressions, I will respond to some of your other comments: i.e., I am not trying to continue an argument with you by what follows; only trying to clarify my position.

So B is a way to "test" the validity of our explanation for A, iff, my interpretation of the Dr. D explication of B, is correct...

No! B constitutes that information which is used to verify the validity of our expectations. It is not the "way" to test the validity. The way to test the validity is to generate expectations for B a subtly different issue.

Ambiguity rears its ugly head once again Dr. D. Why are you saying that mathematical "definitions" are beliefs?

Yes, English is quite ambiguous! The belief I was referring to was the belief that the specific definitions are acceptable: i.e., that they do indeed fulfill the requirements of a definition. If you are a rational person, you must accept the fact that errors can be made. It is entirely possible that, via some subtle thing accidentally missed, a presumed valid definition will later turn out to be internally inconsistent. Acceptance that the definition is without error clearly constitutes a "belief". In fact, thinking you have made no deduction errors constitutes a "belief"; any mathematics and/or logic is just chock full of "beliefs"!

Therefore A is an undefined variable, an identity operator, or an entity, such, that what relations can be known about A, must be necessarily true on logical or analytic grounds. If you can't mentally grasp that logical necessity, then, with all due respect, "your construction" is "SOL".

What my fundamental equation says, it says about our expectations of B. It only applies to A because of the relationship that the significant aspects of B which can be referred to are, by definition, constrained to be significant aspects of A which can be referred to! The fundamental equation is a logical consequence of the fact that the significant aspects of B may be labeled and nothing else!

At no point do I ever say anything about knowing something about A! Whatever A is, it is a totally open issue! If you close that issue in any way, you remove the generality of the deduction.

No, B is neither the abstract model nor the equations! B is whatever it is that we are going to use to defend our model's validity!

B is a subset of C about which we need to create "expectations", ...your words. Make up your mind Doc. You can't have yer cake and eat it too

It appears here that you are confusing a subset of the information we have to work with, with our abstract model and/or the equations specifying that abstract model. They are very different things.

Thanks for the clarification Dr. D. Yes, I wasn't completely sure about what you ment by saying "C is the information we have", and I assumed it was a set of known/understood quantities. You are correct IMHO, information can exist without understanding.

Communication can sometimes be very difficult. Somehow I have failed to communicate the idea that A, B and C are all completely unknown. This is very different from our model which, since we created it, must be known. Likewise, the fundamental equation is also a very known thing!

I hope I have cleared something up here. I would like to believe we are getting somewhere. I would seriously like to get to the defense or the fact that the fundamental equation is indeed a necessary consequence of the "labeling axiom.

Have fun -- Dick

 

[PFanalog57]

Belief and/or non-belief is always an issue in any communication because people invariably believe they know what the words they are using mean. Very few people are aware of the shear volume of assumptions in that belief. That is, in fact, the first hurdle we have to get over. Once we can get the discussion into mathematics proper, communication should get much easier.

If my interpretation is correct, the communication must be as free from ambiguity as possible; ergo, we must communicate via "mathematics", since it is currently the least ambiguous language possible. It is a "meta-language".

The real difficulty here is that I am doing the very best I can to make no assumptions at all and you find that approach very difficult to comprehend. That is exactly the reason why I cannot get the attention of any professional scientist. His mind is utterly closed to the idea that any success is to be found down that rabbit hole!

That "rabbit hole/success/failure" is a whole discussion/debate within itself Dr. D. It asserts or ...assumes? that physical existence is isomorphic to a mathematical structure.

I have said, several times I think, that I want to show you a derivation of physics from first principals. In order to do that, I must first get across exactly what I mean by "first principals". That is what I have been attempting to do. In actual fact, the entire derivation is presented in messages #3 and #4 of this thread. Once you understand exactly what is being said there, the only problem which remains is to actually examine the solutions to that "fundamental equation".

Here is the relevant quote from post 3.

The first fundamental component is, "what is to be explained"; thus our first problem is to find an abstract way of representing anybody of information. Let "A" be what is to be explained and proceed with the following primitive definitions:
1. A is a set.
2. B is a set, defined to be an unordered finite collection of elements of A
3. C is defined to be a finite collection of sets B.
The specific problem is to create an abstract model which will model any explanation of A obtained from C. As an aside, it should be obvious that the necessity of defining C arises because, if all the elements of A are known, then A itself is a model of A and the problem posed is trivial. (Nevertheless, please note that the trivial case where C is identical to B which is identical to A is not excluded in this presentation.)

The second fundamental component is the definition of "an explanation" itself: we must establish an abstract definition of exactly what is meant by "an explanation of A". We will hold here that an explanation of A will consist of the following elements.
1. A set of reference labels for the elements of A (so that we may be able to reference those elements and thus know and discuss what it is that we are dealing with prior to achieving an understanding of those elements).
2. An algorithm which will yield the probability of any specific set B derived from A which is consistent with the distribution of B in C (this is required to assure the explanation yields rational expectations: i.e., so that our explanation will be consistent with the available information "C").
Construction of a model:

Since B is finite, its elements may be labeled.
1. Let labeli be the label of a particular element of B.
2. Let all labeli be mapped into the set of real numbers xi.
3. Let all numbers xi be mapped into points on the real x axis.

All I really ask of you is that you accept, as first principals, the four things that derivation is based on. The word used for that acceptance is a rather mundane issue; whether it be "belief", "acceptance", "understanding" or whatever, the real issue is, will you work with it? The first thing is acceptance of mathematics as a good communication medium: i.e., that mathematical terms are well understood. From our current discussion, I don't think you have any real argument with that so, please, let's drop opposition to the suggestion that it is a fundamental first principal.

The other three issues are the definitions of A, B and C. I think you want these issues to be clarified when, in actual fact, clarifying them essentially amounts to making assumptions about them. If I make any assumptions, then I am limiting the applicability of my deductions and I have no wish to do so. In order for you to seriously argue with my deduction, you must show that some step in my deduction is not possible without clarifying what A, B and C stand for (beyond the definitions I have specified).

The final critical lynch pin in the deduction might be called a "labeling axiom". That would be the fact that I assume all significant issues represented by A, B or C can be referred to with labels. That it is not necessary to make any specification as to what these labels actually refer to beyond the fact that they are significant issues. The central issue of the deduction is that I can deal with all significant issues without knowing what they actually are.

If an issue is significant then it is labeled. If X then Y.

If that is my intention, just exactly how do you expect me to explain to you what they are? I have identified the categories they refer to and the relationship between them: i.e., why I want to talk about three different aspects of explanation. Beyond that I cannot go.

1) A is what is to be explained!
2) C is what we have to work with!
3) B is a subset of C which we will use to test the validity of our model.

The first step is to accept the "first principals" as I have presented them. The second step is to understand, in detail, the derivation given in message #3 and #4: how it is a direct consequence of being able to label the significant elements of A, B, and C and nothing else.

Once you understand the necessity of the fundamental equation, then we can look at the solutions to that equation and learn a lot about what we can and cannot know.

1.] A is the unknown

2.] C is the information

3.] B will be used to test the validity of the mathematical model. B is not the test itself.

Please proceed.

 

[Doctordick]

Maybe we are getting some place!

I am going to presume your last post signifies understanding of my "first principals" though I am still confused by some of your comments.

If an issue is significant then it is labeled. If X then Y.

You state this as an if/then procedure: "if it is significant then label it". That is not exactly what I am saying. What I am saying is "label all elements of B". By definition, the number of elements is finite so the process can be completed. The only possible complaint with the instruction is that there is some aspect of B which cannot be labeled. My solution to that problem is "if you can refer to it, I can use your reference as a label". The only place where "significance" comes in is, "if it cannot be referred to, how can it be significant to your solution to the problem?"

A very real issue exists here: your solution to the problem is to explain C (you have nothing else to work with)! It is an assumption that your best explanation of C is an explanation of A. Certainly there is no proof that A can be explained; we are trying to lay out a road map of the best we can do given what we know (whatever that might be)!

What I am saying is that your statement of significance implies one needs to know whether or not it is significant. My statement is quite the other side of the coin: if you cannot refer to it, how can it be significant to your solution?

That "rabbit hole/success/failure" is a whole discussion/debate within itself Dr. D. It asserts or ...assumes? that physical existence is isomorphic to a mathematical structure.

Again, I am completely baffled by you insertion of that comment. I can only attribute it to lack of communication between us due to the ambiguity of English!

I will none the less proceed as if you understand the labeling issue. Quoting from message #3:

Construction of a model:

Since B is finite, its elements may be labeled.

1. Let label_i be the label of a particular element of B.
2. Let all label_i be mapped into the set of real numbers x_i.
3. Let all numbers x_i be mapped into points on the real x axis.
​

Thus it is seen that any set of labels for the elements of A available to the explanation (i.e., appearing in any set B) may be mapped into points on the real x axis; however a minor problem exists in any attempt to use this as a general model.

Sub Problem number 1:

Since all possible explanations must be modeled and B may contain the same element of A more than once: i.e., the points x_i need not be unique. There is a problem in modeling the elements of B as points on the real x axis. It should be clear that points with the same location can not represent multiple occurrences of the mapped label and information contained in B is lost in step three as put forth.
​

Solution to Sub Problem number 1:

1. Add to the model a real $\tau$ axis orthogonal to the real x axis.
2. Attach to every x_i an arbitrary $\tau_i$ such that every pair of identical x_i points have different $\tau_i$ attached. Our model can now display the fact of multiple occurrences of identical x_i.
​

​

The abstract model of any possible explanation is now a set of points (one set for each B) mapped into a set of (x,$\tau$) planes (one plane for each set B making up the set C).

We have now accomplished the first step: we have established a specific way of modeling all possible references to the elements in B in the set C...

Do you understand exactly why the possibility of problem number 1 arises and how the introduction of an orthogonal axis and the "manufactured" information resolves the difficulty? Secondly, do you understand that such a move does not constrain the possible model at all but rather expands the representable possibilities?

I ask that question because, right here, my attack goes counter to everything any scientists has ever been taught. The scientific attack is to do one's best to constrain the situation to the one applicable to the problem they have in mind; whereas my attack is the make absolutely sure that, whatever I might do, I must never constrain the possible solution of the problem in any way as I know neither what the problem is nor what the solution is!

If anything about this step bothers you, let me know and I will try to do a better job of making the step clear. If you tell me you understand the step, I will continue.

Have fun -- Dick

 

[PFanalog57]

Do you understand exactly why the possibility of problem number 1 arises and how the introduction of an orthogonal axis and the "manufactured" information resolves the difficulty? Secondly, do you understand that such a move does not constrain the possible model at all but rather expands the representable possibilities?

I ask that question because, right here, my attack goes counter to everything any scientists has ever been taught. The scientific attack is to do one's best to constrain the situation to the one applicable to the problem they have in mind; whereas my attack is the make absolutely sure that, whatever I might do, I must never constrain the possible solution of the problem in any way as I know neither what the problem is nor what the solution is!


Have fun -- Dick

Here is an explanation of the scientific method:


http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html


The scientific method has four steps

1. Observation and description of a phenomenon or group of phenomena.

2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.

3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.

4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.

If the experiments bear out the hypothesis it may come to be regarded as a theory or law of nature (more on the concepts of hypothesis, model, theory and law below). If the experiments do not bear out the hypothesis, it must be rejected or modified. What is key in the description of the scientific method just given is the predictive power (the ability to get more out of the theory than you put in; see Barrow, 1991) of the hypothesis or theory, as tested by experiment. It is often said in science that theories can never be proved, only disproved. There is always the possibility that a new observation or a new experiment will conflict with a long-standing theory.



So your approach has more freedom from constraint[even more than the scientific method] and is highly abstract. It appears that by adding more degrees of freedom with the "tau" dimension, the problem is solved... if my interpretation is correct.

Please continue.

 

[Doctordick]

Since you brought it up, let me comment on the scientific method and how it relates to what I am doing. By the numbers:

1. Observation and description of a phenomenon or group of phenomena.

Find out all you can about C!

2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.

Conjure up a possible rule! – (Also, open your mind to the possibility of the existence of unseen things that might make that rule useful: i.e., electrons, gods, phlogiston or maybe even "strings".)

3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.

Deduce your expectations on the assumption the rule is correct and that those unseen things do really exist!

4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.

Check your expectations against C!

Note here that my index on B, mapped into that real axis t, does indeed correspond to time: i.e., C may be divided by t into two sets. We can define B_j to be a member of one of the two sets by the following rule: if B_j is known we put it in the first set, if it is not known we put it in the second set. We then just attach the tag "the past" to the first set and the tag "the future" to the second set. Now we can talk about "predictions": i.e., B in the future! Certainly if our "expectations" are not consistent with "B in the past" the hypothesis is obviously ridiculous (that is why they don't even mention that particular case in the "official scientific method").

Perhaps they should mention it as, from reading this forum, it appears to be the major omission in crackpot theorizing.

If the experiments do not bear out the hypothesis, it must be rejected or modified.

Yes; perhaps we could come up with a new particle to save conservation of energy! If the trick works, does that prove neutrinos exist? I am not complaining about neutrinos, I am merely trying to get you to think about proof of existence itself. In particular, the existence of unseen things and all the vague ambiguous concepts therein!

So your approach has more freedom from constraint[even more than the scientific method] and is highly abstract. It appears that by adding more degrees of freedom with the "tau" dimension, the problem is solved... if my interpretation is correct.

I would disagree with that statement. My approach has nothing in it which is not done by the standard scientific method. The only real difference is that my description of the procedure is not vague and ambiguous! I have made a serious effort to be exact.

Scientists quite often introduce new "unseen" things that they feel makes what they see make more sense. They then convince themselves that they can see these things by interpreting their apparently valid expectations as evidence that their creations exist! A rational person should keep in mind the fact that future knowledge might destroy those self same creations. Think of phlogiston!

I don't think you understood why tau was introduced. My problem was that I wanted to record references to elements of B as points on the real x axis. Think of the problem of inventing a language; one needs symbols for the things to be expressed in that language. I have simply chosen my symbol to be a point on the x axis; the positional value of x becomes the symbol for the specific element of B. If you define exactly what the symbol (or a collection of symbols) stands for, this is as good as any other language. However, when I try to do that, I found a difficulty cropped up. If a particular element showed up twice or more in a given B_j it would only appear once in my proposed symbol system and the mapping system would fail.

I solved that problem through the addition of a second orthogonal axis and attaching a "manufactured" tag to the problem element. In essence, this is no different than conjuring up neutrinos. However, we need to think about a problem this solution creates. We have created an aspect of B which is totally in our mind. We have already defined C to be what we have to work with and thus we are not "guessing" about what might actually exist; we know this coordinate does not exist. It is a pure figment of our imagination.

Now, I will comment here that the scientist doesn't "know" that neutrino exists either but I want to be more exact than he is; I want to maintain awareness that this is an aspect of a mental model of A and not at all a part of A. Consider the impact this fact has on that algorithm we are looking for which is supposed to yield our expectations. There exists no way that the value to be used for tau can ever be obtained from any specific B. If that is true just how are we to evaluated the mathematical algorithm which is to yield our expectations.

Ok, I have a solution to that problem. Let us say that I am able to find a solution to the original problem which yields the correct expectation for B given any arbitrary value for each and every tau_i which could possibly be attached to x_i in that B. Now clearly that is a much more difficult problem than the one we started with; but, if I can find the solution to that problem, the solution to the original problem is obtained by integrating that found solution over all tau_i.

I will presume you understand the existence of sub problem #2 and also understand my resolution of that problem. If you can think of any reasons why my solution to these problems will not work, let me know.

I need to make one more comment on the addition of that tau axis. I will continue to add "manufactured" data to my model. Doing so is completely analogous to the procedure of inventing entities used in every scientific field known to man. The only difference between my procedure and theirs is that, in the interest of being exact, I must always maintain the conceptual difference between C and the added "manufactured" data. The issue is that the logical rules which must be applied to the two different categories are significantly different.

In order to have a simple way to refer to that conceptual difference, I would like to define two terms: "knowable" and "unknowable". When I refer to something as knowable, I will mean that it is information contained in C and is outside my control. When I refer to something as unknowable, I will mean manufactured information created to make my explanation work. Please do not confuse my use with the common usage. I hope I have made it clear that I am working in the abstract and nothing I say is based on anything known about C as I am not allowing myself the freedom to make any assumptions whatsoever about what can be known about C.

The fundamental difference between knowable data and unknowable data is the fact that knowable data is absolute and unchangeable as it must be explained in any and all future theories; whereas unknowable data is fundamentally part of the explanation, and not really part of the phenomena being explained. The most important aspect of unknowable data is that it must obey exactly the same rules as the knowable data. If it does not, then the proposed explanation will fail the fourth step of the scientific method.

It should be clear to you that $\vec{\Psi} (\vec{x},t)$ is an absolutely general representation of any possible algorithm for transforming one set of numbers into a second. This means that the representation has placed no constraint whatsoever on the possible solutions. And, in message #25, I have already showed everyone how to deduce the first three constraints on $\vec{\Psi}$.

This brings me to that "corresponding set D" mentioned on message #4. If you feel everything I have said makes decent sense, I will get into some important aspects of that set D which is in fact more "manufactured" information.

Have fun – Dick

PS Please note that we now have eight defined terms: mathematics, A, B, C, past, future, knowable and unknowable. We will define time to be the point on the t axis which separates past from future (remember, t was an arbitrary label assigned to B_j so using it to provide this separation requires no assumptions).

 

[PFanalog57]

Scientists quite often introduce new "unseen" things that they feel makes what they see make more sense. They then convince themselves that they can see these things by interpreting their apparently valid expectations as evidence that their creations exist! A rational person should keep in mind the fact that future knowledge might destroy those self same creations. Think of phlogiston!

Excellent point Dr. D. Can the introduced "unseen things" be called "useful fictions"?

I don't think you understood why tau was introduced. My problem was that I wanted to record references to elements of B as points on the real x axis. Think of the problem of inventing a language; one needs symbols for the things to be expressed in that language. I have simply chosen my symbol to be a point on the x axis; the positional value of x becomes the symbol for the specific element of B. If you define exactly what the symbol (or a collection of symbols) stands for, this is as good as any other language. However, when I try to do that, I found a difficulty cropped up. If a particular element showed up twice or more in a given B_j it would only appear once in my proposed symbol system and the mapping system would fail.


I solved that problem through the addition of a second orthogonal axis and attaching a "manufactured" tag to the problem element. In essence, this is no different than conjuring up neutrinos. However, we need to think about a problem this solution creates. We have created an aspect of B which is totally in our mind. We have already defined C to be what we have to work with and thus we are not "guessing" about what might actually exist; we know this coordinate does not exist. It is a pure figment of our imagination.

I am going to go back and seriously study your previous posts Dr. D. until I completely understand. I sincerely hope that someone with more experience and training than I have, can continue this important discussion with you.

Now, I will comment here that the scientist doesn't "know" that neutrino exists either but I want to be more exact than he is; I want to maintain awareness that this is an aspect of a mental model of A and not at all a part of A. Consider the impact this fact has on that algorithm we are looking for which is supposed to yield our expectations. There exists no way that the value to be used for tau can ever be obtained from any specific B. If that is true just how are we to evaluated the mathematical algorithm which is to yield our expectations.

Ok, I have a solution to that problem. Let us say that I am able to find a solution to the original problem which yields the correct expectation for B given any arbitrary value for each and every tau_i which could possibly be attached to x_i in that B. Now clearly that is a much more difficult problem than the one we started with; but, if I can find the solution to that problem, the solution to the original problem is obtained by integrating that found solution over all tau_i.

It would probably take a very advanced supercomputer to generate the algorithms of which you speak.

I need to make one more comment on the addition of that tau axis. I will continue to add "manufactured" data to my model. Doing so is completely analogous to the procedure of inventing entities used in every scientific field known to man. The only difference between my procedure and theirs is that, in the interest of being exact, I must always maintain the conceptual difference between C and the added "manufactured" data. The issue is that the logical rules which must be applied to the two different categories are significantly different.


In order to have a simple way to refer to that conceptual difference, I would like to define two terms: "knowable" and "unknowable". When I refer to something as knowable, I will mean that it is information contained in C and is outside my control. When I refer to something as unknowable, I will mean manufactured information created to make my explanation work. Please do not confuse my use with the common usage. I hope I have made it clear that I am working in the abstract and nothing I say is based on anything known about C as I am not allowing myself the freedom to make any assumptions whatsoever about what can be known about C.

Of course. There can be no definitive constraints on C. Therefore the constriants are on the interpretive definitions within the minds of the theorists, the ambiguous "unknowable" that can only be refined with time.

Or not?

The fundamental difference between knowable data and unknowable data is the fact that knowable data is absolute and unchangeable as it must be explained in any and all future theories; whereas unknowable data is fundamentally part of the explanation, and not really part of the phenomena being explained. The most important aspect of unknowable data is that it must obey exactly the same rules as the knowable data. If it does not, then the proposed explanation will fail the fourth step of the scientific method.

If I make the statement: "all grey horses are grey", it must be accepted as "absolute"; an analytic proposition?

It should be clear to you that $\vec{\Psi} (\vec{x},t)$ is an absolutely general representation of any possible algorithm for transforming one set of numbers into a second. This means that the representation has placed no constraint whatsoever on the possible solutions. And, in message #25, I have already showed everyone how to deduce the first three constraints on $\vec{\Psi}$.

This brings me to that "corresponding set D" mentioned on message #4. If you feel everything I have said makes decent sense, I will get into some important aspects of that set D which is in fact more "manufactured" information.

Have fun – Dick

PS Please note that we now have eight defined terms: mathematics, A, B, C, past, future, knowable and unknowable. We will define time to be the point on the t axis which separates past from future (remember, t was an arbitrary label assigned to B_j so using it to provide this separation requires no assumptions).

Please proceed.

 

[Doctordick]

Excellent point Dr. D. Can the introduced "unseen things" be called "useful fictions"?

Certainly; however, I have already put forth a suggested tag: "unknowable data". I would prefer using my tag to "useful fictions" but clearly "useful fictions" would be easier for the common reader to pick up on. For the moment, internal to this discussion, is the tag "unknowable" acceptable to you?

I am going to go back and seriously study your previous posts Dr. D. until I completely understand. I sincerely hope that someone with more experience and training than I have, can continue this important discussion with you.

Now I take that comment right there as a very strong indicator that you are beginning to understand what I am doing. Take heart, I am not a very bright or imaginative person (in fact I could almost be called slow witted), but I am a very careful person (at least when it comes to thinking things out). I think what I am saying can be followed by anyone if they just take the care to think out each step. And I also hope others are reading this. I would love to hear any comments about my thoughts or my presentation.

It would probably take a very advanced supercomputer to generate the algorithms of which you speak.

That is why we are speaking in the abstract. It is never possible to take everything into account in any real problem; but, once the problem is reduced to a finite number of elements (and C is, by definition, finite) we actually can handle everything from an abstract perspective. All we need do is lay out the specific procedure. Speaking of which, I have tried to interest AI people in this (for some very specific reasons which we might get to later) but I am thoroughly regarded as a crackpot agent. You know, the "yes yes, that's nice!" response.

If I make the statement: "all grey horses are grey", it must be accepted as "absolute"; an analytic proposition?

Well, in my opinion, English is sufficiently vague and ambiguous that an argument could be raised against acceptance of that statement; however, in my mind, true by definition (presuming a decent definition) is the only possible defendable "truth". If we agree to use the definition then it is "true"; if we don't agree to use the definition, they we are not communicating and the truth of the statement is immaterial.

And now to get to that "corresponding set D" already mentioned! Let me get to it in a slightly round about way. I will presume you will give me permission to manufacture "unknowable data" to my hearts content so long as I recognize that it is indeed different from C. Therefore, let us be very specific in the exact impact of that difference.

All data, knowable or unknowable, must obey exactly the same rules, except for the fact that it is utterly unknowable (otherwise, as I said, the solution will fail at step four of the scientific method. It follows that the only place where unknowable data impacts the solution of my problem is when I actually numerically evaluate the expectations implied by $\vec{\Psi}$. When I go to evaluate P(B(t)), I must integrate

$$P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv$$
​

over all possible values of any $\vec{x}_i$ which corresponds to "manufactured data"; "useful fictions"; "unknowable data" or "unseen things". What ever it is one wishes to call the reference that x_i refers too. Other than that, the manufactured data can be regarded to be as real as any other data.

Analogous to that, think of Feynman's integrals over all possible virtual transitions in an interaction. This is no more than the standard way of handling those "useful fictions" as you called them.

Since the difference between knowable and unknowable data arises only in the calculation of final results, I will make no effort to differentiate between knowable and unknowable when setting up my collections of information to be used to evaluate the validity of my final solution. That is, just as I added the $\tau_i$ argument to B in order to obtain a model I found convenient, I will simply add these additional arguments to B.

I might comment that ignoring the difference here is a very reasonable thing to do as, since everything has to obey the same rules, the only difference is the fact that I must take into account the fact that I have no way of knowing the correct value of this particular variable. Now, that circumstance is handled the same way whether the particular value is knowable or unknowable so why worry about it? What I am pointing out here is that a "knowable" reference which I just don't happen to know is handled by integrating over all possibilities. Essentially, the difference between "knowable" and "unknowable" is a conceptual difference, not an evaluate-able difference.

Thus, as a first step, let me add arguments to every B_j such that the number of arguments in all B_j are exactly the same. I just do that to simplify the structure of my model. As an aside, since j is being mapped into t (which we have defined to be "time"), the consequence of that step is identical to the assumption that these things being referred to exist whether they are being referred to at one particular time or not. Or, it can be seen as assuming something you knew existed at t₁ and at t₂ also existed at all t between those two values. A very common scientific assumption. The only issue to remember is that, if you make that assumption, your solution to the problem must be consistent with that assumption and it shouldn't be hard to remember that.

I am going to quit there because I want to give you time to digest what I have just done. The next step is very important and, I think, needs to pretty well be examined as a conceptual whole.

Looking forward to your attention -- Dick

Please note that, whenever I use the symbol $\vec{x}$ without any index, I mean the entire collection {$\vec{x_1} ,\vec{x_2} , \cdot \cdot \cdot ,\vec{x_n}$} where $\vec{x_i}\, \equiv \, x_i \hat{x}+\tau_i \hat{\tau}$.

 

[Doctordick]

Russell,

I am sorry to see you go. When I said that you were beginning to understand what I am doing, I didn't really expect you to run off to think about it all by yourself. I had much more background in physics when I got to where we presently are and I wandered in that wilderness for many years before I saw the light. I am afraid that you just haven't enough information to completely understand all of my previous posts. Many of the particular comments I made are based on things you are not yet aware of. My purpose in many of those comments was to interest you in plodding through the details so that you could see the view from the other side of the jungle.

I am sorry but I don't think the direction you have chosen will lead anywhere useful. The first step is to fully understand why my fundamental equation has to be true and exactly what is behind that issue. I knew enough fundamental physics to realize that the equation possessed deep promise long before I was able to prove it had to be valid. And even when I was able to prove that it was valid, with my background in theortical physics it still took me another five years before I managed to wring out the first solution.

If you want to do it all by yourself, starting at your age, you will be an old old man before you will even begin to see the light and I doubt you will have the patience to stay the path. I think you need to understand exactly what is behind the equation and then see at least that first solution in order to comprehend where this thing is going. The concept is quite simple but fulfilling the promise of that concept is not a simple issue at all. You must be able to understand how deep this issue runs. If what I am telling you is correct, there must be an extremely complex path from here to there. The universe is a very complex thing.

Even with my help, it isn't a trivial issue to be mastered in an afternoon. There really is a swamp of ambiguity we have to cross before reaching the dry land on which we can seriously lay the foundation of that first equation. And even then, there is a jungle of possible misunderstandings to cross before we reach that open meadow where we can see beyond the trees. We need a number of definitions yet before we can start to speak rationally about the consequences of that equation.

Now is really not the time to go wandering off by yourself.

Talk to me, please -- Dick

 

[baffledMatt]

Wow,

Dr Dick, I must say I heartily agree with you that it is impossible to discuss what you have presented unless we all understand it.

Great.

My question to you is therefore this:

What did you hope in posting it here in the first place?

First of all, most of us here do not (yet!) have the training or experience to deal with the mathematics or the logic of your argument. And besides, it is incredibly difficult to get across such complicated ideas with this kind of medium. This is why scientists still prefer to stand around chalk-boards when discussing their ideas.

And of course, there are also the ones who understand it perfectly and, perhaps because they see how silly it all is, are staying well out of it.

Is this just meant to be some big ego trip for you?

Matt

p.s. I hope nobody (else) gets offended by this as I appreciate what I'm saying can be interpreted as 'Don't talk to us we're a bunch of thickies'. This is not what I mean!

 

[baffledMatt]

Plus I have some observations to add:

P(B) cannot be dependent on the labeling procedure (the must yield results consistent with the actual distributions of the elements of B in C independent of the chosen mappings). It follows that, since adding a number "a" to the value of every xi reference label does not alter the reference relationship between any xi and its associated element of B in any way at all, it cannot change the function P in any way. Thus if we replace every xi in that expression of with (xi) and look at the resultant calculated value of the probability as a function of a, we know that P(a+a) = P(a). This implies that:

$$\frac{P(a+\Delta a) - P(a)}{\Delta a}\,\,=\,\,0.$$

How do you go from P(B), which is probability of a 'specific B' (whatever you mean by that - see a later comment) to this equation for the derivative? Is 'a' meant to be a real number or a member of B? In the former, what do you mean by P(a), and in the latter, what do you mean by dividing by $$\Delta a$$?

$$\sum_i^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa_x \vec{\Psi}\,\,,\,\,\sum_i^n \frac{\partial}{\partial\tau_i}\vec{\Psi}\,=\, i\kappa_{\tau}\vec{\Psi}\,\,and\,\,\frac{\partial} {\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$

What is $$\kappa_x$$?

What is $$n$$?

You define B as:

B is a set, defined to be an unordered finite collection of elements of A

But you also say that B is not a subset of A. Does this mean that $$x\in B \Rightarrow x\in A$$
is not true?
Finally, could you please define what you mean by "Probability of any specific B"?

Perhaps people would have a better chance understanding you if you were a little clearer.

Matt

 

[PFanalog57]

Russell,

I am sorry to see you go. When I said that you were beginning to understand what I am doing, I didn't really expect you to run off to think about it all by yourself. I had much more background in physics when I got to where we presently are and I wandered in that wilderness for many years before I saw the light. I am afraid that you just haven't enough information to completely understand all of my previous posts. Many of the particular comments I made are based on things you are not yet aware of. My purpose in many of those comments was to interest you in plodding through the details so that you could see the view from the other side of the jungle.

I am sorry but I don't think the direction you have chosen will lead anywhere useful.

[...]

Now is really not the time to go wandering off by yourself.

Talk to me, please -- Dick

With all due respect ...don't, jump to conclusions Dr. D. :surprise:

How can Maxwell's equations for gravity not be useful?

 

[PFanalog57]

And of course, there are also the ones who understand it perfectly and, perhaps because they see how silly it all is, are staying well out of it.

:zzz:

 

[PFanalog57]

Dr. D. I also found this website that presents your ideas/discoveries:

http://home.jam.rr.com/dicksfiles/reality/PREFACE.htm

The category I refer to as postulated relationships are usually referred to as theories. Inventing theories and developing their logical deductions is the central work of the most esteemed in the scientific society. Errors in those theories are discovered through comparison to reality: i.e., experimentation. The process of designing and performing the experiments critical to a theory may take time but it is, none the less, a well understood process and sufficient diligence will eventually discover those errors.

That brings us to the errors in assumptions. Errors in these assumptions are a completely different issue. The primary problem with finding errors in the kind of assumptions I am referring to here is that the scientist usually has no idea of what they are. Remember, the kind of assumptions I am referring to here are those things which he assumes are true without thinking about them at all. If one reviews the history of science one will find that most of the major breakthroughs can be seen as flowing from the realization that their predecessors had made some subtle unexpressed assumption which was actually without foundation. Errors in these kinds of assumptions usually betray their presence by allowing seemingly contradictory results to be well defended(2).

http://home.jam.rr.com/dicksfiles/reality/CHAP_I.htm

I will make much use of Mathematics without defense or argument. In essence, it is quite clear that mathematicians are very concerned with the exactness of their definitions and the self consistency of their mental structures. I suspect mathematics could probably be defined to be the study of self consistent systems. At any rate, their concerns are exactly those which drive my work; I am merely attacking a slightly different problem. I hold that the reason mathematics is so important to science is that we are attempting to map the real universe (which is assumed to be self consistent) into a mathematical system (which is self consistent by construction). In accordance with this view, I will hold that the fundamental mathematical relations require no defense by me.

Part II -- The Problem:

What follows was begun, back in the 1960's, with the realization that human intelligence is totally isolated from the outside world. The only contact which exists is via interactions, the real meaning of which cannot be known a-priori. Our mental image of the universe is constructed from data received through mechanisms (our senses) which are also part of that image. I think any scientist in the world would hold it as obvious that one could not possibly model the universe until after some information about that universe were obtained. The problem with this position is that we cannot possibly model our senses (the fundamental source of that information) until after we have modeled the universe.

This may appear to be another silly presentation of the old chicken-egg paradox but it really isn't. There is a fundamental problem here which needs to be addressed as it points out a very important aspect of our mental image: we have constructed a mental image of the universe given totally undefined information transcribed by a totally undefined process. How can we hope to comprehend the possible errors in that image if we cannot comprehend a mechanism through which such an image can be constructed.

The first step we must take is to admit the possibility of error. I have found that people will admit of the possibility of error in their mental image of the universe but I have not met one who will easily admit of the possibility of error in their mental image of reality itself; they do not find that issue sufficiently abstract to honestly consider. Come, try to be objective: you either have absolute faith in your perceptions of the universe or they are subject to examination. To set any part of those perceptions above examination is to scuttle rational science.

I hold that, if I can show the existence of the fundamental transform for all conceivable representations of true reality, then my alternate reality can be held to be a totally valid representation of true reality. It should be clear to the reader that, for all intents and purposes, what is enclosed in the dotted line becomes identical with my alternate view of our senses and no data provided by our senses via any experiment can invalidate my alternate representation of reality.

Thus it is that I come to define reality to be a set of numbers. Clearly, the fundamental transformation must exist for any communicable concept of reality. That is, any concept which is communicable can be represented by a set of numbers as the communication itself can be so represented. What is of significance here is that, under this representation, no assumptions (other than that it be a communicable concept) have been made concerning the true nature of "reality". All possibilities are included in the representation and, at the same time, the representation can be clearly regarded as "exact": i.e., very specifically defined. The nice thing about an exact definition is that it is only after one has accurately defined a concept that one can begin to speak of truth with regard to that concept. It is only truth by definition which can be spoken of with any confidence worthy of abstract reason.

What follows from here are truly "the consequences of defining reality" . Fundamentally, what I will present is often referred to as a tautology: strictly, "a needless repetition of the same idea in a different word, phrase or sentence". It would indeed be needless repetition were everyone brilliant enough to see those consequences; however, any decent education in mathematics will assure one that the consequences of definition can easily far outstrip the capabilities of common intuition.

Everything I will present will be true by definition. It thus becomes very important that my definitions be clearly understood and that my deductions be followed with extreme care. Even the smallest error is of extreme consequence as, in accordance with the world view of modern science, under the constraints I have placed on myself, I should be able to deduce absolutely nothing of significance! Either my deductions are in error or the truth of my results is absolute.

http://home.jam.rr.com/dicksfiles/reality/CHAP_II.htm

http://home.jam.rr.com/dicksfiles/reality/CHAP_III.htm

http://home.jam.rr.com/dicksfiles/reality/CHAP_IV.htm

http://home.jam.rr.com/dicksfiles/reality/CHAP_V.htm


It will take a while to absorb this information Dr. D. Thanks for putting it on the internet.