Why you should like my perspective

[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![/color]

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".) [/color]

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![/color]

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

Check your expectations against C![/color]

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

<br /> P(\vec{x},t) = \vec{\Psi}^{\dagger}(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv<br />
​

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}.[/color]

 

[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?

<br /> \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.

 

[PFanalog57]

Here are more relevant quotes:

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

If you take the trouble to follow (and understand) what I present, you will find that what I present is an alternate explanation of the universe which, by construction, fits every fact exactly without any recourse to those facts at all. In essence, I do exactly what any competent scientist would hold as impossible: I construct a model capable of modeling any closed body of undefined data which is guaranteed to fit that data exactly.

The only instance where equation 1.22 cannot enforce any arbitrary rule is the case where two arguments (two knowable numbers in a explicit observation) are to be identical. It was to prevent exactly that occurrence within our knowable data that the(tau) axis was originally introduced; it follows that equation 1.22 is a useable representation of any conceivable rule in our model of the universe. For those who are confused, note that what has actually occurred is that I have shown that it is always possible to conceive of unknowable data such that equation 1.22 will constrain the universe to exactly what is actually seen no matter how arbitrary that universe may be.

 

[Doctordick]

Matt,

I notice in your profile that you are a "Ph.D. student"; could I ask what field you are studying?

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.

And it is impossible to present something complex unless one has some idea of his audience's comprehension of what he is saying: i.e., if nobody responds to a post just how am I to know what they understood or didn't understand?

Why do I post here? It's a math physics help forum isn't it? Perhaps I would like a little help understanding the physics community's inability to understand what I am saying. And, as a matter of fact, I think it has helped quite a little.

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.

The mathematics is only slightly beyond high school calculus and easily explained if you understand calculus. And I find it difficult to understand your complaint with the logic. Logic is logic! All one has to do is carefully think about what is being said.

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.

That would be great! You know, in my life, I have brought this thing up with a good dozen Ph.D. physicists. Fifty percent don't even want to talk about it to start with and the rest of them either tell me it's over their head (which I interpret to mean they realize they don't want to talk about it) or, after I get to about where we are in this thread now, they just stop talking to me and won't discuss it anymore. I have no idea what is going on in this third groups mind. I do suspect that what has happened is that they "know" I can't possibly be right and can't actually see any error themselves and they become afraid I might turn them into "crackpots".

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.

Well, if that is the case, I sure would appreciate someone pointing out an error. They sure seem to be willing to spend time debunking the other "crackpots". Why do I get slighted?

And I cannot comprehend how you can think it's an ego trip to bear the brunt of derisive comments and be categorized as a crackpot?

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 \Deltaa?

I do not understand what you are having a problem with. Did you read the definition of B and the construction of the numbers x_i? And a is just a number added to all x_i and \Deltaa is a change in a. Do you understand the definition of a derivative? In P(a) I have merely suppressed writing any of the arguments of P other than a itself since I am, at this particular point, concerned only with the a dependence.

The symbols \kappa_x, \kappa_{\tau} and m are all just real numbers. Substitute those results into the definition of P and you will get exactly the result that the derivative of P with respect to a is zero. That makes them solutions to the constraint that derivative of P with respect to a is zero.

The point on the x-axis called x_i is a reference to an element of B and as such it can also be interpreted as a reference to an element of A. But the reason I say B is not a subset of A is that B is nothing more than a collection of elements of A. It is possible that A does not contain any repeated identical elements while a B might. Technically I don't believe B could, in that case, be considered to be a subset of A. I guess it is all in your interpretation of the rules.

Finally, could you please define what you mean by "Probability of any specific B"?

It is nothing more than a measure of the expectations of that specific B occurring as per the theory which is to explain A. I use the term probability as that is the term usually used to refer to a measure of expectations. Absolutely the only constraint I put on that "probability' is that it is a number bounded by one and zero. Other than that, the theory which is to explain A can define it anyway it wants.


I could be a lot clearer if I had a little feed back on what is being understood and what is being missed.

Have fun -- Dick

 

[Doctordick]

Hi Russell,

I was hoping to keep that website away from you until after I proved to you that the fundamental equation had to be valid and why it had to be valid. Most of what is in that website I wrote well over twenty years ago and I really don't like the idea of editing it as to do so gives the appearance of "fixing up the problems people point out", a typical tact of crackpots.

However, I have discovered, since posting it on the web, that there are many ways that what I am saying can be misinterpreted. Actually, I have found it quite astonishing how much people can distort what that paper says. I have a very strong suspicion that no one really reads it. I think they just scan it, picking up bits and pieces here and there. Since many of the conclusions I reach will never be found in any professional journal, it is very easy for them to conclude I am a crackpot.

At any rate, the issue is moot now. I would comment that the main page can be reached via:

http://home.jam.rr.com/dicksfiles/

Clicking on the picture of the book will take you to the presentation.

One thing I will say is that you have chosen to quote some significant points which makes me think you might be reading it more carefully than others. Nevertheless, please let me know about anything you find difficult to understand or anything in the presentation which appears to you to be unnecessary to say. Everything I put in there, I put in for a reason and it is entirely reasonable that you might miss something subtle. Don't think of it as a criticism of your ability to follow me but rather as an admission by me that I am not a "great communicator".

I am sure that you have noticed that my presentation of the basic argument for the fundamental equation in this thread is quite different from the presentation in the original paper. Which one is better depends on how it is taken by the reader. Anything which is really true can be explained a "dozen ways from Sunday" so please help me make it clearer.

As I said where you quoted me, "It thus becomes very important that my definitions be clearly understood and that my deductions be followed with extreme care." As far as I am concerned, the worst possible outcome would be for you to become convinced that I am right without really understanding some subtlety imbedded in the presentation. Please make sure each and every step makes complete sense to you.

If I am a crackpot, I want to know about it more than anyone. If I have made an error, someone will discover it someday. If I have actually made a stupid error, I would like to know about it before I die. As I said, "either my deductions are in error or the truth of my results is absolute." I would also like very much to discuss the philosophical consequences. It seems to me that there are some very interesting issues there.

Just as an aside, I have always found it funny that my physics diploma says specifically that I was awarded the degree of "Doctor of Philosophy" while the physicists invariably discount my attack with the comment "that's not physics, that's philosophy." Who's lost sight of what?

Have fun -- Dick

 

[baffledMatt]

I notice in your profile that you are a "Ph.D. student"; could I ask what field you are studying?

The short answer is: condensed matter theory. (Only just started though)

And it is impossible to present something complex unless one has some idea of his audience's comprehension of what he is saying: i.e., if nobody responds to a post just how am I to know what they understood or didn't understand?

Why do I post here? It's a math physics help forum isn't it? Perhaps I would like a little help understanding the physics community's inability to understand what I am saying. And, as a matter of fact, I think it has helped quite a little.

I think part of the problem is that on a forum if people don't understand something they are a lot more likely to leave it alone as opposed to try and ask questions. I'm hoping to avoid that trend where possible.

And I find it difficult to understand your complaint with the logic. Logic is logic! All one has to do is carefully think about what is being said.

Ever read anything by Descartes? Apparently that's 'just logic', but I defy anyone to say that his writings are easy to understand. The problem is that if you try to present a purely logical argument the thread of what you are trying to say can easily get lost. It would be easier if you put in little wordy explanations in between to help us along.

Of course, I'm not asking you to replace the formal argument with handwaving, I'm asking you to help it along a bit with a few well thought out analogies/examples.

That would be great! You know, in my life, I have brought this thing up with a good dozen Ph.D. physicists.

Hehe, sounds to me what you need are a dozen good PhD physicists!

I have no idea what is going on in this third groups mind. I do suspect that what has happened is that they "know" I can't possibly be right and can't actually see any error themselves and they become afraid I might turn them into "crackpots".

It might be because they are comfortable to believe that you are wrong but can't be bothered to think it through into a thorough argument - even more so when the idea is one as abstract as yours. I can empathise with this in the sense that you can't take time to try and debunk each and every theory that comes your way.

Well, if that is the case, I sure would appreciate someone pointing out an error. They sure seem to be willing to spend time debunking the other "crackpots". Why do I get slighted?

Because there might not be an error? Possibly, but until I think I understand your arguments correctly I won't try to judge. (By the way, I apologise if I never reach this point, but I hope you appreciate that I have enough of a job trying to understand my own subject!)

I do not understand what you are having a problem with. Did you read the definition of B and the construction of the numbers x_i? And a is just a number added to all x_i and \Deltaa is a change in a. Do you understand the definition of a derivative? In P(a) I have merely suppressed writing any of the arguments of P other than a itself since I am, at this particular point, concerned only with the a dependence.

Ok, that's all I needed. As i have said before, if people are to understand you properly you need to try and be crystal clear about these things.

The point on the x-axis called x_i is a reference to an element of B and as such it can also be interpreted as a reference to an element of A. But the reason I say B is not a subset of A is that B is nothing more than a collection of elements of A. It is possible that A does not contain any repeated identical elements while a B might. Technically I don't believe B could, in that case, be considered to be a subset of A. I guess it is all in your interpretation of the rules.

I'm still not sure what you mean by 'repeated elements'. I thought each element of B was simply an element of A, so it is not clear how repetition comes into it. Perhaps you could give me a specific example to clarify?

It is nothing more than a measure of the expectations of that specific B occurring as per the theory which is to explain A. I use the term probability as that is the term usually used to refer to a measure of expectations.

Yes, but all these words like 'probability', 'measure', 'expectations' need to be defined.

Absolutely the only constraint I put on that "probability' is that it is a number bounded by one and zero. Other than that, the theory which is to explain A can define it anyway it wants.

Perhaps what you should do is define P(B) through one of the equations you have presented, demanding that P(B)\in [0,1] or whatever, and then only later properly justify calling it a 'probability'.

I could be a lot clearer if I had a little feed back on what is being understood and what is being missed.

Well, I hope this has helped.

Matt

 

[baffledMatt]

I have been looking over the first two chapters and wondered if you could clarify the following:

NB. The quotes are all taken from chapter 1 and 2 of the book. The equations obviously didn't cut-and-paste, but I assume you will have no trouble looking them up in the original text. Hope this doesn't cause confusion!

What I am actually going to do is to suggest that, were I all knowing, there would exist data in the universe which would provide the information necessary to separate the repeated patterns into identifiably different cases (since I can not know this information as the patterns are in fact actually identical, this additional information is clearly unknowable: i.e., a total figment of my imagination).

As it is a figment of your imagination - i.e. does not necessarily have to exist - the theory should work just as well without it, however,

Let me add additional unknowable data such that every possible observation consists of a unique pattern even after any arbitrary element is removed from that observation. If that fact is true, then the value of the removed element may be determined via the rule and the remainder of the pattern. The situation may be represented mathematically in the form

Now you are asserting that this unknowable data exists and you use it to write your first equation.

All conceivable algorithms may be seen as operations defining the transformation of one set of numbers into a second set of numbers. It follows that any algorithm may be represented by the following notation:

where the arrow symbol indicates that the object is a set of numbers.

You are assuming that this algorithm exists (which you have not proved because it requires the existence of your made up unknowable data) and that it may somehow be expressed as a set of real numbers, which you have not proven to be possible.
Also, are these algorithms unique?

If we define the adjoint(7) algorithm, , to be identical to the original algorithm except that each and every number generated by the original algorithm is replaced by it's complex conjugate, then we may define the scalar product

What does the 'adjoint of the algorithm' defined in this way mean?

The same mechanisms we used to define lead to the conclusion that we can define and which will lead respectively to P1 and P2. That being the case, equation 2.2 implies that we may write

If we substitute this expression for in equation 2.1, left multiply by and integrate over all from set #2, we will obtain

But equation 2.2 applies to probabilities. You assert that P is only interpreted as a probability, so you must prove equation 2.2 is true for P.

Equation 2.3 with 2.2 implies that the psi (and their adjoints) commute.

We can assure this will not occur by requiring that be asymmetric with regard to exchange of observable arguments

What exactly do you mean by this?

Finally, I'm not sure if I understand you properly, but you seem to be saying from the very first equation that given all the data (including unknowable - which you assert does exist so therefore if you were 'allknowing' you will know even this) and the algorithm - which is for the data plus one other element of data - you will know what that last piece of data must be. This is all very deterministic, so where does any concept of probability come in? Surely what you are trying to describe is a sort of 'hidden variables' theory so there is no place for probability at a fundamental level.

Matt

 

[PFanalog57]

If I have made an error, someone will discover it someday.

Dr. D. here are more brief quotes from your book:

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

Doctordick:

The final expression above yields exactly the correct gravitational red shift. This assures us that any geometry which yields gravity as a pseudo force must also yield the standard gravitational red shift; or, alternately, gravitational red shift is not a valid test of Einstein's general theory.(19)

[...]

It follows that the equivalence of gravity and acceleration not only requires the speed of light to appear to slow if the experiment is observed from a higher gravitational potential, but it also implies any lower object will appear to proceed in the tau direction at a slower rate. This immediately suggests that we should be using Fermat's principle to establish the metric which will yield the proper geodesics: i.e., we should consider the phenomena of refraction.

[...]


I have certainly shown gravitational forces can be reduced to geodesics in my geometry by virtue of the fact that I have just done so. The fact that my result is not exactly the same as that obtained from Einstein's theory is not too troubling. It is possible that I have made a subtle deductive error in the above as none of my work has ever been checked by anyone competent to follow my reasoning; however, in the absence of an error, my result must be correct as it is deduced and not theorized.

[...]

Though reducing gravity to a pseudo force via geometric effects is a nice exercise, I would also like to point out that it does not necessarily lead to the most convenient geometry. In fact, as may be seen above, the compulsion to make the speed of light constant in all frames is actually the source of the complexity of general relativity. If we relax that constraint (which is easy as time is not a measurable variable anyway) we can attribute gravity to a refractive effect and return to a Euclidean geometry, which is probably the single most convenient geometry conceivable.

The geometrical description of gravitation has much
justification. But what about the electromagnetism? The electromagnetic field is different in character from gravitation. Must electromagnetism be considered as an independent physical field, with its own
characteristic dynamics?

Will the electromagnetic field be forever described as
non-geometrical? Or is it possible to describe both the
electromagnetic and gravitational fields as aspects of the curvature
of spacetime? Or a complementary formulation that describes
gravitation as an aspect of electromagnetism? The variation of the
curvature of spacetime at one point can also be correlated with the
electromagnetic field at one point. The electromagnetic field can be
described relativistically by the Maxwell tensor F^uv with electric
and magnetic field strengths E and B...?

Gravity = pseudo force?

Very interesting!

 

[Doctordick]

Russell,

You are doing exactly what I was afraid you would do: you are scanning my paper without being careful to understand it. As I said earlier, it has to be followed step by step as a logical argument. If one takes the approach you are currently using, you will be looking at the conclusions without the defense thus thinking with the standard conventional paradigm. From the conventional paradigm, the conclusions I come to are ridiculous and totally impossible to defend. But neither is modern physics defendable from the astrological paradigm. The only way to argue against my proposition is to show an error in the logic.

So long as you do not understand the paradigm, you will not understand my presentation. Nevertheless, I will try and explain to you why the comments you are quoting yield no real difficulties.

… or, alternately, gravitational red shift is not a valid test of Einstein's general theory.(19)

However, you omit to quote the reference: "19. It is well known that the gravitational red shift is directly required by conservation of energy and is thus not a true test of Einstein's theory of general relativity." It is a test of Einstein's theory only from the perspective that it does not invalidate his theory: i.e. any theory which does not yield a gravitational red shift is invalid because that red shift is a direct consequence of conservation of energy. Or another way to put the issue is to point out that any theory satisfies conservation of energy will also yield the gravitational red shift thus it is support of Einstein's theory only in the utter absence of any competitive theory.

With regard to the Idea of "Field Theories", I would like to point out Einstead's comment to your thread on sci.physics.research:

Since you raised the topic with the subject header, it's both instructive and revealing to see what Einstein, himself, had to
say on the subject of quantum gravity at the end of his life:

"One can give good reasons why reality cannot at all be represented
by a continuous field. From the quantum phenomena it appears to
follow with certainty that a finite system of finite energy can be
completely described by a finite set of numbers (quantum numbers).
This does not seem to be in accordance with a continuum theory,
and must lead to an attempt to find a purely algebraic theory for
the description of reality. But [sic] nobody knows how to find
the basis of such a theory."

I will point out the "Field Theories" have their origin with Newton's gravitational "field". Even Newton, who invented the idea, said that the gravitational field did an excellent job of explaining gravity even though action at a distance is clearly impossible. (I am paraphrasing him as I do not remember his actual words or where I originally read them; but, believe me, he was well aware of the illogic of "field theories".

Newton was also the source of the idea of forces through geometric effects. Things like centrifugal force or coriolis forces are often called "pseudo" forces as, from Newton's perspective, they arise out of the fact that the coordinate system is not an "inertial" system. Pseudo forces share a very simple characteristic: the forces are always proportional to "inertial mass". This is a consequence of a very simple fact: the observed acceleration is entirely due to the fact that it is the coordinate system which is "accelerating" and not the object being observed.

You drive around a corner with your car and that object on the seat next to you (which, in the absence of a force, follows a straight line; not the path of the car) appears to be pulled to the side by "centrifugal force"! That apparent force, if it is to obey F=ma, must be proportional to m. Well, the fact that the gravitational force is proportional to mass leads one to the idea that it also is a "pseudo" force.

In all innocence I would like to point out something subtle about that idea. Gravitational forces only occur in the presence of "other masses" whereas all the other "pseudo" forces are entirely due to acceleration of the coordinate system and require no other entities be present. That is to say, centrifugal force and coriolis forces can be created and/or eliminated in any problem merely by changing the coordinate system being used. Gravity is not quite the same thing; there are other presumptions which must be made such as the "fact" that only specific geometries may be used to describe reality.

Add to this the fact that the mechanics of creating geometries which change forces into geometric effects is a full blown field of classical mechanics. Go back and look at "Hamiltonian" mechanics, a direct consequence of exactly this view of solving mechanics problems. The relationships developed in that area are the direct precursors to the mathematical relationships behind quantum mechanics. Without understanding this stuff, one can not understand modern physics. When I say "understand" modern physics, I don't mean being able to do the math or understand the meanings and implications of the notation; I mean comprehension of why these things are held to be fundamental relations central to physics itself.

Many people take understanding modern physics to being able to intuit the correct relationship to use to solve a particular problem. In my head, that kind of stuff is little more than practice at rote memory tricks. What are we trying to do here? Develop better "rote memory" tricks to solve problems or are we trying to understand why these tricks work?

The idea that "Field Theories" will explain everything is a rather ignorant attitude considering the arguments against them as being a truly fundamental fact. The complexity of the "fixes" required to maintain the current paradigm is also getting close to those precopernican efforts to adjust the design of the spheres that held the stars and planets. Newton really asked a very simple question (suppose the moon is actually falling) and got ridiculed for it. There is little difference between his position and mine.

No one likes to accept the idea that those personal theories they have put years into studying and learning are not going to yield satisfactory results. Do you think they are going to jump off that band wagon when 99.99% percent of the authorities are still riding? I think Einstein himself essentially admitted that the only reason his theory stood up was that it had no competetion (see his quote above)! This whole issue is little more than maintaniance of the value of expertice which took a lot of years to accumulate.

The geometrical description of gravitation has much justification. But what about the electromagnetism? The electromagnetic field is different in character from gravitation. Must electromagnetism be considered as an independent physical field, with its own characteristic dynamics?

Will the electromagnetic field be forever described as non-geometrical? Or is it possible to describe both the electromagnetic and gravitational fields as aspects of the curvature of spacetime? Or a complementary formulation that describes gravitation as an aspect of electromagnetism? The variation of the
curvature of spacetime at one point can also be correlated with the electromagnetic field at one point. The electromagnetic field can be
described relativistically by the Maxwell tensor F^uv with electric
and magnetic field strengths E and B...?

Essentially, what you are pointing out here is the complexity of trying to explain everything by "field theories" and "geometric effects". As the success of QED has pointed out, the exchange of virtual particles is a much more powerful attack on explaining forces. Please note that QED is not a field theory at all but rather a method of calculating the answers a "successful" field theory must produce; quite a different thing. QED is based directly on quantum mechanics and exchange effects. Exchange forces are a consequence of quantum mechanics and have every indication of being a much more general approach than anything before them.

I really wish you would go back to chapter I and get the details of that presentation under your belt before going on to the solutions my fundamental equation which, I assure you, you do not yet understand.

When I was young, during WWII one would often hear the phrase, "he doesn't know sh*t from shine-ola!" I am sure you comprehend the meaning of the comment; however, have you ever seriously thought about how we tell the difference between things on a fundamental level? Seriously, how does one tell the difference between an electron and a Volkswagen? That is not a joke question; it is a problem fundamental to any analysis of anything and the correct answer is extremely enlightening.

How about we get back to how you know the fundamental equation is right? If you don't understand that, then reading the rest of my stuff is a waste of time!

Have fun – Dick

 

[PFanalog57]

Russell,

Essentially, what you are pointing out here is the complexity of trying to explain everything by "field theories" and "geometric effects". As the success of QED has pointed out, the exchange of virtual particles is a much more powerful attack on explaining forces. Please note that QED is not a field theory at all but rather a method of calculating the answers a "successful" field theory must produce; quite a different thing. QED is based directly on quantum mechanics and exchange effects. Exchange forces are a consequence of quantum mechanics and have every indication of being a much more general approach than anything before them.

I really wish you would go back to chapter I and get the details of that presentation under your belt before going on to the solutions my fundamental equation which, I assure you, you do not yet understand.

When I was young, during WWII one would often hear the phrase, "he doesn't know sh*t from shine-ola!" I am sure you comprehend the meaning of the comment; however, have you ever seriously thought about how we tell the difference between things on a fundamental level? Seriously, how does one tell the difference between an electron and a Volkswagen? That is not a joke question; it is a problem fundamental to any analysis of anything and the correct answer is extremely enlightening.

How about we get back to how you know the fundamental equation is right? If you don't understand that, then reading the rest of my stuff is a waste of time!

Have fun – Dick

There is also a problem with postulating a fixed background of Euclidean space. It probably does not correspond to what is real. If reality is self contained,it is logically consistent. If reality is not self contained, it becomes an infinite system/problem of explanations within explanations. The goal is to eliminate the infinities, and arrive at sensible answers. If my interpretation is correct.


Imagine a homogenous liquid or "fluid" as the fundamental "stuff" of reality. Wheeler's "quantum foam concept?"

The fluid has a small distortion or vortice moving in the fluid. How
can the speed of the "vortice" in the fluid be measured?

Only by inserting an object in the fluid and creating an absolute frame
of reference. That would be breaking the rules of course, because no
outside elements, or fixed backround can be introduced into, or compared with, the fluid, since there is nothing outside of reality. The only way to
measure the speed of the vortice is by comparing its motion with
another vortice within reality itself.

If forces of nature are really just distortions in the space-time
fluid, then the motion of a space-time distortion can only be compared
to the motion of another distortion.

Thanks for your patience Dr. D. ; back to the fundamental equation next post.

 

[baffledMatt]

Dr Dick,

I've been doing some thinking about your work and I think I have the beginnings of a vague comprehension of what you have presented, so I was hoping I could share this with you to test-the-water and see if I am on the right track:

It seems that you have started from some very basic definitions about information and measurement (with an abstraction of what are measurements and what is knowable about them) and building on these simple premises go on to derive your main equation from which you claim you can derive many of the standard results of modern theoretical physics.

Now, by applying certain symmetries and taking various limits we are able to derive all sorts of things. You have demonstrated that we can obtain Dirac's equation and GR from this, but I wonder how many other equations can be derived? Is it not the case that if we push the equations in the right way we can obtain any equation that is consistent with your initial definitions of measurement/algorithms etc, so potentially any viable 'physical' theory? I would expect it to be the case given the very rigorous approach you have pursued (give or take the sort of things I pointed out in my last post).

By a strange coincidence a colleague of mine told me today about a very similar thing which apparently happens in conformal field theory. Here we are also dealing with the most general abstract mathematical tool we can think of and, amongst other things, this can be used to derive critical exponents for systems near a critical point (I assume you know what I am talking about but if you want me to remind you what these are just ask.) however, the thing is that it will derive all 'viable' combinations of critical exponents. It is then the job of the physicist to make theories on how the method should be pushed in order to obtain the ones s/he wants. Often this amounts to looking at the table, saying 'ooh, 187/91, that's pretty much what i wanted, now to think of how the physics might push the mathematics to give me this group of exponents'. Do you see what I am getting at? The mathematics you have presented gives us a formalism that any mathematically consistent physical theory must obey. However, it is then the job of the physicist to know which of the solutions apply to which physical process. So, assuming what you have is correct, it will give us all the physics we observe plus possibly a whole lot that we don't.

So, assuming I am sort of on the right track so far, I would propose that wheras your formalism (if you would allow me to call it that) may be a very useful thing mathematically, it tells us little about physics. We need to put physics into it to obtain any information about our universe.

Does this make sense? Or have I missed the point completely?

Matt

 

[baffledMatt]

however, have you ever seriously thought about how we tell the difference between things on a fundamental level? Seriously, how does one tell the difference between an electron and a Volkswagen?

Hmm, that's a funny thing isn't it! You would have to think up a set of measurements you could make on your object which would determine which one of these objects it is. (But now I think we run into trouble, because wouldn't we have to then define each object as precisely the entity which will give us this set of measurements?) Assuming we get through this unscathed, I would think that you tell the difference by determining what measurements will differ between the two. The only problem is that in a sense you have again defined the difference to be this. Or is this not a problem? Also, if your measurements will be the same for each entity that means these things are equivalent and are - for all you can tell - the same thing, so you should reject the existence of one of them to build a well defined picture of the universe.

That is not a joke question; it is a problem fundamental to any analysis of anything and the correct answer is extremely enlightening.

Hmm, somehow I don't feel enlightened so I guess I've missed the point yet again?

Matt

 

[Doctordick]

Sorry if I seem to be difficult to understand.

What I am trying to do is to get you guys to think on an abstract level. The most difficult answer to fight is one which is accepted as true without thought. You really have to understand that our heads are just chock full of ideas about which we never think. Our thoughts are focused in directions which are consequences of things we "know" are true. When I asked how one tells the difference between an electron and a Volkswagen, I had that very issue in mind.

For the moment, pretend the common everyday mental image of Einstein's space time is absolutely correct and I tell you that I want to talk about what to expect if I knew an event had occurred at some specific point in that coordinate system. Most scientists would say, "well that depends on what kind of event it was!" So the question then arises, "what was it?" My lab assistant says it was an electron but my secretary said it was a Volkswagen. I can't go back in time and look for myself (if that could really help) so I quizzed them for more information. Well they both agreed it came down a huge highway so I decided it must have been a Volkswagen. But then he said the highway was the inside of a glass tube many times larger than the event. So maybe it was an electron; I guess you could think of the neck of an electron gun as a highway. She said she still thought it was a Volkswagen and that the street lights reflecting off the rain made it look like a big glass tube.

The example is clearly silly but what it points out is that the identification of an event is a constraint on acceptable surrounding events. When we define an event to be an electron (or a Volkswagen) we are actually using the tag to constrain surrounding events to a known collection of expectations of already defined events. In fact, it is usually a very vast collection and generally impossible to delineate by any mechanism other than by presuming the listener is familiar with the general nature of the associated events indicated by the very act of naming the event of interest.

The central issue here is that, if we explicitly specify our expectations for events at all the coordinates surrounding the event of interest, we have in fact, identified the event of interest; putting a name on it is no more than a convenient reference tag. What is important here is that the specification of expectations in general is all we need to know! Naming events is actually a route to compartmentalization; a path I wish to avoid at all costs.

So, assuming I am sort of on the right track so far, I would propose that whereas your formalism (if you would allow me to call it that) may be a very useful thing mathematically, it tells us little about physics. We need to put physics into it to obtain any information about our universe.

In a sense, you are absolutely right: it tells us nothing about the universe around us; however, it tells us quite a bit about physics. As I commented in my opening of Chapter I,

There is a subtle aspect to science unrealized by many scientists. When one designs an experiment, one must be careful to assure that the result is not predetermined by definition: that is, that one is actually checking something of significance. A simple example of what I am talking about can be illustrated by thinking about an experiment to determine if water runs downhill. If one begins that experiment by defining downhill with a carpenter's level, one has made a major error. They have clearly predefined the result of the experiment as downhill has been defined to be the direction water runs (the bubble being the absence of water). In such a case, it is rather a waste of time to finish carrying out such an experiment no matter how well the rest of the experiment is designed. It should be clear that to do so is nothing more then checking the consistency of one's definitions.

As a graduate student I was very bothered by the failure of the faculty to be careful about their definitions. The whole thrust of my thinking was begun in an attempt to get things well defined. Everything I present is a direct consequence of careful definition (definitions constructed carefully to insure they place no constraint on the possibilities). I would not have been surprised at all if nothing new had come from the effort; all I really expected was a little clarity. But what I discovered was that most of what the physicists told me was true by definition. Now I found that quite astonishing. Essentially, physics tells us nothing about the universe; or at least very little. In many respects it is little more than a story; sort of like how the leopard got its spots: its elephants all the way down.

Now I don't ask you to believe me; I ask you to look at my definitions and carefully consider (with me) the consequences of those definitions.

As I said in message #64, "The next step is very important and, I think, needs to pretty well be examined as a conceptual whole." Since my original paper is now available, I refer you to part IV of Chapter I where I show that absolutely any rule may be reduced to the form F=0. I will read that section over carefully and post a few comments about issues which might be easily missed on a simple reading of that section.

Have fun -- Dick

 

[baffledMatt]

For the moment, pretend the common everyday mental image of Einstein's space time is absolutely correct and I tell you that I want to talk about what to expect if I knew an event had occurred at some specific point in that coordinate system. Most scientists would say, "well that depends on what kind of event it was!" So the question then arises, "what was it?" My lab assistant says it was an electron but my secretary said it was a Volkswagen. I can't go back in time and look for myself (if that could really help) so I quizzed them for more information. Well they both agreed it came down a huge highway so I decided it must have been a Volkswagen. But then he said the highway was the inside of a glass tube many times larger than the event. So maybe it was an electron; I guess you could think of the neck of an electron gun as a highway. She said she still thought it was a Volkswagen and that the street lights reflecting off the rain made it look like a big glass tube.

So, would you say that my comment earlier:

The only problem is that in a sense you have again defined the difference to be this.

is in fact getting to the core of the issue?

As a graduate student I was very bothered by the failure of the faculty to be careful about their definitions. The whole thrust of my thinking was begun in an attempt to get things well defined.

Yes, I only wish more people shared this attitude!

But what I discovered was that most of what the physicists told me was true by definition.

I think this statement is vastly understating the effort of physicists. What you are saying is true, but becomes non-trivial as soon as we don't know exactly what these definitions are, which is exactly what physicists are trying to discover. For instance, I know that a VolksWagon is not an electron because I define it that way. However, this requires me to have a definition of an electron. So, I write something down and say that anything which has these properties is that entity I call an electron - QED. However, in the meantime an experimentalist might make a measurement of that thing we usually accept is an electron (because thus far it fits into the definition) but the measurement is incompatible with our definition. We now have two choices, either change our definition to fit this observation or deduce that this thing we have observed is not an electron - and perhaps then by our defintion electrons do not exist!?

So, the job of the physicist is not simply to see how objects we define interact with each other, but to try and figure out what these definitions should be in order to make sense. I think this is a highly non-trivial exercise and you should not treat it lightly.

To give an example:

where I show that absolutely any rule may be reduced to the form F=0.

This is true given your initial definitions (all of them mind you, not just definitions of sets A and B). however, something you have not shown is whether your definitions correspond to anything in the physical world.

Another example more close to my heart can also be found in the field of condensed matter physics - in fact, it is all of condensed matter physics. We know that in principle we can write down the Schroedinger equation for a solid and hence logically deduce all its properties. This may lead to statements like 'a metal conducts electricity because we define a metal to be blah and, again by definition of blah, it follows directly that a metal is a conductor'. So, we have not really done anything special...

...except to be in the position to make such a statement you will have had to solve the many (many!) body Schroedinger equation which is to all intents and purposes impossible. So the job of the physicist is to make the 'logical deduction' some other way which is no longer the trivialisation you seem to be describing.

Matt

 

[Doctordick]

Hi Matt,

I have no real argument with what you say at all; however, I do have an argument with the idea of adding definitions before first establishing exactly what is meant by the words we are already using. You seem to have missed the point of my electron/Volkswagen question. Or perhaps I have missed your reason for the response you gave. Cest la vie, communication is not an easy thing.

What you are saying is true, but becomes non-trivial as soon as we don't know exactly what these definitions are …

As I always say, anyone who uses a word which he cannot define, does not know what he is talking about. Not knowing what these definitions are is a major burden to carry. As a graduate student, I felt that knowing exactly what I was talking about was the first step in understanding the world. All my teachers told me that was philosophy, not physics so I didn't say much to them about it but it certainly colored everything I learned.

So, the job of the physicist is not simply to see how objects we define interact with each other, but to try and figure out what these definitions should be in order to make sense. I think this is a highly non-trivial exercise and you should not treat it lightly.

But the first question they should ask themselves is "exactly what basis do they have for the foundation of their ideas". Any builder knows that if you cannot lay your foundation on solid ground, you cannot expect your constructs to be stable: i.e., much of your work is apt to be for naught.

This is true given your initial definitions (all of them mind you, not just definitions of sets A and B). however, something you have not shown is whether your definitions correspond to anything in the physical world.

No, I haven't. You should understand that I cannot; not without sacrificing the abstract generality of my attack.

We know that in principle we can write down the Schroedinger equation for a solid and hence logically deduce all its properties.

Now Matt, exactly how did you come to "know" this? Exactly what principle are you referring to? What makes you think Schroedinger's equation is the correct attack? (That is, other than the fact that the authorities tell you it is; or the fact that it gives you the expectations you expect for the cases you, or some experimenters, have examined.) What I am asking you to do is to examine the foundations of your beliefs.

Yes, I understand the difficulties of finding solutions to a many body Schrödinger equation. My Ph.D. thesis was intimately involved with mathematical analysis of the dependability of proposed methods of approximating the solutions.

I think you over react to my supposed "trivialization" of physics. I suspect the reason is that you are trying to give yourself an excuse for not following my thoughts. If you do take the trouble to follow me, you will find that I will, one by one, increase the number of defined terms I use (making sure that no definition ever puts a constraint on the theoretical possibilities[/color]). As the process advances, what they correspond to in the real world will become more and more obvious.

I hope I have not run you off – Dick

PS You still haven't told me your field!

 

[Doctordick]

Just as a reminder, I have at this point, defined nine terms:

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).

The last thing I did before we got off track was to create "unknowable data" sufficient to make the number of arguments in my expectation algorithm the same for all t. As I said, this was done only for the sake of convenience; without it, the issue of how one handles differences crops up and I just really don't want to have to worry about the problem. After all, I am free to add hypothetical entities (referenced by a \vec{x_i} not in C) so long as they obey the rules that the theory (to be someday proposed) requires.

In order to provide a convenient reference to that growing collection of \vec{x_i} attached to the "knowable" elements of C referred to as B_j or B(t), let me call the entire collection (including both knowable and unknowable data) an observation. Secondly, let me call a specific point \vec{x_i} an event. (This brings the number of defined terms to eleven.)

Now I get to that second issue. In the model for explanation I am building (through definition), the rules cannot depend upon t as t is a complete figment of my imagination. But I wanted t to map into the common conception of time used by scientists. Since a lot of phenomena discussed in physics are explained as time dependent phenomena, the specific time of an observation has to be recoverable from that observation: i.e., there must be a way of recovering the proper t from each and every observation. Essentially, this means that t must be implicitly defined by the observation itself (it cannot be explicitly defined as t is a complete figment of the model).

I can use the mechanism of adding unknowable data to assure that t is an implicit recoverable variable by adding sufficient bogus information to the observation to make every observation unique. If every observation is unique, then a list of observations with all the \vec{x_i} defining each observation can be seen as a tabular definition of a function defining t: i.e., you give me a particular observation (in detail) and I can look in the table and tell you the time to be associated with that observation.

The only question which exists is, "can that process always be accomplished?" Since the number of observations is finite and the number of \vec{x_i} attached to each observation is finite, the answer is yes. All one need to is find any case of n identical observations; pick n different points in the (x,\tau) plane which appear in no observation and distribute these n references, \vec{x_i}, to the entire collection of observations making sure the n identical observations get different points, adding one unknowable event to each observation.

Since the process is finite and the number of identical observations is finite, the procedure will eventually eliminate all identical observations and time will become implicitly defined by observations themselves. Before you accept that totally, think about it a little. There is an aspect of that which you should find bothersome. It is not a real problem but you should be bothered by it unless you can argue it out of existence.

There is a much more significant step which may be taken in exactly the same direction. One can use exactly the same procedure to make every observation unique even if any arbitrary event is removed from each and every observation. The significance of that step is that, if every observation is still unique after any arbitrary event is removed, the exact point which corresponds to that removed event is recoverable from the tabular representation of the original observations.

<br /> \vec{x_n}\,=\,f(\vec{x_1},\vec{x_2},\cdot \cdot \cdot ,\vec{x_{n-1}})<br />
​

Where f is defined by that table just described. The beautiful thing about that expression is that it immediately implies that the rule specifying the events seen in the observations can be written as F=0 where F is simply defined as,

<br /> F(\vec{x})\,=\,f(\vec{x_1},\vec{x_2},\cdot \cdot \cdot ,\vec{x_{n-1}})-\vec{x_n}\, \equiv \,0.<br />
​

By construction, every element B_j of C must obey that equation and all unknowable elements are just figments of our imagination anyway so there cannot be any evidence that they disobey it! That is, it is the assumption of any science that the objects they have conceive of obey their rules when they are not looking!

What I have really pointed out is the fact that there is a duality in common construction of theories. The rules are a consequence of the things which are conceived of as existing and the things which must exist are a consequence of the rules. Changing the rules changes what must exist. Changing what you allow to exist changes what rules these things must follow. If you are really after the simplest explanation, leaving both these issues open just complicates the problem. I have just shown that the rule F=0 can explain any arbitrary circumstance and F=0 is certainly a very simple rule. Can any of you give me a good reason why we should not simply say the rule is F=0 and consider what has to exist to make the rule true?

In fact, I can go through the effort of showing that any explanation with any rule can be mapped into an explanation relying on F=0. If that is true, then it seems to me that allowing any other rule does little more than complicate your explanation, particularly if that explanation is dependent on vague and ambiguous definitions.

Looking to hear from you -- Dick

 

[baffledMatt]

I have no real argument with what you say at all; however, I do have an argument with the idea of adding definitions before first establishing exactly what is meant by the words we are already using. You seem to have missed the point of my electron/Volkswagen question. Or perhaps I have missed your reason for the response you gave. Cest la vie, communication is not an easy thing.

Hmm, it is very possible I have misunderstood you. I've never been terribly good with that sort of question. The way i saw it is that you have an entity and you wish to determine whether it is a VolksWagon or an electron. Now, that question requires us to define what a VolksWagon and an electron are, which will also define the difference between them. Now I ask the question "where did these definitions come from?" and I get the answer "well, we looked at an entity made some observations, came up with a definition, and now call that an electron. Same for the VolksWagon." So what I can now do is look at the entity I have and say whether or not my observations are consistent with it being the same as what the other guy calls an electron, or if it is what he calls a VolksWagon.

Although this wasn't my initial reaction. My gut reaction to your question was in fact:

-------
but what do you mean by saying 'something is or is not something else'? Is the statement 'a VolksWagon is not an electron' equivalent to 'an electron is not a VolksWagon'? How do we know how to tell the difference between two things?
-------

which I think goes even further than what you are saying!

As I always say, anyone who uses a word which he cannot define, does not know what he is talking about.
Not knowing what these definitions are is a major burden to carry. As a graduate student, I felt that knowing exactly what I was talking about was the first step in understanding the world. All my teachers told me that was philosophy, not physics so I didn't say much to them about it but it certainly colored everything I learned.

The problem is that as soon as you define what an electron is you are no longer talking about a physical entity. All you can now sensibly talk about is that thing you have defined - any calculations you make only apply to this definition of an electron and there is no reason why you should observe this behaviour in nature. However, the hope is that if you have picked your definition carefully then you will observe that there is a physical entity out there which behaves in the same way as the thing you have defined. You then call this thing an electron, but you don't know whether or not it really is because you don't know how nature defines this entity (although whether we can say nature actually defines anything is unknown).

But the first question they should ask themselves is "exactly what basis do they have for the foundation of their ideas".
Any builder knows that if you cannot lay your foundation on solid ground, you cannot expect your constructs to be stable: i.e., much of your work is apt to be for naught.
No, I haven't. You should understand that I cannot; not without sacrificing the abstract generality of my attack.

[...]

Now Matt, exactly how did you come to "know" this? Exactly what principle are you referring to? What makes you think Schroedinger's equation is the correct attack? (That is, other than the fact that the authorities tell you it is; or the fact that it gives you the expectations you expect for the cases you, or some experimenters, have examined.) What I am asking you to do is to examine the foundations of your beliefs.

Well, obviously the only answer is that I believe this. But I think it is a well founded belief and certainly a useful one. I think we differ very much in our philosophies here. It does not bother me to think that we never really will know anything about the universe - at least at a fundamental level of 'knowing' something. I see physics as a way to make descriptions and predictions about our observations of what we like to think of as reality, but I don't think that it really tells us any more than that. Philosophically speaking I see myself somewhat like the man who rules the universe at the end of the Hitchhikers' guide to the galaxy:

Zarniwoop:
"How do you know [your cat] exists?..."

Man who rules the universe:
"I don't. I have no idea. It merely pleases me to behave in a certain way to what appears to be a cat. What else do you do?"

I know it's not much of a philosophy but I think it allows me to get on with my science.

I suspect the reason is that you are trying to give yourself an excuse for not following my thoughts.
If you do take the trouble to follow me,

Hmm, I have been trying, although I guess it might not be obvious because of my lack of understanding!

PS You still haven't told me your field!

I've currently been working on the statistical mechanics of membranes as well as doing things on self-organised criticality. So if you know anything about SOC you should realize that I can be very open to new and crazy ideas!

Matt

 

[Doctordick]

Matt,

I think I owe you a serious apology. I was in the process of answering your message #85 when I got to a point where I wanted to express something I thought I had said quite well once before. I was searching the various threads to find that specific post when I ran across some posts by you which I had totally missed (messages #74 and #75). I think the reason I missed them was the fact that there was a page shift immediately afterwards and I had gone directly to "last page" after seeing that Russell had made a post. At the rate people post here, I did not expect to find anything behind Russell's post and didn't look. Of course that erroneous expectation was reinforced by finding two posts from you the next morning.

I sincerely apologize for appearing to ignore those posts; it was not intentional. My wife is yelling at me to come to bed at the moment. (I have already wasted an hour responding to #85) so I will respond to all three tomorrow morning. I haven't read #74 or #75 in detail yet but I do have the feeling you are serious; something #85 almost convinced me you were not.

Again, I am very sorry -- Dick

 

[baffledMatt]

No problems! :)

I assure you I am taking your stuff seriously - don't let my occasional sarcasm and cynical nature fool you, I guess that's just the part of me that is waaay too English.

Matt

 

[Doctordick]

Response to Message #74

Hi Matt,

I got up early to have a look at your posts.

"Condensed matter" is pretty close to my thesis subject; however, that was some forty years ago and I a sure things have changed quite a bit since then. I always kind of disparaged my thesis as it was little more than number crunching busy work. I calculated the result of an approach suggested by some authority at the time (G. R. Satchler to be exact, I just googled him and discovered he is still apparently a decent reference). After I got my degree, I told my thesis advisor that I thought the whole thing was a waste of time; the way computers were improving our best bet was to wait twenty years and do the calculations directly. The campus computer we used had roughly the computing power of an Intel 286, if that. Twenty years later, I did see some graduate students using the appendix of my thesis as a teaching reference on angular momentum algebra so I guess it wasn't a total waste.

With regard to asking questions, I think physicists seem to be somewhat intimidating. Certainly my thesis advisor was regarded as unapproachable by most of the graduate students. I think I was the only one he didn't intimidate. Not that I am so strong but rather that I am just impossible to intimidate. I always just assume criticism is well intentioned. I think my father was kind of an intellectual bully; he tried to control the world through intimidation. I just took it as a teaching tool; I just assumed he was trying to prepare me for life. At any rate, the only way to gain understanding is to question everything anyone tells you.

The problem is that if you try to present a purely logical argument the thread of what you are trying to say can easily get lost.

Yes, I have noticed that. Nobody seems to have a very long attention span. The problem with inserting explanations of what one has in mind is that it often becomes a point of departure from the main idea. People get tired of thinking and would rather argue another issue suggested by that explanation. In particular, I have noticed a very strong tendency to build "straw men" from such comments; essentially implying the real subject was that explanation.

It would be easier if you put in little wordy explanations in between to help us along.

The real problem is that it helps people get off subject. And well thought out analogies or examples are difficult to come by when one does not understand exactly why what they are saying is not clear. My mother always told me that one learns a lot more by listening than by talking. The problem is that I have spent most of my life listening and asking questions and little time explaining what is going on in my head. As a consequence, I am not good at it; I suspect my way of thinking is quite alien to most.

Hehe, sounds to me what you need are a dozen good PhD physicists!

Yeah, and they're rarer then hen's teeth.

It might be because they are comfortable to believe that you are wrong but can't be bothered to think it through into a thorough argument - even more so when the idea is one as abstract as yours. I can empathise with this in the sense that you can't take time to try and debunk each and every theory that comes your way.

Yeah, it is sort of a "Catch 22" situation. The world is "chock full of nuts" so the really intelligent people need a barrier to protect them from a deluge. The problem is, that the barrier is constructed from the bulk of those with lesser minds. The presumption is "if you can't convince them, you certainly can't have a very good argument!" Reasonable except when the real problem is they just don't have the attention span to follow a complex thought. In forty years, I have never gotten anyone seriously into the details of Chapter II. They get close to the end of Chapter I and they begin asking "where are you trying to go with this?" If I tell them, the reaction is universal: essentially, "if you had any brains you would know that can't be done!" By By – games over!

(By the way, I apologise if I never reach this point, but I hope you appreciate that I have enough of a job trying to understand my own subject!)

Oh yes! Don't let me put a crimp in your studies. But I would appreciate your following me down the path a ways.

I'm still not sure what you mean by 'repeated elements'. I thought each element of B was simply an element of A, so it is not clear how repetition comes into it. Perhaps you could give me a specific example to clarify?

I am just trying to be very careful. I don't want to make any constraints on A at all; I want it to be absolutely open to all possibilities. The possibility certainly exists that every element of A is specifically different from every other element of A. If B is a finite collection of elements taken from A then it is entirely possible that B could consist of one element of A taken three thousand times. Now, in that case, could one say B is a subset of A? The point here is to make sure that no possibility is eliminated; I want to maintain the position that no possible theory is outlawed by the model.

Yes, but all these words like 'probability', 'measure', 'expectations' need to be defined.

I regard "probability" and the concepts related to it to be included in the field of mathematics.

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. I will leave that defense to others far more qualified than myself.

In particular, there do exist some arguments as to the fundamental basis of "Probability Theory". Thus the question as to exactly what is meant by "probability" is also an issue to be left open. However, I do assume that, whatever the eventual valid theory defines it to be, the measure of expectations will still be a number bounded by zero and one. If you think I am making an error there, I would appreciate hearing your reasoning. Unless you can give me a good reason for rejecting that position, "I will leave that defense to others far more qualified than myself".

Well, I hope this has helped.

Well, if my answers have helped you understand, then it has helped. Thank you for asking the questions.

Have fun -- Dick

 

[Doctordick]

Response to Message #75

Back with some more!

As it is a figment of your imagination … Also, are these algorithms unique?

I believe this whole section is a consequence of the fact that you do not understand what I am doing. I am setting up an abstract model of a theory; I am not proposing a theory but rather a way of looking at a theory. The central issue is to make sure that there exists no theory which can not be represented by the model I am constructing.

It is pretty clear that, at least at this point, you have failed to comprehend what I meant by the terms "knowable" and "unknowable". I think it would help you a lot if you went back and read my message #62 (on page 5 of this thread) to Russell. If you still feel there is a difficulty, let me know and perhaps I can clear it up.

What does the 'adjoint of the algorithm' defined in this way mean?

Essentially, I am defining it to be whatever is necessary to make sure the inner product (the dot product) is a positive definite number. The purpose of the definition is to provide a mechanism to get to or produce a positive definite number from absolutely any possible mathematical algorithm to assure that the model I am building does not eliminate any algorithm which could possibly be the answer to our question: "how do we calculate our expectations?" In essence, I have removed the constraint that the only algorithms which interest us must yield an answer bounded by zero and one. I want my model to be free of any constraint which might cause us to omit a possible theory.

But equation 2.2 applies to probabilities. You assert that P is only interpreted as a probability, so you must prove equation 2.2 is true for P.

Again, I think you have the horse on the wrong side of the cart. I don't "assert that P is only interpreted as a probability"; what I say is that the possibilities are open to any algorithm which (through the mechanisms I have described – essentially a normalized inner product) can be interpreted as a probability. This is a subtly different statement.

Equation 2.3 with 2.2 implies that the psi (and their adjoints) commute.

I don't believe that is true at all. Before you can talk about commutation, you have to define how the product is obtained. I have not defined a product operation between the algorithms \vec{\Psi_1} and \vec{\Psi_2} nor do I use one. The only product defined between these algorithms is the inner product between a given \vec{\Psi} and its ajoint.

We can assure this will not occur by requiring that be asymmetric with regard to exchange of observable arguments

What exactly do you mean by this?

If you go back to my original definitions of x_i you will note that I commented that order had nothing to do with interpretation of the references denoted by those numbers (it cannot as order is not recorded in the mechanism of mapping label numbers to points on the x axis). This means that reordering of the x_i cannot change P. Exchange of two arguments constitutes a reordering operation. If \vec{\Psi} is "asymmetric with regard to exchange", that means the only consequence of exchange is a change in sign. If x_i and x_j are identical then there is absolutely no difference in \vec{\Psi} when the exchange is performed; however, if it is asymmetric with regard to exchange, it changes sign by definition. This simply means that the output numbers of the algorithm change sign and by doing that, do not change! The only number which can change sign without changing is zero! The inner product of a set of zeros is zero. It follows that the probability of x_i and x_j being identical is exactly zero!

Finally, I'm not sure if I understand you properly, but you seem to be saying from the very first equation that given all the data (including unknowable - which you assert does exist so therefore if you were 'allknowing' you will know even this) and the algorithm - which is for the data plus one other element of data - you will know what that last piece of data must be. This is all very deterministic, so where does any concept of probability come in? Surely what you are trying to describe is a sort of 'hidden variables' theory so there is no place for probability at a fundamental level.

First, let me say that communication of my concepts "knowable" and "unknowable" has been difficult. What you are reading was written some twenty years ago; I think the post in message #62 does a better job of defining what I mean. Again, I am not at all trying to describe a theory; I am laying out a model which is capable of modeling any theory, something quite different.

Hope I have cleared some things up -- Dick

 

[Doctordick]

Finally, a response to Message #85

Well Matt, you may think you are honest but this post tends to lead one to suspect the main motive behind your response is to get off the hook without sacrificing your own opinion of your objectivity. You have done exactly what most every professional does when confronted with my work: change the subject! The art of misdirection of attention is well practiced in your chosen profession and a rather habitual move by most.

I had dropped the issue of my question as you had so completely missed the point that it seemed to be a waste of time to continue; it appears in this post that your real purpose was to change the subject. Notice that you did not even comment on my explanation of what I meant.

The example is clearly silly but what it points out is that the identification of an event is a constraint on acceptable surrounding[/color] events. When we define an event to be an electron (or a Volkswagen) we are actually using the tag to constrain surrounding events to a known collection of expectations of already defined events. In fact, it is usually a very vast collection and generally impossible to delineate by any mechanism other than by presuming the listener is familiar with the general nature of the associated events indicated by the very act of naming the event of interest.[/color]

Instead, you go out of your way to re-express the standard catechism on definition. I can only assume your intention (perhaps on a subconscious level) was to avoid thinking about what I said. You very definitely seem to be trying to introduce philosophical issues. Sort of along the lines of "that's philosophy, not physics".

This is true given your initial definitions (all of them mind you, not just definitions of sets A and B). however, something you have not shown is whether your definitions correspond to anything in the physical world.

You agree with what I have deduced so far but then you seem to have a very strong compulsion to imply I am saying more. What is that all about? It tends to come across as if you are trying to construct a straw man you can knock down so you can get off the hook.

I think we differ very much in our philosophies here.

Yes, you are a new student in a field you highly respect. It is easy to believe the authorities have a hold on the right way to attack the problem. I've been there and done that.

It does not bother me to think that we never really will know anything about the universe - at least at a fundamental level of 'knowing' something. I see physics as a way to make descriptions and predictions about our observations of what we like to think of as reality, but I don't think that it really tells us any more than that.

You seem to be putting forth the idea that the job of the theoretical physicist is to come up with short cut methods to calculate results of specific experiments. As a "job" I wouldn't argue with you at all (that's why I haven't earned my living in phsics). But as an interest, I think there are much deeper things to think about here.

When I say "understand" modern physics, I don't mean being able to do the math or understand the meanings and implications of the notation; I mean comprehension of why these things are held to be fundamental relations central to physics itself.

Many people take understanding modern physics to being able to intuit the correct relationship to use to solve a particular problem. In my head, that kind of stuff is little more than practice at rote memory tricks. What are we trying to do here? Develop better "rote memory" tricks to solve problems or are we trying to understand why these tricks work?

Philosophy has very little to do with what I am saying. If you want to, just look at what I am doing as an assemblage of tricks which yield surprising results. Essentially, I am defining things and procedures which, in the final analysis, if they are followed to the letter, will lead inexorably to a very large percentage of modern physics.

To show that I am wrong, all you need to do is show that there exists a theoretical procedure which cannot be mapped into my procedure or that some step I make violates the definitions I have set forth. Anything else seems to be little more than name calling.

Have fun -- Dick