Conservation Of Inherent Ignorance!

[Rade]

Rade I have doubts about your example and the statement that there's no cause of the restriction. Are you sure the correct figure isn't rather 1.022 MeV and coudn't it be due to the formal relation between electron coming in and positron going out?

Yes, I wrote it wrong, it is 1.022. And, I was under the assumption that DD was saying the causality was known to be correct, same way expectations of the explanation are known to be correct--not some hypothesis about what the cause might be. Well whatever he meant to say, what he did say I do not agree with, and I see a pattern that this results often because DD uses common terminology in uncommon ways.

 

You two make me feel compelled to fish up the same quote and address it:I would put the third sentence differently: an explanation assumes causality in the things being explained. I think that what Modest says means he wouldn't use the word explanation if it isn't based on some assumption of causality' date=' i. e. if it is only an algorithm that assigns a probability to each outcome.[/quote']This make sense, but do we "assume" causality in the things being explain, or "know" causality as fact. Is not causality a law inherent (as corollary) to the given (an axiom) that a thing A is a thing A (the law of identity), that it is something A that acts, as its unknown essence constraints it to act ?

 

It seems to me that perhaps DD wants the "cause" of explanation to be "another action" [unknown repetitive patterns of energy as action] rather than the entity [unknown as to the thing in itself] that causes the action of the repetitive patterns. This is what I do not agree with. My thinking is that entities are the cause of all actions, the entity may be undefined, it may be defined. Now, this does not mean that 100% of entities have a cause, most do, a limited few do not. Only those entities that are not forever have a cause. Eternal entities have no cause, that is a definition of what it means to be eternal. For example, one could argue the universe itself is eternal, thus it is an entity without cause. A single human, not being eternal, is an entity with a cause. Now, if you take the view that the "cause" of causality itself is an action, and not an entity (which I think is the view of DD), then I can see how you could reach the conclusion that 100% of entities (things) do not require a cause. Since I do not hold this view, I cannot agree with it.

[Qfwfq]

It seems to me that perhaps DD wants the "cause" of explanation to be "another action" [unknown repetitive patterns of energy as action] rather than the entity [unknown as to the thing in itself] that causes the action of the repetitive patterns.

That's not the impression I get at all. When he talks about his opinions on what physics is, I get the impression he regaards our worldview as being nothing but an arbitrary interpretation of what he believes to be utterly random noise. I strongly disagree with this, but of course that's only cuz I feel my profession being endangered which of course is why I keep concocting so many flimsy objections). :doh:

[Rade]

That's not the impression I get at all. When he talks about his opinions on what physics is, I get the impression he regards our worldview as being nothing but an arbitrary interpretation of what he believes to be utterly random noise.

As I understand it, there is no intrinsic difference between noise or message as input for interpretation. Variety as input is variety no matter what form. Suppose over a wire is both conversation and some irregular pulses of energy, at the same time. To someone that wants to hear the conversation, the irregular pulses are "noise". But, to someone that want to measure the pulses, the conversation is "noise". Thus, interpretation of noise does not have to be arbitrary, but a matter of choice of what you want to ignore.

 

My question, if your worldview is not ...an arbitrary interpretation of what DD believes to be random noise"...what would you say it is in the affirmative ?

[Qfwfq]

As I understand it, there is no intrinsic difference between noise or message as input for interpretation.

In an all too strict sense, sure you could say this, but it isn't so simple. You could say that the text of Kafka's Metamorphosis is just one of countless character sequences of the same length; the monkey at the keyboard could type it out just like any other single one of them. However, not all of the possible sequences are lexically and grammatically correct German language (let alone semantically having a content of any high value).

 

So, German lexicon and grammar constitute a format with a quite low entropy for a given sequence length. Only a tiny fraction of all (random) sequences of a given length are valid for the format. It is equivalent to say that, if German is a candidate explanation for given sequences, it will only be valid for a small fraction of possible ones. These two opposite points of view are, respectively, like asking either:

1. Is the monkey typing in good German?
   
2. Which language is the monkey typing in?
   

IOW the qualifier valid may as well be regarded as mutual, like a binary operator between the data and the format/explanation; we can see either one as potentially refusing the other. However, when we talk about explanation, we see it as something which the data might refute, whereas if we talk about a format, we see it as something for which the data might be rejected.

 

Suppose over a wire is both conversation and some irregular pulses of energy, at the same time. To someone that wants to hear the conversation, the irregular pulses are "noise". But, to someone that want to measure the pulses, the conversation is "noise". Thus, interpretation of noise does not have to be arbitrary, but a matter of choice of what you want to ignore.

Neither the conversation nor the pulses are actual white noise, which was what I meant. Even the pulses, as you describe them, have a format of their own; they aren't nearly as random as white noise. They might e. g. be the signal from a scintillator at CERN labs, where a cable in unfortunately receiving interference from a nearby phone line. Both things are recongnizable and each is distinguishable from utterly random (white) noise. But then, of course, there's no ruling out that the causes of white noise in a stereo system might just happen to give a signal that sounds like Mozart's

, despite the fact that a stretch of that length is far, far, far more likely to have a flat and fairly constant spectrum, at the time scale we perceive... nothing but a dumb hiss.

 

My question, if your worldview is not ...an arbitrary interpretation of what DD believes to be random noise"...what would you say it is in the affirmative ?

A very, very, very, extremely low entropy format.

[Rade]

Again, I will insert a preamble in the hope that it assists the reader in understanding exactly what I am doing and why the issues I bring up are essential. If you have not digested my post “Laying out the representation to be solved” I would suggest your first make a good effort to understand the details of that post.

DD and AnssiH, I have moved to this thread from the one you cite above.

 

What I would like to point out is that any symmetry is essentially an expression of a specific ignorance: i.e.' date=' something very specific [b']is not known[/b]. In Baez's case, he is essentially asserting that the “correct position” of q is not known information (i.e., that actual true position has no impact on the problem being solved). In the same manner, mirror symmetry means that there is no way to tell the difference between a given view of a problem and its mirror image: in effect you are in a state of enforced ignorance as to which view is being presented. If one makes a careful examination, every conceivable symmetry can be seen as a statement of some specific instance of enforced ignorance.

I do not understand how you can say that mirror symmetry means there is no way to tell the difference between (1) a view of a problem and (2) the mirror image of the view--for all possible conceived problems.

 

For example, consider the various mirror nuclei that exist. By definition, mirror nuclei have perfect symmetry, they are two nuclei that have interchanged numbers of protons [P] and neutrons [N]. The most simple example would be the mirror symmetry between helium-3 [PNP] and hydrogen-3 [NPN].

 

So my question, where is the "enforced ignorance" between these two views ? No matter which view of the problem I decide to start with, it is crystal clear what must be meant by the mirror image of the view, there is 0.0% ignorance and 100% certainty.

 

So, I have no idea what you are claiming when you say 'every conceivable mirror symmetry' results in a state of enforced ignorance--I do not see how what Baez is talking about has anything to do with the complete lack of ignorance between mirror symmetry of [PNP] vs [NPN] ??

 

I will ask one question at a time, wait for reply, as I move forward with this thread.

 

===

 

Edit: I also see that Baez has this to say about Noether theorem:

 

"Of course the proof uses Lagrangians, but a proof can't help using the concepts which the theorem is about. In other words: if someone claims Noether's theorem says "every symmetry gives a conserved quantity", they are telling a half-truth. The theorem only applies to certain classes of theories."

 

Thus, one cannot use Noether theorem in any application related to explanation in general, nor the relationship of symmetry and conserved quantity in general, because, as Baez makes very clear, the theorem only applies to a certain class of explanations (i.e., theories).

 

So, there must be many, many examples of mirror symmetry that have nothing to do with conserved ignorance of quantity.

[Rade]

In Baez's case, he is essentially asserting that the “correct position” of q is not known information (i.e., that actual true position has no impact on the problem being solved).

But, is this "really" what he is saying ?

 

It seems to me that what Baez says about the particle in his example is: (1) he is explaining a real particle . that can be measured to be at some start and end locations along a line ________, it may be at any possible two positions (an infinity of possible positions since a line is a continuous infinite), but it must be at some actual two positions, otherwise dq/dt is meaningless because it could never be measured (2) the particle is an entity that moves along the line with Lagrangian L(q,q'), (3) he knows exactly the first location of the particle along the line out of the infinite number of possible locations where it may be, he puts a label on what he knows as q, which he calls "its position" (this means, its position is "known" to Baez, otherwise why would he label an unknown position), and (4) q' is the velocity of the particle when it moves from that known q position to some second possible q position. In other words, dq must have space translation symmetry after a translation for a known particle within a known space (the line space from first q position to second q position along the line, such as q1________q2) to say that the particle follows the law of conservation of momentum along the initial space and the translated space.

 

What am I missing here ?

 

===

 

Second, when you say "shift symmetry" in your presentation, this is the same as saying "space translation symmetry"--correct ? I believe clarity would be added to your presentation if you substitute the words "space symmetry" for "shift symmetry" throughout the presentation. The word "shift" can be thought in many senses, a shift in time, a shift in space, a shift in parity, etc.--but your "shift" in this presentation is limited to the condition of momentum (p), and this (p) is what relates to space translation symmetry. It appears you want to disguise (?) the fact that you are talking about "space" symmetry when you say "shift" ? But, it is called "space-time" and not "shift-time" by Einstein, so, why do you change the wording for your presentation ?

Edited December 4, 2010 by Rade

[AnssiH]

I'll give a short response to the earlier posts;

 

With this statement you answer a previous question you had concerning how you can come to know that anything real exists as an object. See how you conclude that the approach of DD will prove that something "exists" as "procedure", and that it exists in some abstract "possibility space", with a space being a place. So, all we need to do is think about what type of primary substance as "object" could include the possibility of "procedure" to be contained within, in such a way that it could interact with some "information" found outside, and logically we conclude that it must be within the mind.

 

This world view is of critical philosophic importance, because it means that the presentation holds as true that there "exists" some faculty of the mind that can be applied to this "possibility space", that is, there exists within the mind an object that contains the possibility space. There are few philosophies that take the position that within the mind there can be faculties that exist as possibility space, DD appears to be one of them, and I agree completely with this view.

 

Let me take this one step forward. If we agree that within mind at least one faculty as object must exist (i.e., the mind faculty with possibility space internal dealing with explanation procedure), then it is a logical step to conclude that this form of existent can interact with other similar forms of existent external to it--other minds. But, given that what is external to the faculty as input is |undefined information (data)|, all that can be said about the external, no matter what its source, is that while it must be in some whatever form as repetitive patterns of energy open to explanation, it is impossible to attach to it any specific existence as a specific real object.

 

This is levitating towards the philosophy of the mind, and such speculations are irrelevant to this analysis. The analysis does not require an assumption that mind is or contains a real ontological object of some sort (or anything else specific about the structure of the mind).

 

Yes, because it is impossible for consciousness to understand it. Logically, the |undefined information| MUST yield repetitive patterns of energy, otherwise explanation itself would be a moot point.

 

Yes, or impossible to produce.

 

(Be careful of your choice of word "energy" there, because that word will be used with a different meaning in the analysis later on (the ordinary physics definition of energy will be derived from the universal constraints))

 

When a physicist says they observe repetitive patterns of energy as a wavefunction or state-vector, they are not saying they understand "how" the wavefunction collapses after observation, they are saying the wave function does so collaspe, and this change in the evolution of the wave function, as a disruption of the repetitive pattern, is "what they observe".

 

That's not exactly what I was referring to. I was just making a comment about, in what sense there is no such thing as "raw" or "direct" or "unadulterated" observation. Just the fact that you are conscious of something means it has undergone some sort of transformation or interpretation.

 

You do not have to know anything at all specific about the |undefined information|to know that any "given observation" of it must logically be some undefined interruption of the "pattern" of the repetitive pattern of data input that you wish to explain. This is what the physicist means when they say they "collaspe the wavefunction" of the unitary evolution. It would be an incorrect assumption of the DD presentation to assume you "know" whether or not the state-vector reduction (the collaspe) is a "real" action of the physical world, for this would imply that you hold as true the presumption that the state-vector does describe an actual quantum physical reality. It may, it may not, and whatever the answer, it has nothing to do with the presentation of Doctordick. Quantum experiments may indicate that reality is not local, but this does not mean they conclude that reality does not exist, nor does it mean that that quantum reality is influenced by, the human mind. The human can only make a choice "how to measure" and "what to measure", a choice of what instruments to use to measure. Thus, every time you observe or measure, what any "given observation" "really is" is a confirmation of the abstract nature of the dialectic {reality + knowledge}.

 

This speculation is also going into the details of quantum mechanical explanation of reality. But I should mention that the analysis will actually say something very interesting about why that sort of explanation is valid, and universally so, and it sounds like you should find it all quite reasonable. There are some very good epistemological reasons why the objects we define would behave in quantum mechanical manner, having to do with the interplay of some universally applicable definitions.

 

About the comments on causality, you guys just walked away from the definition given for explanation... We are looking for procedures that give expectations. If you have specific expectations, they are a function of some specific circumstance. I.e. that circumstance is thought to be the "cause" of what happens next. That is what we call "causality". On the other hand, to have no causality means you don't have useful expectations either. It's that simple.

 

When he talks about his opinions on what physics is, I get the impression he regaards our worldview as being nothing but an arbitrary interpretation of what he believes to be utterly random noise. I strongly disagree with this, but of course that's only cuz I feel my profession being endangered which of course is why I keep concocting so many flimsy objections).

 

I don't think he feels that way about you exactly, but I think there's a point to his complaints that many people feel so strongly that his result must be impossible, that they don't go through the trouble to think it carefully through.

 

I'm talking about exactly that part of the result which says that any data with unknown meaning can become interpreted/understood in the same terminology as we currently understand reality.

 

I do get the sense from your questions and objections, that you feel there can't really be much of a wiggleroom because we have little bit too solid grounds as the basis of our physics models. Like "real direct information" in some sense, or that we must have made good guesses, or that evolution must have made those guesses for us, or something like that.

 

It does require some thinking to actually see why and how there actually is all the wiggleroom. You could say, that the wiggleroom lies in the very first translation from the "completely unknown meaning" to some defined categorization that is based on any sort of recurring activity.

 

The reason I keep repeating that point about recurring activity is to get your focus onto the fact that "the actual real meaning" of the information never needs to become an issue in the task of predicting it. And that finding epistemological grounding to our definitions would just make them handy shorthand references to some (any) familiar recurring activities, rather than real objects themselves. That is also the key in understanding why quantum mechanical behaviour can be found from epistemological requirements.

 

I'm not an idiot you know, and I have walked through the analysis very carefully. I did not know where it is headed and what the conclusions are when I started, but I did see them myself, DD purposely did not point them out to me. So I am very certain you could pick it up too.

 

-Anssi

[AnssiH]

I do not understand how you can say that mirror symmetry means there is no way to tell the difference between (1) a view of a problem and (2) the mirror image of the view--for all possible conceived problems.

 

For example, consider the various mirror nuclei that exist. By definition, mirror nuclei have perfect symmetry, they are two nuclei that have interchanged numbers of protons [P] and neutrons [N]. The most simple example would be the mirror symmetry between helium-3 [PNP] and hydrogen-3 [NPN].

 

...

 

"Of course the proof uses Lagrangians, but a proof can't help using the concepts which the theorem is about. In other words: if someone claims Noether's theorem says "every symmetry gives a conserved quantity", they are telling a half-truth. The theorem only applies to certain classes of theories."

 

..

 

So, there must be many, many examples of mirror symmetry that have nothing to do with conserved ignorance of quantity.

 

The whole section about symmetries is essentially pointing out, that when you generate a representation of a problem (or a circumstance), that representation can contain properties or facets that are not known. They are not known because they are not part of the problem itself, they are part of how the problem is represented.

 

For instance, if you represent a problem whose solution depends on the spatial relationships between some objects (let's say, you are representing the solar system), you have to represent those relationships somehow. Representing them by laying the objects on a coordinate system means you also introduce a facet that is not part of the problem at all, i.e. the location of that entire solar system is immaterial to how you expect it to behave.

 

Noether's theorem is somewhat of an analogy about the ability to draw conserved quantities from various symmetries. Understanding it is not actually required to understand the analysis itself; the symmetries and conserved quantities we will be looking at are very simple.

 

That being said, the crux of the symmetry section is in its last paragraph. We have laid down a notation that contains immaterial facets, simply because we are laying down "what exists" at a given moment (something that any explanation has to do). Thus, we want to express the constraint, that forces any valid explanation (when mapped to this notation properly), to ignore those facets when it comes to the expectations it gives.

 

-Anssi

[Rade]

The whole section about symmetries is essentially pointing out, that when you generate a representation of a problem (or a circumstance), that representation can contain properties or facets that are not known. They are not known because they are not part of the problem itself, they are part of how the problem is represented...We have laid down a notation that contains immaterial facets, simply because we are laying down "what exists" at a given moment (something that any explanation has to do)

OK, thanks. So you agree with me that there is a way to tell the difference between (1) a view of a problem [what you call material facets that are not known] and (2) the mirror image of this view [what you call immaterial facts of "what exists"]--would this be correct ? If true, then this is my problem, for the presentation indicates this is not possible, so my confusion.

 

For instance, if you represent a problem whose solution depends on the spatial relationships between some objects (let's say, you are representing the solar system), you have to represent those relationships somehow. Representing them by laying the objects on a coordinate system means you also introduce a facet that is not part of the problem at all, i.e. the location of that entire solar system is immaterial to how you expect it to behave.

But, is it really immaterial ? Does not the fact that you must (as you say) represent the relationships of objects "somehow", and the fact that that you can transform this representation to a different "somehow" along the coordinate system, result in great importance because these two "facts" combined represent the information that must be used to derive the conservation laws of interest (time, space, etc.)? So, I just do not understand how the possibility of the transformation itself (as transformation) is not "part of the problem"?

 

That being said' date=' the crux of the symmetry section is in its last paragraph. Thus, we want to express the constraint, that forces any valid explanation (when mapped to this notation properly), to ignore those facets when it comes to the expectations it gives.[/quote']Question, what facets do you mean ? (1) The facets that are unknown (2) immaterial facets you have laid down (3) both types of facets ?

 

Finally, if, as you say, Noether Theorem is not required to understand the presentation then it should be eliminated from the presentation, because as now written making reference to it only adds confusion. When you think about it, Noether logic has nothing at all to do with a presentation about all possible types of explanation--Noether logic has very specific application ONLY to those explanations dealing with Langrangian and/or Hamiltonian type explanations. Since DD presentation is ALSO about the set of all valid explanations that do not require use of Langragiann and/or Hamiltonian, discussion of Noether only adds confusion to the "general" presentation. Not a complaint, a suggestion to improve clarity for the non-physics reader.

[Qfwfq]

Yes, or impossible to produce.

Exactly what do you mean here?

 

That's not exactly what I was referring to. I was just making a comment about, in what sense there is no such thing as "raw" or "direct" or "unadulterated" observation.

So what is the stuff to be explained? What is it that the algorithm should be applied to?

 

About the comments on causality, you guys just walked away from the definition given for explanation...

No, Anssi, we were referring to something said by Dick. You keep losing track of things in the discussion, but of course you decide what is admissible and what isn't. :doh:

 

I don't think he feels that way about you exactly,

About who? Me? Us? I think you simply missed my point.

 

I'm talking about exactly that part of the result which says that any data with unknown meaning can become interpreted/understood in the same terminology as we currently understand reality.

Do you mean even if the data is utterly random?

[AnssiH]

OK, thanks. So you agree with me that there is a way to tell the difference between (1) a view of a problem [what you call material facets that are not known] and (2) the mirror image of this view [what you call immaterial facts of "what exists"]--would this be correct ? If true, then this is my problem, for the presentation indicates this is not possible, so my confusion.

 

Heh, no... You are saying something a bit strange there... I'm not calling a view of a problem "material facets that are not known", nor am I calling a mirror view of that "immaterial facts of what exists", so I'm not sure what you have in mind...

 

At any rate, this should be pretty trivial subject, you seem to be thinking of something far more complicated than what it is... Mirror symmetry refers to pretty much the same thing as it refers to in ordinary physics. It means;

 

If you have a circumstance, which you can mirror (flip an axis), without affecting your own expectations as to how that circumstance works (e.g. which elements will come to interact with each others and how and when), then you have mirror symmetry to your representation.

 

That is the definition of mirror symmetry, so conversely it means quite explicitly that you can't tell the difference between mirrored versions of the same circumstance. (Unless of course you compare them to something you did not flip, but that is the same as only flipping some part of the circumstance, not the whole thing)

 

Of course it also means, that if you have mirror symmetry to your representation, flipping the entire universe is immaterial (you are part of entire universe, remember).

 

And before you ask, yes, this analysis will say something very interesting about parity violations in weak nuclear force. But let's talk about that when we get there.

 

But, is it really immaterial ? Does not the fact that you must (as you say) represent the relationships of objects "somehow", and the fact that that you can transform this representation to a different "somehow" along the coordinate system, result in great importance because these two "facts" combined represent the information that must be used to derive the conservation laws of interest (time, space, etc.)? So, I just do not understand how the possibility of the transformation itself (as transformation) is not "part of the problem"?

 

It is "part of the problem" in the sense that you want to make sure it doesn't affect the expectations. If that is what you mean, then yes, that is also what I meant. That is what the OP is all about, how to represent this exact constraint. That is also exactly what I said in the text you quoted next...

 

That being said, the crux of the symmetry section is in its last paragraph. Thus, we want to express the constraint, that forces any valid explanation (when mapped to this notation properly), to ignore those facets when it comes to the expectations it gives.

Question, what facets do you mean ? (1) The facets that are unknown (2) immaterial facets you have laid down (3) both types of facets ?

 

The facets that are properties of our representation of the circumstances, not properties of the circumstances themselves.

 

Finally, if, as you say, Noether Theorem is not required to understand the presentation then it should be eliminated from the presentation, because as now written making reference to it only adds confusion. When you think about it, Noether logic has nothing at all to do with a presentation about all possible types of explanation--Noether logic has very specific application ONLY to those explanations dealing with Langrangian and/or Hamiltonian type explanations. Since DD presentation is ALSO about the set of all valid explanations that do not require use of Langragiann and/or Hamiltonian, discussion of Noether only adds confusion to the "general" presentation. Not a complaint, a suggestion to improve clarity for the non-physics reader.

 

Yeah, we have talked about this just recently. It was pretty helpful for me when I was first reading this (as a non-physicist), but then it seems everyone else just start complaining about it even being mentioned before they walk onwards and make sure there actually is something worth complaining about in the analysis itself... So, we'll see...

 

-Anssi

[AnssiH]

Exactly what do you mean here?

 

That if no recurring activity of any sort can be recognized in any way, then no expectations can be formed either.

 

So what is the stuff to be explained? What is it that the algorithm should be applied to?

 

Why do you ask? When you come across something in the analysis that requires knowing that answer, let's talk about it then.

 

No, Anssi, we were referring to something said by Dick. You keep losing track of things in the discussion, but of course you decide what is admissible and what isn't. :doh:

 

I was referring to the responses of Modest and Rade, not yours.

 

About who? Me? Us? I think you simply missed my point.

 

You.

 

Do you mean even if the data is utterly random?

 

Yes, but there is of course the topic of whether and how recurring patterns can be recognized. (I'm not familiar with the topic and I don't know if or when large enough volumes make it expected that even "utterly random" data contains repetitive things) It is a bit complicated topic all by itself, so for the purposes of this analysis, I am settling with "somehow, some sort of recurring patterns are recognizable". If this wasn't the case, we would not have any expectations about anything.

 

So this analysis does not really concern "why" (or in what sense) there are recurrences. It concerns the categorization of any sorts of recurrences.

 

The point is simply that whether there really are real reasons behind those repetitive things, or whether we just assign reasons to them, does not affect our explanation at all. I think the way you put it and the way DD put it sounded almost the same to me.

 

-Anssi

[Qfwfq]

That if no recurring activity of any sort can be recognized in any way, then no expectations can be formed either.

Exactly. Furthermore, the expectations lie on making assumptions about those recognized recurrences, otherwise one runs the risk of being Russell's chicken.

 

Why do you ask? When you come across something in the analysis that requires knowing that answer, let's talk about it then.

No, Anssi, you simply aren't following me and I don't have much more patience.

 

I was referring to the responses of Modest and Rade, not yours.

I had mentioned it too, and my point remains.

 

You.

Indeed, this confirms that you missed my point. When I said "our worldview" I did not mean mine. But this is obsolete, because you have now given me your reply:

Yes, but there is of course the topic of whether and how recurring patterns can be recognized. (I'm not familiar with the topic and I don't know if or when large enough volumes make it expected that even "utterly random" data contains repetitive things) It is a bit complicated topic all by itself, so for the purposes of this analysis, I am settling with "somehow, some sort of recurring patterns are recognizable". If this wasn't the case, we would not have any expectations about anything.

As long as you insist on ignoring points about information theory you only show me that your judgement is inadequate; considering this, when you say:

I think the way you put it and the way DD put it sounded almost the same to me.

I question why you consider his conclusions to be certain and my judgement wrong. Instead of insisting for me to examine his proof better, why don't you follow my points and see what I mean?

 

Apparently you believe the fundamental laws of physics and all our understanding of reality is nothing more than the manner in which we interpret random noise. If this is so, what does it mean to say whether an explanation is valid? It would be the exact same thing as saying that, so far, the monkey's typing just happened to be correct Finnish sentences and even meaningful about some topic.

[Bombadil]

Before asking questions about the opening post I will make a few comments to Rade and Qfwfq.

 

Finally, if, as you say, Noether Theorem is not required to understand the presentation then it should be eliminated from the presentation, because as now written making reference to it only adds confusion. When you think about it, Noether logic has nothing at all to do with a presentation about all possible types of explanation--Noether logic has very specific application ONLY to those explanations dealing with Langrangian and/or Hamiltonian type explanations. Since DD presentation is ALSO about the set of all valid explanations that do not require use of Langragiann and/or Hamiltonian, discussion of Noether only adds confusion to the "general" presentation. Not a complaint, a suggestion to improve clarity for the non-physics reader.

 

Firstly I have to wonder if you have followed the opening post far enough to see where the presentation is going with this idea?

 

Secondly do you realize that all you really need to represent is all possible explanations in which a probabilistic function exists which satisfies some smoothness requirements at which point you can approximate those that don’t have these requirements. That is, there exists an interpretation of any explanation that will have those requirements. In which case the use of Langragiann and/or Hamiltonians that you aren’t liking can be looked at either as a consequences of these or as a strengthening of these assumptions used in some cases to rewrite the problem. I don’t think that they result in the removal of any possible interpretations. Trying to prove otherwise would be, I suspect in no way be a trivial endeavor.

 

Not to mention that they haven’t been defined for this derivation so that the actual application of the theorem is not even noticed and is only there for a background and mathematical completion of an idea.

 

Apparently you believe the fundamental laws of physics and all our understanding of reality is nothing more than the manner in which we interpret random noise. If this is so, what does it mean to say whether an explanation is valid? It would be the exact same thing as saying that, so far, the monkey's typing just happened to be correct Finnish sentences and even meaningful about some topic.

 

Qfwfq I think that you and AnssiH are too worried about recurring patterns. So far none of the actual derivation that this thread is about seems to matter if the data is random or not. This is important to realize I think, because at this point the idea of recurring patterns doesn’t seem to play a part in asking if an explanation of some data exists. On the other hand I wonder if it isn’t going a little too far to say that random noise could be looked at as generating Newtonian mechanics. I suspect that the assumption of the existence of objects is in fact part of the derivation of the Schrödinger equation.

 

I say this because I think that the topic is worth careful examination. In short I suggest that rather then constantly saying the same thing you make a mathematical proof based on the fundamental equation that says that what you are saying is right or wrong. Other wise you are going to have a hard time getting to the point that you seem to be trying to get to.

 

Now to the opening post.

 

There is a very important relationship between symmetries and conserved quantities first laid out in detail via a theorem proved by Emmy Noether sometime around 1915. The essence of the proof can be found on John Baez's web site. This is a fundamental theorem accepted as valid by the entire physics community.

 

In particular it appears that Noethers theorem can be applied any time that we are looking at a differentiable symmetry that doesn’t change the problem of interest. Coordinate transformations seem to be the obvious thing of interest here and it seems to be what you are using it for. It seems like a more general statement about mappings from one space into another space could be made here for generating the symmetries that we are interested in but the best that I can come up with is the question. Can any one-to-one mapping of the plane into it’s self in which a problem is unchanged under the mapping be looked at as generating a symmetry? The requirement of the mapping being differentiable appears to be a relatively minor although necessary addition for the application of Nothers theorem, which is what we are interested in.

 

The fundamental issue behind the power of symmetry arguments is the fact that information which is not available can not be produced by any algebraic procedure. This is a direct consequence of the fact that no proof does anything more than verify that what is being proved is actually embedded in the axioms required by the proof: i.e., it can not be false; the essential definition of a tautology. That being the case, how in the world can someone state the solution to a problem in terms of a specific variable when changing that variable has no impact on the problem? For example, consider a common physics problem where the solution is given as some function x(t). If one moves the origin of their coordinate system, the value of x can be shifted to any value desired. (Such a circumstance is commonly referred to as “shift symmetry”.) Clearly, if the problem does not specify where the origin is, how in the world can the solution specify what x is?

 

Then could we go so far as to say that all tautologies must be imbedded with some kind of symmetry relation which in a sense generates them? Or in other words a tautology is nothing more then a symmetric structure combined with some kind of equivalence relation.

 

Also might we not say that the problem specifies X up to a certain symmetry Y. Meaning that a function might define a location for X with the added requirement that the point X is symmetric under the transformation Y.

 

Since even if a problem is symmetric there may be requirements supplied by the remainder of the problem that must be satisfied. In particular it seems possible that if someone ever defined the location of an element in a problem containing some set of symmetries (say reflection about some point) then the location of the remainder of the elements in the problem is defined up to the symmetries (up to the reflection about the point which it is symmetric about). But still after we have solved the relationship needed by the symmetry we have solved part of the problem. The problem is still symmetric but the symmetries have now defined part of the problem. Instead of the problem defining the symmetries.

[Qfwfq]

Not to mention that they haven’t been defined for this derivation so that the actual application of the theorem is not even noticed and is only there for a background and mathematical completion of an idea.

I really don't get you, up to here. All that is more of a reason for us to say he shouldn't be calling Emmy into cause. You seem confused as to what our objection is; it is the lack of any kind of action (Hamiltonian or Lagrangian) that makes it pointless to call her theorem in cause.

 

Qfwfq I think that you and AnssiH are too worried about recurring patterns.

Who, me? Anssi talks about them and I was raising points about his statements. I am not concerned with "so far" and there's no use in telling me what to do. If they give me a reasonable version of the presentation from the OP of this thread, till the Famous Equation, in which the right details are clear, without being lost in a plethora of confused rambling, then I will address them.

 

I suspect that the assumption of the existence of objects is in fact part of the derivation of the Schrödinger equation.

Ask John von Neumann.

 

In short I suggest that rather then constantly saying the same thing you make a mathematical proof based on the fundamental equation that says that what you are saying is right or wrong.

I don't need to start from his equation. I have been discussing some mathematical topics which cast serious doubts on his contentions. But of course, before saying this, you were telling me not to talk about things that come further down the road.

 

In particular it appears that Noethers theorem can be applied any time that we are looking at a differentiable symmetry that doesn’t change the problem of interest.

Except that it might not be the same thing as Noether's theorem. Perhaps you would find it helpful to study some classical analytical mechanics and then the von Neumann quantum formalism, before drawing conclusions and making so many speculations. Edited December 7, 2010 by Qfwfq
omitted detail inserted

[Doctordick]

Hi Bombadil,

 

You need to read my post to “Answering Qfwfq”. The central issue here is “what follows from the definition of an explanation and nothing else”. Anything outside that issue is essentially “off-subject”.

 

Qfwfq I think that you and AnssiH are too worried about recurring patterns.

That is a consequence of Qfwfq's insistence on discussing what is represented by the numerical labels. Clearly one cannot explain anything which entirely lacks recurring patterns and all explanations contain such things. The problem is that people easily confuse “what is being explained” with “what follows from the definition of an explanation”.

 

So far none of the actual derivation that this thread is about seems to matter if the data is random or not. This is important to realize I think, because at this point the idea of recurring patterns doesn’t seem to play a part in asking if an explanation of some data exists.

You are quite correct here.

 

On the other hand I wonder if it isn’t going a little too far to say that random noise could be looked at as generating Newtonian mechanics. I suspect that the assumption of the existence of objects is in fact part of the derivation of the Schrödinger equation.

Here you are getting into some subtle issues which are very interesting but actually have little or nothing to do with the proof of my equation.

 

In particular it appears that Noether's theorem can be applied any time that we are looking at a differentiable symmetry that doesn’t change the problem of interest.

Noether's theorem really isn't paramount here. The only reason I brought it up is the fact that it exists and is held in high esteem by the physics community. The issue of significance is that all symmetries can be used to generate what can be called “conservation laws”. The power of symmetry arguments (often held to be the most powerful arguments which can be made) actually lie in the fact mathematics cannot produce any result that does not lie either in the axioms of the mathematics or in the actual given facts being processed (symmetries being absence of specific information must be coincident with specific constraints).

 

Can any one-to-one mapping of the plane into it’s self in which a problem is unchanged under the mapping be looked at as generating a symmetry?

Yes, I think that could be seen as an excellent definition of a kind of symmetry. But the “plane” really isn't the issue. Any one-to-one mapping of the parameters of a problem from one form to another which leaves the problem unchanged can be seen as a symmetry.

 

Then could we go so far as to say that all tautologies must be imbedded with some kind of symmetry relation which in a sense generates them? Or in other words a tautology is nothing more then a symmetric structure combined with some kind of equivalence relation.

First, the issue is completely off-subject and second, I would not agree at all. Symmetries are not an aspect of generating tautologies at all; they are a specific area of mathematical analysis (which is actually a specific complex tautology). tautology is nothing more than repetition of an idea which is true by internal definition. The real issue here is that tautologies can get extremely complex. So complex that the fact that they are tautologies can get lost in the rhetoric. Religious arguments for the existence of God presented in the dark ages are today seen as tautologies and, in my opinion, mathematics itself is the very best example of a very very complex tautology. But that is just an opinion.

 

Also might we not say that the problem specifies X up to a certain symmetry Y. Meaning that a function might define a location for X with the added requirement that the point X is symmetric under the transformation Y.

I wouldn't put it that way. It may be clear to you but it doesn't seem clear to me.

 

Since even if a problem is symmetric there may be requirements supplied by the remainder of the problem that must be satisfied. In particular it seems possible that if someone ever defined the location of an element in a problem containing some set of symmetries (say reflection about some point) then the location of the remainder of the elements in the problem is defined up to the symmetries (up to the reflection about the point which it is symmetric about). But still after we have solved the relationship needed by the symmetry we have solved part of the problem. The problem is still symmetric but the symmetries have now defined part of the problem. Instead of the problem defining the symmetries.

Again, I think you are over complicating the issue. That statement seems to me to add nothing but confusion to the issue.

 

Have fun -- Dick

[AnssiH]

I wasn't supposed to respond at first because you were making less and less sense, but now I'm thinking perhaps that was because you'd misread my responses, so;

 

Indeed, this confirms that you missed my point. When I said "our worldview" I did not mean mine.

 

I was responding to "...but of course that's only cuz I feel my profession being endangered which of course is why I keep concocting so many flimsy objections", with "I don't think he feels that way about you exactly".

 

No, Anssi, you simply aren't following me and I don't have much more patience.

 

I said "why do you ask?", because it makes absolutely no difference what the information-to-be-explained is, as long as its undefined at the beginning of this puzzle. When you ask that, you are thinking about some specific algorithm working for some specific data, while we are trying to analyze universal aspects of epistemology.

 

I think the way you put it and the way DD put it sounded almost the same to me.

I question why you consider his conclusions to be certain and my judgement wrong.

 

Like I said, I was not commenting on what you had said. And when you thought I was, I then even clarified that your comment and DD's comment sounded almost the same to me, i.e. I was not saying your judgment is wrong, but pretty much the opposite.

 

Let me be explicit; I was saying that, DD's "It is the explanations which require causality not the things being explained." and your "an explanation assumes causality in the things being explained.", sounded like the same statement to me, semantical ambiguities aside.

 

Instead of insisting for me to examine his proof better, why don't you follow my points and see what I mean?

 

Because I don't get the feeling that you understand what is under discussion, and I do think I understand how entropy in information theory relates, or does not relate, to this analysis (at least the impossibility of relating an entropy analysis to the undefined information, as oppose to some defined form of it).

 

The feeling I get from your objections is similar to what you would probably get, if you were to argue about relativity with someone who clearly doesn't understand what the theory actually says. I mean that nagging feeling of receiving very obscure and strange objections, that just keep telling you that there is something very wrong in their idea of how the definitions of relativity actually play out in the theory. I believe you know what I mean, at least if you have ever followed any relativity debates on these forums.

 

On that note;

 

Apparently you believe the fundamental laws of physics and all our understanding of reality is nothing more than the manner in which we interpret random noise. If this is so, what does it mean to say whether an explanation is valid? It would be the exact same thing as saying that, so far, the monkey's typing just happened to be correct Finnish sentences and even meaningful about some topic.

 

That is absolutely crazy complaint. What we are talking about is not at all the same thing as a monkey hitting keyboard and accidentally writing something meaningful. I guess I should feel insulted in some way, if you actually think that is how the analysis plays out. This is why I already said before, "I am not a total idiot you know".

 

Once more in a nutshell; recurring patterns of any sorts enable one to attach expectations to the information without knowing its meaning. Expressing those expectations in terms of some defined entities, requires some symmetry features to the mapping of those defined entities, whatever they may be. The consequential relationships are very interesting, in that they resemble modern physics down to a tee (or incredibly close anyway). That implies that the entities that the world is made of - according to our comprehension - are not ontological entities, but rather an efficient method of mentally handling those underlying recurring patterns, whatever they were. I.e. same defined entities can handle any recurring patterns, it's just a matter of generating a proper translation. Do not take my word for it, investigate the analysis itself.

 

If that still sounds to you like the same thing as "accidentally" interpreting something very specific very correctly, then I really don't think you should waste your time on this.

 

-Anssi