Laying out the representation to be solved.

[AnssiH]

just let it be said that to add new "t"'s in between the existing ones would mean to assume additional information, i.e. "what would be there according to some specific explanation".

Yes, and it also then means there is a concept of "between" the two "t"'s, and that this in-itself can play a role in the representation, given that each "t" represents a type of change (from what is undefined to what is defined), and all change represents a type of motion. I can appreciate that my interpretation and use of words here may have no meaning or interest to you, but again, my interest in the topic is to see how this presentation of Doctordick can be applied to my worldview. And the concept of between any two "t" moments has great importance to my worldview, and I may bring it to discussion as I read more.

 

First things first; I sense a possible misconception about the terminology when you say "t represents a type of change from what is undefined to what is defined".

 

This could be related to the earlier semantical confusions with the terminology of "future" being what is not known and "past" being what is known.

 

Well, that issue simply had to do with "future" being what you have expectations of, as oppose to having actual "undefined information" of. Past is something you have "undefined information" of (the information is "known" even if you don't know its meaning), and it is your explanation (i.e. world view or interpretation) of that information, which gives you some expectations about the future.

 

Maybe this is what you meant, but I wasn't sure.

 

Then to the issue of "in between t's"; Since "t" is something used by the universal notation to refer to changes to the information (which plays an important role in the algebraic analysis) in absolutely general terms, it is just defined as an index that each accumulated "present" (in terms of information accumulation) is indexed with. Without it, the notation would allow just one giant static piece of information, with nothing changing at all. All we want is to allow any sort of "change" to be mapped, no matter what kind of explanation we'd map to this notation.

 

Now, in terms of a specific explanation, yes, some explanations can, and do, assume (undefendably so) continuous properties to the information they are explaining. But as far as the actual available information goes, all information can always be indexed by a "t". The notation itself doesn't define the meaning of "in-between t's", so as far as the analysis goes, it is as meaningful as saying "the area between t's is blue"; it just never comes to play.

 

Like you are saying, you are trying to fit this to an idea you have about "time", with hopes that it would end up telling you something about whatever issue you have in mind. Perhaps the analysis will tell you something about it (it does tell you something about continuity arguments in general), but I would say the best bet to get there would be to just follow the analysis by itself, instead of coloring it with personal views too early. To do so would make things harder for you to interpret properly.

 

Yes, I understand you have no interest in what is inside the black box, but, clearly there does exist two block boxes in your explanation of the process undefined information ---> explanation. I thank you for clearly stating them, this is the type of detail that really helps with understanding.

 

Well yes the reason I mentioned "unknown mechanism of recognizing patterns" at all, was to avoid people asking "how do we recognize things". Because having an answer to that question never comes to play, for the exact reason that we are keeping things so general that we never have to answer that question. Offering an undefendable answer to that question would, on the other hand, take away the universality of this analysis (and thus all conclusions would also be suspect to the validity of those undefendable answers)

 

At the same time, stating it separately has got the problem that it can be taken as implying a lot more than what I actually wanted to communicate.

 

One aspect of |undefined information| that is not a guess is that the source of repetitive patterns that require explanation is directly from |undefined information|, thus in black box terminology, it serves as an input to the first black box you discussed--this we know, not guess.

 

I didn't actually understand what you are saying there...

 

...that is sort of what this analysis is. It does concern what we can actually know epistemologically or ontologically. And that is very little! but also very revealing.

 

Well, perhaps, but you would need to define what you mean "to know".

 

Well in that sentence, I meant it in a strong sense. So ontologically we can know pretty much nothing, but epistemologically we can at least know things like "valid explanations are not self-contradictory" and "all explanations are based on finite amount of information" and "all explanations define persistent elements" (those that can make predictions, which is part of a definition of explanation here), and "all explanations have some dynamics to them" (or at least it's pretty pointless to analyze completely static explanations)

 

The whole analysis is built on arguments like that, none of which could ever lead to conclude any specific representation be ontologically correct.

 

I have not done much investigation but the "probability constraint" of expectation to be greater than or equal to 0 and less than or equal to 1 does not apply to at least one situation, where the (xi) defined elements would represent Cauchy variables (see Google on this name). The Cauchy function has no probability expectation--the word expectation has no meaning to this type of circumstance. Thus, if the goal is to represent expectations generated by explanation of a circumstance dealing with a set of Cauchy (xi) variables, the "probability constraint" presented would not be appropriate. At least this is my read of the situation.

 

Well it's a bit off;

 

[math]

0\;\leq\; P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\;\leq \;1

[/math]

 

i.e. if you have an explanation, you have some expectations; Mathematically speaking, you have a function that returns some expectations, to the input of "some specified circumstance" or "state". (note that "t" is one of the input arguments)

 

He wants to constrain our interest to functions that return the probability in normalized fashion. The text following that statement in the OP is there just to point out that this does not rule out any possible explanations (or any possible "set of definitions"), as we can always have a transformation to any probability function returning its probability in any other scale.

 

Actually relatively simple issue, but DD is laying it down in very analytical fashion in the OP. (Plus he is deliberately moving to the kind of terminology used in quantum mechanics already at this point, but it's all kept absolutely universal until we get to the fundamental equation)

 

I see no problem with proceeding using the "probability constraint" to see how it is applied. It relates nicely to the topics of the past, future, present, and the "t" index moments where some repetitive pattern from |undefined information| [what is unknown] becomes a defined element and is placed into the memory of the past [what is known].

 

This is related to the commentary I made in the beginning of this post, and here also I can't be sure if you are exactly on the same page with me. Perhaps you are, but then that's a bit sloppy way to put it because it sounds like you equate "future" with "undefined information".

 

I mean, of course there is undefined information underlying the "past" too. Your comprehension of that past that comes in the terminology of your explanation, but any new information can potentially spark a change to that explanation, and to your comprehension of your past. The underlying undefined information doesn't change, just your interpretation of it. If that sounds right to you, then good :)

 

Hello AnssiH. Going over the posts for review and saw this comment you made about the puzzle circumstance I presented, and my suggestion that it cannot be represented by the (xi) notation:

 

I would like to point out that the (xi) in my circumstance do not refer to "dynamics", they refer to elements.

 

The [imath]x_i[/imath] indices always refer to elements. The progression of changes through "t"'s is an expression of the dynamics of the situation.

 

So, even if by some way the "dynamics" of the puzzle pieces could be represented, the pieces as elements could not. This is clear because you find it impossible to present even one example, out of perhaps 10,000+ possibilities. So, I can see absolutely no way the (xi) notation could be applied, it is not possible even in principle.

 

Actually it's pretty important that you'd see how any sort of circumstance would be representable in principle. You can probably understand that you won't get a nuclear physicist to draw you a representation of that puzzle room circumstance in terms of elementary particles, and I'm pretty sure you won't be able to do it yourself either. :) But practical difficulties aside, you should be able to understand that in principle the behaviour of all those things is representable in terms of modern physics.

 

Like I said, actual practical analyses of situations like that are performed through all kinds of approximations, as oppose to through modeling the situation in terms of the most fundamental elements of physics. At the same time you should understand that, if those approximations are appropriate, you should get consistent answers through all different ways of modeling the situation.

 

Note in addition that the universal notation is not laid down to be valid notation just for modern physics, but for any explanation. If there actually was a valid explanation where "puzzle pieces" and "persons" were indivisible elements, then we could trivially just assign an [imath]x_i[/imath] indices to them. But then they would not behave at all like the puzzle pieces or "people" you meant them to be. The persons would not have any moving parts, as they would just be a single "point" sitting there, doing nothing. And the puzzle pieces wouldn't have a defined shape if they are a single index, so they don't lock onto each others. Just for starters.

 

So instead of trying to get to these mind bogglingly complex examples, perhaps think more about the fact that, arriving at the validity of the most fundamental elements of modern physics (whose behaviour is very simple compared to "people"), also means that anything that can be seen as a composite object of those elements (like "people"), is representable in principle.

 

But, this is OK, because neither could the (xi) notation be applied to explain why I had bacon this morning for breakfast, if I explained the reason of the circumstance was my expectation that it exists in my kitchen. Just wanted to make sure my position on this point was clear. It is of absolutely no importance that the (xi) notation is not universal for all possible senses of the word explanation, it works where it works as defined. I am moving on to the next section to review.

 

Yeah, as long as you can understand in what sense it is applicable for representing any sort of circumstance of any sorts of defined elements, in principle, and that individual indices are by definition the indivisible elements of a given explanation, and thus their behaviour is also likely to be very, very simple.

 

Ok, suppose the mother of a friend dies. You decide not to attend the funeral because you know you will cry and you do not want to upset your friend. However, your decision evokes an emotional negative response about the truth of your decision because you have a sadness of not being present. According to Doctordick your decision was not rational, that is, does not make sense, where it clearly does make sense to you.

 

That's exactly the kind of semantical confusions I am a bit worried about there. What he means to say with his definition of "rational" is that the decisions are in some way a function of the past, but not necessarily 100% logical analyses of the entire accumulated information. For instance, so-called "intuititive" decisions are something we don't understand entirely logically, but they are still decisions made "by" some reasons in our world view. It's a worry that people see the word "emotional" there and start thinking about psychology or something like that. So I'll just refer to my comments about this same issue few posts back.

 

Anyway, have the questions coming if there's anything else in the OP confusing you. DD will post the next bit soonish.

 

-Anssi

[Bombadil]

I thought that I would start this thread from the beginning not because I don’t have some idea of what it is all about but because I can’t say that I have thoroughly gone though the entire derivation before asking any questions that come to mind and this seems the place to start. With that said I will start at the beginning of the thread and try to help out if I happen to think that I can.

 

I would like to point out that the (xi) in my circumstance do not refer to "dynamics", they refer to elements. So, even if by some way the "dynamics" of the puzzle pieces could be represented, the pieces as elements could not. This is clear because you find it impossible to present even one example, out of perhaps 10,000+ possibilities. So, I can see absolutely no way the (xi) notation could be applied, it is not possible even in principle. But, this is OK, because neither could the (xi) notation be applied to explain why I had bacon this morning for breakfast, if I explained the reason of the circumstance was my expectation that it exists in my kitchen. Just wanted to make sure my position on this point was clear. It is of absolutely no importance that the (xi) notation is not universal for all possible senses of the word explanation, it works where it works as defined. I am moving on to the next section to review.

 

Rade, AnssiH already replied to this but I thought that I would try to add something. Do you realize that the reason that you are seeming to think that an explanation of the puzzle example that you give doesn’t exist is because you see the puzzle pieces as elements in an explanation. Clearly such a view is impossible if you actually are trying to represent a puzzle. As this would not define what a puzzle piece is unless of course you think that a single point can have some kind of structure capable of representing the ordering characteristics needed to describe a puzzle piece.

 

Furthermore you would need some way of describing the manipulation of these pieces. This is an even more complicated problem if you just realize that there is no information that can be supplied that is not already part of the explanation. That is, you cannot just say that the pieces fit together like this and expect them to arrive like that without very carefully defining how you know when they are like that and why they must be like that.

 

If you can realize that the puzzle pieces on there own can’t possibly be single elements I think that you might realize that an explanation of what you describe will exist but that there is no simple way to represent it in an explanation.

 

A “procedure” constitutes some sort of instruction, “expectations” constitute an estimated probability of yes/no decisions and “circumstances” constitute a description of whatever it is we are concerned with expecting. As for my meaning of “rational” see my post Defining the nature of rational discussion! In that post I explain why I feel “rational” means that the the result does not generate an emotionally negative response as to its truth. I will presume the meaning of “hypothetical” is understood.

 

Then what we are interested in is the requirements and constraints needed for a function to be able to give probabilistic expectations to a set of undefined elements. The word undefined element here can in fact refer to any thing that can be associated with a definition to which expectations can be given but which not yet has a definition.

 

We are not actually trying to derive such a function but rather the consequences of such a function and what requirements are needed for the existence of such a function.

 

I use “x” (the common mathematical symbol for an unknown) as a label for the actual underlying element behind the explanation as this label is essentially undefined: i.e., there exists no way of defining this label in the absence of an explanation so it essentially has the character of an unknown. I use “i” as a label for the same element as referred to by the explanation as these labels are specifically defined by the explanation and I show it as an index on x to establish the connection. Thus the expression, [math]x_i[/math], is to refer to a specific underlying element appearing in and identified by the specific explanation being represented.

 

In a sense then the “i” label will do nothing more then tell how many elements are being represented in the notation. That is, it tells how many element are being represented. If this is the case I am somewhat puzzled by how this number can only be given by the explanation, is it that this number must also correspond an element from one set with one from a different set. That is it supplies a sort if correspondence of one element to some other element? Now the actual “x” could be looked at as defining the i’th element in the explanation. Perhaps not like a definition of an element would ordinarily be looked at as this supplies no additional information on its own. But a definition more in the sense of an arbitrary definition defining the location of a point in an arbitrary coordinate system.

 

There is one thing about this that I am somewhat puzzled by. That is if all elements must start as undefined and the definition of the elements is given by the explanation being used what is it that can set up an initial condition for an explanation to satisfy. That is, how can one explanation be considered different from some other explanation when explaining something as. Doesn’t the actual location of an element have to be defined by the explanation that is being used even in comparison to the other elements that are part of the explanation?

 

There is a subtle difficulty with the notation suggested above which needs to be handled carefully. The difficulty I am talking about arises because I am essentially using the notation [math](x_1,x_2,x_3,\cdots,x_i,\cdots)[/math] which, taken at face value, implies that every labeled element defined by the explanation (as referenced by the numerical index “i” on x) is different: i.e., whatever is being referred to (and defined by the explanation) by [math]x_{i_a}[/math] is different from what would be referred to by [math]x_{i_b}[/math]. Such an interpretation would make my notation disallow multiple occurrences of any defined elements. The problem could certainly be solved by using a more complex notation; however, there is an easier way to handle that possibility which will satisfy any and all such complications generated by different explanations designed to explain a given set of “undefined underlying facts” referred to by the numerical labels denoted by “x”.

 

That is to avoid the possible problem of the same x label being needed to represent separate elements in the same explanation. The emphasis being put on them “being separate elements“, since if they are truly the same element this is not a problem, we allow the same x to appear multiple times in the notation associated each time with a different values of i.

 

The reverse situation can also occur: it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by [math]x_i=x_j[/math]: i.e., the numerical reference to the undefined underlying element refers to exactly the same “x” element while the associated numerical index “i” may or may not refer to specifically different defined elements. The point here is to handle all possibilities. It must be recognized that, since the "x" label is undefined, we absolutely can not know if this is or is not the case; however, if the notation disallows such a thing we can't really say "all possibilities" can be represented by the notation: i.e., we cannot require [math]x_i \ne x_j[/math] for any given pair of given defined i, j elements.

 

This seems like the same problem to me and it seems to be using the same solution. This leads me to think that I must be missing something.

[Rade]

I sense a possible misconception about the terminology when you say "t represents a type of change from what is undefined to what is defined"..."t" is something used by the universal notation to refer to changes to the information...it is defined as an index that each accumulated "present" (in terms of information accumulation) is indexed with...as far as the actual available information goes, all information can always be indexed by a "t"...The notation itself doesn't define the meaning of "in-between t's... Without it [the "t"], the notation would allow just one giant static piece of information, with nothing changing at all.

Hello again. Based on your explanation above, I sense we are on the same page. Notice that my understanding was that "t" represents a type of change, and you explain that yes, it is indeed a "change to information". So, yes, this is what I was saying, each "t" is an index of some change in information, and I assume this change refers to possible change (1) in |undefined information| to --> defined information, and (2) a change in defined information to -->other defined information.

 

Next, you say each "t" is index to "each accumulated present". Now, I have a question. Is it not true that each (xi), which is an index of some unique defined element, is also directly associated with some unique "t", which itself is associated with either some unique change in the |undefined information|to defined information OR a unique change in some defined information to another defined information ? This makes sense to me as a way to understand the notation, not sure however if it is what the notation is claiming ? --help needed here.

 

About the word between. It is a word used in the representation by DD, it is stated that new "t" can be placed between old "t" to allow for the sequence of defined information to be represented. So, I refer to the nice example of DD of the archeology research. Suppose 10 old items have been found at the dig (these are in your past as known defined information). Each new find represents a change in information, and each change can be assigned a unique "t" to index that find and place it in the proper logical archeological order with all other past information. So, as DD explained, we would not give the most recent find a "t" index where it is just added to the end of the list of past finds. The reason is because there is a possibility that it would need to be placed "in between" two previous "t" index values.

 

So, while I agree with you that the concept of "in between two t" is not of importance to the notation as it is being discussed by DD, there is such a concept of "between" that I or anyone could have an interest in, that we may want to explain. That is all I am saying, that in my philosophy I can explain exactly what it means to say that there is a concept of between two "t" index values.

 

Well' date=' that issue simply had to do with "future" being what you have expectations of, as oppose to having actual "undefined information" of. Past is something you have "undefined information" of (the information is "known" even if you don't know its meaning), and it is your explanation (i.e. world view or interpretation) of that information, which gives you some expectations about the future. Maybe this is what you meant, but I wasn't sure[/quote']. Yes, exactly as I see it. The future is what you have expectations of "for" some |undefined information|. The past is something you have |undefined information| "of", the defined (xi) elements. And then, all you can "know" about the |undefined information| is this, except that you also know that |undefined information| serves as the input source "of" all repetitive patterns of energy that are part of your future. So, yes, I think I have this down pat, I just use different words to explain how I understand.

 

I didn't actually understand what you are saying there...

Not sure how else to say it. My point is that |undefined information| is' date=' what it is. And, whatever it is, it "is" the source of those undefined repetitive patterns of energy you have an interest to explain, maybe not all of them, but at least some of them.

 

Well in that sentence, I meant it [to know] in a strong sense. So ontologically we can know pretty much nothing,

. Sure, but that one thing we can know I find to be very pretty as a statement, it is "existence exist". This is the only one thing we can know ontologically. We know it as an axiom, I mean, if there was no existence, we would not be having this conversation. Let me ask this--DD has clearly said that |undefined information| must include all of non-existence for the reason that even non-existence requires explanation. Well, let us eliminate from |undefined information| everything except non-existence as a mental exercise. From where then would your undefined repetitive patterns derive from ? So, in this sense, this what you can know about |undefined information|, it is the source of undefined repetitive patterns of energy (and thus matter via Einstein equation), and this source is what we call "existence". One thing I like about the presentation of DD is that it has made me to realize that information is prior to both energy and matter (E and M derive from I), and all of it was undefined at the get go. I find this to be a radical yet exciting new way to look at what exists and what does not exist. I am sorry if this is not how you and DD see things.

 

but epistemologically we can at least know things like "valid explanations are not self-contradictory" and "all explanations are based on finite amount of information" and "all explanations define persistent elements" (those that can make predictions' date=' which is part of a definition of explanation here), and "all explanations have some dynamics to them" (or at least it's pretty pointless to analyze completely static explanations)[/quote']I agree without argument the first and last claim. But, when you say all explanations are "based on" finite information--depends what you mean by "based on". For examples, without |undefined information| no explanation would be possible, and |undefined information| is infinite--correct ?

Second, why must elements be "persistent" ? Many particles of decay physics have lifetimes on order of 10^-15 or greater seconds, not what I would call "persistent", and of course at least some explanations need to define these "non-persistent" particles.

 

The whole analysis is built on arguments like that' date=' none of which could ever lead to conclude any specific representation be ontologically correct.[/quote']Yes, this is one reason why I like the presentation, it presents in a mathematical way that what humans claim they understand about ontology, each specific claim by each human is only their representation of ontology, no one specific representation can be viewed as being correct as to the essence of the ontology, that essence remains forever off limits (at least to humans). As a side note, I think this may be so because the essence of ontology may lie to the other side of the Planck limits (of time, space), which we know from quantum theory humans can never penetrate. But see that, while I agree with what you say, this does not mean to me that there is not in fact some essence to ontology, it is just that we can never know what it might me. Thus, the essence of ontology is prior to any explanation of it. But, the presentation of DD has nothing at all to do with "essence of ontology" so we are getting very off topic.

 

Well it's a bit off;i.e. if you have an explanation' date=' you have some expectations[/quote']Not according to Cauchy mathematics, there are many explanations of it, but, by definition, none of them have any expectation.

 

So, as you say,

He wants to constrain our interest to functions that return the probability in normalized fashion.

The Cauchy mathematics are not such functions' date=' thus by definition they are outside the notation of DD, they represent a type of explanation his notation cannot address. As you said, the notation is under this "constrain", this limitation, showing where it cannot be applied. This is all I was trying to say.

 

I mean, of course there is undefined information underlying the "past" too. Your comprehension of that past that comes in the terminology of your explanation, but any new information can potentially spark a change to that explanation, and to your comprehension of your past. The underlying undefined information doesn't change, just your interpretation of it. If that sounds right to you, then good :)

Yes, exactly as I was thinking of it--that |undefined information| stands behind both the future (directly) and the past (indirectly). And yes, it makes perfect sense to me to say the |undefined information| doesn't change, and see that this is true even though it provides a source of undefined repetitive patterns of energy that need to be explained. I think it gets nicely to the understand that energy can never be created or destroyed(why ?--because energy (and matter) itself derives from the unchanging |undefined information|. The only possibility is for |undefined information| to allow for undefined repetitive pattern of energy--which then energy itself to undergo change, to form defined elements, ultimately back to |undefined information| given entropy.

 

If there actually was a valid explanation where "puzzle pieces" and "persons" were indivisible elements' date=' then we could trivially just assign an [imath']x_i[/imath] indices to them. But then they would not behave at all like the puzzle pieces or "people" you meant them to be. The persons would not have any moving parts, as they would just be a single "point" sitting there, doing nothing. And the puzzle pieces wouldn't have a defined shape if they are a single index, so they don't lock onto each others. Just for starters.

I do not agree, mostly because I have no idea what you mean by "indivisible element" as would relate to the set of all possible explanations of puzzle pieces and individual humans. For me, each human and each puzzle piece is a "primary substance", which would be your concept of "indivisible element". Each could be assigned an (xi) in a non-trivial manner. Having or not having moving parts, or shapes, has nothing at all to do with being a primary substance, the primary substance is what allows for all parts and all possible shapes, both inside and outside the primary substance. So, for me, each primary substance in the puzzle element could be assigned a unique (xi)label, so, I just have no idea why you think such a possibility of explanation is outside the notation--sorry.

 

Perhaps if you define exactly what you mean by "element", and "persistent" that would help. At this point we clearly are talking about two completely different things, and thus makes me wonder if we find yet another constraint to the definition of explanation used ?

 

So instead of trying to get to these mind bogglingly complex examples' date=' perhaps think more about the fact that, arriving at the validity of the most fundamental elements of modern physics (whose behavior is very simple compared to "people"), also means that anything that can be seen as a composite object of those elements (like "people"), is representable in principle.[/quote']I'm not sure I would say the behavior of an electron is simple. For example, we cannot measure both the position and momentum at the same time, very easy to do for any human. Then, quantum theory tells us the behavior of an electron is such that it can be at two places at the same time, which seems not so simple--something I often wish I could do but find very difficult if not impossible. So, it seems to me that representing a person in the notation should in principle be much more simple than applying it to something that can be in two different places at exactly the same time.

 

What he means to say with his definition of "rational"...

Yes, but what he meant to say is not what "he said", thus nothing is added to what he said but confusion. My point is that the word "rational" is completely and absolutely unnecessary to the definition of explanation presented by DD. It only leads to these types of misunderstanding between what "is said" and what "is meant".

 

Thank you for working with me.

[Kriminal99]

could you give an example?

[Rade]

If you can realize that the puzzle pieces on there own can’t possibly be single elements I think that you might realize that an explanation of what you describe will exist but that there is no simple way to represent it in an explanation.

Thank you for your help. OK, if the puzzle pieces are not single elements, please give one example of a single element that would apply to the circumstance. An element has to be an element of something, even if that something is undefined. My problem is that the word element is being used without any definition of it. It was my understanding that the element is what is defined, and since the puzzle piece is so defined as a puzzle piece each one must be a single element by definition. The common sense meaning of element would be for example the He atom. Now, although it is an element, it has both internal structure and diversity of types (isotopes). My roadblock with this issue is I have absolutely no idea how the English word element is being used here.

[Rade]

Ok, I have moved on to the next section, and find this quote of Doctordick, just after the introduction of the probability constraint of >= 0 and <= 1:

 

As such' date=' it is in our interest to express that constraint by mathematical means outside the definition of the circumstance under examination as it cannot be a constraint upon the circumstances themselves...There exists a simple method of avoiding that constraint...[/quote']A major roadblock for me. I do not understand why we "must" avoid that constraint. Does this mean that if we do not avoid the constraint we have a circumstance that is outside use of the notation ? Are we not looking for a general notation that can be used to explain situations not only outside the definition of the circumstance, but also inside the definition of the circumstance under examination ? Is not any circumstance (that is, the list of questions) by definition within the probability constraint, that is, you have all of them, none of them, or some percentage of all of them other than 0%?

 

As you can see, I have no clue why we "must" avoid the constraint, and exactly what would be the consequences if we do not. Seems to me that if we are at this junction of the presentation to move the mathematics down one of two possible statistical paths (by mathematical means outside the definition), it would be helpful to show the mathematical outcome of the other possible path (mathematical means inside the definition). Major help needed here.

[HydrogenBond]

Another way to do this is start with a solution you know and use that to practice the procedure. The idea is to reach the result in the fewest steps. Check mate is four moves instead of four days. If you need to rationally interate one may still reach the solution but that meandering procedure is energy inefficient.ince it takes too much energy to learn and follow.

 

With meandering although it may work, it limits the usefulness to others. The log winding the road, may come down to only a few experts who have the energy to follow. The problem this can create is the prestige of expertise can be leveraged to institute an energy inefficient dogma, that can't be questioned very easily. since very few can follow the meandering, With simplicity more opinions count and progress is faster.

 

E=MC2 lingers due to simplicity. It has practical value to almost anyone would wishes to use it. A long and winding alternative could also have been developed. That could have become a dogma only a very few can see, allowing it to resistant change simply because of too few opinions. There is a certain snob appeal to the long and winded road, since it keeps out the riff-raff. The straight lines welcomes all to particpate. With more particants comes faster progress.

[AnssiH]

Then what we are interested in is the requirements and constraints needed for a function to be able to give probabilistic expectations to a set of undefined elements. The word undefined element here can in fact refer to any thing that can be associated with a definition to which expectations can be given but which not yet has a definition.

 

Yes, emphasis onto "...a definition to which expectations can be given..."

 

It is important that the reader understands that no expectations can exist until some definitions have been created. I.e. there is always a translation from something undefined to some specific definitions, and the expectations only exist in that specific terminology.

 

Indeed we are only interested of explanations of undefined information, and in that sense it is correct to say "probabilistic expectations to a set of undefined elements". Just as long as the reader understands the expectations are not directly referring to undefined elements themselves. (That would be somewhat oxymoronic)

 

Also it is important to keep in mind that if you talk about this in terms of "undefined elements" and "defined elements", you should expect a very large collection of undefined elements (i.e. a large amount of undefined information) to stand behind any single defined element.

 

I am actually not a big fan of the term "undefined element" because it implies something recognizable. I find it easiest to just think of "undefined information" as some sorts of events or patterns of unknown meaning and origin. As long as you can take the undefined as something that doesn't limit the possibilities for specific definitions, you should be okay.

 

We are not actually trying to derive such a function but rather the consequences of such a function and what requirements are needed for the existence of such a function.

 

Yes, or perhaps it's clearer to say, we are looking for common features of all valid functions.

 

In a sense then the “i” label will do nothing more then tell how many elements are being represented in the notation. That is, it tells how many element are being represented. If this is the case I am somewhat puzzled by how this number can only be given by the explanation, is it that this number must also correspond an element from one set with one from a different set. That is it supplies a sort if correspondence of one element to some other element? Now the actual “x” could be looked at as defining the i’th element in the explanation. Perhaps not like a definition of an element would ordinarily be looked at as this supplies no additional information on its own. But a definition more in the sense of an arbitrary definition defining the location of a point in an arbitrary coordinate system.

 

I'll explain this in terms of "undefined elements" and "defined elements", where "undefined element" is some, let's say "indivisible piece of information", and "defined element" is some indivisible fundamental element of an explanation (such as photon).

 

So, for instance in [imath]x_1[/imath], the "1" tells us which specific photon it is, and in every "t" where that index appears, it means we suppose that particular photon appears in each of those "t"'s.

 

It would have a different "x" value to it in each "t", so yes this can be interpreted in terms of "x" determining its position in a coordinate system.

 

Now, if you think about the same thing in terms of undefined elements, there does not exist a connection between, what in your terminology would be [imath]5_1[/imath] and [imath]6_1[/imath]. I.e. in terms of undefined information, that cannot be taken as "a photon moving from 5 to 6", it is taken as two different elements of information. (Every new bit of information would always just mean new elements came into existance)

 

And of course a different specific explanation might look at the same undefined elements through definitions that would cause it to say it was "[imath]5_1[/imath] and [imath]6_2[/imath], where "1" and "2" are different defined elements having their own histories and futures in the evolution of consequent "t"'s.

 

That is what DD means by the "i" index being given by an explanation.

 

And again, the unwanted implications of the concept of "undefined elements" or even "elements of information" is that it sounds like something recognizable in itself. It is not, we are just talking about any sort of information whose meaning is unknown, and it can be treated as "elements" simply by the virtue that there can only be finite amount of information standing behind any explanation.

 

There is one thing about this that I am somewhat puzzled by. That is if all elements must start as undefined and the definition of the elements is given by the explanation being used what is it that can set up an initial condition for an explanation to satisfy. That is, how can one explanation be considered different from some other explanation when explaining something as. Doesn’t the actual location of an element have to be defined by the explanation that is being used even in comparison to the other elements that are part of the explanation?

 

I'm not entirely sure what you are asking about, but does it suffice if I say that different explanations simply interpret the undefined information in terms of different defined elements, and thus see a wildly different "subjective reality" as well?

 

There is a subtle difficulty with the notation suggested above which needs to be handled carefully. The difficulty I am talking about arises because I am essentially using the notation [math](x_1,x_2,x_3,\cdots,x_i,\cdots)[/math] which, taken at face value, implies that every labeled element defined by the explanation (as referenced by the numerical index “i” on x) is different: i.e., whatever is being referred to (and defined by the explanation) by [math]x_{i_a}[/math] is different from what would be referred to by [math]x_{i_b}[/math]. Such an interpretation would make my notation disallow multiple occurrences of any defined elements. The problem could certainly be solved by using a more complex notation; however, there is an easier way to handle that possibility which will satisfy any and all such complications generated by different explanations designed to explain a given set of “undefined underlying facts” referred to by the numerical labels denoted by “x”.

That is to avoid the possible problem of the same x label being needed to represent separate elements in the same explanation. The emphasis being put on them “being separate elements“, since if they are truly the same element this is not a problem, we allow the same x to appear multiple times in the notation associated each time with a different values of i.

 

Your interpretation of that paragraph is wrong. It is something that should be probably clarified in the OP. It already was once but there's still a difficulty there with the ambiguity of the words "different" and "same".

 

What he means by "same" there is that two different photons are "the same".

 

So he is just saying that both "[imath]x_1[/imath] and [imath]x_2[/imath] are allowed to both refer to "a photon", for instance. They are just two different photons.

 

The reverse situation can also occur: it is possible that the explanation may presume the specific elements are different whereas it is possible that the actual underlying elements are, in reality, the same. In this case, the situation is easily represented by [math]x_i=x_j[/math]: i.e., the numerical reference to the undefined underlying element refers to exactly the same “x” element while the associated numerical index “i” may or may not refer to specifically different defined elements. The point here is to handle all possibilities. It must be recognized that, since the "x" label is undefined, we absolutely can not know if this is or is not the case; however, if the notation disallows such a thing we can't really say "all possibilities" can be represented by the notation: i.e., we cannot require [math]x_i \ne x_j[/math] for any given pair of given defined i, j elements.

This seems like the same problem to me and it seems to be using the same solution. This leads me to think that I must be missing something.

 

Then your interpretation of this is correct :) In the final analysis it basically means that explanations can have separate defined elements that occupy the same position simultaneously.

 

Btw;

http://topnews.us/content/225376-stephen-hawking-introduces-model-dependent-realism-world

 

Why is it that when an authority figure says it, it is suddenly being "introduced to the world"? :shrug: Well anyway, it always strikes me as a bit odd how hard it is for people to see this model-dependent realism thing. Just the fact that you can take any representation of any dynamic behaviour, and just choose to represent the same behaviour (semantically) differently, is to me the same thing as model-dependent realism.

 

I have not read the book but I can pretty much tell what he is getting at, and this analysis is very much an exact scientific proof of Stephen Hawking's musings about model-dependent realism. But I think it would very much surprise Stephen how much of our idea of reality really is traced to be entirely model-dependent.

 

-Anssi

[AnssiH]

Next, you say each "t" is index to "each accumulated present". Now, I have a question. Is it not true that each (xi), which is an index of some unique defined element, is also directly associated with some unique "t",

 

Yeah, a specific explanation representing some circumstance would have some collection of [imath]x_i[/imath] elements associated with a specific "t".

 

And there would be a different collection associated with another "t". And/or the "x" values of the represented elements would have changed. (something always has changed between "t"'s, by definition)

 

which itself is associated with either some unique change in the |undefined information|to defined information OR a unique change in some defined information to another defined information ?

 

The latter. For instance, the predictions made by modern physics are obviously giving some expectations in terms of its own definitions.

 

It is not possible to give expectations in terms of undefined information itself, by definition (look my above post to Bombadil)

 

(ps. undefined information = undefined elements = undefined elements of information... each of those choices capture the intented meaning but also carry unwanted baggage)

 

About the word between. It is a word used in the representation by DD, it is stated that new "t" can be placed between old "t" to allow for the sequence of defined information to be represented. So, I refer to the nice example of DD of the archeology research. Suppose 10 old items have been found at the dig (these are in your past as known defined information). Each new find represents a change in information, and each change can be assigned a unique "t" to index that find and place it in the proper logical archeological order with all other past information. So, as DD explained, we would not give the most recent find a "t" index where it is just added to the end of the list of past finds. The reason is because there is a possibility that it would need to be placed "in between" two previous "t" index values.

 

Yes, it means that newly accumulated information can be interpreted, by a specific explanation, in some whay that we think it tells us something about the past.

 

Another explanation might take the same information and argue that it does not tell us anything about the past, or assign them somewhere else in the supposed past.

 

The point is that there is an explicit order when the information was actually received, and implicit order; how our specific explanation orders the supposed meaning of that information.

 

Sure, but that one thing we can know I find to be very pretty as a statement, it is "existence exist". This is the only one thing we can know ontologically. We know it as an axiom, I mean, if there was no existence, we would not be having this conversation.

 

I really like to avoid the word because people understand it in so different ways, and since we are talking about possibilities in interpreting some undefined information, it is not correct to say that any of our defined entities "exist", even if the information behind those definitions "exists".

 

Whenever people say "photons exist", I can never tell which meaning they use. Do they mean that the concept of photons appears in every valid way to comprehend reality? Or that our definition of a photon is aligned exactly with the same kind of real object? Or just that it is one valid way to categorize reality this way? There are also valid ways to categorize reality in terms of aether. It's just very unpopular, and that's why people say it doesn't exist. So, what's the difference, when multiple valid explanations exists? I'm sure that's exactly what Hawking is talking about in his book.

 

Let me ask this--DD has clearly said that |undefined information| must include all of non-existence for the reason that even non-existence requires explanation. Well, let us eliminate from |undefined information| everything except non-existence as a mental exercise. From where then would your undefined repetitive patterns derive from ? So, in this sense, this what you can know about |undefined information|, it is the source of undefined repetitive patterns of energy (and thus matter via Einstein equation), and this source is what we call "existence". One thing I like about the presentation of DD is that it has made me to realize that information is prior to both energy and matter (E and M derive from I), and all of it was undefined at the get go. I find this to be a radical yet exciting new way to look at what exists and what does not exist. I am sorry if this is not how you and DD see things.

 

It is how we see things epistemologically (from "what and how can we know" stand point), but we are trying to be careful to not sound like we are making any ontological implications.

 

Epistemologically, of course information precedes any mental idea of reality (which contains the idea of energy and matter). Ontologically, who knows? I have my beliefs, but I can't objectively defend them.

 

I agree without argument the first and last claim. But, when you say all explanations are "based on" finite information--depends what you mean by "based on". For examples, without |undefined information| no explanation would be possible, and |undefined information| is infinite--correct ?

 

You are probably thinking the potential amount of undefined information, i.e. that there's no upper limit to how much can accumulate. That's true, but in terms of forming explanations from undefined information, it is important to keep in mind that the amount of information that can actually be taken into account in the formation of an explanation, is always finite. That is what I mean "based on"; your accumulated past is always of finite amount, and your explanation is a function of your past, not your future.

 

That argument is actually used in the analysis; that is why the undefined information that is standing behind an explanation, can be referred to as "elements", i.e. some discreet "points" of information. We don't know what that information is actually like at all, but then none of the further arguments rely on knowing something like that. They do rely on knowing it is of finite amount though.

 

Second, why must elements be "persistent" ? Many particles of decay physics have lifetimes on order of 10^-15 or greater seconds, not what I would call "persistent", and of course at least some explanations need to define these "non-persistent" particles.

 

I don't mean persistent as in existing throughout the history of the known universe, but just persistent as in surviving at least through 2 consequent "t"'s. Without definitions, each "t" just contains new "elements of information" without any connection to anything in the previous "t" (and that is why no predictions can be made either). With definitions, different elements of information in different "t"'s can be associated with each others, i.e. some "defined elements" are thought to have persistent identity to themselves.

 

That is universal to all explanations that can make predictions; you need that in order to be able to think about where some element will be in the future.

 

Yes, this is one reason why I like the presentation, it presents in a mathematical way that what humans claim they understand about ontology, each specific claim by each human is only their representation of ontology, no one specific representation can be viewed as being correct as to the essence of the ontology, that essence remains forever off limits (at least to humans).

 

Yes, and isn't it annoying that people always use the validity of their specific definitions as "proof" that their definitions are somehow "like" ontological reality... This is very much on the topic of "model-dependent reality".

 

As a side note, I think this may be so because the essence of ontology may lie to the other side of the Planck limits (of time, space), which we know from quantum theory humans can never penetrate. But see that, while I agree with what you say, this does not mean to me that there is not in fact some essence to ontology, it is just that we can never know what it might me. Thus, the essence of ontology is prior to any explanation of it. But, the presentation of DD has nothing at all to do with "essence of ontology" so we are getting very off topic.

 

If you manage to walk through this thing, you will see there are some very good epistemological reasons for why our idea of reality is so model dependent, and why the model called "modern physics" contains all those interesting and elusive features to it (all those seemingly idealistic features associated with observations etc)

 

I do not agree, mostly because I have no idea what you mean by "indivisible element" as would relate to the set of all possible explanations of puzzle pieces and individual humans. For me, each human and each puzzle piece is a "primary substance", which would be your concept of "indivisible element". Each could be assigned an (xi) in a non-trivial manner.

 

Maybe Bombadil's reply helped already, so I'll just comment that what you mean by "a human" cannot be taken as primary substance because it's behaviour needs to be represented somehow (you know, everything that stands behind your definition of what "a human" is), and a single index cannot capture that.

 

Perhaps if you define exactly what you mean by "element", and "persistent" that would help. At this point we clearly are talking about two completely different things, and thus makes me wonder if we find yet another constraint to the definition of explanation used ?

 

a "defined element" of an explanation is something an explanation takes as indivisible. To give an example from modern physics, the fundamental particles listed here: http://en.wikipedia.org/wiki/Elementary_particle are all elements thought to not have sub-structure.

 

If an explanation takes some object as divisible into two simpler elements, then it would also be represented in the notation as a composite object of two indices neighbouring each others.

 

When I refer to more complex defined objects, I tend to call them "defined objects". Maybe a terminology clarification would be in order.

 

I'm not sure I would say the behavior of an electron is simple. For example, we cannot measure both the position and momentum at the same time, very easy to do for any human. Then, quantum theory tells us the behavior of an electron is such that it can be at two places at the same time, which seems not so simple--something I often wish I could do but find very difficult if not impossible. So, it seems to me that representing a person in the notation should in principle be much more simple than applying it to something that can be in two different places at exactly the same time.

 

If you manage to walk this thing through, you will understand why the concept of superposition is valid and necessary from the underlying definitions of elements.

 

What I meant by the behaviour of human being mind bogglingly complex is that to capture everything that is "a human" is to capture the orchestrated behaviour of a mind boggling number of simpler elements. That includes very large number of electrons too.

 

(Actually in your example you were only referring to decision making mechanisms of a human being, but that too entails defining how a human being makes definitions in some sufficient detail, in terms of indivisible elements)

 

-Anssi

[AnssiH]

Ok, I have moved on to the next section, and find this quote of Doctordick, just after the introduction of the probability constraint of >= 0 and <= 1:

 

A major roadblock for me. I do not understand why we "must" avoid that constraint. Does this mean that if we do not avoid the constraint we have a circumstance that is outside use of the notation ? Are we not looking for a general notation that can be used to explain situations not only outside the definition of the circumstance, but also inside the definition of the circumstance under examination ? Is not any circumstance (that is, the list of questions) by definition within the probability constraint, that is, you have all of them, none of them, or some percentage of all of them other than 0%?

 

As you can see, I have no clue why we "must" avoid the constraint, and exactly what would be the consequences if we do not. Seems to me that if we are at this junction of the presentation to move the mathematics down one of two possible statistical paths (by mathematical means outside the definition), it would be helpful to show the mathematical outcome of the other possible path (mathematical means inside the definition). Major help needed here.

 

He means simply that, his requirement that the probability function gives its expectations in normalized fashion, should not (and does not) limit the possibilities when it comes to explaining some information.

 

At the face of that constraint, some readers might be prompted to think that "gee, obviously there can exist explanations that give their probabilities in some other range, like between 1 and 10, and thus they are not taken into account anymore".

 

DD is laying down a simple mathematical procedude that takes any explanation and translates its probability "range" into range between 0 and 1.

 

In other words, he is just saying that requiring that constraint of normalized probability, does not steer our analysis towards some specific set of explanations; we are still analyzing properties that are common to all explanations.

 

If [imath]\vec{G}[/imath] corresponds to probabilities given by "some valid explanation", then;

 

We merely integrate (or sum) the function [math] \vec{G}^\dagger\cdot\vec{G}[/math] (which is [math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math] times some constant) over all possibilities and use the fact that P integrated (or summed) over all possibilities has to be one to establish that constant of proportionality. We then merely divide [math]\vec{G}[/math] by the square root of that integral (or sum) and obtain a new function (which I will call [math]\vec{\Psi}(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math]). At this point the correct probability for the expectations predicted for our explanation can be written

 

 

[math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t) \equiv \vec{\Psi}^\dagger(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\cdot\vec{\Psi}(x_1, x_2, x_3,\cdots, x_n, \cdots, t)[/math]

 

 

-Anssi

[Rade]

Thank you AnssiH for the clarity of your explanations.

 

One question about this comment you made

 

If an explanation takes some object as divisible into two simpler elements' date=' then it would also be represented in the notation as a composite object of two indices neighbouring each others[/quote']OK, so suppose an explanation that takes some object as divisible into three simpler elements, then one way the "defined object" could be represented is (x1y1z1)--would that be correct ? Also, I assume one could have a mixture of "defined elements" + "defined objects" for any given explanation--correct ?

 

Next I would like to comment on this comment

 

a "defined element" of an explanation is "something" an explanation takes as indivisible...not to have sub-structure

OK' date=' I agree completely. You gave a list of such defined elements from physics, such as the "photon", OK, I agree. But, of course we cannot limit our understanding of "element" to these physical examples, because the word has other meanings.

 

One such meaning was given by Aristotle, it is what he called the "primary substance". So, here are some statements made by Aristotle [Categories, Chapter 2']

..."everything except primary substances is either predicable of a primary substance or present in a primary substance"..."and if these last did not exist, it would be impossible for anything else to exist". "Primary substances are most properly called substances in virtue of the fact that they are the entities which underlie everything else"..."no one primary substance is more truly substance than another"..."all substance appears to signify that which is individual. In the case of primary substance this is indisputably true, for the thing is a unit"..."substance has no contrary. What could be the contrary of any primary substance, such as the individual man or animal ?. It has none." ..."no single substance admits of varying degrees within itself"..."one man [as primary substance] cannot be either more or less man than another"..."the most distinctive mark of substance appears to be that, while remaining numerically one and the same, it is capable of admitting contrary qualities".

 

My point here is that, it is my opinion that the "defined element" of DD is the same concept as the "primary substance" of Aristotle, in the sense that it is a "defined primary substance". Thus, a "defined" individual man as a primary substance, as a unit, is as much a "defined element", as a unit, as would be the photon of physics. This is why, in the puzzle example I presented, each puzzle piece represented an indivisible "defined element" and has no sub-structure, and thus could be represented in the (xi) notation of DD. If this understanding is not correct, then please explain exactly how the concept of "defined element" disagrees with any of the claims made by Aristotle as to what could be called "defined primary substance".

 

As you can see, I find the following to be true by definition" element = primary substance. So, I need you to explain why this is a false claim.

 

Moving on to this conclusion of DD

 

We then merely divide [math]\vec{G}[/math] by the square root of that integral (or sum) and obtain a new function (which I will call [math] \vec{\Psi}(x_1' date=' x_2, x_3,\cdots, x_n, \cdots, t)[/math']

So, is DD using Greek [math]\vec{\Psi}[/math] with future goal of relating this new function to the "wavefunction" [math]\vec{\Psi}[/math] of quantum theory ? Also, I see that imaginary numbers now enter the presentation as being possible, and of course "i" is critical to quantum theory. So, I wonder, is it possible that DD developed use of Greek symbol notational presentation for explanation working backwards from the concept of the quantum "wavefunction" [math]\vec{\Psi}[/math] ? It makes sense given that DD is a trained physicist, and it also would help explain why the notational approach will ultimately lead to deriving the [math]\vec{\Psi}[/math] as it is today used by quantum physics ?

[Rade]

Moving on, I see this quote

 

Another possibility is that integration (or sum' date=' considering possible singularities) over [math']\vec{G}^\dagger\cdot\vec{G}[/math] is undefined. In that case, I would hold that the offending function simply cannot be seen as equivalent to an explanation: i.e., if one cannot define a probability from that function it simply cannot serve as a representation of an explanation

Well, this would certainly be a major problem for explanation itself if this situation is common when an explanation is put forward. Would anyone know how common such a problem would be ? I mean, would <1% of all possible explanation meet the [math]\vec{G}^\dagger\cdot\vec{G}[/math]"undefined" criterion or >99%, or some % between ?

[Rade]

Moving to the end of the presentation, there is this very cryptic statement

 

 

mathematically speaking that would be for all circumstances where t is less than the current present (whatever index the explanation puts upon that present)' date='

 

[center']

 

[math]P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)dV_x=\vec{\Psi}^\dagger \cdot\vec{\Psi}dV_x[/math]

 

[/center]

 

 

where dV_x is the differential volume [math]dx_1dx_2\cdots dx_i \cdots [/math] if the possible circumstance constitute a continuous field or one if the circumstances are discreet.

What does this mean.. "t is less than current present" ? Does this mean the "past", so, if present "t" was today, less than today would be yesterday, and greater than today would be tomorrow ? Why use the words, "less than" (which implies a "greater than") in reference to a "present" ? Would it not be better to say "t is before current present" and "t is after current present" ?

 

Also, why is the word "volume" being introduced at this end point of the presentation where the circumstance under consideration is a "continuous field" ? How do we jump from discussing probabilities of expectations to "volume" of something ? I also have no idea how we got to the conclusion that something called [math]dV_x[/math] can take two forms (1) a differential volume [if circumstances constitute continuous] or (2) the number 1 [if circumstances constitute discrete]. And, it seems that this: [math]\vec{\Psi}^\dagger \cdot\vec{\Psi}dV_x[/math] appears completely out of the blue, it makes no sense to me. Also, what exactly is a "continuous field", and how did we get to discussion of a "field" concept ? Could you please give an example of where circumstances are "discrete" as opposed to "continuous field". Finally, should it be "discrete field" to match "continuous field" ?

 

I am left with the feeling, after reading the above section, that there is a chapter of information about physics that the reader is assumed to have knowledge of, so many physics terms (volume, densities, fields, etc.).

 

Well, it looks like I am at the end of this thread, I have no further questions or comments.

[AnssiH]

OK, so suppose an explanation that takes some object as divisible into three simpler elements, then one way the "defined object" could be represented is (x1y1z1)--would that be correct ?

 

No, it's more like having [imath](x_1, x_2, x_3)[/imath] (each element having their own "x"-variable of course) sticking in close proximity together through some evolution of "t"'s. Think of an ordinary definition of something like an atom. Just like an atom is by definition some specific number of specific sub-elements stuck together in some specific way, that's also how such things would be mapped in this notation. It is some specific interaction (represented through an evolution of "t"'s) between some defined elements, which actually defines a more complex object.

 

Also, I assume one could have a mixture of "defined elements" + "defined objects" for any given explanation--correct ?

 

Definitely.

 

OK, I agree completely. You gave a list of such defined elements from physics, such as the "photon", OK, I agree. But, of course we cannot limit our understanding of "element" to these physical examples, because the word has other meanings.

 

Definitely.

 

One such meaning was given by Aristotle, it is what he called the "primary substance". So, here are some statements made by Aristotle [Categories, Chapter 2]

..."everything except primary substances is either predicable of a primary substance or present in a primary substance"..."and if these last did not exist, it would be impossible for anything else to exist". "Primary substances are most properly called substances in virtue of the fact that they are the entities which underlie everything else"..."no one primary substance is more truly substance than another"..."all substance appears to signify that which is individual. In the case of primary substance this is indisputably true, for the thing is a unit"..."substance has no contrary. What could be the contrary of any primary substance, such as the individual man or animal ?. It has none." ..."no single substance admits of varying degrees within itself"..."one man [as primary substance] cannot be either more or less man than another"..."the most distinctive mark of substance appears to be that, while remaining numerically one and the same, it is capable of admitting contrary qualities".

 

My point here is that, it is my opinion that the "defined element" of DD is the same concept as the "primary substance" of Aristotle, in the sense that it is a "defined primary substance". Thus, a "defined" individual man as a primary substance, as a unit, is as much a "defined element", as a unit, as would be the photon of physics. This is why, in the puzzle example I presented, each puzzle piece represented an indivisible "defined element" and has no sub-structure, and thus could be represented in the (xi) notation of DD. If this understanding is not correct, then please explain exactly how the concept of "defined element" disagrees with any of the claims made by Aristotle as to what could be called "defined primary substance".

 

As you can see, I find the following to be true by definition" element = primary substance. So, I need you to explain why this is a false claim.

 

Well I just read the "Categories" from here;

http://plato.stanford.edu/entries/aristotle-metaphysics/#Cat

 

And what Aristotle refers to as primary substance (of categories) is not analogous to indivisible elements of an explanation. He is talking about categorization of definitions, e.g.;

 

"Musical instrument" has hyponyms such as "guitar", "piano", "flute".

"Guitar" has hyponyms like "electric guitar", "acoustic guitar"

And so on;

Electric guitar -> Gibson Les Paul -> "this individual Gibson Les Paul"

 

When you get to an individual object, i.e. something that doesn't have hyponyms, that is what he calls primary substance (of categories), because he is getting to the fact that without a single individual Gibson Les Paul guitars, their hypernym or genus category - Gibson Les Paul - doesn't exist either. Obviously, if you don't have a single sample of some "type", there's no categorization for those types either. I.e. without a single sample of something that has got "color", the category "color" doesn't exist either.

 

What he is getting at doesn't mean that what he calls "primary substance" is same as fundamental elements of all understandable structures (unless of course you just so happen to be categorizing the fundamental particles and end up with "this individual photon" :)

 

If you wanted to represent a Gibson Les Paul guitar in DD's notation, your representation needs to capture what is actually taken as Gibson Les Paul guitar. You can't just put down a single index, and expect that can be understood as an electric guitar, because a single index doesn't in any way represent anything like the behaviour understood as "electric guitar".

 

A representation that would capture all that is needed to take something as an electric guitar, would contain a lot of indices doing very specific things temporally and spatially.

 

That's the basic problem with these kinds of thought experiments (like the puzzle room), that the representation in universal notation actually needs to represent what is meant by something being "a person"; the mapping needs to contain that specific behaviour taken as "person". Regardless of what you think a person is actually ontologically made of, it is never enough to refer to a person as a single index, because it doesn't capture what "person" means in the setup of that thought experiment. The only thing we could possibly say about a person as a single index is where he is positioned in our coordinate system in different "t"'s. To actually say all those other things that are required for something to be "a person", would require a lot more indices and very specific interaction between them through "t"'s.

 

So, is DD using Greek [math]\vec{\Psi}[/math] with future goal of relating this new function to the "wavefunction" [math]\vec{\Psi}[/math] of quantum theory ? Also, I see that imaginary numbers now enter the presentation as being possible, and of course "i" is critical to quantum theory. So, I wonder, is it possible that DD developed use of Greek symbol notational presentation for explanation working backwards from the concept of the quantum "wavefunction" [math]\vec{\Psi}[/math] ? It makes sense given that DD is a trained physicist, and it also would help explain why the notational approach will ultimately lead to deriving the [math]\vec{\Psi}[/math] as it is today used by quantum physics ?

 

He is using the same symbols because he knows what they end up corresponding to in the final analysis. It is just convenient to not have to change the symbols in the end.

 

And he is deliberately making moves that get us to identical representation as modern physics (especially when we get past the point of "fundamental equation"), which is sort of the point; we get to analyze the epistemological roots of the definitions of modern physics.

 

The important point is that each of those moves is valid universally to any set of definitions, regardless of what the underlying undefined information is like. Meaning, that any recurring patterns in any sort of undefined information can be processed through transformations that make it look exactly like modern physics. But I'm getting ahead of things now, so don't worry if that doesn't make sense to you yet.

 

Another possibility is that integration (or sum, considering possible singularities) over is undefined. In that case, I would hold that the offending function simply cannot be seen as equivalent to an explanation: i.e., if one cannot define a probability from that function it simply cannot serve as a representation of an explanation

Well, this would certainly be a major problem for explanation itself if this situation is common when an explanation is put forward. Would anyone know how common such a problem would be ? I mean, would <1% of all possible explanation meet the [math]\vec{G}^\dagger\cdot\vec{G}[/math]"undefined" criterion or >99%, or some % between ?

 

Like DD says, that case is essentially outside the definition of an explanation; if the output of a function cannot be interpreted as probability at all, it simply is not a function that predicts a future.

 

So as long as we stick with our definition of an explanation, 0% of explanations have that problem :)

 

What does this mean.. "t is less than current present" ? Does this mean the "past", so, if present "t" was today, less than today would be yesterday, and greater than today would be tomorrow ?

 

Yes that is what he means. A probability function needs to give correct probabilities for your known past. If it violates your past, it is known to be invalid.

 

Also, why is the word "volume" being introduced at this end point of the presentation where the circumstance under consideration is a "continuous field" ? How do we jump from discussing probabilities of expectations to "volume" of something ?

 

It's a mathematical concept used in describing probability densities. DD uses [imath]dV_x[/imath] to refer to [imath]dx_1dx_2\cdots dx_i \cdots[/imath], i.e. all possibilities, or all possibilities of some specific range (in which case we get relative probabilities to that range, instead of absolute probabilities).

 

Like;

http://en.wikipedia.org/wiki/Probability_density_function#Densities_associated_with_multiple_variables

 

That's related to what he was saying earlier in the OP; as per the definition of probability, the sum of "all possibilities" is required to yield the probability of "1". In the case that the specific explanation assumes the possible values for those variables are continuous, mathematically that is cumbersome because it means that any single possibility is 0. That is when you have to use the idea of probability density to represent your probabilities.

 

Secondly, the specified integral (or the specified sum) might be infinite and division by infinity is exactly zero causing the defined function (which is to be our explanation) to vanish exactly. From the perspective of probabilities, this second case actually appears to be quite reasonable. Anytime the number of possibilities goes to infinity (i.e., there are an infinite number of possibilities which do not vanish) the probability of a specific result must vanish. In that case, we concern ourselves not with specific cases but rather with ratios between integrals (or sums) taken over various ranges.

 

For a more detailed explanation of that same issue, read this old post;

http://www.physicsforums.com/showpost.php?p=1345013&postcount=441

 

and this from the "as far as dV is concerned" onwards;

http://www.physicsforums.com/showpost.php?p=1387960&postcount=478

 

DD can probably explain this better to you once he gets back, since I am also familiar with the idea only in so far that it is used in this analysis.

 

I also have no idea how we got to the conclusion that something called [math]dV_x[/math] can take two forms (1) a differential volume [if circumstances constitute continuous] or (2) the number 1 [if circumstances constitute discrete].

 

Because in the case the possibilities are taken to be discrete (by the explanation), i.e. of finite number, then we can get absolute probabilities instead of relative to some range of possibilities.

 

And, it seems that this: [math]\vec{\Psi}^\dagger \cdot\vec{\Psi}dV_x[/math] appears completely out of the blue, it makes no sense to me. Also, what exactly is a "continuous field", and how did we get to discussion of a "field" concept ? Could you please give an example of where circumstances are "discrete" as opposed to "continuous field". Finally, should it be "discrete field" to match "continuous field" ?

 

It is entirely up to the specific explanation whether it supposes the possible values to its defined elements are discrete or continuous. The notation just needs to allow a representation of both cases, that's all.

 

I am left with the feeling, after reading the above section, that there is a chapter of information about physics that the reader is assumed to have knowledge of, so many physics terms (volume, densities, fields, etc.).

 

Well it's more that the reader is required to have some knowledge of the mathematical concepts used (physicians would have that knowledge too though). But remember, I had no knowledge of those concepts either, at the end of the day it's all up to the reader to educate themselves of necessary concepts when they arise. That's what I did anyway.

 

Well, it looks like I am at the end of this thread, I have no further questions or comments.

 

Yup, DD will continue from where the OP left, once he gets back. Next up the expression of the universal symmetries, and the combination of those expressions into the fundamental equation. After that we get to the real meat. (in a way that you'll actually understand the implications :) )

 

-Anssi

[Rade]

Thank you AnssiH, again, clear explanations, even if some of the math transformations I must just take on faith (I assume they are correct otherwise some mathematician would have destroyed this presentation long ago).

 

I see only one issue that remains, I do not agree with this comment you made

 

And what Aristotle refers to as primary substance (of categories) is not analogous to indivisible elements of an explanation. He is talking about categorization of definitions' date=' [/quote']Yes, and that is exactly my point. The presentation of Doctordick also is about "categorization of definitions"--they are what you call "defined elements". The presentation places (defined elements) that derive from |undefined information| into categories, such as the set of all defined elements that are in the category called "the past", the set of all defined elements that can be indexed by a unique (t), etc.

 

So, yes, each unique "defined element" would be the same as each Gibson Les Paul guitar as a "primary substance", as a thing that is an individual, as a UNIT, it is indivisible. I cannot take away any part from the Gibson Les Paul guitar and claim to have the same. It can no more be divided than a photon can be divided, this is what "primary substance" means. Only higher order substances, such as secondary substances, can be divided.

 

In discussion of an object, you said that a defined object with three defined elements can be represented (x1,x2,x3). In the same way, a three piece band (an object) can be represented as three defined Gibson Les Paul guitars (each a primary substance), attached to three humans (each three other primary substances), as (xiy1,x2y2,x3y3). I just do not understand your reluctance to accept the universal sense in which the English word "element" can have meaning, especially as relates to the presentation by Doctordick concerning his "defined elements" ? From my perspective your worldview adds a massive constraint on the application of the presentation, it does not allow for explanation of circumstances where each (xi) represents a unit of a primary substance as being the same as a defined element.

 

So, I am left with this one rather major concern with the presentation.

[Kharakov]

Secondly, the specified integral (or the specified sum) might be infinite and division by infinity is exactly zero causing the defined function (which is to be our explanation) to vanish exactly.

You might want to correct this part as division by infinity is not exactly zero. It's an infinitesimal. [math]\frac{2}{\infty}[/math] does not equal [math]\frac{1}{\infty}[/math].

[Qfwfq]

I am actually not a big fan of the term "undefined element" because it implies something recognizable. I find it easiest to just think of "undefined information" as some sorts of events or patterns of unknown meaning and origin.

Actually, I have been cringing whenever you write "undefined information" because I find it meaningless and oxymoronic, I think unknown meaning makes more sense and, strictly, data rather than information. If you start with "data of unknown meaning" and somehow arrive at a meaning of it, you have "turned it into information" or, more precisely, it becomes possible to extract information from it.

 

I'm not entirely sure what you are asking about, but does it suffice if I say that different explanations simply interpret the undefined information in terms of different defined elements, and thus see a wildly different "subjective reality" as well?

I might caution against confusing "different descriptions" with "different realityies" and in the latter case, it is a quite debatable matter but definitely not a new idea. Monism hasn't always been the dominant opinion. So:

Why is it that when an authority figure says it, it is suddenly being "introduced to the world"?

Well, journalists are always journalists.

 

Just the fact that you can take any representation of any dynamic behaviour, and just choose to represent the same behaviour (semantically) differently, is to me the same thing as model-dependent realism.

Caution, caution, caution...

 

I have not read the book but I can pretty much tell what he is getting at, and this analysis is very much an exact scientific proof of Stephen Hawking's musings about model-dependent realism. But I think it would very much surprise Stephen how much of our idea of reality really is traced to be entirely model-dependent.

I would be even more cautious about saying these things. First of all, the old adage: Never judge a book by its cover. Mostly, I have doubts about Dick's analysis being "very much an exact scientific proof of Stephen Hawking's musings about model-dependent realism" and about it being even more than Hawking would dare to think (and how can you make the comparison anyway?).

 

For instance, the predictions made by modern physics are obviously giving some expectations in terms of its own definitions.

 

It is not possible to give expectations in terms of undefined information itself, by definition

Yeah, in terms of the second statement, the first is obvious and it goes even if you don't specify "modern physics" so what implications can it have?

 

Whenever people say "photons exist", I can never tell which meaning they use. Do they mean that the concept of photons appears in every valid way to comprehend reality? Or that our definition of a photon is aligned exactly with the same kind of real object? Or just that it is one valid way to categorize reality this way?

I would say most certainly the first, hardly the third, while the second is a very subtle matter that I am not inclined to go into in this thread. Suffice it to say (repeat, actually) that you should be wary of taking things that you hear here and there about modern physics as being the way all physicists see it and always meant so plainly and literally.

 

There are also valid ways to categorize reality in terms of aether. It's just very unpopular, and that's why people say it doesn't exist. So, what's the difference, when multiple valid explanations exists? I'm sure that's exactly what Hawking is talking about in his book.

I find you are being very arbitrary.

 

Yes, and isn't it annoying that people always use the validity of their specific definitions as "proof" that their definitions are somehow "like" ontological reality... This is very much on the topic of "model-dependent reality".

Yes, it's annoying, isn't it? Very much like presuming to interpret what the author of a book means, without having read it. Well, I guess I won't be spending more time on these posts, I would have more interest if the thread could concisely clarify the steps from what's in the OP to Dick's Famous Equation, enough to make a critical examination possible (more than in past times) for me,