What I believe an explanation is!

[modest]

Hello DoctorDick. I reread the thread hoping to gain a firmer footing. Unfortunatly, like quicksand, I think I just got swallowed up a little deeper

 

:)

 

I'm exaggerating :) hopefully :D

 

It is quite simple actually, anytime one has a theory one must be able to compare the consequences of that theory to the actual information on which it is based. To the casual observer, it might appear that the “i” index is sufficient to that purpose; however, that is not quite true. The problem with the “i” index is that it is defined by the specific theory being examined and that theory could be incorrect. The fact that the theory might be incorrect implies that the “i” index identification could also be incorrect. It should be held in mind that being correct is actually quite a different classification than is “flaw-free”.

 

If we are to include all possible “flaw-free” theories, we must allow for all possible mappings from each of those theories to the actual information which is to be explained. Our model must allow such a comparison without specifying what the actual labels are.

 

Yes, I understand the difference between being correct and being flaw-free. Actually, you'll see I introduced the issue in this thread in post 18 ;)

So, I'd say it's true that "given an arbitrary prediction, an acceptable explanation could tell us if that prediction were acceptable or not", but that would not necessary mean the prediction would be correct.

I do understand that an explanation may be flaw-free yet incorrect. What I was a bit unclear on was the need for 2 labels for an element ("x" and "i") and also two lists. If the information list is the past, the actual information, then I don't see why it needs or why it should contain "i". On the other hand, if the explanation list contains "x" then I see no purpose for the information list at all. It's already represented in the explanation list.

 

You are correct; there are indeed going to be three different lists here serving three very different purposes

 

Oh, my.

 

The “knowledge list” (as I intended to use it in the quotation you referred to) is an excerpt from the information list which is used for the purpose of analyzing the actual use of the “explanation”.

 

Ok. Would you say the knowledge list is part of the past while the information list is the whole past (where the past is defined as what is known)?

 

Also, does the knowledge list contain unknowable information as implied here:

From that perspective, we can conceive of “having the explanation list” (no mention of how that result was achieved) without actually having the “knowledge list”.

It's also difficult for me to imagine what the information list and the knowledge list are going to be practically used for if their information will always be indeterminate.

The fundamental purpose of an explanation is to allow one to deduce the constraints imposed upon the answer to a question when given only small part of the relevant information. The essential situation is that if we actually knew the entire “information list” an explanation is rather beside the point; we could simply refer the questioner to the ”what is”, is “what is” explanation.

 

What is important here is that other, quite simple, explanations exist. Explanations which do not require memorization of the entire “information list” and it is these explanations which are of interest to us.

 

Right. I agree, a rather small explanation can explain a rather large set of information.

 

In the absence of persistence, I suspect the simple ”what is”, is “what is” explanation is the only possibility: i.e., we have the information list and nothing more.

 

But, I can conceive of information where there is no persistence such as (x)_t = {(1)₁, (2)₂, (3)₃...} yet an explanation such as dx=dt is possible. By my thinking this would be like a timer—not persistent, but explainable by means other than a list of each tick.

 

So, presuming you understand everything up to this point, that brings me back to the question I asked earlier. The one I referred to in post #35.

Let us go back to that original question, suppose we are given a set of numbers (a supposed “present”) and are asked, “what is the correct t index assigned to that set?” The possibility certainly exists that there are multiple presents with exactly the same set of reference numbers associated with different “t” indices. In that case, our ”what is”, is “what is” explanation (as currently defined) will fail to provide us with an answer.

This thread has now exceeded fifty posts and I was unable to find the post where I originally asked that question which is somewhat troubling. Nevertheless, this is a very important question and resolving it will lead to more subtle issues. We need to be able to handle this kind of question. Let me know that you understand the issue I am bringing up.

I suspect this is where tau gets introduced. To be honest, the development of this model is not feeling like a deductive method to me.

 

The "t" index distinguishes different presents. Only by arbitrarily ignoring the value of "t" for a given set does one have trouble telling in which of two otherwise identical presents it belongs. Arbitrarily ignoring one index doesn't seem like a good reason to add another.

 

~modest

[Doctordick]

Sorry to be so slow. I have been having some minor electronics problems. Modern technology seems to be getting the upper hand on me.

Hello DoctorDick. I reread the thread hoping to gain a firmer footing. Unfortunately, like quicksand, I think I just got swallowed up a little deeper

I had wondered why you had taken so long to respond to my last post. Thank you for making it clearer for me.

I do understand that an explanation may be flaw-free yet incorrect. What I was a bit unclear on was the need for 2 labels for an element ("x" and "i") and also two lists.

It is quite clear to me that you are missing the very essence of what I am doing. You are thinking in terms of specific explanations; not in terms of the general problem of creating a mechanism capable of representing any and all possible explanations: i.e., not knowing anything about what they are or what is being explained. We have a problem here which absolutely no one (except for myself and Anssi) has made any attempt to come to grips with. The underlying problem is, how does one represent something when they have utterly no idea as to what it is they are talking about. You have to confront that problem before we can even begin to talk about how to solve it.

 

We need both x and i for the very simple reason that we have two very different collections of concepts to deal with here. First there are the concepts needed by a specific given explanation. We need an extremely general way of specifying these ideas (concepts, ontological elements, noumenon, ... or whatever you desire to call them) which stand behind our explanations: the things on which the flaw-free theories (or explanations) and their epistemological constructs are built. No explanation serves any purpose if that explanation can not be understood. In order to be understood, the explanation must be expressed in terms of meaningful labels. The first question to be answered is, what mechanism are we going to use to represent these undefined “things”. We need some kind of language to do such a thing: i.e., the definition of the language itself is part and parcel of the explanation. The labeling mechanism must be independent of the language used (this must be so because the language itself, and that would be any language, is a presumed explanation of sounds, marks and ideas). It should be clear that we may use numerical references to identify these “things”. That is the essence of the index “i”.

 

If we have a specific explanation (which includes everything necessary to understand that explanation) and do indeed understand that explanation, we can specify each and every elemental component of that explanation (and that includes the language necessary to that explanation) with specific numerical values for all references “i”. If you wish, you can think of that collection of numerical references as a computer file containing the entire body of that specific explanation (every document including the descriptions of all phenomena associated with that explanation, including an entire complete presentation of the language necessary to understand the explanation and every bit of information standing behind the explanation.) That is to say that a complete collection of the necessary information requires all connections and relationships within that data to represent a specific pattern: the specific explanation being represented. In essence, the existence of a specific explanation implies possibility of generating a specific set of indices “i”.

 

Now, under the assumption that you understand what I have just laid out, let me ask you a simple question. Is that collection of indices “i” sufficient to label all possibilities of interest here? When I say “all possibilities” I don't mean “any” specific explanation; I instead mean “each and every possible flaw-free explanation”. I must assume that you are bright enough to realize that the answer to that question is quite clearly “no” as the “i” indices represent a specific (possibly known) explanation.

 

Try and look at it from the following presumption. Suppose, for the sake of argument, you have a “correct explanation” (that presumes such a thing exists but we really need not worry about that issue for the moment). Clearly, that “correct” explanation could be set forth via some set of indices “j” totally and completely analogous to the index “i” just discussed. The next question which should arise in your mind is, does there exist a one to one correspondence between each and every possible specific index in the set “i” and the set “j”? The answer has to be a resounding no as, if there were, the collection represented by the indices “i” would be exactly that “correct explanation” represented by the set “j”: i.e., all information contained in the complete set "i" would be identical to the set "j".

 

To go off on a tangent for a moment, I am of the opinion that (among almost all people) there is a major misunderstanding of exactly what the conflict between “science” and “religion” is all about and it has to do with comprehending exactly what a “flaw free explanation” is. An excellent example of what I am talking about is the simple explanation, “It is no more than what God wants it to be!” That is a perfectly flaw-free explanation of everything. There exists not a whit of evidence to counter that assertion. The flaws occur not with the explanation itself but rather with those who claim to know the “will” of God. The real problem with such an explanation is that it is not really a very useful explanation (except perhaps for controlling the behavior of gullible people, but that is not the central issue being discussed here): i.e., scientists perceive scientific explanations as better than religious explanations for the simple fact that they provide much more useful deductions. In fact, I could comment that there exist scientific explanations known to be flawed which are commonly used every day for the simple fact that they are so useful. This is exactly the issue lawcat brings up in the following post (though I wouldn't suggest he understands what I am talking about).

I must disagree with this categorical statement. And not to beat a dead horse, but as everyone knows, science is probabilistic. For example, take Octet Stability Rule which is well accepted Materials Science and Engineering/List of Topics/ Octet Stability by Electron Sharing - Wikiversity. The rule states that satellite atoms will combine to form 4 bonds with the central atom. Yet, this is not always true. For example, in Sulfate Hexafluoride (SFl6), Fluorides form 6 pair-bonds with the sulfate atom. There are exceptions. The SFl6 is inconsistent with Octet Rule, yet the science is probabilistic and accepts this theory.

When I was a graduate student, I had many an argument with both other students and with faculty concerning this very issue. I always asserted that, “any theory which, when pushed to the limits of its supposed applicability, gave incorrect answers”, was wrong. They all essentially took the position that I was pushing the said theories outside the realm assigned to them. What they didn't understand (and I guess I never made clear) was that I wasn't saying these theories were not useful (as they were all quite useful); I was simply pointing out that they were wrong (a totally different issue). Science is chock full of “compartmentalized thought”. The first requirement of a valid explanation is that it must start by being flaw free. Otherwise it is actually little more than “a rule of thumb”. Being useful is a totally different issue entirely.

 

The question here (in the logic of creating a representation of an arbitrary flaw-free explanation) is, can a one to one correspondence between all the elements of the ancient Roman gods (and what consequences can be attributed to them by those who believe such an explanation) be established with all the elements of modern physics? It should be clear to you that we certainly cannot use the same set “i” for every possible flaw-free explanation.

 

But, back to the set “j” defined to represent that correct explanation. That would appear to be a rather unique set. If that is indeed a correct explanation, then the collection of the entire set of “j” indices is a correct representation. It follows from that assertion that it must be possible to map each and every “i” index contained in a given "present" to a specific “j” index (however, it should be clear that the reverse is not true as the persistence assumed in the flaw free explanation might be in error). Since we clearly do not know this “correct” explanation and its elements are totally unknown, I use “x” to refer to those elements and thus “x_i” refers to the correct unknown element standing behind that reference index “i”.

 

Is that picture clear to you?

If the information list is the past, the actual information, then I don't see why it needs or why it should contain "i".

We need to be able to refer the elements in the explanation to the actual elements in the information list; without that information, how are we to prove the explanation is flaw-free? Without the subscript “i” how are we to know which elements in the information list actually correspond to which elements in our explanation?

On the other hand, if the explanation list contains "x" then I see no purpose for the information list at all. It's already represented in the explanation list.

We are only beginning the examination of the problem. Since most "useful" explanations are not ”what is”, is “what is” explanations, we cannot presume this relationship will continue into more complex explanations. That is why I wanted you to separate, in your mind, the explanation list from the information list. As I said earlier, it is that move which allows me to talk about the issue of answering questions given less than complete information. And, if we are going to conceptually separate the two, the problem of identifying the explicit elements of the specific explanation with the general elements in the underlying information list resurfaces. A general model of a general specific explanation of generalized information cannot be accomplished without having a way of referring to these different structures of the elements.

Oh, my.

I don't understand your difficulty here. It seems to me that three categories should not be a hard thing to comprehend.

Ok. Would you say the knowledge list is part of the past

No I would not! The knowledge list consists of the information about which the (soon to be asked) question is to be asked. I suppose I should have said,”The “knowledge list” (as I intended to use it in the quotation you referred to) is a supposed excerpt from the information list which is used for the purpose of analyzing the actual use of the “explanation”.

 

Returning, for a moment, the the first question I proposed

Let us go back to that original question, suppose we are given a set of numbers (a supposed “present”) and are asked, “what is the correct t index assigned to that set?” The possibility certainly exists that there are multiple presents with exactly the same set of reference numbers associated with different “t” indices. In that case, our ”what is”, is “what is” explanation (as currently defined) will fail to provide us with an answer.

The information being given here is that “supposed present”. At the moment, we are dealing with a ”what is”, is “what is” explanation so there is no difference between the “information list” and the “explanation list”. That will begin to change soon.

while the information list is the whole past (where the past is defined as what is known)?

I don't really know what you have in your mind when you say, “the whole past”. Let us just say that the “information list” consists of the information on which the explanation is based. I have just defined that to be “the past” and no additional qualities are intended at all.

Also, does the knowledge list contain unknowable information as implied here:

I apologize. I was responding to Rade's comments and began using the word “knowledge” in places where I had already established I would use the word “information”. I have edited that post and replaced “knowledge list” with “information list”. I am very sorry to have confused you. I will try to do better in the future.

It's also difficult for me to imagine what the information list and the knowledge list are going to be practically used for if their information will always be indeterminate.

All I am talking about here is a general representation of “an explanation”. It is going to be used as a mechanism to represent an undefined explanation so that I can examine a generalized expression of the underlying implications.

Right. I agree, a rather small explanation can explain a rather large set of information.

This is a somewhat caviler statement as even the simplest explanation includes the presumption of a language within which that explanation is posed. In that sense, no truly small explanations of any value exist. It is worthwhile to point out that the ”what is”, is “what is” explanation is actually quite universal: i.e., it covers the entire gamut of possibilities. Even the most sophisticated explanation can be mapped into a ”what is”, is “what is” explanation (we tend to call such an explanation “reality itself”). In fact, it could perhaps be seen as the only “correct” explanation of anything.

But, I can conceive of information where there is no persistence such as (x)_t = {(1)₁, (2)₂, (3)₃...} yet an explanation such as dx=dt is possible. By my thinking this would be like a timer—not persistent, but explainable by means other than a list of each tick.

As a general example, you are omitting unbelievably large volumes of information. In particular, you are omitting an explanation of the words you are using to express what you have in mind. It is an excellent example of compartmentalized thinking: i.e., you are presuming the validity of most everything you know.

I suspect this is where tau gets introduced. To be honest, the development of this model is not feeling like a deductive method to me.

No, tau is quite down the road from here and, at the moment, I haven't begun to deduce anything. I am merely laying out a method of representing the general basis from which valid deductions can be made. The only thing of interest at this point is that no possibility be eliminated by the design of the representation of that general basis. I am sure you have heard the old adage, "the trick to finding the right answer is asking the right question". All I am doing here is laying things out so I can ask the right questions.

The "t" index distinguishes different presents. Only by arbitrarily ignoring the value of "t" for a given set does one have trouble telling in which of two otherwise identical presents it belongs. Arbitrarily ignoring one index doesn't seem like a good reason to add another.

You misunderstand the issue I am bringing up. The issue is the ability to answer questions given less than complete information. This is a characteristic we would like a useful explanation to posses; a characteristic quite absent from the simple minded ”what is”, is “what is” explanation. As I mentioned earlier, that explanation could certainly be “correct” but, even if it is “correct”, it has a few problems when it comes to usefulness.

 

I hope I have made myself a little clearer. And I apologize again for confusing you.

 

Have fun -- Dick

[Doctordick]

Hi modest, you are clearly confused over an issue that seems quit clear to me. As I know you are well aware, I have had great difficulty communicating the central issue of my numerical labels x_i. I have just finished reading The Rosetta Stone The Decipherment of the Hieroglyphs, by Robert Sole, Dominique Valbelle and W.V.Davies (or rather, a translation into English by Steven Rendall). Perhaps an example cast as an analogy to Champollion's translation of the Egyptian Hieroglyphs would make the issue clearer.

 

To put the problem in a nutshell, the Rosetta stone (it was found in Rosetta Egypt in 1799) had three inscriptions on it. One in Greek which could be read by the finder, Pierre Bouchard (a French army officer under Napoleon) and two others he could not read. The clue to its importance was in the last sentence of the Greek inscription: “This decree shall be inscribed on stelae of hard rock in sacred characters, both native and Greek, and they shall be erected in each of the temples of the first, second and third category, next to the image of the king living eternally”. No known person had been able to read Egyptian Hieroglyphs for more than one thousand four hundred years. (As an aside, the last document known to be written in hieroglyphs was written around 394 AD. The Byzantine emperors had prohibited the practice of pagan cults. The last Egyptian temple was actually closed around 551 AD.)

 

So there was the problem, they had a text (the English translation of the Greek runs roughly eight pages of type written composition) written in three different languages Greek, Coptic and Egyptian which claimed to say the same thing. Now, let's cast the problem in an abstract form which I hope you can follow. The Greek inscription is the explanation (what it says is really unimportant; what is important is that it can be understood). The Coptic I will lay aside for the moment; its real value is pronunciation as the inscription is essentially a cursive representation of the hieroglyph language about the time of Alexander.

 

The problem then is to associate each and every significant element of the Greek inscription (our explanation) to each and every supposed significant element of the Hieroglyph inscription (what we are trying to explain). First, let us take every element of the Greek inscription (every letter, every word, every phrase, every sentence: every element to which we can assign a meaning) and assign a numerical label to that element (those numbers are analogous to my index “i”). Secondly let us examine the Hieroglyphic inscription and lay out each and every distinct feature of that inscription we can recognize and assign a numerical label to that element (those numbers are analogous to my index “x”). Note that we have no proof that any of those specific features are significant nor can we be sure any one of them actually was intended to convey a meaning but we do know that we have included all features capable of communicating meaning (because any we have not labeled can not be seen as different).

 

Now, our problem is to establish an association between the collection of i indices and the collection of x indices. If we can do so, we have solved the translation problem. How we do that is totally immaterial here; the point is that the solution can be expressed by that collection of numbers called x_i. Note that I have totally thrown away those numbers (both i and x) for which no connection can be made. It is possible that some of my “i” indices serve no purpose: i.e., perhaps there are ideas in Greek which cannot be expressed in Hieroglyphs. Likewise, it is possible that some of those “x” indices serve no purpose: i.e., perhaps there are features of the Hieroglyphs which convey no meaning (say like the angle of a particular line in a specific glyph which is somewhat different in two similar glyphs).

 

The important thing here is that the solution of the problem is in that collection of numbers called x_i. Now, suppose one finds another bilingual document and one does the same thing with that document. Let us call our first solution (x_i)₀ and our solution for the second (x_i)₁. This additional index is to allow changes in the meanings of some glyphs from one document to another (think in terms of context; certainly you must include the possibility of changes). Changes in “i” can certainly also exist; however, those are known (because that is the language the translator understands).

 

The whole object here is to have a way of representing any flaw-free solution of the problem of translating some unknown information into an explanation of that information.

 

Let me know if this analogy clarified anything for you.

 

Have fun -- Dick

[modest]

Thank you for bumping the thread. Perfect timing as I have a couple hours today to spend on this :)

 

It is quite clear to me that you are missing the very essence of what I am doing. You are thinking in terms of specific explanations; not in terms of the general problem of creating a mechanism capable of representing any and all possible explanations: i.e., not knowing anything about what they are or what is being explained. We have a problem here which absolutely no one (except for myself and Anssi) has made any attempt to come to grips with. The underlying problem is, how does one represent something when they have utterly no idea as to what it is they are talking about. You have to confront that problem before we can even begin to talk about how to solve it.

 

Perhaps I've not been specific enough with my comments. It's really not the purpose of the model nor the reasons behind the formalism that are giving me pause. I understand that (and even agree with your fundamental motivation) better than you probably think. My lack of footing is situated at the mechanics, the nuts and bolts, of the model and the model's formalism itself. You might say I understand the reasoning behind the things you've done thus far, but don't feel comfortable in my understanding of their execution.

 

To help solve that problem I'm going to back up and try to make some specific comments on the main developments so far.

 

At this point, “the past” (that which is to be explained or the collection of presents) is a labeled set of ontological elements and the explanation itself is that self same set of labels. The first thing I want to bring forth is the fact that the labels of the ontological elements are themselves a fundamental part of any explanation. If you have no way of referring to those ontological elements (or whatever title you wish to place on the known information) then you cannot build a epistemological construct based upon them. In effect, once you tell me we are discussing a specific explanation, you are confirming the existence of a set of specific labels you have placed upon these elements.

The past is a set. It contains ontological elements which are represented, regardless of their nature, with numbers.

[math]\mathrm{Past} = \mathbf{P} = \{9, 24, 3,... \}[/math]

The elements of the set P contain labels

[math]\mathbf{P}_i = \{9_{128}, 24_{17}, 3_{812},... \}[/math]

In a ”what is”, is “what is” explanation, that same specific set of labels constitutes your explanation. Using numerical labels is no more than a convenience and constitutes no assumption concerning the character of those elements.

In a “what-is is what-is” ‘explanation’ the “set of labels” are the explanation.

[math]\mathrm{What \ is... \ Explanation} = \mathbf{I} = \{128, 17, 812,... \ i,... \ \}[/math]

We then have,

[math](\mathbf{P}_i)_{i \in \mathbf{I}} [/math]

where P is the past

[math]i[/math] is an index which labels elements of P

I is an index set containing [math]i[/math].

 

The [math]t[/math] index is essentially an index of subsets of P and I.

 

I am, by the way, trying to put this in the language of set theory in hopes that our communication might be a little more precise (or, at least more-precisely understood).

 

Your next post:

Essentially that means that every ontological element in the ”what is”, is “what is” “explanation” requires two indices: one which is consistent with the explanation under examination and another which maintains the generality of the model. Clearly the “past” must actually consist of only the general index (so that all possible explanations are still included) but, for the moment, we are concerned with analysis of the specific “explanation”. I will denote the general index with the number “x” and the "explanation" index (possible presumptive persistence) with the number “i”. Thus it is that every element in the current ”what is”, is “what is” explanation will be represented by the number x_i and each present in that explanation will be represented by a specific collection of numbers. As an example,

[math](x_2,x_{151},x_{293},x_{10591},\cdots,x_i,\cdots)_t.[/math]

 

I would like to point out that one must include the possibility that the past might actually include real persistence and we don't want to eliminate that possibility from our model: i.e., the same x index might appear at different times.

 

Ok, the idea is to add another index. If I were to continue with the P example, [math]\mathbf{P}_i = \{9_{128}, 24_{17}, 3_{812}...\}[/math], I might enumerate this a little differently than your example,

[math]\mathbf{P}_{i,x} = \{9_{(128,x)}, 24_{(17,x)}, 3_{(812,x)}... \}[/math]

Such a difference may be trivial. I'll see what you have to say.

 

What we have now is "the past" (P) which is a "set of ontological elements". The elements are divided into subsets which are labeled [math]t[/math] and [math]q[/math]. The elements are numbers each of which is labeled by two indices: [math]x[/math] and [math]i[/math]. In the what-is is what-is explanation the index [math]i[/math] makes a set (an index set) which I've called I.

 

But, having gone through that, I'll say I suspect the explanation list is, in fact, not the set I, but the whole compilation of:

[math](X_i)t_q[/math]

 

At this point I've probably written enough for a half a dozen you-don't-understand-what-I'm-doing objections, so I will stop and return to the body of your post.

 

I do understand that an explanation may be flaw-free yet incorrect. What I was a bit unclear on was the need for 2 labels for an element ("x" and "i") and also two lists.

It is quite clear to me that you are missing the very essence of what I am doing. You are thinking in terms of specific explanations; not in terms of the general problem of creating a mechanism capable of representing any and all possible explanations: i.e., not knowing anything about what they are or what is being explained. We have a problem here which absolutely no one (except for myself and Anssi) has made any attempt to come to grips with. The underlying problem is, how does one represent something when they have utterly no idea as to what it is they are talking about. You have to confront that problem before we can even begin to talk about how to solve it.

 

We need both x and i for the very simple reason that we have two very different collections of concepts to deal with here. First there are the concepts needed by a specific given explanation. We need an extremely general way of specifying these ideas (concepts, ontological elements, noumenon, ... or whatever you desire to call them) which stand behind our explanations: the things on which the flaw-free theories (or explanations) and their epistemological constructs are built. No explanation serves any purpose if that explanation can not be understood. In order to be understood, the explanation must be expressed in terms of meaningful labels. The first question to be answered is, what mechanism are we going to use to represent these undefined “things”. We need some kind of language to do such a thing: i.e., the definition of the language itself is part and parcel of the explanation. The labeling mechanism must be independent of the language used (this must be so because the language itself, and that would be any language, is a presumed explanation of sounds, marks and ideas). It should be clear that we may use numerical references to identify these “things”. That is the essence of the index “i”.

 

If we have a specific explanation (which includes everything necessary to understand that explanation) and do indeed understand that explanation, we can specify each and every elemental component of that explanation (and that includes the language necessary to that explanation) with specific numerical values for all references “i”. If you wish, you can think of that collection of numerical references as a computer file containing the entire body of that specific explanation (every document including the descriptions of all phenomena associated with that explanation, including an entire complete presentation of the language necessary to understand the explanation and every bit of information standing behind the explanation.) That is to say that a complete collection of the necessary information requires all connections and relationships within that data to represent a specific pattern: the specific explanation being represented. In essence, the existence of a specific explanation implies possibility of generating a specific set of indices “i”.

 

Now, under the assumption that you understand what I have just laid out, let me ask you a simple question. Is that collection of indices “i” sufficient to label all possibilities of interest here? When I say “all possibilities” I don't mean “any” specific explanation; I instead mean “each and every possible flaw-free explanation”. I must assume that you are bright enough to realize that the answer to that question is quite clearly “no” as the “i” indices represent a specific (possibly known) explanation.

 

Try and look at it from the following presumption. Suppose, for the sake of argument, you have a “correct explanation” (that presumes such a thing exists but we really need not worry about that issue for the moment). Clearly, that “correct” explanation could be set forth via some set of indices “j” totally and completely analogous to the index “i” just discussed. The next question which should arise in your mind is, does there exist a one to one correspondence between each and every possible specific index in the set “i” and the set “j”? The answer has to be a resounding no as, if there were, the collection represented by the indices “i” would be exactly that “correct explanation” represented by the set “j”: i.e., all information contained in the complete set "i" would be identical to the set "j".

 

To go off on a tangent for a moment, I am of the opinion that (among almost all people) there is a major misunderstanding of exactly what the conflict between “science” and “religion” is all about and it has to do with comprehending exactly what a “flaw free explanation” is. An excellent example of what I am talking about is the simple explanation, “It is no more than what God wants it to be!” That is a perfectly flaw-free explanation of everything. There exists not a whit of evidence to counter that assertion. The flaws occur not with the explanation itself but rather with those who claim to know the “will” of God. The real problem with such an explanation is that it is not really a very useful explanation (except perhaps for controlling the behavior of gullible people, but that is not the central issue being discussed here): i.e., scientists perceive scientific explanations as better than religious explanations for the simple fact that they provide much more useful deductions. In fact, I could comment that there exist scientific explanations known to be flawed which are commonly used every day for the simple fact that they are so useful. This is exactly the issue lawcat brings up in the following post (though I wouldn't suggest he understands what I am talking about).

When I was a graduate student, I had many an argument with both other students and with faculty concerning this very issue. I always asserted that, “any theory which, when pushed to the limits of its supposed applicability, gave incorrect answers”, was wrong. They all essentially took the position that I was pushing the said theories outside the realm assigned to them. What they didn't understand (and I guess I never made clear) was that I wasn't saying these theories were not useful (as they were all quite useful); I was simply pointing out that they were wrong (a totally different issue). Science is chock full of “compartmentalized thought”. The first requirement of a valid explanation is that it must start by being flaw free. Otherwise it is actually little more than “a rule of thumb”. Being useful is a totally different issue entirely.

 

The question here (in the logic of creating a representation of an arbitrary flaw-free explanation) is, can a one to one correspondence between all the elements of the ancient Roman gods (and what consequences can be attributed to them by those who believe such an explanation) be established with all the elements of modern physics? It should be clear to you that we certainly cannot use the same set “i” for every possible flaw-free explanation.

 

But, back to the set “j” defined to represent that correct explanation. That would appear to be a rather unique set. If that is indeed a correct explanation, then the collection of the entire set of “j” indices is a correct representation. It follows from that assertion that it must be possible to map each and every “i” index contained in a given "present" to a specific “j” index (however, it should be clear that the reverse is not true as the persistence assumed in the flaw free explanation might be in error). Since we clearly do not know this “correct” explanation and its elements are totally unknown, I use “x” to refer to those elements and thus “x_i” refers to the correct unknown element standing behind that reference index “i”.

 

Is that picture clear to you?

 

I understand the conceptual difference between [math]i[/math] and [math]x[/math]. It’s the functional difference between the indices and the lists which I was asking about. In the quote above you use the term “set of indices [math]i[/math]” or just “set [math]i[/math]”—is that equivalent to saying “the explanation list”? If so then I think I see where you're coming from.

 

My only trepidation at this point is the structure you're giving the information list. Am I correct that it is to be represented with subsets [math]q[/math]? A change in information happens from one [math]q[/math] to the next?

 

If this is the case then it seems you've already given the information list a kind of Euclidean character with a single dimension of time. The rate of change of any element in the information list must be some exact multiple of this index [math]q[/math], and there is only one index allowing for change translating into one dimension of time.

 

Let's see... I guess that's all.

 

Oh, yeah, the Coptic thing. The Rosetta stone could only be translated because people still spoke modern Coptic. The more modern of the two Egyptian texts on the stone was rather close to this modern language allowing it to be translated with both phonetics and meaning. The Egyptian Hieroglyphs had similar phonetics allowing its translation. Had there been no phonetic connection between the Hieroglyphs and the newer of the Egyptian languages on the stone or had we not known modern Coptic, I don't believe the stone could have been translated.

 

But, that's immaterial for your purpose in using the example. It was a good example and I understand what you mean to convey. Like I said, I do understand quite well the purpose of the model.

 

~modest

[Doctordick]

Hi modest, I have read your whole post and, as you say, we are having a lot of difficulty understanding one another. Trying to explain my view of the necessity of those two indices is not an easy thing to do. I think that my example with the Rosetta stone was probably the best I have done. By the way, I am really not that proficient in set theory notation that such a representation would be useful here. One thing I think might be worth talking about is exactly what stands behind my interpretation of “time”.

If this is the case then it seems you've already given the information list a kind of Euclidean character with a single dimension of time.

I think this makes some assumptions I am not ready to presume. Perhaps I can make my position a little clearer.

 

I have always been bothered by the general lack of interest in Zeno's paradox. Most modern mathematicians and physicists dismiss it as the confused ravings of someone who does not understand mathematics. Personally, I think they miss his point entirely. The issue is that “motion” is a presumed characteristic of reality. You absolutely cannot “prove” any motion took place as, to do so, would require examination of an infinite amount of data; it is induction (the very essence of presumption itself) which must be brought in to defend applying the continuity of mathematics to the data: i.e., it amounts to, “the conclusion is correct because I have assumed it is correct”. Newton introduced time as a evolution parameter in his dynamics and from that day to this, the intellectual community simply considers “time” to be an obvious continuous aspect of reality. Personally, I think that is a rather presumptuous assertion.

 

I see it quite differently. I see “time” as a reference index telling me what information we are talking about; talking about “yesterday”, “1942” or “one nanosecond ago” is no more than specifying what specific information we are going to talk about. This is utterly no different, conceptually, than specifying “mathematics”, “music” or “that book over there”. I think it is the failure of the intellectual community to recognize this issue that drives a wedge into the whole logic of their world view.

 

So I bring the issue in early, in the form of reference notation, because I want to get a very specific problem out of the way. The issue central to my adoption of this ordering index is to remove “order of information” from the representation. If you leave order in as meaningful, it generates some very bothersome problems. On the other hand, interpreting it as “time” generates no difficulties that I am aware of. The issues of “time” and “motion” are so embedded in our world view (and thus in almost any explanation) that they need to be very carefully defined.

It was a good example and I understand what you mean to convey. Like I said, I do understand quite well the purpose of the model.

Then you should understand that the collection of numbers “x_i” constitute a representation of an explanation as a translation from some unknown information (represented by the collection “x”) to something which is understood (represented by the collection “i”).

 

As I said, this index “t” brings to the representation the idea of “order”. If it is going to represent order, let us use it to represent all order (that gets the issue of order into one specific index; a substantial simplification of what could otherwise be quite complex). In particular, it removes “order” from the characteristics of the subsets [imath]\left(x_i\right)_t[/imath].

 

Now you could complain that such a thing is in violation of my Rosetta stone example as the order of the hieroglyphs on a particular bilingual document clearly have meaning so attaching the index t to different documents does not eliminate “order” as an issue. This is true, but let us instead attach a different t to each and every element where order is significant. The point being that the entire “translation” (which you understand amounts to an explanation of the hieroglyphs) can be represented by the complete set x_i divided into subsets such that “order” within a subset is of no consequence.

 

My point is that order is order and, so long as the collection is finite, the actual order need not have any relation to a fixed Euclidean representation: i.e., the order within the hieroglyphs need not map directly to the order in the translation. That is why I brought up the issue of t_q: i.e., different explanations might use a different ordering.

Ok, the idea is to add another index. If I were to continue with the P example, [math]\mathbf{P}_i = \{9_{128}, 24_{17}, 3_{812}...\}[/math], I might enumerate this a little differently than your example,

[math]\mathbf{P}_{i,x} = \{9_{(128,x)}, 24_{(17,x)}, 3_{(812,x)}... \}[/math]

Such a difference may be trivial. I'll see what you have to say.

I really don't understand the impetus behind this example. You apparently want to use three references for each element. My question would be, why would you want to do that after complaining about my arguments that one should use two? (It has occurred to me that this may be an attempt to answer my question. If that is the case, I think I have a somewhat simpler approach which fills the need completely.)

 

I have a distinct impression that most everyone, including you, are operating under the assumption that I am presenting some method which is to be used to generate explanations. This is entirely false. What I am laying out is a specification of a logical structure which is capable of representing any and all possible explanations of anything. Quite analogous to Turing's idea of a universal calculating machine: i.e., Turing's ideas do not, in any way, tell us what is to be calculated, but rather that anything that can be calculated can be calculated by his logical machine. My model tells us nothing about how to come up with an explanation, but rather that any flaw-free explanation can be represented by my model. Now it does yield some very interesting constraints which I personally think are well worth thinking about; but, at the moment, that is totally beside the point.

 

My reason for relating order to the concept of “time” is quite simple. Any order of any kind can be essentially connected to the concept of time. When reading hieroglyphs (when the order is significant) we look at one first and then the other.

 

That brings up something I remember from graduate school. We had a Chinese graduate student whom I asked to teach me a little about Chinese characters. I was young, full of vim and vinegar so to speak, and I kind of teased him about the order of the strokes. He would show me how to write a Chinese character and, instead of “writing it” per his instructions, I would instead draw the character: i.e., I would set down the strokes in the “wrong order”. The finished character looked just like the one he wrote but he always got extremely upset because I put the strokes down in the wrong order. (Actually I did it intentionally because it really drove him up the wall; I would usually pretend that I could not remember the proper order.) I don't think he ever did comprehend that I was actually pulling his leg regarding order in the expression of the characters. As I think back about the issue now, I can only think that somehow he saw the order as actually embedded in the character. Perhaps I was missing some important part of the representation. Perhaps there was a real subtle consequence of writing them in the correct order which was not being perceived by me; kind of like foreign accents are missed by people not brought up in a language.

But, that's immaterial for your purpose in using the example. It was a good example and I understand what you mean to convey. Like I said, I do understand quite well the purpose of the model.

If that is true, then you should be capable of understanding both the reason for the question I asked and the answer I now provide.

 

Suppose we are given a set of numbers (a supposed “present”) and are asked, “what is the correct t index assigned to that set?” The possibility certainly exists that there are multiple presents with exactly the same set of reference numbers associated with different “t” indices. In that case, our ”what is”, is “what is” explanation (as currently defined: i.e., the entire collection of sets x_i) will fail to provide us with an answer. What can we do 'to our explanation' in order to solve this problem?

 

What we can do is to add fictional information (fictional elements) to our ”what is”, is “what is” explanation. Or, as you put it, add the t index back into the information. What we can do, to assure that the problem just described cannot arise, is to examine the entire ”what is”, is “what is” explanation (determining all cases where we have “exactly the same set of reference numbers associated with different specific t index” and then add a different number to the each such list, never using a number which has already been used anywhere in our explanation. The problem then can not arise;not within that explanation anyway.

 

This is the first time I add fictional information to that ”what is”, is “what is” explanation. I choose this case because it is the simplest case and the fact that it does provide a solution is pretty obvious. To review what I have done, I have added fictitious information to my “explanation” for the sole purpose of answering a specific question concerning the problem of obtaining the correct flaw-free answer given a specific case of incomplete information. The important point here is that this is something we want our explanation to be able to accomplish. (Please note that after adding this “fictitious” information to our ”what is”, is “what is” explanation, it is now explicitly part of that explanation.)

 

Let me know how that hits you.

 

Have fun -- Dick