Science Forums 2

[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.

Originally Posted by modest

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.

Originally Posted by modest

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).

Originally Posted by lawcat

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?

Originally Posted by modest

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?

Originally Posted by modest

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.

Originally Posted by modest

Oh, my.

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

Originally Posted by modest

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

Originally Posted by Doctordick

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.

Originally Posted by modest

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.

Originally Posted by modest

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.

Originally Posted by modest

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.

Originally Posted by modest

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.

Originally Posted by modest

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.

Originally Posted by modest

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.

Originally Posted by modest

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