Science Forums 2

[Doctordick]

Originally Posted by Eclogite

To me an explanation is an accounting of a process; a description of how and why things are as they are. In short, it deals, as directly and clearly as possible with what is.

Yes indeedy do! That is certainly the first requirement of an explanation. If the "explanation" is not one hundred percent consistent with "what is" (i.e., the information being explained) then it's a bogus explanation from the get go. But there is more to "an explanation" than that. If your explanation has nothing to say about what is to be expected it is a rather worthless construct. As the older generation used to tell me, "what is, is what is, and don't worry about it!" That "deals, as directly and clearly as possible with what is" but I doubt many people would regard it as an explanation.

Originally Posted by Eclogite

Your definition seems to address what will or might be. Now these two are related, but they are also different. That difference, and the jarring effect of trying to fit your 'explanation' into a hole in my linguistic symbology, that does not want to accept it, are making it difficult for me to focus on where you want to take this idea.

I think that what you are missing is the necessity of that prediction of expectations. Even in a case where there is nothing to predict, (i.e., the story which constitutes the explanation is completely finished at its conclusion) the construct itself unfolds through the issue of prediction. Point by point, the explanation sets up a process for establishing expectations for the next step until the finished state is established.

Secondly, I would say that you are jumping the gun by worrying about where I want to take this idea. I think the "jarring effect of trying to fit [my] 'explanation' into a hole in [your] linguistic symbolism is a consequence of the common perception that explanations are "correct": i.e., a failure to take into account the fact that all explanations of anything must be taken as tentative and possibly erroneous. I have found in my life that everybody is willing to admit that they could be wrong; but never about the case under discussion.

And, where do I want to take it? Well, I think the idea of an explanation is a rather basic concept (a first principal thing if you would be so kind as to consider it such). What can we talk about without the concept of an explanation? If we are going to talk, we are going to use words and how do I know what you are saying if I don't know what the words mean? That is the first explanation required. It is entirely possible you are speaking in a secrete code and I am missing the entire import. Probably not; but certainly possible and any errors in communication essentially arise from exactly the same fundamental phenomena (your meanings for words and my meanings may not be exactly the same).

That's why I like mathematics. Mathematicians have labored for centuries trying to make sure their systems are internally self consistent. As a consequence, it really makes no difference if I have misunderstood their intended meaning. It is the internal consistency of the defined procedures which establish the system (secrete code or not). That is, my construct (since it obeys the same internally self consistent collection of rules) is an analog of his and we know we will arrive at the same conclusions. (Or one could face the real issue and admit that, logically speaking, mathematics is pretty dammed simple to understand.) In short, we can communicate.

But back to the issue of assigning numbers to meanings. Turtle, you are assigning numbers to meanings and, as you mention, the assignment is arbitrary. In order to make an assignment such as you propose, the meanings being referred to have to be understood (and meaningful, so to speak). In essence, you have already made assignments of the connections and relationships between these many "defined entities" you are assigning numbers to. But, understanding a language is a complex thing. It is very hard to keep in mind all the various usages of these entities and thus quite difficult to be absolutely sure that the inferred connections and relationships are indeed internally consistent.

On the other hand, mathematical relationships are pretty well guaranteed to be to be internally consistent so I can be rather caviler in any manipulations based on those mathematical operations. What draws me to the issue is the fascinating things which happen when you don't set it up any internal connections or relationships (outside those mathematical operations already well defined): i.e., I presume there is no information outside the language usage itself (which is actually quite a reasonable proposition). In many respects, I am looking at the problem of finding the possible internally consistent connections and relationships which can be inferred from a finite set symbols, signs, concepts ... (what ever one wishes to call these meaningful things). In many respects this is the very essence of the problem of learning a language.

As an aside, notice that I said, "there is no information outside the language usage itself" (the "language" being this collection of "things" which can be referred to). If there is no information outside the collection, we can refer to the collection as "a universe unto itself" (a mathematician might refer to it as a "closed" universe). On the surface it sounds like I am asking the impossible: find all the possible internally self consistent connections and relationships which can be inferred from an undefined collection of supposedly meaningful references. But it certainly isn't impossible, millions of babies come into the world (a closed universe of experiences) every year and within a few short years, they manage to infer, for themselves, whole collections of internally self consistent connections and relationships between symbols, signs and concepts which were unknown to them only a matter of months before.

I have already said that I am interested in "explanations" because I think that is the central issue of understanding (my first principle so to speak). As I have mentioned in my first post above,

Originally Posted by Doctordick

The first thing we need is a collection of meaningful symbols to which we can attach these numbers. A good name for a collection of meaningful symbols is the word "information". So, what I am proposing is attaching numbers to information.

Now turtle, you make a habit of listing out numbers and their assignments; but the sheer volume of information being talked about here precludes the step of writing down symbols for the basic elements of this information. It is much easier just to plant the concepts of doing so in your head. For this reason, I will simply refer to the information to be explained as A, the set of supposedly meaningful "things": i.e., the meaningful things themselves are "the elements of A. So our purpose is to explain A (a pretty simple statement).

However, we have a slight problem there. As I explained to Eclogite, one of the essential properties of an explanation is that it must make predictions: i.e., it must predict things about A before they are known. This implies that, for the purpose of analysis, A (our universe) cannot be thought of as "known". Now certainly some elements of A need to be known (which we could call the basis of our explanation) and our model of the circumstance must include changes in the collection of known elements. These changes must consist of elements of A. What else can they consist of if we are talking about a closed universe? So I will simply refer to a change in the base information as B and the base information (the sum total of all changes from our opening position of zilch) as C.

At this point I have some meaningful entities to which I can attach numbers: the elements of C or "the elements of the collection of B's which go to make up C".

The second element of "an explanation" must be that prediction. As laid out above, all of the information on which the explanation is based is contained in the set C. Again, as I explained to Eclogite, even if the explanation concerns itself only with C making no predictions concerning unknown portions of A the construct itself still unfolds through the issue of predictive steps. In essence, what is desired is a prediction of the next set B which is to be added to the known collection C. Think of it as an answer to the question, "Ok, what's next?" Obviously the answer needs to be a collection of elements of A (or a new set B) as there is nothing else available (that's the definition of a "closed universe").

Designing an abstract model of a question is probably the hard part of the whole thing. Sure, if the set A constitutes everything, both the question and the answer are comprised of elements of A. However, the problem is that both questions and answers can be quite complex and may involve strings of sets B. We can get around the answer complexity by requiring a "twenty question" format (think of it as a multi-billion question game). In that case the answers become a simple binary yes/no but the questions can still be complex.

I hold that the most complex questions which can be asked can be seen as collections of changes in information (think of it as a sequence of concepts represented by sets B). In that case, the question can be reduced to a yes/no answer on each hypothetical set B. Another way to view the same issue is to see the answer as a collection of possible sets B with the question being, "can this collection of possible sets actually be expected as real changes in information?" Can they actually be possible valid sets?

That reduces the question answer problem down to, "given a particular arbitrary set B, can that set be accepted as a real possibility?" The answer is clearly either yes or no or something in between (a probability: a number bounded by zero and one). Since the whole issue was begun with the prospect of assigning numbers to the elements of B, the question answer problem has now been reduced to finding a mathematical function where "validity" = Probability (B). If I knew exactly what that function was, I could use it to explain A. If you refuse to accept that notion, I think I could at least say I understood A as I would know my expectations exactly and I could not possibly be surprised in any new information.

Believe it or not this is no more than setting the stage; but, before I go on I would like a little feed back on the clarity of what I have said. I admit it is a rather abstract opening but one shouldn't be afraid of abstraction. Abstraction is a powerful tool as it frees one to rationally examine things they do not understand. And I certainly don't understand exactly what this set A is! All I really know is that I have to come up with an explanation of it and, to do that, I need a road map to organize my thoughts.

Have fun -- Dick

Knowledge is Power
and the most common abuse of that power is to use it to hide stupidity