Modest, I appreciate your interest and you have moved me to respond.
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Originally Posted by modest
I wonder if whatever definition we give "information", the explanation itself must also qualify as information under that definition. If that were the case then an explanation could be seen as additive. Let me explain,
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I agree; however, I would deny that it is part of the information to be explained. That conclusion is arrived at through the following reasoning.
I have elsewhere divided the information standing behind an explanation (i.e., the information being explained) into two very different categories: valid and hypothesized information. Valid information is defined to be the actual information to be explained and hypothesized information is an essential part of the explanation. That is to say, hypothesized information must be true if the explanation is to be valid; however, if the explanation is removed (discounted or disproved) the hypothesized information may also be removed. Valid information, on the other hand, being the actual information to be explained can not ever be removed: each and every explanation must explain that information.
From this perspective, the explanation itself qualifies only as hypothesized information; thus it does not add to the “valid” information.
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Originally Posted by modest
I posit that an explanation transforms non-comprehensible and non-understandable information into comprehensible and understandable information.
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I would not argue with this statement at all; however, it does require we define exactly what is meant by the quality “understood”. (I am presuming here that “comprehensible” simply means that “it can be understood” thus the issue of determining that an explanation makes the information “understood” covers both ideas.)
So, how do we come to the conclusion that a body of information is “understood”? Actually, this is a problem faced by every teacher in the history of the world. They attempt to discover the answer to that question by testing their students. The tests can easily be seen as an interaction where the teacher provides some information and then examines the students response to that information (that is why they call them “examinations”
). If the student's response is consistent with the possible responses the teacher would give to the same information, then the teacher will presume the student understands the information. I think any conceivable test which can be given can be cast into that format.
Thus it is that “I” come to the conclusion that “understanding” has to do with predicting information. There is one subtle cavil which needs to be brought up. If “all” the information is known then any question about the information can be answered; but that doesn't really fit the common concept of “understanding”; “knowing” and “understanding” are usually thought of as different concepts. Modest is bringing up that issue when he says
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Originally Posted by modest
The process of the explanation (whatever that is) would transform the information such that predictions about a portion of the information could be made given the remaining information and patterns within the information could be identified.
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I would like to simplify that argument a bit. Let me put forth the idea that anything which would allow one to predict information not known from information which is known could be called an understood explanation. Now again I bring up another subtle cavil. That idea, as specified, seems to require actual prediction. Let me suggest that an explanation need not actually do such a thing. If we turn the proposed solution around, one could say that, given an arbitrary prediction, an acceptable explanation could tell us if that prediction were acceptable or not. I do this because this point of view turns the situation to a relationship which can be easily expressed.
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Originally Posted by modest
I therefore propose that one thing which an explanation does to (or for) information is to expand its size.
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I would agree with that; however, I would put it a little differently. Any explanation of anything would, of necessity, add “hypothesized information”.
Would you agree modest or do you have some serious complaints with my position at this point?
Twenty years ago I wrote,
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I will suggest that what an explanation does for information is that it provides expectations of subsets of that information. That is, it seems to me that if all the information is known, then any questions about the information can be answered (in fact, that could be regarded as the definition of "knowing"). On the other hand, if the information is understood (explainable), then questions about the information can be answered given only limited or incomplete knowledge of the underlying information: i.e., limited subsets of the information. What I am saying is that understanding implies it is possible to predict expectations for information not known; the explanation constitutes a method which provides one with those rational expectations for unknown information consistent with what is known.
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Does anyone have a suggestion for clarifying what I said twenty years ago: i.e., anything I have omitted that you think should be there?
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Originally Posted by Turtle
Don't run off Doc. I have no objections as you say, so I withdraw to watch.I see you have other respondents already as it is. Carry on.  |
No need to withdraw; I take your opinions rather seriously. I just didn't want to be the motivating force behind another “Spacetime” thread.
Have fun -- Dick
