What I believe an explanation is!

[lawcat]

I agree. There must be something to be explained.

I also agree that the next thing is to define the nature of explanation--either, who, what, how, when, why?

Generally, the WHO, and WHAT, is empirical. Once we observe the WHO and WHAT, we can proceed to the important question of HOW--because HOW-explanation is predictive of all future observed WHOs and WHATs.

The easiest way to approach HOW-explanation is to define it as algorithm that connects WHO1 and WHAT1, to WHO2 and WHAT2. In essence, the HOW-explanation is the knowledge of the "process" between state1 and state2--and often it holds true regardless of how we define WHO and WHAT.

[Doctordick]

There seems to be a major misunderstanding going on here. The purpose of this thread was to try to explain my definition of “an explanation” and I was intending to cover objection to that definition.

Originally Posted by Turtle

I started small & intend to build my definition around your objections as we go.

I have no intention of objecting to your definition. If you have something important which you can deduce from your definition, have at it. I was taking your comments to be objections to my definition which apparently was not your intention. So this whole thread is based on misunderstanding.

It appears that the thread has become a place for people to present (or work out) their personal definitions of “an explanation”: i.e., quite analogous to the “Spacetime” thread. I now understand lemit's post

Originally Posted by lemit

I am curious about the genesis of this thread. Since the quote above could be inserted into almost any page of the "Spacetime" thread without being out of place, I can't help wondering if this is a response to something said elsewhere.

Am I right?

--lemit

I think lemit is quite right!

So, since this thread is not concerning itself with the issue I tried to bring up, I will abandon it to you all and start another (on another day) which might be more to the point I was trying to bring up.

Have fun -- Dick

[modest]

Originally Posted by Doctordick

First of all, in order to have an explanation, one needs something to explain. Whatever it is that is to be explained, it can be certainly be categorized as some kind of information. It thus follows that "an explanation" is something which is done to (or for) information. The central issue is then, if we are to define "an explanation" in general, we must lay down exactly what an explanation does to (or for) that information.

If anyone wants to discuss that issue, I will respond.

I agree with this paragraph and I'd be interested in discussing the issue.

You say that an explanation does something to (or for) information. I agree. 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,

I posit that an explanation transforms non-comprehensible and non-understandable information into comprehensible and understandable information. By this rational we could give qualities to unexplained information (were we to analyze it) such as not being able to predict a portion of the information from the remaining information or not being able to sort the information into patterns which exist within the information. 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.

If the explanation is itself information then the transformation involves (but would not necessarily be limited to) adding information to the set of unexplained information. For example, here is some unexplained information:

1 1 2
2 2 4
3 3 6
4 4 8

To explain the information we add additional information:

1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
4 + 4 = 8

Of course, this is not a complete explanation of arithmetic. It is only meant to represent a limited set of unexplained information vs. a set of partially explained information. My point being: one quality of an explanation is that it is additive. The set of unexplained information is necessarily smaller than an equivalent set of explained information.

I therefore propose that one thing which an explanation does to (or for) information is to expand its size.

Would you agree Doctordick, and what else would you propose the explanation does?

~modest

[Turtle]

Originally Posted by Doctordick

There seems to be a major misunderstanding going on here. The purpose of this thread was to try to explain my definition of “an explanation” and I was intending to cover objection to that definition.
I have no intention of objecting to your definition [Turtle]. If you have something important which you can deduce from your definition, have at it. I was taking your comments to be objections to my definition which apparently was not your intention. So this whole thread is based on misunderstanding.

Yes I agree with all, save humbly suggesting the thread is based on misexplanation.

Originally Posted by Hickory Dickory Doc

So, since this thread is not concerning itself with the issue I tried to bring up, I will abandon it to you all and start another (on another day) which might be more to the point I was trying to bring up.

Have fun -- Dick

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.

[Doctordick]

Modest, I appreciate your interest and you have moved me to respond.

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,

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.

Originally Posted by modest

I posit that an explanation transforms non-comprehensible and non-understandable information into comprehensible and understandable information.

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

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.

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.

Originally Posted by modest

I therefore propose that one thing which an explanation does to (or for) information is to expand its size.

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,

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.

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?

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

[watcher]

Originally Posted by Doctordick

Valid information is defined to be the actual information to be explained

are not these valid info what we called as self-evident?

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.

so hypo info that is based in a valid info is also a worldview?

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.

how do know that a established valid info is always valid.

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.

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?

isn't this , what we called theory?

[arkain101]

I believe I follow what you are saying about what explanations do to information. And although I will respond via words, I decided to, on top of words, also represent this visually (redundant, obvious or not). The framework is an explanation.

A simple set of diagrams that show, a starting point of information (the circle, the left most point) that provides a framework for a varies set of predictions.

In knowing, predictions are 1) made 2)checked and 3)validated.

In understanding, the predictions are 1)made 2)not-checked 3)not-validated

In misunderstanding, predictions are not valid, not made....

I even colored it for, Green is a go! Orange is a Caution! Red is a zzzz wrong stop! (lol)

So.. is the doodle worthless? or helpful? They say a picture says a thousand words.

[modest]

Originally Posted by Doctordick

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.

Yes, that seems a reasonable way to categorize the information. Would I be correct that a parallel is to be made between hypothesized information (including the explanation) and a worldview?

Originally Posted by Doctordick

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.
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?

Yes, I do. The only possible sticky point:

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.

An explanation would indeed tell us if a prediction were acceptable or not, but I prefer testing the prediction as a means of "testing" the explanation. I say this because additional information can invalidate a seemingly sound explanation. An obvious example is Newtonian mechanics. Michelson and Morley provided information that tested the mechanics (or the explanation) which had previously seemed acceptable. Actually, that may not be the best example given recent discussion. Let's say geocentrism used to be an acceptable explanation for the apparent motion of the sun and moon but that additional information invalidated the predictions and the explanation and required heliocentrism.

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.

~modest

[Doctordick]

Hi modest, you seem to be awfully close to understanding what I am saying.

Originally Posted by modest

Would I be correct that a parallel is to be made between hypothesized information (including the explanation) and a worldview?

Well, I wouldn't put it that way (I think it oversimplifies the issue) but I guess the comment is not totally “off the wall”. Suppose we just let that idea slide for the moment as I don't really see that it adds anything to what I am saying.

Other than that, I find your response to be very acceptable except for one subtle misunderstanding. That has to do with my comment!

Originally Posted by Doctordick

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.

You seem to think that specification is insufficient and I think you are wrong for a very important reason.

Originally Posted by modest

I prefer testing the prediction as a means of "testing" the explanation.

First of all, we are not talking about “testing the explanation” here. If we are going to “define” an explanation via the assertion, “an explanation transforms non-comprehensible and non-understandable information into comprehensible and understandable information” (which, by the way I agree with completely), we are directly faced with the problem of determining if an explanation is understood. This is a subtly different question and your constraint is just not sufficiently general to include all possibilities. At the same time, that very constraint is actually included in my specification. Let me try to clarify the situation with an example taken from the circumstance I have already presented.

Originally Posted by Doctordick

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.

There are many circumstances in many explanations where a specific answer does not exist (understanding something does not always lead to a single incontrovertible response to a specified circumstance). Furthermore, if you constrain the possibilities for a specific circumstance to a single specific answer (essentially a specific prediction) then you are actually testing the information available to the respondent, not his or her understanding of that information.

That is why I suggest turning the proposed solution around. Instead of allowing only one specific answer, allow all possible answers and require the explanation to tell us if the obtained response were acceptable or not. Your case, allowing only one specific response, is included in such a definition (all the explanation need do is yield “unacceptable” for all responses except the one specific response desired for the specific circumstance under examination) while at the same time the more complex circumstances mentioned above are still included.

Originally Posted by modest

I say this because additional information can invalidate a seemingly sound explanation.

Once again, you indicate that you do not understand what Anssi and I are talking about. We have mentioned many times that the explanations we are talking about are “flaw-free”; that means that no information is available which invalidates the explanation. New information invalidating an explanation merely makes that explanation no longer flaw-free and thus no longer a member of the possibilities we are interested in.

Originally Posted by modest

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.

Nowhere have Anssi or I suggested that any explanation under consideration was “correct”. What we said was that it was flaw-free, a very different matter. This whole presentation has to do with designing a flaw-free explanation of arbitrary given information. To do that, I need to define exactly what is meant by “an explanation”. I very much like your definition: “an explanation transforms non-comprehensible and non-understandable information into comprehensible and understandable information” (it is very much exactly what I have in my mind for the definition). And that definition requires a method of determining whether the explanation is understood.

An explanation which is either not understood or not flaw-free is a pretty worthless construct. Does any of this make sense to you?

Have fun -- Dick

[modest]

Originally Posted by Doctordick

Hi modest, you seem to be awfully close to understanding what I am saying.

Thank you. I have understood fine everything you've said in this thread. Moreover, I've not yet disagreed with any of it.

Originally Posted by Doctordick

That is why I suggest turning the proposed solution around. Instead of allowing only one specific answer, allow all possible answers and require the explanation to tell us if the obtained response were acceptable or not.

That's fine. If information is explained then the explanation provides a means of relating a subset of information (A) to another subset of information (B). With the explanation in hand a person could predict the contents of B given A and given some arbitrarily predicted B the explanation would say if it is indeed a valid prediction of A.

You seem to open up the possibility that there is more than one possible B given A and the explanation and I'd agree with that. I can certainly think of examples... so, yeah, I'm OK with that.

Originally Posted by Doctordick

Your case, allowing only one specific response...

I really didn't mean to imply that, but given there are multiple valid predictions that can be generated with some information and an explanation, I'd agree the most concise way to express what we're saying would be: "given an arbitrary prediction, an acceptable explanation could tell us if that prediction were acceptable or not".

Originally Posted by Doctordick

Nowhere have Anssi or I suggested that any explanation under consideration was “correct”. What we said was that it was flaw-free, a very different matter.

Good. Then we agree. I don't mean as a criticism that "given an arbitrary prediction, an acceptable explanation could tell us if that prediction were acceptable or not" does not make the explanation correct [edit:does not mean the prediction is "correct"]. It's simply true, and you agree. So, there's no need for you to get along with your "you don't understand what I'm doing" thing.

Originally Posted by Doctordick

This whole presentation has to do with designing a flaw-free explanation of arbitrary given information.

Good. That makes sense.

So, how do we model this explanation?

~modest