If you don't like to read long involved posts with subtle logic, don't bother reading this: you'll probably be severely disappointed.
The Turtle has posted an interesting thread called "Katabatak Math-An Exploration In Pure Number Theory". In it he brings up the idea of attaching meaning to the numbers (colors, musical notes, ...) yielding some very interesting patterns. But he does not mention the possibility of considering the converse. That would be attaching numbers to meanings and then looking at internal relationships implied by mathematical processes. I have personally looked at that issue and found the results quite enlightening.
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 this really isn't a very alien concept at all; it's done with computers on a daily basis.
What I would really like to do is find something of interest I could do with this information by applying mathematical ideas to these numerical "labels".
Before going any farther, I would like to separate the problem into two different issues. Suppose I could answer any questions about the information so labeled. It seems to me that I could define that as knowing the information: i.e., if I "knew" it all, I could recover any of it with little more than knowing the pattern to be located. Now this is a very uninteresting thing to do. In fact, that's what computers do all the time. On the other hand, "understanding" the information is quite a different issue. Now that would be an interesting computer operation and one I don't think has been seriously considered.
So how does one know when they understand something? Well, you could say they get a little light that goes on in their head and they then "know" they understand it, but I think you would be kind of gullible if that were all you wanted to ask of them. I personally would require an explanation before I would accept anyone's claim to understand. That being the case, let me give you my definition of "an explanation".
Quote:
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Originally Posted by Doctordick
If the information is understood, 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 itself constitutes a method which provides one with those rational expectations for unknown information consistent with what is known.
Thus I come to define "An explanation", from the abstract perspective, to be a method of obtaining expectations from given known information. If you have any arguments with that definition, it seems to me that you need to show me either a method of obtaining those expectations which can not be conceived to be an explanation or an explanation which provides no method of obtaining expectations. If you cannot show one of those circumstance, than you should agree that it is a usable definition of an explanation consistent with the common meaning of the term.
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The above is taken directly from an
earlier post on another thread.
Still looking for serious complaints.
Have fun -- Dick
Knowledge is Power
and the most common abuse of that power is to use it to hide stupidity
