Science Forums 2

[Doctordick]

Hi modest, I have read your whole post and, as you say, we are having a lot of difficulty understanding one another. Trying to explain my view of the necessity of those two indices is not an easy thing to do. I think that my example with the Rosetta stone was probably the best I have done. By the way, I am really not that proficient in set theory notation that such a representation would be useful here. One thing I think might be worth talking about is exactly what stands behind my interpretation of “time”.

Originally Posted by modest

If this is the case then it seems you've already given the information list a kind of Euclidean character with a single dimension of time.

I think this makes some assumptions I am not ready to presume. Perhaps I can make my position a little clearer.

I have always been bothered by the general lack of interest in Zeno's paradox. Most modern mathematicians and physicists dismiss it as the confused ravings of someone who does not understand mathematics. Personally, I think they miss his point entirely. The issue is that “motion” is a presumed characteristic of reality. You absolutely cannot “prove” any motion took place as, to do so, would require examination of an infinite amount of data; it is induction (the very essence of presumption itself) which must be brought in to defend applying the continuity of mathematics to the data: i.e., it amounts to, “the conclusion is correct because I have assumed it is correct”. Newton introduced time as a evolution parameter in his dynamics and from that day to this, the intellectual community simply considers “time” to be an obvious continuous aspect of reality. Personally, I think that is a rather presumptuous assertion.

I see it quite differently. I see “time” as a reference index telling me what information we are talking about; talking about “yesterday”, “1942” or “one nanosecond ago” is no more than specifying what specific information we are going to talk about. This is utterly no different, conceptually, than specifying “mathematics”, “music” or “that book over there”. I think it is the failure of the intellectual community to recognize this issue that drives a wedge into the whole logic of their world view.

So I bring the issue in early, in the form of reference notation, because I want to get a very specific problem out of the way. The issue central to my adoption of this ordering index is to remove “order of information” from the representation. If you leave order in as meaningful, it generates some very bothersome problems. On the other hand, interpreting it as “time” generates no difficulties that I am aware of. The issues of “time” and “motion” are so embedded in our world view (and thus in almost any explanation) that they need to be very carefully defined.

Originally Posted by modest

It was a good example and I understand what you mean to convey. Like I said, I do understand quite well the purpose of the model.

Then you should understand that the collection of numbers “x_i” constitute a representation of an explanation as a translation from some unknown information (represented by the collection “x”) to something which is understood (represented by the collection “i”).

As I said, this index “t” brings to the representation the idea of “order”. If it is going to represent order, let us use it to represent all order (that gets the issue of order into one specific index; a substantial simplification of what could otherwise be quite complex). In particular, it removes “order” from the characteristics of the subsets .

Now you could complain that such a thing is in violation of my Rosetta stone example as the order of the hieroglyphs on a particular bilingual document clearly have meaning so attaching the index t to different documents does not eliminate “order” as an issue. This is true, but let us instead attach a different t to each and every element where order is significant. The point being that the entire “translation” (which you understand amounts to an explanation of the hieroglyphs) can be represented by the complete set x_i divided into subsets such that “order” within a subset is of no consequence.

My point is that order is order and, so long as the collection is finite, the actual order need not have any relation to a fixed Euclidean representation: i.e., the order within the hieroglyphs need not map directly to the order in the translation. That is why I brought up the issue of t_q: i.e., different explanations might use a different ordering.

Originally Posted by modest

Ok, the idea is to add another index. If I were to continue with the P example, , I might enumerate this a little differently than your example,

Such a difference may be trivial. I'll see what you have to say.

I really don't understand the impetus behind this example. You apparently want to use three references for each element. My question would be, why would you want to do that after complaining about my arguments that one should use two? (It has occurred to me that this may be an attempt to answer my question. If that is the case, I think I have a somewhat simpler approach which fills the need completely.)

I have a distinct impression that most everyone, including you, are operating under the assumption that I am presenting some method which is to be used to generate explanations. This is entirely false. What I am laying out is a specification of a logical structure which is capable of representing any and all possible explanations of anything. Quite analogous to Turing's idea of a universal calculating machine: i.e., Turing's ideas do not, in any way, tell us what is to be calculated, but rather that anything that can be calculated can be calculated by his logical machine. My model tells us nothing about how to come up with an explanation, but rather that any flaw-free explanation can be represented by my model. Now it does yield some very interesting constraints which I personally think are well worth thinking about; but, at the moment, that is totally beside the point.

My reason for relating order to the concept of “time” is quite simple. Any order of any kind can be essentially connected to the concept of time. When reading hieroglyphs (when the order is significant) we look at one first and then the other.

That brings up something I remember from graduate school. We had a Chinese graduate student whom I asked to teach me a little about Chinese characters. I was young, full of vim and vinegar so to speak, and I kind of teased him about the order of the strokes. He would show me how to write a Chinese character and, instead of “writing it” per his instructions, I would instead draw the character: i.e., I would set down the strokes in the “wrong order”. The finished character looked just like the one he wrote but he always got extremely upset because I put the strokes down in the wrong order. (Actually I did it intentionally because it really drove him up the wall; I would usually pretend that I could not remember the proper order.) I don't think he ever did comprehend that I was actually pulling his leg regarding order in the expression of the characters. As I think back about the issue now, I can only think that somehow he saw the order as actually embedded in the character. Perhaps I was missing some important part of the representation. Perhaps there was a real subtle consequence of writing them in the correct order which was not being perceived by me; kind of like foreign accents are missed by people not brought up in a language.

Originally Posted by modest

But, that's immaterial for your purpose in using the example. It was a good example and I understand what you mean to convey. Like I said, I do understand quite well the purpose of the model.

If that is true, then you should be capable of understanding both the reason for the question I asked and the answer I now provide.

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: i.e., the entire collection of sets x_i) will fail to provide us with an answer. What can we do 'to our explanation' in order to solve this problem?

What we can do is to add fictional information (fictional elements) to our ”what is”, is “what is” explanation. Or, as you put it, add the t index back into the information. What we can do, to assure that the problem just described cannot arise, is to examine the entire ”what is”, is “what is” explanation (determining all cases where we have “exactly the same set of reference numbers associated with different specific t index” and then add a different number to the each such list, never using a number which has already been used anywhere in our explanation. The problem then can not arise;not within that explanation anyway.

This is the first time I add fictional information to that ”what is”, is “what is” explanation. I choose this case because it is the simplest case and the fact that it does provide a solution is pretty obvious. To review what I have done, I have added fictitious information to my “explanation” for the sole purpose of answering a specific question concerning the problem of obtaining the correct flaw-free answer given a specific case of incomplete information. The important point here is that this is something we want our explanation to be able to accomplish. (Please note that after adding this “fictitious” information to our ”what is”, is “what is” explanation, it is now explicitly part of that explanation.)

Let me know how that hits you.

Have fun -- Dick