Hi Tim,
I have moved to the top in order to make this easier to find. I have mentioned to John Huggins on a number of occasions that this forum has a higher "post" density than any other I have seen. It needs some mechanisms to keep continuity on the threads. Now that is a real "AI" project! I think it would require some kind of well thought out cookie control together with a well thought out file structure. But that is another story. Harv has made some very rational suggestions for the meanwhile.
Yes, it is clear that you are seriously contemplating what I have tried to say and seem to have a good feeling for many of the critical issues. I appreciate the work very much. It is clear to me that you are trying to follow my thoughts and the implications carefully. Just as an aside, I think the issue of understanding words (essentially creating the concepts to be attached to those words) is a very serious aspect of puzzle solving itself. The great puzzle of course being the universe we find ourselves in. The depth and complexity of this puzzle is clearly beyond our comprehension on a conscious level yet we all have some solution or another (including Alan's) which bears a surprising similarity to solutions expressed by those about us. This fact alone should be seen as surprising.
I just read your exchange with Paul and Harv (far below) and am very reassured that you are taking the correct tack. If I may quote my preface: "It should be clear, even to the uninitiated, that errors in the logical deductions only occur when an attack is newborn and are quickly eliminated by careful examination of those deductions. Errors in deduction are the easiest to eliminate and, in fact, seldom persist long enough to pervade the field. Certainly, if any idea survives long enough to be part of the body of knowledge passed from one generation to another, one can expect to find few if any errors in the deductions; too many people will have been led through those deductions to allow anything but extremely subtle errors to stand for long."
It is in exactly this area where I do need help as almost no one has been led through my deductions. Nothing is harder than finding your own errors. When I was a graduate student, working on my thesis, there was a point where my result was off by a factor of 10 and I could not understand the problem. I finally sat down my wife (who knew no physics at all) and explained the derivation line by line (trying to do it in terms she could follow)  my error just jumped out and bit me on the nose. When you read your own stuff, your mind just seems to jump across those things. Paul is the only other person who has seriously examined my deductions and that endeavor brought forth a number of errors (all actually minor but important none the less). I just want you to know that I appreciate your interest very much.
I would like to make one comment which I believe no one here has clearly understood. I regard language to be a vague and poorly defined mechanism for communication; however, as it is all I have, I try to express my ideas and concepts in terms consistent with common usage, not always a successful process. The only way I have to know whether the idea has been properly communicated is to see it reexpressed in another's words. I think you have made an excellent contribution. Thank you very much.
"truth as we know it is dependent upon our definitions:
hence we must be meticulously correct in our definitions."
****The meaning of correct is vague. We must do our best to avoid relying on context as the context itself may be misconstrued. That is why I move to context free labels provided by numbers. (This appears to be an issue beyond Harv's comprehension!)
"reality is comprehensible and communicable therefore:
reality can be represented by a set of numbers. "
****I presume you understand here that the set of numbers are nothing except a representation of a message in meaningless labels and that we possess no information not provided by that message. Again, as an aside, I fully realize that I am using a mental model created by my subconscious for the purpose of discussing and thinking about the problem. Now Harv barfs all over me for that. My position is that if one takes Harv's advise, there is simply nothing which can be done as logic itself vanishes from our vocabulary. Harv's advise amounts to telling us to leave the solution up to our subconscious. As I have said many times, our subconscious may be brilliant but there is certainly no evidence it can be trusted to be logical. My only defense on the issue is that I am doing my very best to be objective with the information available for conscious consideration. Mathematics is the only "language" where the vocabulary and its meaning are decently accepted by most everyone knowledgeable of the field.
"this set of numbers can be divided into subsets. those subsets can be construed as transformed by our senses for analysis via the fundamental transform of the model we construct."
****Now here there seems to be a slight misunderstanding. I hope you are not referring to the "fundamental transform" I mention in figure 2. If you are referring to what I call an "Alternate view of our senses" in that same figure, then you are correct. I would rather say "via the transform performed by our subconscious in the model we will construct". Let me know if this seems confusing to you.
"because these subsets are examinable they must be finite.
because our purpose is to establish a mental image of the universe the number of subsets examined must be finite.
because the mental image must allow for the existence of another subset not yet examined the number of subsets that make up the universe must be infinite. "
****Seems clear to me!
"since the examined subsets (of which we shall construct our mental image) are finite they can be ordered.
they can be ordered by the continuous parameter 't' which shall be defined as time. where a specific value of t will indicate a specific subset available to be examined. time has a definite direction: the past consists of those subsets available to our senses whereas the future consists of those subsets which are not available for examination. The past is what we know and the future is what we do not know. "
****The need for the continuity of 't' is omitted here. If we are to develop a mental model of the universe based on a collection of examined subsets (i.e., not all of it) and every examination of any possible collection must yield the same model (reality is what reality is: i.e., that which we are trying to model), then it follows that our analysis must allow the possibility of an observation between any two given observations. This implies that the parameter 't' is a continuous variable. Again, if this seems confusing to you let me know.
"an observation is defined to be a member of the set of examined subsets of reality."
****Seems reasonable to me!
"the task at hand is to determine from a sequence of observations, exactly what the rules of the universe are: that is, we are interested in constructing a mental model which will separate the actual observable universe from the set of all possible universes.
In order for that result to be possible, the sequence must be produced by some unknown algorithm (i.e., it is presumed that the sequence is not random or without rules)"
****I presume you have no argument with that.
"if we knew the algorithm it would have to be independent of time since independent observers in time must be able to apply the algorithm and still be able to construct the rules of the universe or our mental model. since the algorithm is independent of time we can not predict any particular observation unless the time of the observation is contained in some implicit manner."
****Again, the term "independent observers" seems to me to bring in a concept of something specific existing in this model (these other observers). I would rather say that the resultant model can not depend on that ordering referred to in the definition of 't'. If it did, the model would depend on that ordering and that would violate the definition of 't'.
"If there is information implicitly embedded in the data, it must be presumed that there are patterns of data which are possible (uncontradictable) and patterns of data which are not possible(contradictable). This is the essence of what a scientist means when he says there are rules. If all things are allowed then there are no rules."
****The patterns of data which are not possible are those which would constitute a contradiction of some sort. Of course there is a certain vagueness in either statement. Of essence is the fact that any "rule" must make something possible and something else impossible as that is essentially what one means by a rule.
"upon examining our observations (our set of numbers) we can have a collection of patterns that are unique or some patterns that may appear more than once. if we were all knowing we would know what data to add to those sets so as to make those sets unique. since we are not all knowing we will just say we will add unknownable data to those sets so as to make the collection of patterns unique."
****I really don't know how to make the idea of "knowable" and "unknowable" classifications clear enough to avoid Harv's tendency to barf all over what I say. His complaint here is that there exists no way to identify the "knowables". He is of course correct; however, what he misses is that the conclusion is not dependent upon being able to make that identification and I have no idea of how to make that fact clear to him.
"now let us add further unknowable data such that every possible observation consists of a unique pattern even after any arbitrary element is removed from that observation. If that fact is true, then the value of the removed element may be determined via the rule and the remainder of the pattern.
this situation can be represented mathematically as below:
Xn = f(X1,X2,X3,...Xn1)
so this is where i stop and ponder for a while.... "
Fundamentally, I do not think you have made any errors or omission of real significance. I get the impression that you are following my presentation quite well. I would like to add a little which might clarify my presentation a somewhat.
The discussions over the last few years have been very helpful to my thoughts. On review, of the exchanges, I am beginning to suspect that the single most significant thing I have discovered in my analysis of the problem of understanding the universe is that the conventional scientific attack on explaining reality is actually excessively free. (One could say disorganized.)
I conceptually divide "things which exist" into two categories: "knowables" (things which will turn out to actually exist in that final analysis way down the road) and "unknowables" (things which will turn out to be figments of our imagination, created to allow our rules to explain our observations). Now Harv always barfs on that concept because it is clear that we fundamentally do not have the power to determine if any given idea belongs to one or the other category; however, I hold that the two different categories require different logical consequences. That issue has no bearing whatsoever on whether the categories exist or not.
So, from that perspective, one can understand that as science advances, there are two things which can change. Actual facts (the knowables) cannot change, but both the "unknowables" (what we think exist) and "what we think the rules are" can change. As scientists, we are free to create any "unknowables" we wish so long as all the "knowables" and "unknowables" (all the things we think exist) obey "all the rules". And we are free to theorize any "rules" we wish so long as all the "knowables" and "unknowables" (all the things we think exist) obey "all the rules". This is no more than an abstract statement of what scientists do all the time. They continually invent new entities which provide explanation of the phenomena they examine and then check to see if those invented entities obey the rules they believe to be true. At the same time, they occasionally change the rules a little. (On some very rare occasions, the rules have changed quite a little and I guess I am proposing a basic change in the rules.)
Getting back to what I have done: I have explicitly proved that, if you accept that both the rules and the entities are variable (that is, subject to change by advancement of science), then it is always possible to put the rules in the form of a solution to the expression F=0. That is, there exists a very specific rule for the functioning of the universe which does not constrain the universe in any way. That rule is in fact my fundamental equation. The result of that constraint is that the only question left to answer is "what entities actually exist?" The equation itself is entirely content free and imposes no constraints whatsoever on the universe.
Furthermore, anything deduced from my work must be content free. A considerable volume of modern physics is directly deducible from my fundamental equation. As I comment in my paper, physicists seldom worry much about the consequences of their definitions and I think I put forward very strong evidence that they should take the issue seriously. I state once again, I have presented no theory whatsoever; all which I have deduced, I have deduced directly from definition.
Essentially (depending on how one cares to view my work), I have either invented or discovered a very powerful abstract tool for organizing any serious scientific investigation.
Have fun  Dick
