Well, I stay away for a week and you guys post so much trash that I can't find my last post. By the way, Paul, don't argue with Yanniru. He is a recognized authority and should not be questioned. So, Tim, I post once more to the top of the collection. I would remove some of these guys from what I can see but I worry that someone might say something intelligent.
Sorry you are old Tim! Where are the young people interested in understanding? I don't think the modern school system really encourages kids to think. My dad said that the school system in the US was destroyed when they closed the one room schoolhouses and opened the baby sitting institutions we currently have! Sometimes I think he had a good point. According to him, the great thing about the one room schoolhouse was that everybody got to hear everything going on with every class right from the get go, yielding a much better understanding of the what's and why of education.
No, I won't hold being old against you. Explaining things to someone else is always the best way to clarify things in one's own mind. From your statement, "the data of reality as it impinges upon our senses is collected first through the filter of our senses and then we feed that filtered data through the fundamental transform (of fig 2) which yields the divided subset of numbers", certainly clarifies the fact that your picture of what I am saying and mine are not alike at all.
As I said earlier, "the existence of the fundamental transform mentioned in figure 2 goes to the issue of representing reality as a set of numerical labels and has nothing to do with explaining our "senses". The explanation of our senses is left open as an unanswerable question." You imply you understand that statement and then proceed to apply aspects of figure 2 to my further deductions. This is my fault for not being entirely clear with my arguments. I apologize; however, sometimes it is not as easy to be as clear as one thinks one is being.
I will try to be a little more careful. Figure 2 goes only to the issue of representing "reality" via a set of numbers being universally applicable. The only thing lacking from that definition is the step of giving meaning to those numerical labels. This I leave open as I have no way of proving that any meaning which I attach to any of those labels is correct! I only wish Harv could understand that. I use numerical labels because they possess no connotations at all and the problem of connotations in the English language (and probably all other "languages") is what I want to avoid at all costs. The problem with those connotations is that they imply more relationships then can be checked (for consistency) on a conscious level.
At this point, you should be able to comprehend the definition of "reality" as a set of numbers. If you can understand that, then most all aspects of the figures drawn may be laid aside. Only one issue still outstanding might be seen as represented in that diagram (but it has nothing to do with the so called fundamental transform). That issue is the fact that all information available to us is obtained through our senses. That we have absolutely no way to check the veracity of our perceptions by any means outside of our perceptions themselves.
Now I am totally astonished that everyone in the scientific community is not immediately bothered by that truth (a truth which seems to me to be accepted by everyone). It is absolutely clear that my awareness is on the wrong side of the pipeline of perception to allow any testing of the veracity of the pipeline itself! From 60 years experience with the scientific approach, it has become clear to me that the common scientific position on this question is very simple. Essentially their position is: if it can not be tested it must be believed to be true. With regard to this universal unexamined belief, I need to comment: on occasion, when belief in that perception leads to totally inconsistent results (consistency being a central issue of "truth") we assign the title "illusion" to the effect and go back to believing everything else.
Whenever I bring this issue up the most common barf I obtain is "well, if you are going to take that position, then everything is "illusion!" I say there is no more proof of that than there is that it isn't "illusion". My personal opinion of the reaction is that people like Harv just don't like to think about the problem and use that common response to cut off debate.
At this point, I would like to make a side point. As Harv quite often makes quite clear, my deductions are based on logic which is of course directly dependent upon my own subconscious solution to the problem of creating a mental image; however, my position is that the deductions themselves rely only on that logic itself and not at all on the particular solution my subconscious has achieved. Logic itself is perhaps the only issue upon which almost the entirety of the human race agree: i.e., it appears to be one of the thing which everyone's mental image contains (if not, we do not categorize them as rational but rather tend to lock them up in the funny farm).
The issue of this discussion is the fact that the problem we face is one of deciphering the puzzle which is reality. If we are to decipher that puzzle we must first establish exactly what we have to work with. Dam near nothing! And Harv, that's not very much; in fact, it may be exactly nothing. (Excuse me if I talk to Harv in the background because I know he's there and, no matter what I say, he will spout forth some unthoughtout cavil!) The only thing I do know about reality itself is that (if it is communicable) it can be presented as a set of numbers.
On the other side of this puzzle is the fact that I possess a mental model of reality (whether it is right or wrong is not an issue at all). Just as reality can be seen as a set of numbers (that objective set of labels with no assigned meaning) that mental model can also be seen as a set of numbers (again, an objective set of labels with no assigned meaning). Now right here I think there is a major communication problem. I suspect that no one out there has any concept of what I am talking about. Let me go off for a moment and try to explain my mental image in terms of a set of numbers.
My subconscious (my intuition?? whatever you want to call it) has provided me with a mental image of reality (what I think or rather "feel" reality is). Within that mental image is a thing I call the "tip of my finger". In every memory I have of any examination (every observation) of "the tip of my finger" I found associated with it another thing which I call "my fingernail". Now, in that mental image, both of these things are made up of a great number of other things (the category of which I have attached the name "molecules" and "atoms"). The quantity of things I am talking about here well exceed 6 times 10 to the twenty third items (Avogadro's number). Now Harv may want me to name each of these things but I don't know how to come up with that many names. How about we just give them numerical labels Harv?
Now let's look at all those observations I referred to (the tip of my finger and my finger nail)! Are all those things I observed (or at least thought I observed) fifty years ago the same gadzillian things I observed two seconds ago? Even my subconscious (my intuition) says "probably not", I have cut off a good foot of it since then! What my subconscious tells me is that every time I observed a collection of "things" to which it attached the title "the tip of my finger" I also observed another collection to which it attached the title "my fingernail". So the various English names which we give to things are really to defined cases; situations involving not only a large number of things but referenced to a great many more things. Concepts are even more deeply involved and complex things.
The issue here is that my mental image of reality consists of so many things that naming them in English is not only impossible, but not even conceptually reasonable. Naming them with numerical labels on the other hand is at least achievable on a conceptual level. Just take each separate observation, establish some coordinate system (after all, my mental model consists of these things being in different positions in a three dimensional space) and then name each thing by its particular coordinates. Having made no commitment to use the same coordinate system in any two observations, the names (coordinates) of these many gadzillion things won't even be the same from one observation to the next. However, that thing I called "my fingernail" will probably be identifiable to some collection of things in every observation.
So there, I have just explained a conceptual transformation of my mental image of reality into a set of numbers. I could just as well (conceptually thinking) have put forth a complete description of every observation I ever made (including each and every detail of everything I presumed to be true at the time of each observation) in English, naming and identifying everything in every observation in complete detail. Then calculate the ASCII representation of each and every word. That also would transform my mental image of reality into a set of numbers. The information content of the two sets of numbers would be fundamentally equivalent. I personally like the coordinate system put forth first as it is conceptually quite simple and correlates quite well with the overwhelming intuitive illusion put forth by my subconscious that I live in a three dimensional world.
I hope that clarifies the puzzle a bit. We have this thing called "reality" about which we know almost nothing (which I hold can be represented by a set of numbers) on one side of that pipeline called our senses or perceptions. We, as aware individuals, work with a mental image (also representable by a set of numbers) provided to us by that pipeline. We know that the pipeline creates illusions and we have utterly no way to examine the pipeline itself. So reality is the source of the information entering the pipeline and what we are consciously aware of comes out the other end. To presume that what comes out (minus known illusions) is an exact valid representation of reality is foolish to say the least. If we have any interest in understanding reality at all, we should at least examine the logical possibilities here.
The puzzle then is the transformation which takes place in the pipeline. Whatever goes on in that pipeline, we have one word which certainly applies. That word is "definition"! What goes in certainly cannot be defined and yet, if we knew what it was and could communicate it, it certainly is representable as a set of numbers (if it cannot be known and communicated then there is no reason to even think about it).
What comes out is very specifically defined; a whole slew of defined perceptions, concepts and ideas commonly referred to as our mental image of the world we find ourselves in.
I will quote myself again, "Of issue is exactly what part of our observations are meaningful statements about "reality" (i.e., actual consequences of our observations) and what part is nothing more than self consistent consequences of our definitions." Our actual observations are what goes into that pipeline, not what comes out! In my paper, I specifically identify my purpose: "In this presentation, I will attempt to construct a mental image of the universe without presumption and, thus, discover what it is we know and what part of what we think we know which is myth".
That procedure involves careful definition of a number of particular terms. The definitions begin with the primary definition: "reality is a set of numbers". Harv, those are the meaningless numerical labels attached to the "things" which go to make up the "observations" my second defined term. The Ontology is very simple: those labels are labels for the things which actually exist! What comes out of the pipeline? Things I think exist (plus a whole lot of defined ideas so complex that I cannot even begin to enumerate them).
The things I think exist are clearly made up of two components: things which really do exist (reality) and things which do not really exist (illusions created in the pipeline). I refer to these two different components as "knowable" data and "unknowable" data (just names I attach to the conceptually different components). The "unknowable" data is, by definition, not part of reality (that is, it is illusion) so it must be created by the pipeline itself. Clearly, it can be done as we all possess a mental image. The real puzzle is, how can such a thing be done?
The first step in this puzzle is to realize that the freedom to add illusory information to the actual data obtained from reality allows one to specify the rules which control our illusions to be specified as a solution to the equation F=0 without making any constraint at all on what set of numbers appear in the original observation (and Harv, not being able to obtain that original observation has absolutely nothing to do with this conclusion).
The next step in the puzzle is to comprehend that the information available to us cannot answer any questions for sure. All answers must be couched in the form of a probability. This fact also constrains how the answers must be expressed. The sections from equation 1.3 to 1.7 display exactly how to bring this fact to bear on the puzzle such that we assure that we "discover what it is we know" and do not confuse the issue with the illusions our subconscious creates ("what we think we know which is myth").
The final step in the puzzle is to realize the significance of symmetry. This is where I totally lose Yanniru (I worry about his mental competence). Since there is absolutely no way to uncover what processes take place within that pipeline, there is no way to justify any symmetry in the things I think exist to be a valid characteristic of reality itself. It is entirely possible that those symmetries are nothing but an illusion created by the pipeline (our subconscious or intuitive feelings). Since no method exists to prove they are not so generated, attributing to reality is a direct consequence of the standard scientific position: "if it can not be tested it must be believed to be true". Yanniru and the whole lot of posters on this forum use that postulate all the time (without any defense I am aware of).
The solution to the difficulty of symmetries in the things I think exist is to construct an mathematical representation which inherently includes those symmetries. Deviation from that representation then yields important characteristics of reality. Thus it is that the first step in my analysis is to assure that my bare model displays every symmetry that I can think of. By this mechanism I assure myself that my model will not attribute to reality things which could have been generated by the pipeline. Make it easy to "discover what it is we know and what part of what we think we know which is myth" created by our subconscious.
This final step is what leads to equations 1.17. The stuff from equation 1.18 on amount to adding some symmetry considerations to the F=0 constraint. Once you understand everything up through equation 1.17, I will try to clarify the remaining portions of chapter 1.
I hope I have not blown you away with this response.
Have fun -- Dick