I am answering your e-mail on the forum for two reasons: first, you have already mentioned aspects of issues on the forum and second, I think my answers are relevant to the problems many have in understanding what I am saying.
I will begin with your comment, "Re: understanding your paper: I have struggled for some time to understand equations 1.1 and 1.2. Sometimes I felt I had grasped what they were about only to find something didn't seem right."
I am of the opinion that your problem is very specific: it is your failure to appreciate the necessity of understanding mathematics. You want the solution in the form of a subconscious feeling that you understand the whole whereas the only correct answer is that you can follow the logic of any single step.
I have been slow to answer because I do not know how to explain the issue; how to put it so that it will make sense to you. I will try though I do not expect success.
You have a mental picture of reality. You came to have this mental picture of reality, not by conscious effort but by receiving it unrequested from your subconscious mind. You think this mental picture is real when in fact it is actually an illusion. The proof that this is true exists in your mental picture itself.
Let us assume that your mental picture of reality is correct. I will presume that picture includes the existence of your brain contained within your skull and connected to your eyes, ears, muscles and skin via nerves. Now when you see something, your brain is aware of what you are seeing because certain nerves in your optic nerve are discharging electrical impulses (and probably also causing chemical changes). Exactly the same comment could also be made about anytime you hear something or feel something.
Think about that for a moment! When you read this, are you "aware" of exactly which nerve cells in your optic nerve are active and which are not? In fact, are you even "aware" of your own optic nerve at all? When you hear something, are you aware of exactly which nerves are being activated by the action in your inner ear? Now your brain receives this information (various nerves firing) and deduces what is going on! Your brain transforms these signals into representations in your mental image: you see a light, you hear a noise or you feel something. How did you first decide that the firing of a particular nerve meant you were seeing something. You never did any such thing did you? You were aware of "seeing a light", "hearing a sound" or feeling something. So even in your own mental picture of reality, what you see, hear, or feel is an illusion presented full blown by your brain.
Now I say that the illusion was created by your subconscious; certainly by any stretch of the common understanding of the universe, the conversion from nerve impulses to ideas was performed by your brain and you certainly didn't do it on a conscious level so what else could it be but your "subconscious". I only comment about that because Harv gave me such a hard time for crediting the image to my subconscious.
If you understand that then you should understand that comprehending what is actually going on amounts to comprehending what caused those particular nerves to fire. Your problem is that your subconscious stands between you and reality and you have utterly no way of examining what is going on except through the illusions created by your subconscious. We could begin by starting with a large number of nerve connections and try to come up with an explanation of how the brain managed to transform that information into the illusions it creates. The problem is that the idea of nerve connections is another one of those illusions! So I took the step that, no matter what the source of the information was, it could be represented by a set of numbers! That at least gave me a pretty universal starting point.
Thus, my problem became one of figuring out a method of modeling (creating internally consistent illusions) of undefined data transformed by an undefined mechanism (the subconscious). This required working with numbers and logic and nothing else. The whole of what can be seen as numbers and logic is called mathematics.
Back to your difficulty understanding equations 1.1 and 1.2. "Sometimes [you] thought [you] had figured them out but then something seemed wrong". I think your problem stems from your utter refusal to put your faith into logic itself. The problem is that the conscious minds ability to analyze anything is severely limited: I am convinced that no one can consciously consider more than two or three concepts simultaneously. Any more than that and you are, in reality, depending on the accuracy of the illusions created by your subconscious.
Words are themselves one of the major signs of those illusions. When you use a word, you are very often not being exact because there always exists some doubt as to what the words actually mean. What you are actually trying to do is to make your subconscious model what I am doing. You are trying to create a mental image which makes what I am saying make sense to you.
Alan: I asked myself: "why does Dr. Dick call "observation" a specific subset
of an examined set of a set of numbers?
If reality is defined to be a set of numbers then an observation being a specific piece of [look at] reality is a specific subset of numbers and our examination of reality consists of a collection of observations. These are concepts which you should be able to comprehend as basic. We are not talking about "intersections" here, we are simply naming subsets of information: reality is "everything" that we could possibly know, some of it is what we examine and that examination (what we do know) consists of a number of observations. Think of an observation as everything we are aware of at a given moment (labeled with t, the name of the moment). Note that the observation is defined to be what is real, not the illusion created by our subconscious; that's why it must be seen as a set of numbers.
Alan: By adding "unknown data", unknown categories, we insure that whatever "your phone" is, it is exactly specified to be the region wherein all these unknown categories intersect with the known categories to give the definition "your phone".
The unknowable data I refer to is not "unknown categories", it is just pure addition of bogus information created out of my imagination in order to provide the effect I desire. I add this bogus information three different times for three very different reasons. The first time is to make sure that all observations are unique:
On that first occasion, I made a strong attempt to explain what I was doing:
"In order to comprehend my purpose and thus the constraints I must obey to serve that purpose, you must understand that I am constructing a completely general mental model of an unknown universe! What is significant is that there must exist no universe which cannot be represented by my model; that any part of the model is fictitious should bother no one as the entire model is a fictitious construct. To add to my model the possibility of significant information which is not knowable via any direct means does not constrain the ability of that model to represent reality. Most scientific attacks concern themselves with limiting the field under consideration; my attack is specifically concerned with not limiting the field of applicability of my model."
I use the word "bogus" because I want the reader to realize that absolutely no evidence at all exists to make this data part of "reality". In your mental image of reality (that illusion your subconscious has created) "unknowable data" would correspond to the presumption that things you are not actually aware of at a given moment really exist. Essentially, what I am saying is that it is very reasonable to hypothesize things existing even when you have no actual data to defend that existence (except that it makes your explanation simpler than it would otherwise be: i.e., it is part of the explanation, not part of the actual data to be explained). Does the moon exist when you are not looking? That idea certainly is not essential to the fact that you see it when you look but it does make the explanation of your real observations simpler.
On that first occasion, I add "unknowable data" sufficient to make all observations unique. I do this purely for mathematical simplification. As I said, everything I know I obtain from a finite number of observations. Since every observation consists of a finite set of numbers and everything I know consists of a finite set of observations, those observations can be ordered (that is basic mathematics: numbers can be attached to each one). Since, in my analysis, I want to order them, I must include that information in my analysis. Is there any easier way then to attach that additional data to the sets? If I don't make them unique, how do I know where to put them in the series? On what is the order based?
At this point I notice a very valuable consequence of this unknowable data. If I go a little further and add sufficient "unknowable data" to make every observation unique even when one piece of data is removed, I have created a very strange situation. The situation is strange because, if I knew the rule which constrains the observations (controls what data may be seen), and were given all the numbers but one, I would know exactly what observation I was looking at and only one possibility would exist for that missing number. That means that for every set of observations (missing one number) there would exist only one possibility for the missing number. That line itself is expressed by the idea that the missing number is a function of the other numbers --> equation 1.1.
Equation 1.2 is nothing more than a rearrangement of expression 1.1 .
I know that won't clear much up, but I tried!
Have fun -- Dick