Sorry for not replying to your other post. I got tired of talking about Dick's model per se, and I'd rather discuss issues more specifically (due to a lack of time). I'll talk to Dick about his model, since it is afterall... his model.
***What I "so confidently" know about 'ultimate reality' is that it contains thought.***
That only brings the question further back. How do you know that? That is, what if the logic that you apply to understand ultimate reality is faulty? For example, what if there is no real 'now'. That is, what if the world is more like a film reel where each 'slice' of you exists separate from every other 'slice' of you? What you call Thought would reduce to a particular state at any one time, that is, a state of awareness where you feel like you are thinking. In such a world, there is no thought. Now, this a world that we can imagine (and with GR might even be a likely world), but what about the worlds that we cannot imagine? I don't think your premise can hold.
***Thus, it is not vacuous, and there is something. What I also "so confidently" know, is that "I" can, to some extent, control "my" thoughts, and I have excercised that control in many and various ways. ("I" and "my" are in quotes to indicate that I claim to know virtually nothing about what they are or mean.)***
You have perceptive feeling that at any particular time that you can control your thoughts. Again, it could be that all of 'you' exists in a 'slice of time' where the past did not occur which led to this current feeling.
***In particular, I have thought about how to interact with what seem to be other people, and have discovered that I am able to communicate some of my thoughts to some of them, and likewise they to me. So, I have learned to talk, read, write, study, etc. I learned that mathematics is the development of consistent conceptual structures. I learned that I am in posession of a lot of information that I did not consciously dream up and which has a lot of seemingly consistent patterns (people call this 'sense data' putatively coming from the "outside world".)***
These are all memories that you must recall instant by instant. If the only thing that exists is an instant (i.e., the last instant you experienced), then there is no actual events in your past. This is a form of solipsism, but we cannot rule it out. Therefore, we do not absolutely know this about 'absolute reality'.
***I have also learned that some of the patterns which result from mathematics (pure thought), can be put into correspondence with patterns which come from "sense data". If we suppose that there is some connection between some of these "sense data" and some "ultimate reality", and if we can make a correspondence between the "sense data" and some theorems of mathematics, then I think we can be "confident that we are dealing with a portion of 'ultimate reality'".***
We can be confident only in so much that we are willing to make certain assumptions about ultimate reality (e.g., that correspondence with human ideas and human senses can accurately depict ultimate reality). This is not something that we actually know in an ontological sense. We are merely giving ourselves some slack in making these needed assumptions. A leap of faith, if you will.
***And, I think that we have virtually no access to anything true about any "ultimate reality", or at best, if we do, we don't (or even can't) know that we do.***
This is my main point. But, I think you need to apply it to the idea that 'thought exists'.
***But we have discovered, to our great benefit, that we can make correlations between mathematical structures, and patterns of this "sense data", to make useful predictions about the behavior of our world.***
I agree, this is done in light of scientific experimentation. That is, a scientific prediction is only useful when it is showed to be useful. We don't know why a mathematical structure is useful in scientific theory, we just know that it works in the way of theory creation. The nominalist, Harry Field, has attempted to create science without numbers. The idea is an attempt to show mathematics as only a convenience and not some testimony of mathematical necessity existing in the world. For example, people such as myself used to use slide rules until calculators were cheap enough and small enough to afford and carry with them. Some people who only used slide rules had a difficult time moving over to using calculators because they weren't used to any other way of doing their calculations. Perhaps mathematics is our slide rule. Perhaps modal theorists in their attempt to construct mathematics will mistakenly invent some new type of means by which to state theories in non-mathematical language. Perhaps new insights to the universe will come immediately as a result.
The concept of using math and constructing a model with some basic assumptions might seem appealing to depict ultimate reality and answer why physics is the way it is, however math (as far as we know) is just a tool to come to useful predictions. Without new predictions the tool is useless. That is, we might be using our slide rule (with our slide rule assumptions) to validate our concepts of 3-dimensional space and the physics that is 3-dimensional based, however we might be limiting ourselves for higher dimensional calculations. Perhaps we cannot use a slide rule or the assumptions of slide rules to validate the rules of higher dimensional space. In such a case, we should throw away the slide rule and buy ourselves a fancy TI graphic calculator. The point is not this poor analogy, the point is that we cannot use human abstract tools to tell us how ultimate reality must be unless we can at least acquire some predictions that provide more credibility to the abstract method. Otherwise, we are more than likely constructing slide rule Bible Codes which are just epistemological tricks (as Luis mentioned).
***And the correspondence of that theorem with anything that might be "ultimate reality" makes predictions that yield a priori most of the laws of physics.***
Bible Codes are notorious for performing the same trick. How do you tell the difference? Consider this: no one has ever constructed a method such as Dick's method that later did not come to be seen as nothing but a Bible Code.
Warm regards, Harv