First of all, please bear in mind that I wrote this while reading your post, so if my thought process seems to bounce all over the place you'll know why.
"Their position seems to be "Oh sure, people in the past have had erroneous concepts of reality, but that is over now, our concepts of reality are now completely correct!" That has been the position taken by everyone since the beginning of rational thought."
Maybe. I used to think that, but I'm not totally sold on it. I think most people accept that science is a means, not an end, but on the other hand I've rarely discussed that with anyone so I can't be sure.
"Essentially, no one capable of following the mathematics has yet admitted my right to examine the problem. They all do everything in their power to stop me at the opening position. They all fight tooth and nail to defend the correctness of their perspective."
Well, I'll try and wade through your 100+ paragraphs of data and see if I can interpret your data. I'll take it one paragraph at a time to make sure I don't skip anything:
"1. No one knows for sure what reality actually is: i.e., they may have some excellent ideas but there exists no proof that there are no errors in their concepts."
"2, The only way we may know what a word means is by how it is used. Given that fact, the actual letters (or symbols -- Chinese or Egyptian hieroglyphs or pictures etc. or even, for that matter, patterns of electron flow in our brains) used to represent a concept are immaterial, we could just as well simply number these things. Then, translating any communication into patterns of numbers we can work with the numbers instead of the symbols.
3. If everything is so translated, then we have absolutely nothing else to work with. The original meanings of the numbers must be embedded in their usage. Compare this with "The only way we may know what a word means is by how it is used." Is the problem the same or is it not? I believe I have done no more than express the problem in an abstract manner. "
I agree, but I do need to point out that not all human models are respresented through symbols. It would be difficult to represent the sensation of pain into a numeric set capable of being interpreted by the originator of that sensation. So, while reality may be reducable to a set of numbers which represent all reality, realize that we are absolutely incapable of knowing some aspects of that reality in a numeric sense.
0. We may still have an infinity of numbers to search through, but at least we won't be searching through X