Richard,
Since clarity is apparently not my strong suit, let me know if anything seems confused to you. I apologize for my comments on your "reality set"! No, I did not realize it was April first. Sorry, I can sometimes be quite dense.
***** Richard:
...reminds me of how Godel renumbered numbers into a linear set, or somthing like that, my memory is so poor; and then proved his incompleteness theorem using the assigned numbers. You have just assigned numbers to your data.
*****
Yes, that is very analogous to what I have done and it surprised me that Harv would not accept such an abstract representation as rational in that he implied he was familiar with Godel's work. The whole issue in both cases is to assure the absolute generality of the representation.
***** Richard:
So I am wondering if they need to be thought of as a coordinate system. Perhaps some of the mathematical operations that follow require a background space.
*****
I think Paul (apparently our best current authority on the subject of mathematics) will agree that the concept of a coordinate system is actually no more than a mental crutch and is not fundamentally needed in any mathematical representation of any mathematical relationship.
***** Richard:
Another note. Astronomers claim that the universe has scale invariance.
*****
Yes, that is true; however, I think they see it from a macroscopic perspective. I don't think anyone other than myself has actually proposed that the Universe (over the entire range from the microscopic to the macroscopic) needs to be scale invariant. But of course "no one" is a pretty absolute statement to make and is most probably wrong. I have never seen it stated that such a symmetry requires that "action at a distance" is not possible. However, I will comment that I remember reading Newton one time (on his theory of gravity) where he said something to the effect that although action at a distance is clearly impossible the mathematical construct of a gravitational field was a useful mechanism. That seems to imply that "contact" interactions are the only interactions he found rational. It is too bad that I have never actually talked to him so I don't really know what he had mind.
***** Richard:
Also I must confess that I have not yet read your entire paper I was so hung up on the assertion of no assumptions.
*****
I take this to mean that you understand why I feel I have made no assumptions about reality other than the fact that the field of mathematics is valid reasoning. The real central issue is that absolutely any set of numbers (the "knowable data") can be analyzed from the perspective of the representation I present: i.e., that in laying out that perspective, I have not excluded a possibility.
***** Richard:
So I promise tonight to dig your paper out of the big box I poured everything into when I was laid off on 9/11.
Sorry to hear of your problems. I hope you can find something reasonably quickly. I know what it's like as I have been there. I used to have my own business and after that "went away" (technology made my patent worthless) I was essentially unemployed for almost six years! When you work for yourself, you have no job references and age discrimination is very real! "Overqualified" is the standard euphemism for "too old".
By the way, if you can't find your copy, contact me at doctordick01@yahoo.com and I will send you a self extracting zip file which contains the whole thing. I have made some corrections since it was posted on the web (I should probably make some more considering what I have learned in the last year). By the way, that web site no longer exists!
Have fun -- Dick |