Mariko said:
~~Wow impressive-May I ask you what that paper was written for? Was it a class, your job or for the heck of it?
My http://home.jam.rr.com/dicksfiles/reality/Contents.htm where a lot of very important stuff is laid out in easily understood presentations.
I only comment on John's post because I have had a very real personal experience with the issues Lee Smolin is talking about. I have a Ph.D. in theoretical physics. I got there, not because I wanted to "do physics" but, because I wanted to understand the universe (and by the way, "the universe" is everything by definition) and physicists seemed to have a better handle on the problem than anyone else; however, by the time I received my degree, I was throughly disappointed with the physics community. My thesis adviser and I disagreed on the importance of "number crunching" as compared to underlying principals.
Just as an aside, every theoretical physicist I have ever met made it quite clear that they had utterly no doubt as to the correctness of modern theory (all it might need are minor corrections which could be found by careful examination of the predicted results and experiments: i.e., "diligent number crunching"). One once told me (who I do not remember), "don't worry about the logical defense, people much better than you have already examined that issue exhaustively". One day (when I asked my thesis adviser a simple question) he said, "only geniuses ask questions like that and, believe me, you're no genius." I never thought I was but I didn't think you had to be one to ask questions. It did make me think about the meaning of the word "genius" though. I decided that the real purpose of the word is to provide an out for the professional's failure to spot the errors in their own perspective.
One year, when I was taking a Quantum course given by the chairman of the department, I commented to him about something I had noticed. [That would be exactly the same issue I tried to explain to Hurkyl
here (actually consists of three posts because of length)]. The professor looked over my work one evening with me and, after several hours of serious discussion, said, "well, of course you are right, but don't show this to any of the other students, it will just confuse them!" At the time, I respected him and kept what I had noticed to myself (after all, at the time, I knew of no applications anyway so what difference could it make). I only mention this because it reflects the stifling of original thought practiced in US graduate schools.
So, after I got my degree, I earned my living outside physics (no one wanted to support the kind of thing I wanted to think about and I certainly didn't want to teach things I couldn't support). None the less, I continued to think. I had discovered the equation I gave above,
<br />
\left\{\sum_i\vec{\alpha_i}\,\cdot\,\vec{\nabla_i}\,+\,<br />
\sum_{i\not=j}\beta_{ij}\delta(\vec{x_i}\,-{\vec{x_j}})\right\}<br />
\vec{\Psi}\,\,=\,\,K\frac{\partial}{\partial t}\vec{\Psi}\,=<br />
\,iKm\vec{\Psi},
back when I was a graduate student but I could not solve it then. Thus, at that time, it was little more than a useless representation of an idea. However, some twelve years later, I managed to pull out a solution. Once I saw how to solve the thing, everything just fell into place. When I tried to publish my results, every journal I submitted it to rejected it (I don't think a referee ever saw it as they all said it was outside the interest of their publication).
I went to my thesis adviser for help in getting it published. He was very helpful

; he informed me that "no one would ever read my work because I had not paid my dues". Oh yes, he also refused to look at it himself. Well, I didn't believe him and I continued to try to generate some interest. As it turned out that he was quite right. The physicists said it was philosophy; the philosophers said it was mathematics and the mathematicians said it was physics. So I have discovered a new field of interest to no one. I laid it aside and when on with my life.
And that is the way it would probably have ended except for two events. In 1987, I bought an IBM286 PC at a garage sale that happened to have "Word Perfect 5.0" on it. That program could display mathematical equations and had spell check (my spelling is normally atrocious). So I copied my old hand work over to a WP file and sent it out to a few people. The response was no better than before. In 2000, I was cleaning the attic and ran across a copy. I commented about it to my son-in-law who suggested I self publish on the web which I did. Except for some minor corrections, that is exactly what is posted on my http://home.jam.rr.com/dicksfiles/ (click on the book).
The thing on explanation was generated after some conversations with Paul Martin. As I say, it is the underlying essence of the other paper. As I said earlier, anyone who seeks to understand anything is seeking solutions to the fundamental equation given above whether they know it or not. It is quite easy to show that understanding a language (and thus the ability to think) is itself a solution to that equation. Is it philosophy or is it physics or is it mathematics? It is all three as it is an analysis of exact science itself.
Have fun -- Dick