When I first approached the field of numerical
simulation, everything in my models used
“piecewise linear” approximations of functions.
I knew that piecewise approximations using
polynomials existed, but I much preferred
piecewise linear because it was so straightforward
in the calculation of differentials and integrals.
I thought I was pretty smart doing it the “easy”
Then somebody showed me that piecewise quadratic was
“easy” too, and better. Then I started playing with
cubics and so-on. Then conjugates entered the picture
as well. After playing with these mathematical objects
for years, one day in 1985 I discovered the Lorentz
factor in an “approximation”. I put that factor on the
left hand side of the equation and out popped a really
neat identity, the one described above. And it was not
merely an approximation, “piecewise conjugate” was
exact. I know that even “high falooten” math-nuts on
SciAmPF had never seen my identity before; I was
user-name ClamShell at that time and they refused to
absorb what was necessary to understand it, so they
dismissed my work on the basis that they didn’t understand
it. I’m really no Galois, but Galois suffered the same
fate at the hands of his chairman. So I think maybe that
I’m onto a “new” type of analysis, and for lack of better
words, I call it “Conjugate Analysis”.
And if I am wrong, I have little to lose, so I persevere
in the notion that gravity is a “conjugate field”( and so
are the other fields as well); a first principle.