Procedure to generate an equation

          Fourier analysis is decomposition and reconstruction of a wave function, among other things. Fourier analysis processes data. I go one step further. I let the computer create tools which process data -- equations. And if they work, if they yield the right answers, who can question their validity? By the way, my equations, as simple as they may seem, were generated by the Princeton supercomputer.

          Like in the Fourier analysis, I break down the task into its basic components and then allow the computer to sort things out and recombine the components into one small neat package in "the best fit". And the best fit is the right answer.

          This is how it's done.

          The first step. You define the task. The task is to derive a certain equation. You compile a table of variables and constants which influence the equation. You describe each variable. Whether it is directly proportional or reciprocal (it will go either in the numerator or the denominator, accordingly). You define its SI unit and other properties, if present. Then you compile data tables in SI units as well. Finally, you define the range of the observed value known from observations or from experiments (in SI units).

          The second step. You write a program (or modify the existing one) to manipulate the tables – all possible permutations of variables, constants, and data values to find the simplest combination of variables and constants which would yield the observed value within the defined range. The computer prints out the equation.

          That’s it. Then you test the equation manually using a calculator and see if any modifications are necessary. To the best of my knowledge, no one else has ever used this simple method to derive equations.

          Computer? Any computer. Programming language? Your favorite.

          It is not very complex. For example, let’s derive the equation for gravitational redshift z using the Earth as a sample.

          First, compile a table of variables and constants involved.

          D  -  gravitational density or its integral, directly proportional, in gi units

          d  -   distance of gravity limit, directly proportional, in meters

          f  -   gravitational viscosity constant, directly proportional

          m  -  mass, directly proportional, in kg

          c  -   speed of light, inversely proportional, in meters per second

          Add an array of coefficients between 2 and 10. Do not go above 10.

          Define a table of gravity limits. We already have Table 2 in “The math” page. It contains the mass data as well.

          Now, define the range of the observed value from an accepted experiment. The value for Earth is 38 microseconds. Try the range 30 – 40 (in e-notation).

          We are ready to create a program. The gravitational density here is the integral between 0 and 9.83 gi, gravity limit is 9.1993*10**10 meters, and the mass is 5.9736*10**24 kg. We ignore the gravitational influence by the Sun and our galactic black hole because that influence is insignificant. Gravitational viscosity and the speed of light are known constants.

          Spin the program. It spits out  z = 3 D d f / c  =  0.0000347 sec

          The mass is ignored which makes us skeptical. So, we take a calculator and enter the Earth’s data. The answer is 0.0000347 sec or 34.7 microseconds.

          By George, it is correct! It is even more precise than the experiment.