6. Bridging the gap

By convention there is color, by convention there is sweetness, by convention bitterness, but in realty there are atoms and space.

—Democritus

Of course it is conceivable that one could be lucky; simply find the magic equation and in one fell swoop recreate all of physics in a new genre. We, on the other hand, have felt a need to under­stand how more of the simple things could be done before attempting to do everything. In summary, we have worked to knock down, one at a time, the bugaboos that made CAs seem inappropriate, while finding ways to model more and more of the properties of physics. Someday we hope to see it all put together with a grand equation or rule that is the answer to everything, but this process may more closely resemble the progress of quan­tum mechanics as opposed to the theory of rela­tivity. Once we do have the rule we will be able to work with it in two ways: analytically, as with any mathematical equation, and through simulation, where we use computers or specially built cellular automaton machines. The usefulness of simulation will depend on the scale; if it is at Planck's length, then we will be unable to compute much. If how­ever, the scale is closer to a fermi, then we may be able to compute a lot. Surprisingly, the rule would be the only parameter of this model of physics. We assume that the rule includes the specification of the neighborhood. To be complete, everything in our universe (the exact present state) would be a consequence of the rule, the size and shape of the cellular space, the boundary conditions (which can be eliminated if the space wraps; e.g., if cell co­ordinates are treated modulo some number), the initial conditions and the time (which would be an integer, the number of time steps from the initial conditions to the present). From the rule it should be possible in principal to compute every constant of physics and answer every question posed at the appropriate scale. The reason is that given the rule, we need only run a simulation and watch it to determine the values of whatever we are unable to calculate analytically. To be practical (mean­ing that we do not plan on spending much more money on CA machines then we are planning to spend on accelerators) the scale of the rule (of the CA) must not be too far below the scale of the phenomena we wish to model.