Eternal Progression
A “derivation” of the laws of eternal progression
based on work by Dr. John H. Gardner, B.Y.U. Physics Dept.
The following is a "derivation" of the laws of eternal progression and a discussion of their implications, taken from my father's writings. Note that it is not really a rigorous derivation, it is more a motivational derivation—that is, based on similarities and hunches, equations and properties are guessed at. But the exercise is, I believe, still profitable.
An important symmetry in the derivation of modern physics is the "gauge" symmetry (so-named for historical reasons). If, under a change of scale (i.e., size), no other properties of an object change, that object is said to have gauge symmetry. (An example would be the ratio of the circumference of a circle to its radius—it always remains equal to 2π, even if the circle changes size.) Let us designate knowledge by Q and think of it as something learned. The change of Q over time is learning. We will postulate that learning exhibits gauge symmetry.
The motivation for this postulate is taken from the parable of the talents. The servant with 5 earns 5 more, the servant with 3 earns 3 more. We are told that this is what it is like in the kingdom of heaven, implying that it is an eternal law. (Compare also the statements, "where much is given, much is expected" and "if a man gains more knowledge in this life it will be so much the better for him in the next life"—loose quotes.) The reason these show gauge symmetry is because the expectation is independent of the initial size—each servant doubles his goods and is equally rewarded for his efforts, independent of the starting number.
Mathematically, we see that the change in Q is proportional to Q, which we express as dQ/dt = Q. (For those that have forgotten calculus, dQ/dt means "the change in Q over time".) This equation has the solution Q = Q0 et (again, calculus—this says that Q grows exponentially with time). So our knowledge, Q, grows exponentially. A simple example of the power of exponential growth can be seen in this example: suppose an individual receives $1.00 at birth and invests it at 6% compound interest. At 70 his $1 would have grown to about $60. But if he lived to 1000 his $1 would have grown to about $20,000,000,000,000,000,000,000,000! If growth were simply linear, after 1000 years his $1 would grow to just $61.
In order to be exponential, learning must be more than simple accumulation of knowledge. Accumulation, by its nature, is a linear process. Exponential growth occurs during those "aha!" experiences where we assimilate information and transform our understanding.
