There are other non-linear functions which will produce curves similar to the exponential-curve, but with different slopes. These would include quadratic, cubic and quartic, reflecting equations of degrees 2, 3 and 4. Each successive slope of higher-degree formulae would be steeper than the last.
The most important concepts to be gained from this brief discussion pertaining to exponential curves are:
| (1) |
All physical processes occurring in our known universe, including entropy, are doing so at an exponential rate.
|
| (2) |
The curve itself reflects a process which is either accelerating or
decelerating at a constant specified rate.
|
| (3) |
An exponential curve can represent the initial sweep of a sine wave, so
that all concepts presented here would fit either the model of an open universe which will expand forever, or one that is oscillating cyclically.
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The concept that evolving intelligence is related to universal expansion can be expressed mathematically:
|
 In =(Volume of Space)(K2)
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| In = Change (increase) in intelligence
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| K2 = Constant variable which could be unity (1) and cancel out of the equation; but which, however, might not, dependent upon what other properties, yet to be defined, might also be contained within space which compete with intelligence for space. For example, does matter expand to fill space as space itself expands? Is there more to space than we yet realize, so that in the absence of any matter, space is still not a vacuum? Do forces in action across space compete for any of the volume?
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| Volume of Space = Change in volume of space per unit of matter for the same period of time that the change of intelligence is measured.
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Space needs to be more specifically defined as follows:
| Spacec = Space1 + Space2 + Space3
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| Spacec = Total space in closed universe.
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| Space1 = All of space excluding that portion containing matter (mass + energy).
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| Space2 = That fraction of space occupied by matter-energy.
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| Space3 = That fraction of space which might contain potential unknowns (i.e., forces in action that might conceivably occupy part of space, or other unknowns).
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