### The Curse of Dispersion

For the Dispersive Discovery model, the ultimate reserve reaches a bounded value. However, the growth proceeds slow but steady enough that it can fool people into a sense of complacency. The fact that geologists themselves have considered reserve growth "an enigma" indicates that they can't quite make heads or tails of how it comes about. It occurred to me that the rate of reserve growth plays in people's perceptions in rather alarming ways.

Two analogies come to mind: the carrot dangling in front of a horse and the frog being slowly boiled alive.

The fact that no one understands the enigma lets people's imaginations run a little wild as they have no checks to balance their viewpoint. Yet the fact that we have a model allows us to develop a few benchmarks that we can use as a countering influence. One that I will describe briefly comes from considering the running average time it takes to find oil in a region using the simple "seam" variant of dispersive discovery. This average has an interesting tendency to creep upwards over time.

Solving a troubling enigma can lead to a blessing or a curse.We can evaluate this average by evaluating the definite integral of T*exp(-T/t)/t/t multiplied by t. This grows as the logarithm of t for larger times. The positive trend looks at least somewhat encouraging, but then realize that we have to divide by t to properly scale the result. After we do this scaling then we can see the law of diminishing return acting on the result directly, since the divisor t has a greater magnitude than the numerator log(t). This factor log(t)/t becomes a valuable measure to estimate return on investment.

However, non-mathematical analyses and intuition can lead to optimistic outlooks. They may forget that the beneficial dispersed growth gets more than compensated by the effort to find it and that divergence becomes greater with time. Until we get more people on board understanding the real effects we will have to suffer from the "Curse of Dispersion" -- dispersive reserve growth acts as the carrot in front of the horse, while at the same time quietly boiling us alive if we ignore its rather obvious diminishing returns.

"The picture's pretty bleak, gentlemen. ..the world's climates are changing, the mammals are taking over, and we all have a brain about the size of a walnut."

**Update:**Added figure

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