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The hypothesis goes something like this: many natural phenomena follow a bell-shaped curve. I think there's a formal statement of this in the discipline of statistics.
It's hard to get a Normal distribution (i.e. Gaussian/Bell-shaped) from temporal causal phenomena such as oil discovery and production. Bell-shaped curves extend to infinity in both directions, and our minus infinity is not very long ago. I wish we could, but you can't really hand-wave this stuff away unless you consider the problem from first principles.
Of the things wrong with the HL/Gaussian approach, the fact that it erroneously predicts that the Romans would have used 1.5 molecules of hydrocarbon is the least of its problems :-)
1858 is the start as far as I am concerned. Up to that point, there was little active progress in oil exploration.
http://en.wikipedia.org/wiki/Petroleum#History
It kinda suprised me.
Perhaps surprising history but oil (and NG) didn't become a displacing technology until later in the 19th century. Until then whale oil was used predominately for commercial use,