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

Petroleum, in some form or other, is not a substance new in the world's history. More than four thousand years ago, according to Herodotus and confirmed by Diodorus Siculus, asphalt was employed in the construction of the walls and towers of Babylon; there were oil pits near Ardericca (near Babylon), and a pitch spring on Zacynthus.[10] Great quantities of it were found on the banks of the river Issus, one of the tributaries of the Euphrates. Ancient Persian tablets indicate the medicinal and lighting uses of petroleum in the upper levels of their society.

The first oil wells were drilled in China in the 4th century or earlier.[citation needed] They had depths of up to 243 meters and were drilled using bits attached to bamboo poles.[citation needed] The oil was burned to evaporate brine and produce salt. By the 10th century, extensive bamboo pipelines connected oil wells with salt springs. The ancient records of China and Japan are said to contain many allusions to the use of natural gas for lighting and heating. Petroleum was known as burning water in Japan in the 7th century.

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,