HL is a theory without a hypothesis. OK, oil production is never a square wave and it rises then falls, and the area under the curve will equal URR at the limit but so what!

OK, let's see.. I think you have sort of answered your own question there, Alan. 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.

So, what Hubbert was saying, is that oil production will follow this trend regardless of political / economic / etc. issues. Basically we're gonna pump it out and use it as fast as we can in the end. Some of the TOD filk will superciliously say it's a "logistic curve", but they're both just blobs on a graph, near as I can tell. It looks to me like the bell is just the first derivative of the logistic WRT time.

I was trying to explain this in a recent thread, and was duly corrected: Hubbert did not originate "Linearization"; it had been my impression that he did. Anyhoo, the linearization is a clever way of graphing the production curve so that the points (theoretically) fall along a straight line. Furthermore, as time passes and production continues, the estimate gets better (because there is more history [larger Q] in the later points on the graph).

The beauty of linearization is that it allows you to place a ruler on the graph, strike a line, and get an estimate of the URR for the stuff you're trying to predict.

But in the end, it's all just statistics and the actual URR will only be known in hindsight. Many of us have looked at the graphs put together by SS, Khebab, westexas, and others and concluded that peak is probably about now. Since it is a century-long bell curve, there may be as much as 5 - 10 years of uncertainty as to the actual location of the peak — check back in 2025 and we'll know for sure.