I disagree. Pattern recognition of market behavior shows leptokurtic (to the left) distributions when humans act in large groups. There ARE long tails of disorder in the markets, which create great opportunities for some (and this concept backtests all the way to when tick data began - up markets down markets etc). Small moves are mean reverting and large moves tend to persist - this is based on a consistent, first principle prevalence in humans for emotion to dominate rationality in the short run in situations that aggregate collective behaviour (financial markets are perfect proving ground). This is too short term to be based on any fundamental economic theory - which in long term those are all faulty anyhow -this is more based on human behavior. Oil is similar -which is why I disagree with your dismissal of Verhulst equation being applied to oil - 20th century humanity has behaved like a superorganism, and many more aspects than just geology at work. Unfortunately, Mr. Duncan is not responding to my emails at moment (I can understand why) otherwise I would ask him for a more detailed explanation of his heuristic model.

A few more comments a) he and I have our real names out here and you don't, so that is a problem in itself (any 'model' attached to an anonymous person has no personal reputation risk or accountability -i.e. if dispersive discovery turned out to be totally false, you could create a new login ZebBubbleMicroscope and design an anti-dispersive loglet model - no one would know it was same person). b)side note - dispersive discovery has an embedded error in that the small fields found early on were found by accident (we weren't looking for them, c)people with the best models are unlikely to share them with the public, unless it is a 'gift' or some marketing trap. (I've seen far more of latter). All Euan was trying to do here is what any good analyst would attempt - a paper, with data and predictions was made 10 years ago and he wanted to see the results and residuals. His brief essay above is only one data point in any case. Not like Duncan predicted the end of world or anything....;-)

The key to theory is that the theory can be tested in a controlled environment. Unfortunately, we lack an oil depletion control to truly test out the real theories, so it comes down to a matter of who has the most convincing argument or whose intuition you trust the most.

Here we agree. And I trust Duncan/Campbell/Laherrere, etc. more than IEA/EIA or anyone with an economist at helm. (But I trust my own heuristics overlayed on other peoples heuristics even more.)Just to be clear, there will NEVER be a model to test oil depletion that is acceptably sound until it is much too late to do anything about its conclusions. That is achilles heel of science - it works great when it has decades to percolate, hypothesize, test, retest, repeat, etc. but when events change fast we are going to, in very real ways, make decisions using heuristics. This is the way it has always been and I don't see any indications of it changing.

Don't get me wrong WHT - you are brilliant mathematician and provide insight to an important aspect of our problem - modeling depletion -but sometimes everything of salience, even with oil, can't be parsed into math. We now have demand/environment/credit/non-energy input/social equity issues overlayed on top of geology, forever...very tough to model without huge error bands.