Sorry to be clear I meant fragile in the mathematical sense not in the sense that its not a good model given the underlying assumptions. For this type of model I'd argue its probably the best model possible.

The problem with complex systems is we have no way regardless of the type of model to prove its correctly modeling the complex system. How do you know for sure your model made the correct underlying assumption ?

We do know that complex systems in general are capable of rapid change. Statistical mechanics in its simple form can't for example correctly predict phase transitions. I'd argue the theory was extended to include them because we know they exist and the model can readily account for them but the math of stat thermo does not in my opinion actually contain the concept. For that matter liquids are not obvious either although its not a huge leap to go from a gas to a condensed liquid so that transition could in a sense be discovered.
I'd argue that solids would take a stroke of genius and its not "obvious".

What I'm trying to say is this sort of modeling has very little leading hints in the math itself just to complete the model and in general despite the power its a relatively simple problem. I agree 100% that chaotic math itself is intrinsically useless as a model. No problem throwing it out but then what ?

We can of course get into a heated argument on phase transitions and statistical mechanics and if they are what I would call a natural result of the theory. I'd be forced to define what I mean by natural result at that point. The best approach would be to take some smart high school student tech him the stat thermo of gases and see if he discovered water and solids of course it would be nice if this student had never heard of water and solids or mabye the math was cleansed of its physical interpretation :)

When you get into true complex systems that are not homogeneous then its difficult to prove that you have created the correct ensemble.

It the case of the shock model I question one of the inputs which is reserve growth. Is the shock model itself capable of solving for the correct reserve growth given the other input parameters ?
Can it prove or disprove the validity of reserve growth ?

I honestly don't know I've not played with it enough to see if it can be modified to solve for some of its questionable inputs.

This is what I mean by unstable without the perfect model its difficult to know if you left something out or if you can detect questionable input condition or questionable dynamics.

Now with that said I think that the shock model can be extended to only need as inputs the size of the earth and some reasonable constraints on the number of basins. Given its basic premise one would think it could be started with inputs that could theoretically be refined to the point that the input data itself was considered trustworthy.

But even with that you still can't prove you did not miss a shock.

Maybe I can explain it this way if you know quantum mechanics its actually fairly natural to derive classical mechanics most students well versed in quantum mechanics can after a bit hit on the correspondence principle and invent classical mechanics. Of course they would naturally know where the assumptions failed.
The reverse problem was beyond hard and required brilliant insight. Classical mechanics by its nature was really incapable of telling you it was and approximation the true nature of the approximation simply was not intrinsic in the math.

This is what I mean when I say in my opinion the sock model is a good model however its not clear yet whether its classical mechanics or quantum mechanics. I argue we lack a understanding of whatever the real higher level model is and I agree chaos is the wrong route. But then what ?
Under the covers of course we know we are dealing with a complex system dispersive model or not :)

From the dispersive discovery point of view I'd argue a natural extension that not really included is that a single discovery encourages more intensive localized searches. The gold rush effect this does as you correctly point out not ensure that we find the big field first but I'd argue that any find tends to propagate further search from the point of discovery. Some of the first oil fields turned out over time to not be all that important as far as oil bearing basis go. Pennsylvania for example. And of course Hitler was desperate for oil but never even bothered to search the north sea for oil. Why because they did not have the technology so obviously to some extent the search was technically constrained.

Agree or disagree the point is I think these are valid points you could raise vs a pure dispersive search however I'd also argue that the only reason I could raise them was because I happened to know the "right" answer just like the additions of phase transitions to what is really a pure gas model of statistical mechanics I'd argue that these additions would be difficult to add naturally. Its actually a fact that discovery and lack of discovery i.e dry holes influence the search pattern. However how do you model it and even if you came up with the concept on your own since its fairly basic how would you add it ?

Hopefully you agree that there probably is a self propagation term in dispersive search such that success and failure influence the further probability of more searching in the region. Please tell me you at least buy into the concept :)

Assuming you did how could you determine the strength if you will of the variable ?

For gold for example given that the nature of the deposits where well known the search pattern around a gold strike was very intensive same for silver. Finding coal is considered trivial because of the nature of the deposits. Locating good coal seems did not require intensive skill. This is yet another "natural" intrinsice that makes sense but again I'd argue difficult to add. And certainly difficult to consider from scratch.

A simple case lets say that oil deposits hand a big red X on top of them marking their location. I know this sounds funny but rives lakes and streams effectively have this. Most rivers lakes and streams where discovered by simply walking around the area ! A dispersive search for water seems trivial.
However finding the lakes in the Antarctic and Greenland is far from trivial. And of course underground aquifers can be missed for a surprisingly long time.

http://www.uswaternews.com/archives/arcsupply/6nebsan.html

You tell me you created the model how well does it extend if you agree with my concept of what I call stability then how do you feel the model works. I tend to think its a simplification of a higher order but unknown model if you agree what form with the higher one take ? Quantum and Classical mechanics shows that the "higher" model can be radically different yet naturally produce the approximation.

Obviously I think complex systems are computational engines and I think its a natural result of one formulation of quantum mechanics. One of the corrections i.e assuming more or less discovery near a strike or dryhole. Is actually driven by the belief that the underlying system is naturally a computation engine.
This does not require intelligence. Dispersion of seed via wind which one would argue is a perfect dispersive search picks up the selectivity simply because seeds that land in fertile ground disperse more seeds to continue the search while obviously the once that land on rock or water don't propagate so the search is not continued in that direction. Underlying is a rudimentary ability to communicate in the case of seeds it very primitive and the I survived signal is sufficient to alter the search pattern.

You see that communication has this tendency to enter into complex systems even something as simple as crack propagation has the "I survived" signal and cracks can rapidly propagate to the weakest point. You need not even assert biological control.

I'd argue that this feedback is so common and so basic in complex systems that dispersive search without feedback is simply not correct and that because feedback comes from a higher order model that there exists a bigger better model that the shock model is a simplification of a poorly defined meta model.

My own attempts at trying to deduce this has right now resulted in me becoming very concerned about the assumptions we make at least with what I think I know I'd suggest people become very concerned about our situation. This could of course be from lack of understanding or even worse understanding but also overreacting to some of the features that seem to be present.

All I can say right now is I think I know enough to argue that for the case of oil and our economy we are at a crossroads possible in the sense that I really think I've gleaned enough to say that we will know the true nature of our complex system. Either I'm right and we will soon know if we have a oil glut or a fast collapse or I'm really really wrong and the central limit theorem takes the day and we follow a fairly smooth curve.

Whats worse is I might be theoretically right and you can determine if a complex system is following central limit behavior or not but simply messed up the solution with oil. That for me would be the worse outcome :)
But no problem I'll go watch the ice melt at the poles since this is the other complex system that I've decided is going to follow the fast collapse route in fact its what actually lead me to think oil would also follow the same route. It has a similar feedback in that a loose iceberg physically grinds away and shatters the nearby ice. The sandpaper and hammer effect. Same for glaciers once they start cracking they have self propagation built in and of course water moving to the base. I argue that these effects soon overwhelm simple melting.

I've got to be right once or even worse I've got two chances to be wrong. Well three if you count collapse of our civilization which is independent of the rate of decline of oil simply needs it to decline.

Only because complex systems are self similar regardless of the underlying forces do you have to evoke quantum mechanics as providing the most basic feed back channel through extended qubits. A communication theory of complex systems must have a reasonable and basic route for feedback if feedback or computation is indeed the key to complex system behaviors.

At least so far it seems that complex systems in decline rarely follow the central limit theorem once fully constrained. My hearsay is that the central limit theorem only works for complex systems that are still open and have other inputs. Once the system is closed it eventually rapidly moves to and extreme condition.
One would argue that the polar caps are not closed but in my opinion they have transformed to a new system with enough open water to to create a new "closed" water ice sun dynamic. They need no further inputs then what exist now to go to extreme. Closed for complex system just means the feedback loops are no longer varying and thus the system will move to one of its extreme values.

And like I said nothing prevents this from being totally wrong thats one of the problems in my opinion with trying to formulate a higher order theory esp one that based on hidden variables and erroneous measurements :) I can't think of another approach that obviously has the proverbial feet of clay or house built on sand :) It very basis is a collapsing sandpile :)

Given the poor quality of my model that suggest this I'd be excommunicated for suggesting this if I still did science.