Stuart Staniford hadde en post vedr asymmetrisk produksjonskurve for USA forrige dagen. Jeg sendte inn denne kommentaren:
According to Ivanhoe, in his article King Hubbert - Updated(PDF!), Hubbert himself wrote:
"This complete cycle has only the following essential properties: The production rate begins at zero, increases exponentially during the early period of development, and then slows down, passes through one or more principal maxima, and finally declines negative exponentially to zero. There is no necessity that the curve P as a function of t, have a single maximum or that it be symmetrical. In fact, the smaller the region, the more irregular in shape is the curve likely to be. On the other hand, for large areas such as the United States or the world, the annual production curve results from the superposition of the production from thousands of separate fields. In such cases, the irregularities of small areas tend to cancel one another and the composite curve becomes a smooth curve with only a single practical maximum. However, there is no theoretical necessity that this curve by symmetrical. Whether it is or is not will have to be determined by the data themselves." (my emphasis)
Hubbert seems to have drawn symmetrical curves out of expediency; I have read anecdotes by people claiming to have known him that he could get rather irate when people ascribed to him the notion that the curve would necessarily be symmetrical.
Ivanhoe refererer:
Hubbert, M. King, 1980; Techniques of prediction as applied to the production of oil & gas; in Oil & Gas Supply Modeling, Ed. S.I. Gass; Proceedings of a symposium held at the U.S. Department of Commerce, National Bureau of Standards, Washington, D.C., June 18-20, 1980; Report N.B.S. Special Publication #631, May, 1982, p. 16-141. (Extensive summaries of all of MKH’s earlier papers.)
Men så, rett etterpå, leser jeg på Energy Bulletin A note on Hubbert’s hypotheses and techniques (EB, Pierre-Noël Giraud) at
1. Hubbert’s thesis
Hubbert’s thesis can be formulated as follows: “The annual production over time of a mineral resource is bound, for purely geological reasons, to follow a bell-shaped symmetrical curve. The annual production therefore reaches a ‘peak’ when half of the reserves have been produced, then it declines while the remaining half of reserves, more expensive to exploit, is being depleted”.
[figure omitted]
2. Hubbert’s basic assumptions
According to Hubbert’s papers, and papers by his partisans, the three underlying assumptions of the Hubbert’s thesis are:
Assumption 1: The curve: (cumulative discoveries) = f (cumulative exploration effort) is a pure logistic curve. (Fig 2)
[figure omitted]
Assumption 2: Exploration effort is constant over time.
Assumption 3: The time-lag between discovery and production is constant.
If these three assumptions are accepted, then Hubbert’s thesis is logically true.
As the exploration effort over time is constant, the above pure logistic curve
(cumulative discoveries) = f ( cumulative exploration effort) can be rewritten as a second pure logistic curve: (cumulative discoveries) = f ( time).
Thus, the rate of discovery is the derivative of this pure logistic curve of cumulative discoveries over time, which is a symmetrical bell curve. As for the rate of production, it is obtained by merely translating the rate of discovery by the constant time-lag between discovery and production, equally a symmetrical bell curve. Q.E.D.
Arrgh. Skal jeg bli nødt til å selv pløye gjennom alt Hubbert skrev for å finne ut hva han egentlig sa??? Det er åpenbart at enten Ivanhoe eller Giraud har misforstått og/eller over/feiltolket her.
...og jeg skal spise Felleskjøpet-sixpencen min dersom det er Ivanhoe. For det første, Ivanhoe gir faktiske Hubbert-referanser og sitater. For det andre, Giraud sier "according to Hubbert's papers, and papers by his partisans" -- hvem er Hubbert-partisan her, om ikke Ivanhoe??? Og det er ikke akkurat nøytral språkføring av Giraud her, heller. Girauds stykke fremstår både stilistisk og innholdsmessig som et "straw man"-argument; et rent sverteforsøk mot Hubbert.
Når det er sagt... At Hubbert presenterte matte som gir symmetriske kurver, er utvilsomt. Om det var det eneste han la fram skal jeg ikke ha sagt; men det er intellektuellt uærlig (eventuelt innmari dårlig forskning) å kun fokusere på matten og ignorere at forfatteren påpeker at "dette er en grov forenkling av virkeligheten, det er ikke slik at kurven nødvendigvis er symmetrisk, så ta det med en klype salt", og så bombastisk hevde at forfatteren tok feil fordi virkelighetens kurver ikke er symmetriske.
Nei, det er ikke lett å være profet. Marx' utbrudd om sine tilhengere virker á propos: "Hvis dette er Marxisme, så er ikke jeg Marxist".
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