Really Simple

Courtesy of the Morning Seditionists comes this wake-up call:

“If you really want to reduce the amount of oil that you consume, you have to reduce the amount of gasoline you use,” Bush said on a road trip to push energy initiatives he announced last month in his State of the Union address.

Bush also poses the question of how to avoid breaking ... hog farmers.

Piling On

Sometimes it doesn't matter what kind of effort and persistence that you apply to a field of study. In certain circles, if you make one "mistake" then the whole house of cards collapses around you. Take the case in point of legendary sports-hunter Jim Zumbo and his comment on assault rifles as analyzed by Dave Johnson. Because Zumbo had the temerity to question the sanity of using military assault rifles by sportsmen, it looks like his 40+ year career in outdoor writing and hosting has entered an immediate twilight zone. All advertisers, NRA members, and hunting publishers have virtually left him as virtual road-kill. This story has opened my eyes more than any one in recent memory to the mass psychology of specific segments of the population.

As for myself, practicing the sport of fishing much more than hunting, I would suggest a useful analogy would involve the obvious questioning of using dynamite or poison as a fishing technique if that turned into a "popular" practice employed by a rabid fraction of fishermen. Thinking back on someone who showed the same contrarian viewpoint as Zumbo (but didn't back down), I would consider that publisher George Pazik made a similarly bold pronouncement during the oil crisis in the mid-70's. His frequent suggestions in the pages of Fishing Facts magazine that oil would not last did not seem to offend his readers (at least to the extent of calling for his head) even though gasoline serves as the lifeblood of any serious boating angler. But then again, fishermen don't have a lobbying arm quite like the hunters do with the NRA.

I look forward to hearing what the hosts of my local "Bear Facts and Fish Tales" radio show have to say about the situation. At least one of the hosts of the show seems to have that same hateful response to contrary viewpoints, lately launching diatribes against cross-country skiers who venture across his snowmobile path on the way to his favorite ice-fishing hole.

Not road-rage this mind-set, something more akin to a pathetic hobby-rage.

In a land far away

Not too long ago.

A sound-proofed drilling rig in urban Los Angeles.

Modest Proposal Reloaded

As most ideas, no matter how preposterous, will eventually get their day in the court of public opinion, it doesn't surprise me that someone else latched on to the obvious but rather crude approach to reducing the chances for nuclear war. Who else but Instapundit stated:

"Nor do I think that high-profile diplomacy, or an invasion, is an appropriate response. We should be responding quietly, killing radical mullahs and iranian atomic scientists, ..."

Predictably, the unctuous neo-tard radio host Spew Spewitt agrees with the Instapundit. From my earlier post, I thought I demonstrated how easily one can emulate at face-value the thought processes of the keyboard commandos. Fortunately, Greenwald does a nice job in explaining which direction this will take us:

If we are to be a country that now sends death squads into nations with whom we are not at war to slaughter civilians -- scientists and religious figures -- what don't we do? American credibility in the world has fallen to literally unimaginable depths over the last six years, but it is critical to remember that with a President never to face the electorate again, many Bush supporters -- and certainly the White House itself -- are headed in the direction of increasingly extremist and bloodthirsty measures. And it is hard to overstate what a complete disregard they have -- really an intense contempt -- for the values that have long defined this country.

Wait long enough and the satire becomes the reality.

Norway drop

I pasted the latest data from Norway onto the Oil Shock model (generated earlier last year) below.

The TOD linked story cites a drop of 7.8% from the previous year, which approximates the downward slope shown by the model.

Naive quadratic growth

I don't believe that quadratic growth can continue indefinitely in the face of a constrained resource, yet I find it somewhat instructive to see what happens when we force and maintain the acceleration within the context of a contrived example. As a premise, say we have a pool of resources from which we can draw a random sample. The number of draws we get per year follows from an accelerated growth law proportional to t², where t=Time.

  D(t) = a  t2 / 2 = # of chances per year
  N(t) = D(t) * RemainderPool / TotalPool = # of discoveries per year

  RemainderPool(t) = TotalPool - Integral (N) 
 
  dR(t)/dt = - a * t2*R /T/2

  R(t) = T * exp(-a*t3/6)

  N(t) = T/2 * a * t2 * exp(-a*t3/6)

  Cumulative(t) = Integral(N(t)) = T *(1 - exp(-a*t3/6))

(the bottom of this post shows a Monte Carlo program which verifies the math statistically)

N(t) shows the characteristic Hubbert peak of any finite resource. In this case the peak occurs at t = cube root of 4/a. The return-on-investment (ROI) of search for resources comes out of this very simply; we divide the number of discoveries by the acceleration curve of the search:

  ROI(t) ~ exp(-a*t3/6)

Initially, the ROI stays near 1 but then drops down to 0.005 at a date twice past peak. The naive part of the model comes about from the assumption that random draws from the same population will continue indefinitely and within the context of an accelerating population of investors. (kind of like a tri-state lottery?)

This exercise shows that we can't sustain naive quadratic growth -- eventually the acceleration term has to subside as the investors and prospectors start to see diminishing returns as they meet a lower ROI. This realization forms the basis of the more realistic discovery model written up in a recent post, where I suppress the acceleration term as discoveries start to accumulate. This causes a sharper dropoff after peak than the naive model, as it models the potential investors becoming dissuaded from joining the discovery rush as the law of diminishing returns rears its ugly head. In other words, the naive model assumes a very optimistic and persistent investor, someone in fact willing to continue to beat their head against the wall.

---

Monte Carlo program to generate sampled Discovery and Cumulative curves

with Ada.Numerics.Discrete_Random;
with Text_IO;

procedure Ran_Fill is
   subtype Pool is Natural range Natural'First .. 1_000_000;
   package G_Natural is new Ada.Numerics.Discrete_Random (Pool);
   G : G_Natural.Generator;
   Ultimate : constant Pool := 100_000;
   Checked : array (Pool) of Boolean := (others => False);
   Acceleration : constant Integer := 1;
   Draw : Pool;
   Discoveries : Integer;
   Prospectors : Integer;
   Cumulative : Integer := 0;
begin
   G_Natural.Reset (G, 1);  -- use the same seed each time
   for Year in 1..1000 loop
      Prospectors := Acceleration * Year * Year;
      Discoveries := 0;
      for Count in 1 .. Prospectors loop
         Draw := G_Natural.Random (G);
         if Checked (Draw) then
            null; -- Already checked
         else
            Checked (Draw) := True;
            if Draw <= Ultimate then -- Eureka!
               Discoveries := Discoveries + 1;
               Cumulative := Cumulative + 1;
            end if;
         end if;
      end loop;
      Text_IO.Put_Line (Year'Img & 
                        Discoveries'Img & 
                        Cumulative'Img);
   end loop;
end;

Quardratic Linearization

I applied the Hubbert Linearization to the quadratic/shock model on world production and it looks like the following:

It shows a fairly obvious quasi-linear regime indistinguishable from empirical observations and the oft-used Logistic equation heuristic.

Time to ditch the cheap heuristic and use a real model, I'd say.