Wednesday, February 9, 2011

Regression To The Mean

"All truth passes through 3 stages. First, it is ridiculed. Second, it is violently opposed. And finally it is accepted as self-evident."  -Arthur Schopenhauer

Warning: What you are about to read is very likely the insane ramblings of a mad man.  God, I hope that's the case.

Imagine you receive a very large pop bottle that is full of rice at 12:00.  At 12:01 you remove one of those grains of rice.  At 12:02 you remove 2 grains.  At 12:03 you remove 4 grains.  You continue this, taking twice as many grains of rice out of the pop bottle every minute, for one hour.  At 1:00 the bottle is empty.  What's somewhat interesting is that at the 1:00 mark you end up taking over 500 quadrillion (576,460,752,303,423,500) grains of rice.  But we've all learned about exponential growth like that.  Here's what I find the most interesting about the thought experiment: at what point would you start to worry about your limited supply of rice?

If you're taking twice as many grains of rice every minute, and the bottle is empty in one hour, then at 12:59, one minute before you run out of rice, you still have 50% of your total supply of rice left.  At 12:58, you still have 75% left.  Clearly, it would be difficult to plan ahead and prepare for a depleted supply of rice when you still have a vast majority of your total supply 2 or 3 minutes before you run out.  This becomes even more disturbing if you imagine a bottle of unknown size full of an unknown, but finite, amount of rice.  And if you imagine that your entire existence is dependent on the unknown, finite amount of rice in the bottle, the problem becomes dreadfully catastrophic.

Now instead of a huge pop bottle and rice, think about Earth and oil.

Oh shit...

PART 1: OIL AND GLOBAL POPULATION

You can figure out the doubling rate of something with some very simple math.  If you have a continual rate of growth, all you have to do is divide the rate of growth into 72 and you'll get the doubling rate.  So if you had $100 and every year you earned 10% interest on that money, you would have $200 in a little over 7 years (72/10 = 7.2).  Another 7.2 years later you would have $400.  And so on.

We can look at this another way using some more simple math.  Say you start to double the number of apples you eat every year.  The first year you eat 1 apple.  The next year you eat 2 apples.  The year after that you eat 4 and so on.  1, 2, 4, 8, 16, 32, 64, 128.  That's the number of apples you eat for 8 years.  If you start to add these numbers up you'll notice that the number of apples you eat in any given year is one more than the number of apples you've eaten in all the previous years combined. 1+2+4+8+16+32+64 = 127, one less than the total eaten in the next year alone.  This holds true no matter how large the numbers get.  That's why at 12:59, before 576 quadrillion grains of rice are pulled from the bottle, the bottle is still half full.

A quick google search (that's as much effort as I was willing to expend) showed that from 1900-1973 the average growth rate of oil consumption was 7%.  It doesn't seem like much until you figure out that it means you double consumption about every 10 years (72/7=10.3).  That means that in the 1920's we used more oil than the two previous decades combined.  In the 1960's we used more oil than the previous six decades combined.  However, since then, the growth rate has actually declined for a variety of reasons, but if we assume a conservative average growth rate of 3% for world wide oil consumption, that means that we use twice as much oil per year every 24 years.  Instead of taking 10 years to consume more energy than all the previous years combined, it would take 24 years.  That also means that only 24 years before we run out of oil, we'll still have 50% of the world's total oil supply (a lot of oil, relatively speaking) in the ground.

Oh shit...

If you think of a bell curve and imagine that it represents global oil production, the top of the bell curve would represent what is called "Peak Oil".  At that point, the world reaches its peak of oil extraction.  That means that no matter how much money or effort you put into the oil industry, it will be impossible to equal the oil supply that was reached at that point.  That also means that at Peak Oil, you only have 24 years worth of oil left (assuming a continual 3% growth rate, which would be virtually impossible*).  And since we don't know how much oil is present in the planet, we won't know when we've reached Peak Oil until after the fact, when the supply fails to reach the level it was at when it peaked.  In the rice and pop bottle example I mentioned earlier, Peak Oil is 12:59.  And we won't know that we reached Peak Oil until a few seconds after 12:59.


Oh shit...

As of right now, the most oil that was extracted from the earth was 73.72 million barrels per day.  That was in 2005.  Since then, we have failed to reach that level of oil production.  To put it in other terms, our oil production peaked somewhere around 2005.

Shit shit shit! Ohhhh shit!

Now that doesn't necessarily mean that we reached Peak Oil in 2005. 

Phew!!

The declining supply was most likely a result of falling demand due to the worldwide recession we've been going through, among other things.  That same data also shows that oil production peaked in 1979 and we didn't see that same level of production until 1996**, so there are obviously peaks, valleys and plateaus in the curve.  That also demonstrates that we will be on the downward side of the slope for a long time before people are aware of it.

But some optimistic current estimates are that we will reach Peak Oil in 10 to 40 years.  Of course, it's extremely difficult to estimate that with any accuracy because the governments in the Middle East that produce the world's oil supply, and the governments around the world who research these things, would never tell the world that their reservoirs are running dry.  But there will certainly be signs to look for.  Drilling for oil on land is by far the most efficient way to get oil.  The total energy used to drill test wells and everything that goes into finding and extracting oil is very small for land drilling.  Drilling in the ocean is much more inefficient.  You have to expend a lot of energy just to find oil, and you need to find a lot more oil before you start to get more energy than you put in.  So it's very disconcerting to hear that Saudi Arabia, a country that currently has at least 20% of the world's known oil reserves, is investing heavily into offshore oil exploration.  There is only one reason why they would do that, and it's the same reason America started doing it after we reached Peak Oil in 1970: they're running out of places to drill on land.  And then there's this recent story where Sadad al-Husseini, a geologist and former head of exploration at the Saudi oil monopoly Aramco, claims Saudi Arabia overstated its oil supply by 40%.

Maybe the drop in oil production since 2005 wasn't simply due to the global recession.  After all, the recession didn't really start until late '07, early '08.  Oh, and there's the little story that nobody really talked about where the International Energy Agency claimed that we saw Peak Oil in 2006.

Oh shit...

With the laws of supply and demand, it's safe to assume that a global oil shortage will cause prices to go up to a level where the average person cannot afford it.  When that happens, things like electric cars as well as solar and wind power sources will finally become more cost effective, and more prevalent as a result.  But make no mistake, the oil we use to drive our cars and light our homes is only slightly more significant than a drop in the bucket.  It takes 7 gallons of oil to make one tire on your car, electric or not.  It takes several gallons of oil to produce and transport the steel used to make the car.  Nearly everything you buy only exists because of oil.  Plastics, which are found in almost all consumer goods, packaging for food, etc only exist because of oil.  Your toothpaste and toothbrush has oil in it.  Of all the things you use throughout your day, nearly 100% of it only exists because humans have figured out how to use oil to make it and/or get it to you.  Expecting electric cars and solar panels to solve the problem is extremely foolish and extraordinarily naive.  Oh, and there's this little problem.

Probably the single most important reason we have our high standard of living is because a few farmers can effectively feed everyone in the country.  The technological advancements in farming freed up the masses to pursue other interests, like building transistor radios, TVs, satellites, space shuttles and producing steel, cars, computers, cell phones, etc.  If the majority of people had to spend the majority of their time growing food, none of that would have existed.  Modern farming only exists because of oil.  It powers the tractors that plow the field, fertilize the ground and plant the seeds.  It powers the airplane that sprays petroleum based chemicals that increase yields.  It powers the combines that harvest the crop.  It powers the trucks that transport the crops to factories that use energy to make bread, sugar, flour, and so on.  It powers even more trucks that bring the final product to your local grocery store.  It powers the ships that import all the things we want to eat, but are grown on another continent. In one study, David Pimentel and Mario Giampietro concluded that the industrialized world uses 10 calories of petroleum based energy to produce 1 calorie of food energy.

All of this has lead to a population explosion that is difficult to comprehend.  It took all of human history up until 1804 to reach 1 billion people.  It took another 123 years to add another billion people.  It then took 33 years to add another billion people.  We're currently adding a billion people to the planet every 10-15 years***.  It's no coincidence that this population explosion occurred at the same point that humans started to use oil to power their societies.  Humans aren't as unique as we like to think we are.  Whether it be bacteria in a petri dish, caribou on a predator-free island, or humans with a few trillion barrels of oil, any organism that is put into favorable conditions will experience a population explosion.  Remove the favorable conditions and the explosion will be followed by a drastic decline. None of the human population growth of the last century or two would have existed were it not for one thing.  In economics, they call that a bubble.  And every bubble must pop at some point.

Oh shit...


PART 2: UNLIMITED GROWTH AND REGRESSION TO THE MEAN

Every major economy on the planet is only sustainable and effective if continual growth exists.  We all know this without even thinking about it.  We put money in the bank, the banks use that money to invest in new business, growth occurs, wealth is created and banks get their money back with interest.  The growth of the new business creates more people with more money who put it in the bank who can then make more loans to more businesses.  That cycle works wonderfully as long as growth takes place.  Without growth, that system could never exist.  Depositors would lose out on their savings because it would not have grown with the bank's investment.  With their savings depleted, individuals have less money to spend on things they normally buy and banks have less money to invest in business.  Business fails to get credit, they fail to expand, consumers don't spend money and the whole system collapses in on itself.  Continual and infinite growth is absolutely essential for every major economy in the world today.

When house values stopped growing, it exposed major problems.  When GDP remains flat or contracts or does anything other than grow (at a high enough rate, as we're currently learning), it brings a lot of pain to a lot of people because of the inherent effects of zero growth on a system dependent upon growth.  Our entire system, and the system of every industrialized nation on earth only exists because economic growth has always occurred, save for a few temporary but painful dips here and there.

But as I pointed out before, nearly all of the growth that has taken place since the late 19th century, give or take a few decades, has only occurred because of oil.  This leaves us in a very peculiar situation.  Our world demands infinite growth, but that growth is dependent on a finite energy source.  At some point in human history, those two things will collide.  The question that keeps me awake at night is simple: How many more minutes do we have until 1:00?

In a scenario where the world's oil supply shrinks, then it follows that economies will shrink as well.  Formulating the doubling rate works for growing systems just as well as it does for shrinking systems.  You just get negative numbers instead of positive ones.  When home prices started to rise at abnormally high rates because of artificial stimuli, it followed that when the stimuli was removed or conditions changed, the prices would fall to pre-bubble levels.  However, these economic systems have the advantage of politicians who can print money and lower interest rates and bail out financial entities, at least for a period of time.  But a bubble is a bubble, no matter if it's tech stocks, housing prices, population growth or oil dependent civilizations.

In statistics there is a term called "regression to the mean".  Basically, it says that if you see statistical anomalies in a system, something that deviates from "average", the system, when given enough time, will "regress to the mean" or return to normal.  If you hit the jackpot the first three times you play a slot machine, and you play that machine long enough, you'll eventually wind up with as much winnings (read: losings) as the average person ends up with.  If you flip a coin five times there is a chance that it'll turn up heads every time.  Continue to flip that coin for long enough and your results will approach a 50-50 head-tails average.

Now look at the human population chart and the global oil production chart.  Better yet, look at both of them together.  What if that chart was housing prices?  Stock prices?  What if you saw that chart and had no clue what it showed?  How confident would you be that there wasn't an imminent regression to the mean?  A bubble about to burst?  Humans have been on this planet for hundreds of thousands of years.  What are the odds that the last 100 is anything other than a blip?  A statistical anomaly?  Three slot machine jackpots and the heads side of a coin five times in a row?



*In reality, the right half of the bell curve will probably be stretched out over more time than the left half due to supply, demand, rising prices and the end of economic growth.

**Although for much of those years, the relative low supply can be directly attributed to some politically motivated actions taken by the OPEC nations, where they purposely limited the global oil supply to manipulate prices.

***Imagine the pop bottle and rice example in reverse.  Start adding twice as much rice to the bottle every minute for an hour.  At 12:59 the bottle will be half empty.  At 1:00 it will be full.  At 1:01 you could fill two bottles, if you had another one.  Currently, we only have one planet.

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