Weapons of Reason: The paradox of skill

"The race is not to the swift or the battle to the strong, nor does food come to the wise or wealth to the brilliant or favor to the learned; but time and chance happen to them all." ― Ecclesiastes 9:11

Stephen Jay Gould is known not only for his work in biology, but also for a collection of essays on baseball.  In "Why No One Hits .400 Anymore," he explains just that, with a fairly elegant solution.  The pool of talent in baseball has grown since the early days, strategies and tactics have been improved, and players receive better training.  Another way of putting this is that the average skill among players has improved.  However, as they have improved, they are also beginning to approach the natural limits of what the human body is capable of.  When the entire community of players approach this limit, the community looses variation—there is now less room to spread out.

2009 Belmont Stakes photo finish.

This observation is sometimes called the paradox of skill—the greater the average skill level in a community, the less important skill becomes in determining the outcome of competition.  In the above photo finish, the difference between the two horses is only a few inches.  Both the horses were bread and trained to run competitively; however, the outcome was likely determined by essentially random factors that gave one horse a slight edge over the other.  This effect can be seen at work elsewhere.  At one time, higher education would have ensured employment in highly desirable, relatively low stress jobs.  Now, college education is becoming necessary for gainful employment at all.

Population density

What would the population of the United States be, if it were as densely populated as India?  I was under the impression that India's population density is only slightly greater than that of the U.S.  This assumption is wrong.

The answer to the question is 4 billion people.  When will this happen?  The quick way to answer this question is to consider historical growth rates.  During the 20th century, the U.S. averaged 1.3% population growth per year.  At this rate, population would reach 4 billion by the year 2210. A lot can happen in 200 years to affect the actual growth rate.  That being said, the U.S. may reach a population of 1 billion—the equivalent of the population density of Europe—by the year 2100 at a 1.3% growth rate.

Peak oil, part II

"It is sunlight in modified form which turns all the windmills and water wheels and the machinery which they drive. It is the energy derived from coal and petroleum (fossil sunlight) which propels our steam and gas engines, our locomotives and automobiles." ― John Harvey Kellogg

In a previous post, I wrote about peak oil—particularly that answering the question of how much oil is left is not easy.  That said, a new approach has occurred to me.  Oil and coal are the remains of ancient plants, formed 300 million years ago in the carboniferous period—C on the horizontal axis of the chart below.  The periods leading up to this saw the proliferation of plants, which removed massive amounts of carbon from the atmosphere.  At its peak, carbon dioxide made up 7000 parts per million (ppm) of the atmosphere, but today makes up only 180 ppm.  This carbon went somewhere, and for the most part it was sequestered in rocks as coal and oil.  A simple calculation puts the weight of this carbon to be 10 trillion tonnes.

How much is oil and how much is coal?  Consider the proven reserves of oil versus coal.  There are 190 billion tonnes of oil reserves, but there are 860 billion tonnes of coal reserves.  Assuming that this reflects their natural abundance, we'll assume that oil and coal are in a ratio of 5 to 1 of sequestered carbon.  This implies that there have been 3.6 trillion tonnes of oil and natural gas—18 trillion barrels—and 11 trillion tonnes of coal.

How long will this last?  As of 2015, 93 million barrels of oil are consumed per day—about 34 billion per year—which has grown by about 1% per year since the 1980s.  If this continues, there are 185 years of oil.  That being said, consumption must eventually stop growing and begin to decline—that is the notion of peak oil.  Instead, oil rations will eventually be put into effect, which could mean that oil will be here for centuries.  As for coal, 7.5 billion tonnes are consumed per year, growing by about 2% per year since the 1980s.  This implies a 170 year supply.  The same caveats apply.  Many things can change in this time, too.  It's still hard to say how long we will burn fossil fuels.

Guaranteed minimum income

"I care not how affluent some may be, provided that none be miserable in consequence of it." ― Thomas Paine, Agrarian Justice

The concept of guaranteed minimum income—GMI—is relatively self-explanatory.  The government would send periodic payments to households to guarantee a minimum income.  Let's suppose that a program was implemented in which, on average, every person received 6,800 dollars per person per year—this is approximately 100% of the poverty threshold—costing a total of 2.2 trillion dollars.  This program would be difficult to fund.  The government collected 3 trillion dollars in taxes in 2014, but that would probably change when the GMI program is implemented.

There are about 150 million jobs in the United States, which means each job provides, on average, 20,000 dollars in tax revenue.  However, GMI could render minimum wage obsolete.  A large number of jobs would open up, mostly unskilled positions paying a few dollars per hour.  How many is hard to say.  For the sake of argument, let's say a 70% decrease in minimum wage, would lead to a 10% increase in the number of jobs.  The net result would likely be a 66% decrease in taxable wages, if the GMI is not taxed.  Though dubious, my calculations suggest this would cause a 14% decrease in tax revenue.  That is, 2.5 trillion dollars, which would just about cover the costs of the program.

That's not to say that a similar program cannot be implemented.  Giving GMI payments to the bottom 20% of the population would cost less than half a trillion dollars annually—on par with current welfare spending.  Furthermore, solutions such as universal basic income have gained support from both left- and right-wing politicians.

Endangered element: indium

Unlike others in the endangered element series, indium use is not dominated by a single application—indium is employed in a number of applications.  For example, the screen you are looking at contains indium in the form of ITO—indium tin oxide—whose semi-conductive properties make it useful for controlling liquid-crystals.  Indium semi-conductors are also useful for thin-film solar panels, LEDs, and electroluminescent materials.  It is also found in solder, sodium vapor lamps, and nuclear control rods.  Truly, it's a versatile metal.

However, indium is relatively rare.  It comprises only 50 parts per billion (ppb) of the Earth's crust. One author compares indium with silver, claiming that silver is less abundant yet produced in higher quantities.  However, silver comprises 70 ppb of the Earth's crust—still quite rare, but about as common as indium.  Furthermore, silver is commonly found in ores, such as argentite.  Indium minerals are uncommon.  Instead, it is extracted from sphalerite—zinc ore—where it has a concentration of 1 to 100 parts per million.  Fortunately, there has been substantial interest in finding substitutes for indium.  Many of these solutions, however, still rely on non-renewable resources, like petrol chemicals or other endangered elements—e.g. gallium arsenide.

Cost of electricity

"Why, sir, there is every probability that you will soon be able to tax it." — Michael Faraday on the practical value of electricity

We are living in a period of extraordinarily cheap energy—but exactly how much does energy cost?  Fortunately, Open Energy Information—OpenEI—collected data on the costs for different forms of electricity production.  The problem is that different technologies incur different costs.  A coal plant requires a turbine to be built and maintained, but also require fuel.  Solar panels simply need to be constructed, but then collect energy from the sun without additional fuel inputs.  To take these differences into, we'll use a metric called the levelized cost of electricity—LCOE.  The LCOE is the present value of all the costs involved in operating the electrical plant.

Using the OpenEI data and U.S. energy data, we can compare the relative costs of the energy produced in 2011, for example.

Source	LCOE (USD/MWh)	% Production	Cost (b USD)
Hydropower	20	8.0	18.5
Coal, unscrubbed	40	15.3	70.3
Coal, scrubbed	50	30.6	175.9
Natural gas	50	19.7	113.4
Geothermal	60	0.4	2.9
Nuclear	60	21.1	145.3
Wind	60	3.0	20.6
Solar, Photo-voltaic	200	0.4	12.3
Solar, thermal	280	0.02	0.5

What inferences can be drawn from this?  First, we are likely to use primarily coal  and natural gas power for a long time—they are among the cheapest on the list.  However, because they are so low, they are more likely to increase than to decrease.  This could be driven by increasing fuel prices, but this is likely decades away.  Solar power—particularly, photo-voltaic solar power—could still decrease substantially in cost per megawatt-hour.  It is much easier to go from 200 dollars per MWh to 100 dollars per MWh than it is to go from 20 dollars per MWh to 10 dollars per MWh.  The technology to make cheap solar energy available may soon be widely available.

Peak oil

"Life without oil, in fact, would be so different that it is frightening to contemplate. We are addicted, and it is no comfortable addiction. Like other drugs, oil comes with a baggage of greed, crime and filth. Worse, it is smothering the planet."  ― James Buchan

Petroleum is a non-renewable resource. The question we need to ask is just how much is left?  A 2013 OPEC report estimated that there are 1.5 trillion barrels of oil in proven reserves in the world.  At the rate the world consumes oil, this will be gone in only 44 years.  In 2014, BP released a report putting the figure at 1.7 trillion barrels, claiming that this will last 53 years.  New oil is continually being discovered, though—oil companies have an incentive to find these new resources.  How long we can keep discovering new oil, however, isn't clear.

Source data via OPEC.

Understanding this chart is difficult—not what it says, but why it says it.  This requires a more detailed study of the history of oil production and the technologies that have driven discovery.  In the past, intermittent bursts of discovery seem to have been the norm.  This appears to have changed in the 1990s, with a lull that has lasted until the present—I am most interested in finding out why.  However, the size of the earth is finite.  The oil we have already found is low hanging fruit—the remaining oil will be difficult to find.  In addition to slowing rates of discovery, the oil industry will also face increased competition from alternative energy and—one may hope—increased pressure from the public for environmental responsibility.  It is likely that the end of oil will not come from dwindling supplies, but from these other causes.

Livestock

"It may indeed be doubted, whether butcher's meat is any where a necessary of life." ― Adam Smith, The Wealth of Nations

Anti-microbial resistance poses a threat not only to public health, but also to the meat industry.  In recent years, the process of raising livestock has received some attention from the public.  In some cases this has inspired people to adopt a vegetarian—or vegan—diet, due to concerns over animal cruelty.  In order to meet the enormous demand for meat, farmers need to raise animals in a short amount of time and in as small a space as possible.  As a result, animals are raised in squalor and severely restricted in mobility, making them susceptible to disease.

Antibiotics are necessary to this process, but they are also often misused.  Antibiotics are administered in low doses to many animals to stimulate growth.  This means more meat, which means greater profits for processors.  However, this also creates an environment in which anti-microbial resistance can develop.  80% of antibiotics sold in the United States are sold for use in raising livestock.  This is unsurprising when you look at the numbers of animals kept in the United States: 100 million hogs, 250 million turkeys, 8.6 billion chickens, etc.  This contributes to drug-resistant infections in people, but it is likely to negatively impact the meat industry as well.


Policies could be put in place that curb the consumption of antibiotics.  Animals could also be raised with more space, proper food and exercise.  However, this would undoubtedly cause the prices of meat to rise as well.  Before the advent of industrial farming, meat was expensive.  For example, chickens were raised primarily for laying eggs.  There were no chicken farms.  As a result, poultry was expensive, and was only consumed occasionally.  The meat industry also makes extensive use of marketing—essentially manufacturing demand.  It's unlikely that consumers will change their habits; therefore, farmers are also unlikely to utilize different processes.

Endangered element: gallium

Gallium is a metallic element, well known for its low melting point—at 86 degrees Fahrenheit, it will melt in the palm of your hand.  The mechanical properties of gallium make it unsuitable for most manufacturing processes.  In fact, it is even known to weaken steel substantially.  However, its chemical properties lend it to the production of semi-conducting materials.  It is most commonly applied in compounds with arsenic—as gallium arsenide, GaAs—or nitrogen—as gallium nitride, GaN.

Three quarters of gallium is used in integrated circuits.  Gallium arsenide is ideal for semi-conductors that are insensitive to overheating—that is to say, mobile technology, whose compact designs allow waste heat to accumulate.  In the U.S., this accounts for the consumption of 30 tonnes of gallium each year.  If the world consumed gallium at this rate, it would require 750 tonnes of gallium per year.  World production capacity is estimated to be 680 tonnes per year.  As more countries develop, it possible for demand to increase, potentially leading to shortages.

The demand for solar energy will also drive demand for gallium in the coming decades.  In 2014, solar energy provided only 1% of Electricity in the United States.  Photo-voltaic cells that are made with gallium can achieve high-efficiency.  About 30%, compared to 20% efficiency of silicon based solar panels.  In 2014, this required only 700 kilograms in the United States; however, a hundred-fold increase would push this to 70 tonnes.  Again, if the entire world consumed gallium at this rate, the demand would be 1,750 tonnes.  It is likely that a number of solutions will be needed to meet our energy needs.

The doomsday argument

"Since after extinction no one will be present to take responsibility, we have to take full responsibility now."  ― Jonathan Schell, The Fate of the Earth

When will the last person be born?  The question is simple; the answer is difficult.  J.R. Gott tried to answer this question using Bayes' theorem and simple statistics.  The number of people who will be born is likely to be large.  But is it more likely that there will be one trillion people or two trillion?  We expect larger numbers to be less likely than smaller numbers.  We write $\text{Pr}(N) = k/N$ and $\text{Pr}(n) = k/n$, where N is the number of people that will ever be born and n is the number of people already born.  Furthermore, we'll assume that there is nothing special about our position in human history.  We were as likely to be born as the billionth or the hundred billionth person.  Mathematically, this is written $\text{Pr}(n|N)=1/N$.

The likelihood that there will be N people, given that we know there have been n people already—$\text{Pr}(N|n)$—is obtained from Bayes' theorem:$$\text{Pr}(N|n)=\frac{\text{Pr}(n|N) \times \text{Pr}(N)}{\text{Pr}(n)} = \frac{n}{N^2}$$From this, we can calculate the probability for upper bounds on the number N: $\text{Pr}(N \leq z)= \frac{z-n}{z}$.  The first modern census was not conducted until the 18^th century, but we can estimate the number of people who have lived on Earth—it's on the order of 100 billion.  We can be 95% confident that there will be fewer than 2 trillion people.  Given that there are four births every second, this person will be born in 15 thousand years.

There are a number of objections that can be made against the doomsday argument on mathematical grounds; however, the biggest problem is that it fails to address the physical causes of extinction. Genetic mutations will continue to accumulate in human populations, perhaps causing h. sapiens to differentiate into new species.  Disasters may contribute to an early human extinction.  A 2008 report by the Future of Humanity Institute estimates a 1 in 5 chance of humans extinction before the year 2100.  Though, the methodology of this study is questionable.  The doomsday argument may be flawed, but it raises questions in mathematical inference, and has opened the door to managing the risks we face as a species.