Oil and doomsday

Recently, I provided an estimate of the amount of oil that was formed in the Earth—about 18 trillion barrels.  It's always good to tackle these kinds of problems from different angles, and before using the composition of the atmosphere to do the calculation, I had planned to re-purpose the doomsday argument.  It seems much better suited to this type of problem.  After all, there is a finite amount of oil—or, rather, a finite number of barrels of oil—that we are drawing from.

However, before we are able to apply the doomsday argument, we need to know how many barrels of oil have already been consumed. Using data from Energy Trends Insider, it appears that approximately 1.4 trillion barrels have been produced in modern history.  That being said, reliable verifications of this estimate are hard to find.


Using the doomsday argument, we find that we can be 94% confident that there are at most 16.6 trillion barrels of oil remaining, given that we have already consumed 1.4 trillion barrels.

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.

Computers vs. peak oil

Computers have become entwined in our daily lives.  Imagine, if you can, a day in which you didn't interact with a computer in some form or another.  Media, communication, personal finance, and commerce have become reliant on these technologies for success.  Will personal computers remain so readily available to everyone indefinitely?  It is easy to extrapolate form past experiences.  Computers have become steadily cheaper and more powerful for decades, but there is no real guarantee that this trend will continue.  This has also been confined mostly to Western Europe and the Anglophone nations, with computers remaining widely unavailable in developing nations.

Petroleum is very important in the manufacturing of electronics.  Over 40% of the chemicals used for creating semi-conducting devices rely on petroleum in some aspect of their manufacturing.  It is true that in most of these cases substitutes exist, but we don't rely heavily on these substitutes for a reason—either they are more expensive or cannot meet current demands.  Without cheap petroleum, manufacturing of semi-conductors will also rise in price, which will adversely effect the supply of these machines.

The energy requirements for producing electronics is enormous.  For example, one study found that manufacturing a laptop requires between 3000 and 4000 megajoules of energy—the equivalent of 24 and 32 gallons of gasoline, respectively.  Furthermore, these products often contain plastic components, in an effort to reduce costs.  Plastic can be replaced with metals, such as aluminium—many high-end models already use these materials.  But, this increases the price of products, as metals are harder to shape than plastics and are more expensive, in general.

Personal computers will remain available, even as petroleum supply dwindles; however, it is reasonable to expect that the price of these machines will likely increase.  Businesses will continue to rely on computing to run efficient operations, and the wealthy may have access to personal computers.  However, the poor may have to rely on publicly available machines—such as those at libraries.  This may have the effect of widening the gap between these groups of people, contributing to greater levels of wealth inequality.

Population of the United States

Calculating the change in a population is easy:$$\text{Population change} = \text{Births} - \text{Deaths} + \text{Immigration} - \text{Emigration}$$ Estimating the number of births and deaths—and the effects of migration—in any given year is difficult.  The number of births can be estimated from the total fertility rate (TFR)—the average number of children a woman will have during her life time.  The number of deaths can be inferred from a life-table, like those used by actuaries.  I've put these statistics together into a simple model for forecasting populations.  Today, we'll look at two hypothetical futures—two assumptions about the behavior of people in the 21st century.

The darker line assumes a constant fertility rate, equal to that of 2012.  The lighter line assumes a decreasing fertility rate.

In the 1960s the United States entered  a period of relatively low fertility.  The population hasn't decreased, because of immigration.  In the past few years, approximately one million people have come to this country each year—compared to about four million births per year.  In the graph above, the darker line shows the expected population if the fertility rate and immigration continue as they were in 2012.  In this case, we would expect the population to level off by mid-century around 350 million people.

The United States has also experienced declining fertility since the mid 2000s.  The lighter line assumes that fertility will continue to fall to 1.4 by the year 2025—this fertility rate would be similar to that of South Korea today.  If you were born in the 1990s, it is likely that none of your children will be born during the 2040s—the decade where the curves diverge.  The parents of these children already exist though—they are young children today.  After this point, the population would decline rapidly, as those born near the end of the 20th century begin to age and die.  We currently face an aging population, but the effects would be much more pronounced in this scenario.

Schedule

After some thinking—and observing my viewing statistics—I have decided to eliminate two posts per week: Monday and Friday.  Posts will also come earlier in the day.  My hope is that this will benefit the quality and variety of my writing and increase reader engagement.

Until tomorrow.

Endangered element: zinc

Sphalerite is the primary ore for zinc.

Why is zinc an important mineral?  By far the most common use of zinc is corrosion resistance, accounting for 80% of the metal's use in the United States.  Steel has two useful properties; it's strong and light-weight.  It also has the disadvantage of being susceptible to rusting.  Stainless steel doesn't rust, but is substantially weaker than other kinds of steel.  Any steel structure that will be exposed to the elements needs to be protected from corrosion.  The solution to this problem is to simply coat the surface of the metal in zinc, which forms a layer of zinc carbonate over time.  This application, however, doesn't threaten future supplies.

Increased demand for zinc will likely be driven by zinc-air cells, useful for creating electric cars.  In 2012, the United States used 26.7 quads—quadrillion BTUs—of energy for transportation, primarily supplied by petroleum.  Zinc-air cells carry about 1600 BTU per kilogram—c.f. 43,000 BTU per kilogram for gasoline.  To replace every conventional car on the road would require 17 billion tonnes of zinc-air cells.  I don't know how much zinc is used to make these batteries, but there are only 1.9 billion tonnes of identified zinc resources in the world.

Can everyone in the world have an electric car?  Probably not—but this answer is too dismissive.  Everyone may not need to own a car in the coming decades.  Greater availability to public transit and autonomous cars could substantially improve the efficiency of transportation.  However, the United States only has 4% of the world population.  Increased demand from the rest of the world—particularly developing nations—could offset any gains from improved efficiency.  The future population of the world is uncertain as well.  Some countries may experience growth in population; others may experience contraction in population.  No single technology will likely be able to replace petroleum burning cars.  Instead, societies will need to rely on a variety of solutions.

Hydrogen fuel cells

How much energy is needed to make each kilogram of gasoline?  This may sound like an unusual question, because we tend to think of gasoline as a source of energy.  When one kilogram of gasoline is burned it releases about 45 megajoules (MJ) of energy in the form of heat, that can then be converted into other forms of useful energy.  However, 9 MJ are needed to produce a kilogram of fuel.  Though this number is non-zero, the important point is that less energy goes into the fuel than is recovered from it.  This feature makes petroleum good as a fuel source, among other properties.

In a previous post, I wrote about the energy requirements of producing hydrogen.  Every kilogram of hydrogen contains roughly three times as much energy as a kilogram of petroleum—about 140 MJ.  Steam methane reformation requires 135 MJ per kilogram of hydrogen; this represents a net gain in energy, but a very small net gain.  Furthermore, it relies on the same non-renewable resources that it is meant to replace.  However, even if we rely on electrolysis to manufacture hydrogen, the fuel cells extract energy by performing the electrolysis reaction in the opposite direction.  That is to say, the energy recovered by fuel cells is the same as the energy used in manufacturing the fuel.  At best, this only allows electricity to be converted to a more portable form.

There are difficulties in making hydrogen portable, as well.  Because gasoline is relatively dense, it can carry a large amount of energy in a compact space.  Hydrogen pressurized to 5,000 psi, would occupy over eight times as much space as the equivalent amount of gasoline, at room temperature.  Instead, hydrogen is typically cooled to about −400 degrees Fahrenheit.  At this temperature, the same hydrogen would occupy a similar amount of space as gasoline, but this temperature would need to be maintained.  Gasoline can sit for years before being used, but hydrogen would likely need to be used shortly after it is brought to temperature.

Power of the brain

How much power does the human body use?  Evolution is less survival of the fittest, and more survival of the most efficient.  The calculation is simple.  A typical caloric intake is 2500 kilocalories—known simply as Calories, in the United States—per day.  This is the equivalent of 120 watts.  This is rather impressive.  You and I are kept alive with about as much power as in used by a standard incandescent light-bulb.  Furthermore, the brain only requires 20% of the body's energy usage, which comes—that is, 24 watts.

How does this compare to computers?  Personal computers use a modest 65 to 250 watts, but don't possess the ability to match the functions of the human mind.  Artificial intelligence is, for now, run on supercomputers.  For example, WATSON consumes 85 kilowatts—the equivalent of roughly 1,000 PCs.  Koomey's law is similar to Moore's law, but deals with the energy usage of computers.  It states that the number of calculations for every unit of energy doubles every one-and-a-half years.  A quick calculation shows that WATSON could match the human brain in energy usage by the 2030s.  These computers only mimic one aspect of human cognition, but how these technologies will be used remains uncertain—there are a number of possibilities I intend to explore more fully.

That being said, I'm confident that human minds are not at risk of obsolescence.  The human brain is incredibly efficient, and already possesses a powerful set of skills.  Furthermore, the problem solving capabilities of groups of people exceeds the sum of the parts.  What is not clear is the number of people who will be able to take part in these kinds of activities.

Endangered element: helium

In a previous post, I wrote about  the concept of endangered elements—elements whose supply may not be able to meet demand within the next hundred years.  If we expect certain technologies to improve and to reach ever more people, the scarcity of these elements could prove to be a major impediment.  It's important to understand how we currently obtain and apply these materials.  We'll begin with helium.

Most helium found on earth was produced through the nuclear decay of uranium—or other heavy elements—which then dissolved into natural gas and oil over millions of years.  This isn't good news; most fossil fuel resources aren't projected to outlast the century, but bad policy making could produce shortages much sooner.  Helium, despite being common in the cosmos, is rare on Earth, and in the atmosphere.  It's effectively a non-renewable resource, and will be difficult to obtain once our current supplies run dry.

Helium has the lowest boiling point of any material at only 7 Fahrenheit degrees above absolute zero, which allows other objects in contact with liquid helium to be maintained at this temperature.  The next lowest boiling point belongs to hydrogen—at 36 Fahrenheit degrees above absolute zero.  Unsurprisingly, 32% of helium is used for cryogenics, particularly for cooling the magnets used in MRI machines.  Unfortunately, this means that MRI may become less available as helium supplies dwindle.  This could have a large impact on the standard of care, unless a substitute for MRI can be found.  I suspect that this will be problematic for the widespread adoption of quantum computing technologies, as well.  Such technologies my be adopted on a small scale, by wealthy institutions and organizations, but may remain beyond the reach of most.

Antimicrobial resistance

"Infectious disease is merely a disagreeable instance of a widely prevalent tendency of all living creatures to save themselves the bother of building, by their own efforts, the things they require. Whenever they find it possible to take advantage of the constructive labors of others, this is the path of least resistance. The plant does the work with its roots and its green leaves. The cow eats the plant. Man eats both of them; and bacteria (or investment bankers) eat the man" ― Hans Zinsser, Rats, Lice and History

Since the development of modern medicine in the early 20th century, the quality of life has risen greatly.  Ever since people began to live in cities, close proximity has allowed disease to spread easily.  Medicine was able to reverse this trend for the first time; however, an important tool in the fight against disease is rapidly loosing efficacy.  Bacteria are developing resistance to common antibiotics.

Evolution is an incredibly powerful force.  For every bacterium, roughly one genetic mutation will arise every two days.  The number of bacteria in the world is staggering.  In your body, alone, there are on the order of 100 trillion bacteria.  Not all mutations will lead to resistance to antibiotics—in fact, not all of these mutations will even be favorable.  Bacteria, however, also posses the ability to take share genetic information.  With both of these properties, antimicrobial resistance is seemingly inevitable.

This isn't the end of the story.  As I said, antibiotics are only one tool for controlling disease.  Sanitation will become increasingly important.  We already have the ability to treat drinking water and dispose of sewage and other waste.  Hand washing can effectively combat disease transmission, even without antibacterial soap, and alcohol-based hand sanitizer can still be made widely available.  Controlling pests is a second tool at our disposal.  Insects, such as mosquitoes, are perhaps the worst vector for disease, and have been responsible for countless pandemics throughout history.  Vaccination is yet another tool—be sure to share this with any anti-vaxer you know, they certainly are in need of education.  By augmenting our immune systems, certain infectious disease have become very rare, and small pox has been eradicated completely.

At the same time, this is still a substantial problem.  The number of deaths that could occur in the coming decades due to infectious disease is staggering.  Those most susceptible to death by infection are infants, the elderly, or those with otherwise compromised immune systems—three groups whose numbers have grown thanks to antibiotics.  Though otherwise healthy individuals likely won't succumb to infection, the toll in human suffering should not be underestimated.

Weapons of reason: Jevons' paradox

"The Earth provides enough to satisfy every man's need but not for every man's greed." ― Mohandas Gandhi

Jevons' paradox is an example of how economics can defy common sense.  We use energy for useful things, such as manufacturing or transportation.  Creating machines that can use energy more efficiently can help to reduces prices and reduce our consumption of fuel.  However, the latter is not guaranteed.  150 years ago, an economist named William Jevons realized that more cost-effective coal plants resulted in an increased demand for coal.  However, the increase in demand was greater than the increase in efficiency, which meant the industry was consuming more coal, rather than less.

Jevons' paradox is more likely to occur in cases of elastic demand, where demand more than doubles when cost is cut in half.

Price elasticity is necessary to understanding how Jevons' paradox occurs.$$\text {Elasticity} = \frac{\text{Percent change in demand}}{\text{Percent change in price}}$$Elasticity is typically a negative number. More negative values represent more elastic price—that is, the products demand changes faster with a given change in price.  Energy efficiency is not the only contributing factor to price, but more efficient use of energy will cause lower prices.  Because of other factors, Jevons' paradox is likely to occur only in cases of high elasticity when energy efficiency is the only change.  Energy demand is typically inelastic in the short-term; but, it can be substantially higher in the long-term.  If price can be reduced without an increase of energy efficiency, then the corresponding increase in demand will naturally increase overall energy consumption.


The Luddite response—which is too reactionary—would be to never improve energy efficiency.  There are two obvious problems with this.  First, improving energy efficiency doesn't always lead to Jevons' paradox.  Second, society could potentially benefit from increases to energy efficiency.  Instead, new technologies need to be combined with new policies that would help offset any increases in fuel consumption.  An example would be a green tax, which incentivizes manufacturers to create less pollution—perhaps by burning fewer fossil fuels.

Commercial flight

"Thank God, men cannot as yet fly, and lay waste the sky as well as the earth!" ― Henry David Thoreau

Since the 1960s, air travel has surpassed other forms of ridership in intercontinental travel.  In the United States,  1.73 million people travel on domestic flights in the United States on any given day.  However, it is doubtful that flight will maintain this kind of dominance into the century, if commercial flights will remain viable at all.

In some ways, the writing is already on the wall.  The number of air carriers is down 13% from its peak in 2001 as airlines downsized in response to rising oil prices in the past  few years.  Most jets use kerosene as fuel—like other hydrocarbons, its high energy density makes it ideal for this application.

Can other power sources step in?  While there have been a number of achievements in solar powered flight, it is provide passenger air travel on a large scale.  The amount of power required to travel through the air can be easily calculated.$$ \text {Power} = \frac{\text {Weight} \times \text{Speed}}{\text{Glide Ratio}}$$For a Boeing 747, the requirement is at least 3 MW, which would require at least 2,000 square meters of solar panels—an area twice as large as the wings of the 747.

Even if a substitute power source is found, high speed rail is often capable of reaching speeds comparable to jet liners, and could well provide for long distance domestic travel in the future.  Furthermore, if demand for intercontinental flights falls too much, the maintenance of the global infrastructure for managing flights may become untenable.  Flight will likely remain possible for governments, armed forces, and the very wealth; however, my expectation is that cheap commercial flights will become unavailable to most people within the following decades.

Rare metals

Our society is dependent on an abundance of mineral resources.  You are reading this today, because of a number of rare metals that have been used to construct the computer—or tablet, smart phone, etc.  A large amount of time and effort is spent discovering, extracting, and transporting these materials from the Earth.  Let's consider four of them: zinc, gallium, indium, and hafnium.  These are example of so-called endangered elements.

Composition of the Earth's crust.

As much as 95% of the Earth's crust is composed of silicates—minerals that contain silicon and oxygen.  These minerals are not as suitable as the remaining 5% as ores, because the chemical bonds of silicates require more energy to be broken.  However, even a pessimistic calculation estimates that there may be 10 quadrillion tonnes of non-silicates accessible to human mining efforts.

Ores are important for two reasons.  First, they feature higher concentrations of certain elements than the rest of the Earth's crust—often, much higher concentrations.  Second, their chemical purity make them suitable to industrial processes.  Zinc is only the 25th most abundant element in the Earth's crust, but readily bonds with sulphur in an ore called sphalerite.  It comprises 79 parts per million (ppm) of the Earth's crust, which is more abundant than silver, gold, or even copper.  Gallium, indium, and hafnium are not typically obtained from unique ores, but occur in trace amounts in other metals.  They are also substantially rarer at 17 ppm, 49 parts per billion (ppb), and 5 ppm, respectively.

These elements in particular have applications to technologies that will be important during the next century, and will likely experience growing demand in the face of dwindling supply—which would adversely affect their price, and the prices of technologiey.

Electrolysis of water

In a previous post, I stated that steam methane reforming requires only half the energy of the electrolysis of water.  The so-called hydrogen economy will be a topic that I will come back to from time to time, and while doing more calculations, I may have encountered an error in the numbers.  It is important to always present accurate information—my goal is, of course, to promote education and critical thinking.

Steam methane reforming is a process in which natural gas and water are placed under high temperature—up to 1000 degrees Celsius—and pressure.  This ensures that the reactants are fully converted into hydrogen and carbon dioxide.
$$ \text{CH}_4 + 2 \text H_2 \text O + 165 \text{ kJ} \rightarrow \text{CO}_2 + 4 \text H_2 $$This source claims that the process requires approximately 135 megajoules (MJ) of energy.  However, my best efforts cannot reconcile this with naïve thermo-chemistry.  Using the enthalpy of formation, I can only account for 21 MJ per kilogram of hydrogen.  Even including all the heat required to create the high temperatures needed does not reconcile the difference.

Electrolysis, as the name implies, involves the use of electricity to disassociate the oxygen and hydrogen in water.  Though this process can be demonstrated without high temperatures in table-top experiments, industrial applications often require them.$$2 \text{H}_2\text{O} + 484 \text{ kJ} \rightarrow \text{O}_2 + 2 \text{H}_2$$Because of the stability of the bonds in water, the energy requirement is considerably larger than steam reformation.  Naïve thermo-chemistry yields about 120 MJ per kilogram of hydrogen.  I am unable to find sources that give the energy requirements for the industrial state of the art.  From a purely theoretical stand point, though, steam reformation has only one fifth the energy requirement of electrolysis.  Furthermore, if electrolysis could more easily manufacture hydrogen, we would already use this method more widely; though, it remains unclear exactly how different the energy requirements are.

Crossing an ocean

“There is nothing more enticing, disenchanting, and enslaving than the life at sea.” ― Joseph Conrad

Despite the fact that most people travel by air, the majority of trade still travels by sea— as much as 90% of it.  Most commodities have long shelf-lives to begin with, but cargo ships are also one of the most fuel efficient modes of transportation.  But how much energy is needed to cross the ocean?  This is a simple physics problem.  Most fuel will be used to work against the drag of the water against the ship.  The required energy, in horsepower-hours, is $$E \approx \frac{1}{10,000,000} \times \frac{\Delta x^3}{\Delta t^2} \times \text{WSA},$$
where Δx is the distance in nautical miles, Δt is the travel time in days, and WSA is the wetted surface area of the ship in square feet.

The real usefulness of this equation lies in it's ability to estimate the fuel requirement of these vessels, as one tonne of fuel carries 17,000 horsepower-hours of energy.  In general, the numbers will be enormous, especially over long distances and short travel times.  Pull out a calculator, and see how much energy certain trips might cost—use your imagination or use real shipping routes.

The moral of this story is that as our supply of fossil fuels dwindle and their costs rise, it is highly likely that the age of sail will return.  After all, wind was able to supply all the energy needed during the 19th century to transport goods and will supply our electricity during the 21st century.

New technologies

An article in The Atlantic recently featured this graph, though a more detailed version can be found here:

This chart is rather unremarkable, and it doesn't strongly support the idea that consumption spreads faster today.  Why did it take so long for electricity to be adopted, but such a short time for color TV?  The simplest explanation is infrastructure.  Before the homes in an area can have electricity, a power plant has to be built nearby.  After this, a network of transmission lines needs to be built to deliver the electricity to homes.  All of this requires time, effort, and money.

Television—which was distributed wirelessly for much of the 20th century—only required to be put in the homes.  Units could be produced quickly and transported easily.  Once the technology was available, it could be distributed quickly.  Looking closely at the graph, we see that during their periods of quick growth, radio and color TV matched the growth of the Internet.

Furthermore, this graph ignores the early development of electrical appliances.  The impetus for electric power plants was electric lighting.  However, many electronic appliances were first developed before 1930 to make use of electricity.  The data is not shown, but it is possible that these would have grown quickly to match the prevalence of electricity of the time.

Nitrogen

"It is the chemist who must come to the rescue of the threatened communities. It is through the laboratory that starvation may ultimately be turned into plenty... The fixation of atmospheric nitrogen is one of the great discoveries, awaiting the genius of chemists." ― William Crookes, Chemical News

I've tried to avoid equations, but this one is too relevant to today's discussion.  Ammonia is necessary to making fertilizer, and it can be easily made with hydrogen and nitrogen, in the Haber-Bosch process: $$ \text{N}_2 + 3 \text{H}_2 \rightarrow 2 \text{NH}_3 $$

Schematic of the Haber-Bosch process.

Nitrogen is essential to life.  Though only 3% of the human body is nitrogen, by weight—9%, if water is ignored—it gives proteins and DNA much of their chemical identity.  We don't simply absorb nitrogen from the atmosphere, like oxygen.  It is supplied through the food we eat, after it has been collected by other plants and animals.  However, modern agriculture has become dependent on artificial fertilizers.  In fact, 80% of the nitrogen in your body comes from the Haber-Bosch process.

This process relies on hydrogen as a reactant, which is abundant on Earth, in the form of water.  Most of our hydrogen does not come from water, though.  95% of it comes from hydrocarbons, with only 5% coming from the electrolysis of water.  The most common process used to manufacture hydrogen is steam reformation of methane.  This process is able to efficiently produce hydrogen at lower cost than electrolysis, though it does produce a substantial amount of carbon dioxide as a by-product.  It also requires about half the energy as electrolysis per kilogram of hydrogen.

In the United States, most hydrogen in used to refine other hydrocarbons—for example, it is used to remove sulfur from petroleum.  Only 1.6 million tonnes of hydrogen could supply our need for ammonia, which would require three times as much hydrogen to be produced by electrolysis. However, other countries use nitrogen more for the production of ammonia, and meeting the world need for cheap fertilizers could be more difficult.

On autonomous vehicles

"Averroës, Kant, Socrates, Newton, Voltaire, could any of them have believed it possible that in the twentieth century the scourge of cities, the poisoner of lungs, the mass murderer and idol of millions would be a metal receptacle on wheels, and that people would actually prefer being crushed to death inside it during frantic weekend exoduses instead of staying, safe and sound, at home?" ― Stanisław Lem, The Futurological Congress

Though it's still early, I haven't made any real predictions—today seems like a good day to start.  By the year 2025, few people will own cars.  I'll go further, and estimate that there will be only one vehicle for every five people in the United States.  This hinges upon the adoption of autonomous vehicles.

Consider transportation in Europe.  Per capita, the United States consumes 2.5 times as much petroleum as Europe—most likely because there are more than twice as many vehicles per capita.  I've heard anecdotes that Europe, indeed, has much better public transportation than even the best U.S. cities.  European policy makers have tended to favor mass transit and improving walkability over other forms of transportation.  If metropolitan bus fleets in the United States can be automated, they could be operated more cheaply—or expanded to offer more continuous service or more routes.  With increasing petroleum prices, policies will have to favor more efficient use of fuel.

However, let's say you want access to a private vehicle—it may not be necessary to own one, outright.  With cars able to drive themselves, one vehicle could easily serve many people in a day.  There are already car sharing companies that could easily expand their business with fleets of driverless cars.  Improved fuel efficiency may also extend the time that oil will remain cheaply available—at least, it could smooth the transition to a post-petroleum economy.

Replacing fossil fuels

"The future is already here—it's just not very evenly distributed." ― William Gibson

It is trivial to say that wind and solar will replace fossil fuels, because in many places they already have.  Given that these sources produce less pollution and provide more autonomy in energy production, why haven't we been using them all along?  The simple answer is that fossil fuels are just easier to use.  They store a large amount of energy per pound and can provide energy consistently to the grid.  Most of all, they are easy to transport.

via NREL.

There are approximately 48,000 wind turbines in the U.S., supplying 4% of our electricity.  To supply our full electricity demand would require on the order of 1 million wind turbines. However, building these turbines would require a large amount of steel and copper, and they would need to be replaced every twenty to thirty years.  Wind farms also require more space than conventional power plants, and may not provide power with the same consistency.

via NREL.

Solar energy has experienced fast growth, recently, though it suffers from a similar set of disadvantages as wind.  There are other problems with the availability of the materials needed to make more efficient solar panels—though, we will visit this issue later.  We may have to settle for relatively inefficient silicon-based solar panels.



However, this entire discussion ignores that electricity generation is only 40% of our energy usage.  Almost none of the energy used for transportation is electric.  The question then becomes
"How will we provide transportation without petroleum?"

How is energy made?

"It is important to realize that in physics today, we have no knowledge what energy is.  We do not have a picture that energy comes in little blobs of a definite amount.  It is not that way." ― Richard Feynman, The Feynman Lectures on Physics

It is a myth to say that we produce energy.  It is impossible to create—or destroy—energy.  Instead, we extract it from energy-rich sources, like coal or petroleum.  The problem then becomes how to make it do what we want.  In the 18th century, engineers were able to build machines that could turn chemical energy into motion.  In the 19th century, engineers were able to build machines that could turn motion into electrical energy.  And in the 20th century, engineers were able to build machines that could turn nuclear energy into heat.  However, at this point, most methods of extracting energy are in place.

via LLNL and DOE. (Full size).

Above is one of the best infographics I've seen.  It shows the energy sources and uses for the United States—by far, the largest energy consumer in the world.  Let's begin the controversy.  Fossil fuels are, undoubtedly, a limited resource.  The notion that we will reach—or have reached—a point where we are no longer able to increase the available supply of petroleum is called the peak oil hypothesis.  Looking at this chart, though, we see that over 80% of our total energy needs comes from fossil fuels, and over 95% of energy used for transportation comes from fossil fuels.  Tomorrow, we'll look at what sources may replace fossil fuels in the future.

Weapons of Reason

"Never let the future disturb you. You will meet it, if you have to, with the same weapons of reason which today arm you against the present." ― Marcus Aurelius, Meditations

What will happen in the future?  This seems to be a profound question—deep and philosophical.  But, it's actually quite vague.  If we tried to study history by asking "What happened in the past?" we wouldn't get far.  The concept of the future involves not only time, but also place and people, which naturally compounds the difficulty in understanding it.

We need to narrow the scope of this question.  It would be better to ask what will happen in the next century—during our and our children's lifetimes—and to ask where these things will happen.  This question is also wrapped up in personal issues—our desires and aspirations—which makes us susceptible to wishful thinking and other biases that would only confirm our hopes for the future.  This means that it's important to exercise as much objectivity as possible and to put our faith in the weapons of reason: mathematics, science, and logic

What will happen in the future?  This is the topic that I want explore, in the hopes that at least a few more people will think more critically about the experiences we will have and the challenges we will face.