Political Calculations
Unexpectedly Intriguing!
22 December 2023
The value of n is still unknown, but new results constrain it to fall between 8 and 10^500, ruling out popular 'n=1' and 'n=2' theories. - Source: XKCD: https://xkcd.com/2861

We've come to the end of 2023, making it time to take stock of the biggest math stories of the year that was!

In choosing these stories, we've emphasized math stories involving practical applications in selecting the Biggest Math Story of 2023, which we'll present at the end of this year's edition after going through the runners-up.

That's not to say that we don't find other big, pure math stories impressive. For example, 2023 saw both a proof for a nearly-100-year old problem in Ramsey theory and the discovery of the ninth Dedekind number, 286,386,577,668,298,411,128,469,151,667,598,498,812,366, which is also an achievement in computing.

But these aren't examples of the kinds of stories with great potential to affect people's lives or explain the world in which we live. That's what separates practical math from pure math. And as we go through the runners-up before reaching the Biggest Math Story of 2023, what stands out is the connections between the pure and the practical. It's a true bonus whenever there's also fun to be had with that math.

It all starts now! Let's begin with a unusually big story that surprisingly didn't much attention during the year.

An Unexpected Link Between Number Theory and Evolutionary Genetics

Mohanty et al. (2023) Figure 2 - https://doi.org/10.1098/rsif.2023.0169

The biggest math story of 2022 was the discovery that complex numbers, combining real and imaginary components, are essential for the existence of the universe. As practical applications go, it doesn't get much bigger than the universe. This story is a good place to start the 2023 edition of our year-ending series, because it points to a connection between mathematics and biology that potentially affects all life within the universe!

A team of researchers identified a potential application of number theory for explaining some vital characteristics of robustness observed in evolutionary genetics. What makes their findings special is that number theory in mathematics is often limited to applications that are themselves highly math dependent, such as computer coding or modern cryptography. Since evolutionary genetics is inherent to biology, finding a linkage between number theory concept and biology was unexpected.

From here, we'll turn to the University of Oxford's press release because it describes their discovery in layman's terms:

... the team of researchers (from Oxford, Harvard, Cambridge, GUST, MIT, Imperial, and the Alan Turing Institute) have discovered a deep connection between the sums-of-digits function from number theory and a key quantity in genetics, the phenotype mutational robustness. This quality is defined as the average probability that a point mutation does not change a phenotype (a characteristic of an organism).

The discovery may have important implications for evolutionary genetics. Many genetic mutations are neutral, meaning that they can slowly accumulate over time without affecting the viability of the phenotype. These neutral mutations cause genome sequences to change at a steady rate over time. Because this rate is known, scientists can compare the percentage difference in the sequence between two organisms and infer when their latest common ancestor lived.

But the existence of these neutral mutations posed an important question: what fraction of mutations to a sequence are neutral? This property, called the phenotype mutational robustness, defines the average amount of mutations that can occur across all sequences without affecting the phenotype.

Professor Ard Louis from the University of Oxford, who led the study, said, "We have known for some time that many biological systems exhibit remarkably high phenotype robustness, without which evolution would not be possible. But we didn't know what the absolute maximal robustness possible would be, or if there even was a maximum."

It is precisely this question that the team has answered. They proved that the maximum robustness is proportional to the logarithm of the fraction of all possible sequences that map to a phenotype, with a correction which is given by the sums of digits function sk(n), defined as the sum of the digits of a natural number n in base k. For example, for n = 123 in base 10, the digit sum would be s10(123) = 1 + 2 + 3 = 6.

Another surprise was that the maximum robustness also turns out to be related to the famous Tagaki function, a bizarre function that is continuous everywhere, but differentiable nowhere. This fractal function is also called the blancmange curve, because it looks like the French dessert.

First author Dr. Vaibhav Mohanty (Harvard Medical School) added, "What is most surprising is that we found clear evidence in the mapping from sequences to RNA secondary structures that nature in some cases achieves the exact maximum robustness bound. It's as if biology knows about the fractal sums-of-digits function."

A blancmange is a fancy molded gelatin dessert, whose defining feature is its scalloped or wave-like sides. The green curve in this section's illustration is the contour the authors are attempting describe.

Its still early days for this new application however, which keeps this math story from being the biggest of the year.

Buying a Winning Lottery Ticket

Lottery Ticket by Ian Barbour on Flickr - https://www.flickr.com/photos/barbourians/8425673057

Our next contender for the biggest math story of the year involves the maths of probability and statistics, with the side benefit of potentially helping you win money in playing the lottery. Which if you can make it work for you, could be a very practical application!

Starting with the prospect of improving your chances of getting a winning ticket in the lottery, University of Manchester mathematicians studied the United Kingdom's national lottery, in which players choose 6 of 59 possible numbers that might be drawn when numbers are randomly selected. They applied graph theory to determine the minimum number of tickets lottery players would have to buy to get at least one that would win in each drawing.

We should note a "winning ticket" means a ticket that wins any of the possible payouts for the U.K.'s national lottery, not the 'Lotto' jackpot that's the main attraction to players. The University of Manchester's press release describes what they did to find how many tickets they needed to get any payback at all:

Focusing on the National Lottery’s flagship game ‘Lotto’, which draws six random numbers from 1 to 59, Dr David Stewart and Dr David Cushing found that 27 is the lowest possible number of tickets needed to guarantee a win – although, importantly, with no guarantee of a profit.

They describe the solution using a mathematical system called finite geometry, which centres around a triangle-like structure called a Fano plane. Each point of the structure is plotted with pairs of numbers and connected with lines – each line generates a set of six numbers, which equates to one ticket.

It takes three Fano planes and two triangles to cover all 59 numbers and generate 27 sets of tickets.

Choosing tickets in this way guarantees that no matter which of the 45,057,474 possible draws occurs, at least one of the tickets will have at least two numbers in common. From any draw of six, two numbers must appear on one of the five geometric structures, which ensures they appear on at least one ticket.

But Dr Stewart and Dr Cushing say that the hard work is actually showing that achieving the same outcome with 26 tickets is not possible.

The researchers note that buying 27 lottery tickets for the U.K.'s Lotto game will cost players £54. They indicate players will never make back that stake in "almost 99% of cases".

Getting Better Odds to Win a Coin Flip

Researchers at the University of Amsterdam found a trick that could give you a small edge in beating the odds of winning coin tosses. The trick is to see which side of the coin is originally facing up when it is tossed. If you can, there's a 50.8% chances that same side will be the the winner of the coin toss!

Although the same-side bias odds are close to even, it's also enough of a bias that coin flip odds are skewed as much as some casino games are in favoring the house. Here's how corresponding author František Bartoš described it:

Fortunes have been made by casino operators with those kind of biased odds in their favor.

Meanwhile, we built a tool to simulate a biased coin toss, assuming that the side you see up is always "Heads". By all means, take it for a test drive to see if you can put it to your own practical application!

Artificial Intelligence Speeds Math Proofs

Cozy office with a green computer screen showing math formulas and diagrams, highly detailed, photorealistic - generated with Stable Diffusion DreamStudio Beta

2021 was the year artificial intelligence qualified as the biggest math story of the year. 2023 has seen an acceleration of AI systems capable of generating images and writing, but AI in the form of proof assistants also made a mark in advancing mathmatics.

That's the most practical application part of the story of how a team of four mathematicians proved Kati Marton's conjecture, considered by many mathematicians to be the "holy grail" of combinatorics. The invaluable Quanta Magazine covered the story of how the formalization of their proof came together:

Eventually, the group pushed through, and on November 9, they posted their paper. They proved that if A + A is no bigger than k times the size of A, then A can be covered by no more than about k12 shifts of a subgroup that is no bigger than A. This is a potentially enormous number of shifts. But it is a polynomial, so it doesn’t grow exponentially faster as k gets bigger, as it would if k were in the exponent.

A few days later, Tao began to formalize the proof. He ran the formalization project collaboratively, using the version-control package GitHub to coordinate contributions from 25 volunteers around the world. They used a tool called Blueprint developed by Patrick Massot, a mathematician at Paris-Saclay University, to organize the efforts to translate from what Tao called “Mathematical English” into computer code. Blueprint can, among other things, create a chart depicting the various logical steps involved in the proof. Once all the bubbles were covered in what Tao called a “lovely shade of green,” the team was done. They discovered a few very minor typos in the paper — in an online message, Tao noted that “the most mathematically interesting portions of the project were relatively straightforward to formalize, but it was the technical ‘obvious’ steps that took the longest.”

The increasing usefulness of computer-assisted automation tools continued to be one of the biggest math stories of 2023, but not the biggest.

A Unique Tile Makes a Pattern That Never Repeats

It was two breakthrough discoveries in the ancient mathematical field of geometry, of all things, that made for the biggest math story of 2023! March had the first part of the story of the invention of an unusually-shaped einstein ("one-stone") tile, whose pattern would never repeat nor leave any gaps when tiled over a plane.

While that marked an improvement over Roger Penrose's aperiodic tiling, which requires two differently shaped tiles to accomplish the same feat, geometers had still never managed to find one tile shape that would do the same thing.

And in truth, they still hadn't, because the einstein "hat" tile required some tiles to be flipped over to fully "tile the plane", as they say in geometry. If you try doing that with common bathroom tiles, you'll quickly see that something is off with that approach.

In June, the same team tweaked their previous concept and created the "Spectre" tile and completed the solution to the centuries-old challenge.

It's only been months, but the new einstein and Spectre tiles are already making their presence felt in the real world. You can buy a T-shirt to celebrate the concept, or you get actual tiles to play with or that use these shapes as especially challenging puzzles. The kind that's extra hard because all the pieces can fit together no matter which ones you use.

Numberphile's Brady Haran did a half hour video interview describing how David Smith and Craig Kaplan developed their geometric solutions, but here's Ayliean's five-and-a-half minute video summarizing it all at warp speed.

And that one-two punch of discovery is the biggest math story of 2023!

Previously on Political Calculations

The Biggest Math Story of the Year is how we've traditionally marked the end of our posting year since 2014. Here are links to our previous editions and our coverage of other math stories during 2022:

This is Political Calculations' final post for 2023. Thank you visiting us this past year, we hope found the things we wrote either useful, thought-provoking, or entertaining. We'll see you again in the New Year, which we'll kick off with our annual tradition of presenting a tool to help you find out what your paycheck will look like in 2024. Have a wonderful holiday season - we'll only drop in long enough to update this final article of the year with links to other math-related year-end wrap-ups!

Update: Quanta Magazine has put together an article and video with what they consider to be the year's top math stories.

See you next year!

Image credits: Lottery Ticket by Ian Barbour on Flickr. Creative Commons. CC BY-SA 2.0 DEED Attribution-ShareAlike 2.0 Generic. "Cozy office with a green computer screen showing math formulas and diagrams, highly detailed, photorealistic" generated with Stable Diffusion DreamStudio Beta. XKCD: The Value of X. Creative Commons CC BY-NC 2.5 DEED Attribution-NonCommercial 2.5 Generic.

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21 December 2023
A picture of the concept of poor, middle class, and rich people image generated by Microsoft Bing Image Creator

Where do you fall on the distribution of income in the United States?

We can help you answer this question using the data that the U.S. Census Bureau has collected on the total money income earned by individual Americans as well as for the families and households into which Americans gather themselves!

If you're a visual person, we'll first present the U.S. income distribution information with an animated chart, which will cycle through three charts presenting the cumulative distribution of income for U.S. individuals, U.S. households, and U.S. families (follow these links for static versions of the charts).

To use these charts, first find the income that applies for you on the horizontal axis, then move directly upward to the curve that defines the cumulative distribution of income. Once you've found your place on S-shaped curve in each chart, look directly to the vertical scale on the left hand side of the chart to determine your approximate U.S. income percentile ranking. Each of the charts will be displayed for five seconds and will cycle back to the beginning after running through each of the charts. The charts will also indicate the median and average income earned by each category.

Animation: Cumulative Distribution of Total Money Income for U.S. Individuals, Households, and Families in 2022

Now, let's find out more precisely where you really fit into the 2022 distribution of income! To find out where you, your family or your household ranks among each of these categories, just enter your personal income, your family's income, which includes the incomes of your spouse and other family members who live with you, and also the combined income of just the people who live within the walls of the same household that you do, into the following tool. We'll do some quick math and provide a more better estimate of the percentage of all American individuals, families and households that you outrank given the incomes you enter than you can get from scanning the animated chart. We'll also break down the numbers for your Individual income to tell you how you compare to your fellow male and female Americans. If you're accessing this article through a site that republishes our RSS news feed, please click through to our site to access a working version of our tool.

Income Data
Input Data Values
Your Personal Total Money Income
Your Household's Combined Total Money Income
Your Family's Combined Total Money Income

Your Estimated U.S. Income Percentile Ranking
Calculated Results Values
Among All U.S. Individuals with Incomes
 - Among All U.S. Men with Incomes
 - Among All U.S. Women with Incomes
Among All U.S. Households
Among All U.S. Families

Our tool should be able to place most people within half a percentile of their actual income percentile. A percentile of zero indicates that you are at the very bottom end of the U.S. income spectrum, while a percentile ranking of 100 indicates that you are effectively at the very top end. A percentile rank of 50.0 puts you at the median, where 50% of the U.S. population would have a higher income and 50% has a lower income.

For our readers who live outside of the United States, you can still get in on the action if you convert your income from your local currency into U.S. dollars first!

If you want a more precise estimate of your income percentile ranking within the U.S., please check out Don't Quit Your Day Job's Income Percentile Calculator. DQYDJ uses a more refined version of the U.S. Census Bureau's income data to estimate the distribution of total money income within the United States, which means that compared to our tool, which will put you in the right seating section of the ballpark, PK's tool can put you in the right row of that seating section.

Finally, if you're looking for the income data for 2023, please note that the U.S. Census Bureau will report the data it collects for this year sometime in September 2024. The data for 2023 won't even be collected until March 2024, when Americans will be preparing their income tax returns for the 2023 tax year and have all the records needed to do that. The Census Bureau's statisticians will then take the next six months to analyze all the income data they collect before reporting their results.


U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table PINC-01. Selected Characteristics of People 15 Years and Over, by Total Money Income in 2022, Work Experience in 2022, Race, Hispanic Origin, and Sex. [Excel Spreadsheet]. 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table PINC-11. Income Distribution to $250,000 or More for Males and Females: 2022. Male. [Excel Spreadsheet]. 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table PINC-11. Income Distribution to $250,000 or More for Males and Females: 2012. Female. [Excel Spreadsheet]. 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table FINC-01. Selected Characteristics of Families by Total Money Income in: 2022. [Excel Spreadsheet]. 8 September 2023. Accessed 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table FINC-07. Income Distribution to $250,000 or More for Families: 2022. [Excel Spreadsheet]. 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table HINC-01. Selected Characteristics of Households by Total Money Income in: 2022. [Excel Spreadsheet]. 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table HINC-05. Percent Distribution of Households, by Selected Characteristics Within Income Qunitile and Top 5 Percent in 2022. [Excel Spreadsheet]. 8 September 2023.

U.S. Census Bureau. Current Population Survey. Annual Social and Economic (ASEC) Supplement.Table HINC-06. Income Distribution to $250,000 or More for Households: 2022. [Excel Spreadsheet]. 8 September 2023.

Image credit: Microsoft Bing Image Generator. Prompt: "A picture of the concept of poor, middle class, and rich people."

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20 December 2023
Human development stages on Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Human_development_stages_(collage).jpg

Life expectancy in the United States has started to recover after taking a big hit from 2020's Coronavirus Pandemic.

That's the big story following the CDC's release of its provisional life expectancy estimates for 2022 at the end of November 2023. After peaking at 78.8 years in 2019 (76.3 years for males and 81.4 years for females), average American life expectancy at birth dropped during 2020 and 2021, bottoming at 76.4 years (73.5 years for males and 79.3 years for females).

But in 2022, it began to rebound. Average life expectancy at birth rose to 77.5 years, with life expectancy rising by 1.3 years to 74.8 years for males and rising by 0.9 years to 80.2 years for females. The CDC finds "declines in mortality due to COVID-19 were the primary reason for the increases in life expectancy from 2021 to 2022 observed for the total population".

The following chart showing how life expectancy from birth has changed for Americans from 2000 through 2022 is taken from the CDC's report presenting its provisional findings for 2022.

CDC. Provisional Life Expectancy Estimates for 2022. Figure 1. Life expectancy at birth, by sex: United States, 2000-2022

While the decline in COVID-19 mortality led the improvement in U.S. life expectancy, it wasn't the only contributor to it.

The increase of 1.1 years in life expectancy from 2021 to 2022 primarily resulted from decreases in mortality due to COVID-19 (84.2% of the positive contribution), heart disease (3.6%), unintentional injuries (2.6%), cancer (2.2%), and homicide (1.5%) (Figure 4). The increase in life expectancy would have been even greater if not for the offsetting effects of increases in mortality due to influenza and pneumonia (25.5%), perinatal conditions (21.5%), kidney disease (13.0%), nutritional deficiencies (12.6%), and congenital malformations (5.9%).

The CDC's provisional data for 2022 will be finalized over the next months as the agency is still accumulating death certificate data.


Arias, Elizabeth; Kochanek, Kenneth D.; Xu, Jiaquan; Tejada-Vera, Betzaida. Provisional Life Expectancy Estimates for 2022. National Center for Health Statistics (U.S.). VSRR; no 31. [PDF Document]. 29 November 2023.

NAMES. United States Life Tables, 2019. National Center for Health Statistics (U.S.). National Vital Statistics Reports, Vol. 70, No. 19. [PDF Document]. 22 March 2022.

Image credit: Human development stages (collage) on Wikimedia Commons. Creative Commons. CC BY-SA 3.0 DEED Attribution-ShareAlike 3.0 Unported.


19 December 2023
Income trajectory concept image by tuku on Pixabay - https://pixabay.com/photos/graphic-concept-success-successful-1991983/

Your education level can have a profound effect on how much money you can expect to earn throughout your life.

That's one of the major takeaways from the U.S. Census Bureau's data for the average total money income by age for different levels of educational attainment in 2022. This data shows several different patterns:

  • The more education you have, the higher the amount of income you can expect to earn at every age.
  • The amount of income you earn will most likely peak between the Ages of 45 and 64.
  • The more income you earn while you're younger, the earlier you are likely to retire.

Here's the chart illustrating each of these patterns.

Income and Education Level in 2022, Average Total Money Income by Age for Level of Educational Attainment

Let's go through each of the takeaways:

The more education you have, the higher the amount of income you can expect to earn at every age. The chart shows those with more education have higher average total money incomes than those with less education for every age group.

The amount of income you earn will most likely peak between the Ages of 45 and 64. You can see this by where the annual income earned peaks for each level of education. Those with a less than high school level of education peaks at Age 45-49, while those with high school diplomas peaks at Age 60-64. Americans who earn associate degrees see their incomes peak on average at Age 55-59 and those with bachelor's degrees peak at Age 50-54.

The more income you earn while you're younger, the earlier you are likely to retire. This takeaway is all about why the incomes for the different education levels peak at the ages they do. Those with higher incomes can typically afford to retire earlier. After they do retire, the average total money income earned within each education level drops, with the size of that drop increasing with age.

The size of that dropoff for retirement is bigger for those who have earned higher incomes during their lifetimes, which is why it shows up as it does when the income trajectories by age is organized by education level.


U.S. Census Bureau. PINC-04. Educational Attainment--People 18 Years Old and Over, by Total Money Earnings, Work Experience, Age, Race, Hispanic Origin, and Sex. Person Income in 2022, Both Sexes, All Races. [Excel spreadsheet]. Accessed 17 December 2023.

Image credit: Image by tuku from Pixabay.

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18 December 2023
An editorial cartoon of a bull escaping from a pen after the gate has been opened by a Federal Reserve official.

The S&P 500 (Index: SPX) rose for the seventh week in a row. The index closed out the week at 4719.19, almost a 2.5% increase over where it closed the previous week.

Almost all of that upward movement came on Wednesday, 13 December 2023 after 2:00 PM, when the Federal Reserve first announced it would hold the Federal Funds Rate steady in a target range of 5.25 to 5.50%, then signaled in the following press conference by Federal Reserve Chair Jerome Powell that the U.S. central bank would pivot to cut interest rates in 2024. The change effectively reverses the expectation the Fed would continue following a more hawkish policy that had been voiced by Powell as recently as 1 December 2023.

After the bulls were let loose on Wednesday, the S&P drifted slightly higher through the rest of the week as Fed officials sought to walk back some of the change in expectations for the course of how interest rates would change during 2024 they had unleashed.

These changes are captured in the latest update of the alternative futures chart. We've also added a new redzone forecast range to account for the echoes of past volatility that arises from the dividend futures-based model's use of historic stock prices as the base reference points from which it projects the potential trajecgtories of the S&P 500 into the future.

Alternative Futures - S&P 500 - 2023Q4 - Standard Model (m=+1.5 from 9 March 2023) - Snapshot on 15 Dec 2023

This new redzone forecast range assumes investors will shift their forward-looking focus from 2024-Q4, where we established it was in the previous edition of the S&P 500 chaos series, back toward 2024-Q1, which coincides with the expected timing of when investors anticipate the Fed will start cutting interest rates.

That change in the forward time horizon of investors wasn't the only expectation that changed during the past two weeks. The outlook for dividends has also substantially improved during the past month, as shown in the next chart.

Animation: Past and Projected Quarterly Dividends Futures for the S&P 500, 2021-Q4 through 2024-Q4, Snapshot on 15 December 2023

Nearly all of the change in the outlook for dividends in 2024 took place during the past two weeks.

Other things also happened during the trading week ending on Friday, 15 December 2023. Here is our summary of the week's market moving headlines.

Monday, 11 December 2023
Tuesday, 12 December 2023
Wednesday, 13 December 2023
Thursday, 14 December 2023
Friday, 15 December 2023

The CME Group's FedWatch Tool projects the Fed will hold the Federal Funds Rate steady in a target range of 5.25-5.50% until 20 March 2023 (2024-Q1), six weeks earlier than expected a week ago, when the Fed is expected to start a series of quarter point rate cuts at six-to-twelve-week intervals through the end of 2024.

The Atlanta Fed's GDPNow tool's estimate of real GDP growth for the current quarter of 2023-Q4 rose to an annualized growth rate of 2.6% after having held steady at a +1.2% growth rate during the preceding two weeks. The Atlanta Fed's nowcast increased thanks to reports of higher personal and government spending figures along with higher business investments in the past week.

This article is the last for the S&P 500 chaos series in 2023. We'll be back with a new edition covering the last weeks of December 2023 sometime early in 2024!

Image credit: Microsoft Bing Image Creator. Prompt: "An editorial cartoon of a bull escaping from a pen after the gate has been opened by a Federal Reserve official."

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15 December 2023

2023 has been a year of strange maps. For example, San Francisco has its infamous "poop" map, which tracks the locations where human feces have been reported on the streets of the city that came up during a recent political debate.

But other cities have their own maps of shame, which brings us to Datawrapper's Ivan Lokhov's Rats of New York map, which visualizes where New York City transit riders have reported rat sightings at subway stations in the United States' largest city.

Lokhov produced the map as part of the "The Unofficial NYC Subway Rat Census". In any case, we're looking forward to seeing how Martin Scorsese approaches the subject when he makes the definitive, and no doubt critically-acclaimed, Rats of New York movie.

A 'very big rat problem' sign in New York City photo by Robinson Greig on Unsplash - https://unsplash.com/photos/white-and-black-quote-on-brown-wooden-fence-BL6i5uYZuVQ

Image credit: Photo by Robinson Greig on Unsplash.


14 December 2023
Power Plant (Tianjin, China) photo by Shubert Ciencia on Wikimedia Commons

Over the past two months, China's economy has shown signs of greater economic growth. That change coincides with an increase in the rate at which carbon dioxide emissions are accumulating in the Earth's atmosphere. The increase reverses what had been a modest decline that coincided with sluggish economic growth in China.

When we talk about carbon dioxide as an economic indicator, we focus on China because that nation is, by far and away, the world's largest producer of carbon dioxide emissions. Given China's outsize role in global supply chains, these emissions provide can work as an indicator of global economic health in addition to China's.

We can illustrate China's role in producing carbon dioxide emissions by comparing its consumption of coal with the rest of the world. Over two-thirds of China's emissions come from from coal-fired power generation plants, so there's a very direct connection. The following chart summarizes the International Energy Agency's estimates of China, India and the rest of the world's consumption of coal, which is primarily used to generate electricity to support economic activity, for the years from 2020 through 2023.

Global Coal Consumption, 2020-2023 - IEA July 2023 estimates

In 2023, the IEA estimates China's consumption of coal accounted for nearly 56% of the total amount of coal consumed in the world. India, whose consumption of coal ranks second in the world, accounted for a little over 14% of the world's consumption. The entire rest of the world's coal consumption represents a little under 30% of the total.

Examining the chart more closely, both China and India have increased their consumption of coal since 2020, while the rest of the world has seen its consumption of coal decrease over this period (primarily in the U.S. and in the European Union). The increases in China and India however more than offset that reduction, with the result that the world's total coal consumption has increased in each year since 2020.

Unsurprisingly, China is responsible for most of that increase:

Coal power makes up about 70% of emissions in China, which has committed to being carbon neutral by 2060. After 2025, it is unclear whether China will approve new coal plants.

In the third quarter of this year, however, China permitted more new coal plants than in all of 2021, according to Greenpeace, even as most countries have stopped building new coal-fired power and are phasing out plants.

"With energy security becoming a code word for coal in recent years, there is a clear-cut path to receive approval on building more new coal while you still can," Greenpeace project leader Gao Yuhe said.

Xu Mingjun, general manager of Shenhua Energy, China's largest coal company, told investors in September that the company was taking advantage of this window of opportunity to bolster coal development.

More than 95% of the global coal plant capacity that began construction this year was in China, according to U.S. think tank Global Energy Monitor (GEM).

The expansion of China's coal-fired power generation capacity contributes to both economic growth within China, to the extent it does not substitute for other less reliable sources of electricity, and the nation's emissions of carbon dioxide. And by extension, the continuing accumulation of carbon dioxide in the Earth's air, as indicated in the next chart.

Global Coal Consumption, 2020-2023 - IEA July 2023 estimates

All indications point to China continuing to expand its coal-based power generation capacity through the end of 2025. The big question for these next two years is whether the global economy can support it?


International Energy Agency. Global coal consumption, 2020-2023. [Online data]. 28 July 2022.

International Energy Agency. Global coal consumption, 2021-2023. [Online data]. 27 July 2023.

National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [Online Data]. Updated 5 December 2023. Accessed 8 December 2023.

Image credit: Flickr/Wikimedia Commons. Power Plant (Tianjin, China) by Shubert Ciencia. Creative Commons. CC BY 2.0 DEED Attribution 2.0 Generic.

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About Political Calculations

Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

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