Seventy-Three, Yes. Higally-Piggle, No. What Is Math Anyway?

What does it mean that seventy-three is a genuine number, but higally-piggle isn’t? Smithsonian Magazine delves into the old question: What is math? The answer is provided below. (See the original article for all the links.)

It all started with an innocuous TikTok video posted by a high school student named Gracie Cunningham. Applying make-up while speaking into the camera, the teenager questioned whether math is “real.” She added: “I know it’s real, because we all learn it in school… but who came up with this concept?” Pythagoras, she muses, “didn’t even have plumbing—and he was like, ‘Let me worry about y = mx + b’”—referring to the equation describing a straight line on a two-dimensional plane. She wondered where it all came from. “I get addition,” she said, “but how would you come up with the concept of algebra? What would you need it for?”

Someone re-posted the video to Twitter, where it soon went viral. Many of the comments were unkind: One person said it was the “dumbest video” they had ever seen; others suggested it was indicative of a failed education system. Others, meanwhile, came to Cunningham’s defense, saying that her questions were actually rather profound.

Mathematicians from Cornell and from the University of Wisconsin weighed in, as did philosopher Philip Goff of Durham University in the U.K. Mathematician Eugenia Cheng . . . wrote a two-page reply and said Cunningham had raised profound questions about the nature of mathematics “in a very deeply probing way.”

Cunningham had unwittingly re-ignited a very ancient and unresolved debate in the philosophy of science. What, exactly, is math? Is it invented, or discovered? And are the things that mathematicians work with—numbers, algebraic equations, geometry, theorems and so on—real?

Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered—a position known as Platonism. It takes its name from the ancient Greek thinker Plato, who imagined that mathematical truths inhabit a world of their own—not a physical world, but rather a non-physical realm of unchanging perfection; a realm that exists outside of space and time. Roger Penrose, the renowned British mathematical physicist, is a staunch Platonist. In The Emperor’s New Mind, he wrote that there appears “to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some external truth—a truth which has a reality of its own…”

Many mathematicians seem to support this view. The things they’ve discovered over the centuries—that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever—seem to be eternal truths, independent of the minds that found them. If we were to one day encounter intelligent aliens from another galaxy, they would not share our language or culture, but, the Platonist would argue, they might very well have made these same mathematical discoveries.

“I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science . . . . “Working mathematicians overwhelmingly are Platonists. They don’t always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”

Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago. . . .

Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have?

. . . The Platonist must confront further challenges: If mathematical objects exist outside of space and time, how is it that we can know anything about them? Brown doesn’t have the answer, but he suggests that we grasp the truth of mathematical statements “with the mind’s eye”—in a similar fashion, perhaps, to the way that scientists like Galileo and Einstein intuited physical truths via “thought experiments,” before actual experiments could settle the matter.

Consider a famous thought experiment dreamed up by Galileo, to determine whether a heavy object falls faster than a lighter one. Just by thinking about it, Galileo was able to deduce that heavy and light objects must fall at the same rate. The trick was to imagine the two objects tethered together: Does the heavy one tug on the lighter one, to make the lighter one fall faster? Or does the lighter one act as a “brake” to slow the heavier one? The only solution that makes sense, Galileo reasoned, is that objects fall at the same rate regardless of their weight. In a similar fashion, mathematicians can prove that the angles of a triangle add up to 180 degrees, or that there is no largest prime number—and they don’t need physical triangles or pebbles for counting to make the case, just a nimble brain.

Meanwhile, notes Brown, we shouldn’t be too shocked by the idea of abstractions, because we’re used to using them in other areas of inquiry. “I’m quite convinced there are abstract entities, and they are just not physical,” says Brown. “And I think you need abstract entities in order to make sense of a ton of stuff—not only mathematics, but linguistics, ethics . . .”.

Platonism has various alternatives. One popular view is that mathematics is merely a set of rules, built up from a set of initial assumptions—what mathematicians call axioms. Once the axioms are in place, a vast array of logical deductions follow, though many of these can be fiendishly difficult to find. In this view, mathematics seems much more like an invention than a discovery; at the very least, it seems like a much more human-centric endeavor. . . .

But this view has its own problems. If mathematics is just something we dream up from within our own heads, why should it “fit” so well with what we observe in nature? Why should a chain reaction in nuclear physics, or population growth in biology, follow an exponential curve? Why are the orbits of the planets shaped like ellipses? Why does the Fibonacci sequence turn up in the patterns seen in sunflowers, snails, hurricanes, and spiral galaxies? Why, in a nutshell, has mathematics proven so staggeringly useful in describing the physical world? Theoretical physicist Eugene Wigner highlighted this issue in a famous 1960 essay titled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Wigner concluded that the usefulness of mathematics in tackling problems in physics “is a wonderful gift which we neither understand nor deserve.”

However, a number of modern thinkers believe they have an answer to Wigner’s dilemma. Although mathematics can be seen as a series of deductions that stem from a small set of axioms, those axioms were not chosen on a whim, they argue. Rather, they were chosen for the very reason that they do seem to have something to do with the physical world. As Pigliucci puts it: “The best answer that I can provide [to Wigner’s question] is that this ‘unreasonable effectiveness’ is actually very reasonable, because mathematics is in fact tethered to the real world, and has been, from the beginning.”

Carlo Rovelli, a theoretical physicist at Aix-Marseille University in France, points to the example of Euclidean geometry—the geometry of flat space that many of us learned in high school. . . . A Platonist might argue that the findings of Euclidean geometry “feel” universal—but they are no such thing, Rovelli says. “It’s only because we happen to live in a place that happens to be strangely flat that we came up with this idea of Euclidean geometry as a ‘natural thing’ that everyone should do,” he says. “. . . Remember ‘geometry’ means ‘measurement of the earth’, and the earth is round. We would have developed spherical geometry instead.”

Rovelli goes further, calling into question the universality of the natural numbers: 1, 2, 3, 4… To most of us, and certainly to a Platonist, the natural numbers seem, well, natural. Were we to meet those intelligent aliens, they would know exactly what we meant when we said that 2 + 2 = 4 (once the statement was translated into their language). Not so fast, says Rovelli. Counting “only exists where you have stones, trees, people—individual, countable things,” he says. “Why should that be any more fundamental than, say, the mathematics of fluids?” If intelligent creatures were found living within, say, the clouds of Jupiter’s atmosphere, they might have no intuition at all for counting, or for the natural numbers, Rovelli says. Presumably we could teach them about natural numbers—just like we could teach them the rules of chess—but if Rovelli is right, it suggests this branch of mathematics is not as universal as the Platonists imagine.

Like Pigliucci, Rovelli believes that math “works” because we crafted it for its usefulness. “It’s like asking why a hammer works so well for hitting nails,” he says. “It’s because we made it for that purpose.”

In fact, says Rovelli, Wigner’s claim that mathematics is spectacularly useful for doing science doesn’t hold up to scrutiny. He argues that many discoveries made by mathematicians are of hardly any relevance to scientists. “There is a huge amount of mathematics which is extremely beautiful to mathematicians, but completely useless for science,” he says. “And there are a lot of scientific problems—like turbulence, for example—that everyone would like to find some useful mathematics for, but we haven’t found it.”

Mary Leng, a philosopher at the University of York, in the U.K., holds a related view. She describes herself as a “fictionalist” – she sees mathematical objects as useful fictions, akin to the characters in a story or a novel. “In a sense, they’re creatures of our creation, like Sherlock Holmes is.”

But [Leng says] there’s a key difference between the work of a mathematician and the work of a novelist: Mathematics has its roots in notions like geometry and measurement, which are very much tied to the physical world. True, some of the things that today’s mathematicians discover are esoteric in the extreme, but in the end, math and science are closely allied pursuits . . . “Because [math] is invented as a tool to help with the sciences, it’s less of a surprise that it is, in fact, useful in the sciences.”

Given that these questions about the nature of mathematics have been the subject of often heated debate for some 2,300 years, it’s unlikely they’ll go away anytime soon.


Nope, anybody who reads this post (or the whole underlying article) has to accept that math depends on axioms or rules. They are invented, not out of the blue, but because they’re plausible and useful. Once you settle on the axioms or rules, discoveries can follow. Therefore, Platonism is wrong. Its competition, which is usually called “nominalism”, is right. I’m glad that’s finally settled.

On a related note, the National Public Radio site has a short article on time travel. The article cites research in physics that purports to show that paradox-free time travel is possible:

Researchers ran the numbers and determined that even if you made a change in the past, the timeline would essentially self-correct, ensuring that whatever happened to send you back in time would still happen. . . . In other words, a time traveler could make changes, but the original outcome would still find a way to happen — maybe not the same way it happened in the first timeline but close enough so that the time traveler would still exist and would still be motivated to go back in time. [According to one of the authors], “No matter what you did, the salient events would just recalibrate around you.”

I’m not qualified to judge the technical merits of this research, but I doubt it shows that paradox-free time travel is guaranteed in every case. If you went back in time and murdered your grandfather before he met your grandmother, and your grandfather didn’t have an identical twin, I’m pretty damn you’re grandmother would have an insurmountable problem generating your precise DNA, whether or not “the numbers” say otherwise.

On yet another mathematical topic, America’s Electoral College is authorized to determine that 63 million counts more than 66 million. That’s why we all need to vote this year.

Let the Pendulum Swing

Two social scientists predicted that America was facing the Turbulent Twenties, based on their study of historical patterns. History shows how to calm things down and improve people’s lives. Here’s most of their article from Noema magazine: 

Almost three decades ago, one of us, Jack Goldstone, published a simple model to determine a country’s vulnerability to political crisis. The model was based on how population changes [affected] state, elite and popular behavior. Goldstone argued that, according to this Demographic-Structural Theory, in the 21st century, America was likely to get a populist, America-first leader who would sow a whirlwind of conflict.

Then ten years ago, the other of us, Peter Turchin, applied Goldstone’s model to U.S. history, using current data. What emerged was alarming: The U.S. was heading toward the highest level of vulnerability to political crisis seen in this country in over a hundred years. Even before Txxxx was elected, Turchin published his prediction that the U.S. was headed for the “Turbulent Twenties,” forecasting a period of growing instability in the United States and western Europe. . . .

Our model is based on the fact that across history, what creates the risk of political instability is the behavior of elites, who all too often react to long-term increases in population by committing three cardinal sins.

First, faced with a surge of labor that dampens growth in wages and productivity, elites seek to take a larger portion of economic gains for themselves, driving up inequality.

Second, facing greater competition for elite wealth and status, they tighten up the path to mobility to favor themselves and their progeny. For example, in an increasingly meritocratic society, elites could keep places at top universities limited and raise the entry requirements and costs in ways that favor the children of those who had already succeeded.

Third, anxious to hold on to their rising fortunes, they do all they can to resist taxation of their wealth and profits, even if that means starving the government of needed revenues, leading to decaying infrastructure, declining public services and fast-rising government debts.

Such selfish elites lead the way to revolutions. They create simmering conditions of greater inequality and declining effectiveness of, and respect for, government. But their actions alone are not sufficient. Urbanization and greater education are needed to create concentrations of aware and organized groups in the populace who can mobilize and act for change.

Top leadership matters. Leaders who aim to be inclusive and solve national problems can manage conflicts and defer a crisis. However, leaders who seek to benefit from and fan political divisions bring the final crisis closer. Typically, tensions build between elites who back a leader seeking to preserve their privileges and reforming elites who seek to rally popular support for major changes to bring a more open and inclusive social order. Each side works to paint the other as a fatal threat to society, creating such deep polarization that little of value can be accomplished, and problems grow worse until a crisis comes along that explodes the fragile social order.

These were the conditions that prevailed in the lead-up to the great upheavals in political history, from the French Revolution in the eighteenth century, to the revolutions of 1848 and the U.S. Civil War in the nineteenth century, the Russian and Chinese revolutions of the twentieth century and the many “color revolutions” that opened the twenty-first century. So, it is eye-opening that the data show very similar conditions now building up in the United States.

In applying our model to the U.S., we tracked a number of indicators of popular well-being, inequality and political polarization, all the way from 1800 to the present. These included the ratio of median workers’ wages to GDP per capita, life expectancy, the number of new millionaires and their influence on politics, the degree of strict party-line voting in Congress, and the incidence of deadly riots, terrorism and political assassinations. We found that all of these indicators pointed to two broad cycles in U.S. history.

In the decades following independence, despite growing party competition, elites in office often compromised and voted together, and rising national prosperity was broadly shared. But that wave of positive conditions peaked around 1820; from there, political polarization and economic inequality rose sharply in the years leading up to the Civil War. The crisis indicators peaked in the 1860s but . . . they remained high until 1920 (the years of Reconstruction, Jim Crow, the Gilded Age, violent labor unrest, and the anarchists).

Then, the tide shifted, and a second wave of greater unity and prosperity began to gather strength. Contrary to expectations, World War I and the Great Depression did not produce a rise in political instability indicators. Instead, the country pulled together. The reforms introduced during the Progressive Era and clinched in the New Deal reduced inequality and strengthened the economic share of workers; during and after World War II, the country agreed on new tax policies and increased spending on roads and schools.

The 1950s were a golden age of worker progress and party cooperation; even in the 1960s and 1970s, despite serious racial conflicts, the country’s leaders were able to agree on remarkably far-reaching reforms to improve civil rights and environmental protection. However, the 1960s were a high point in our indicators of political resilience; in the 1970s and 1980s, things began to turn, and by the 1990s, a new wave of rising inequality and political divisions was well underway, exemplified by Newt Gingrich’s policies as speaker of the House. In the next two decades, the crisis indicators rose just as sharply as they had in the decades before the Civil War. It was not just that by the late 2010s, overall inequality was rising to the levels not seen since the Gilded Age; median wages in relation to GDP per capita also were falling to historically low levels.

Writing in the journal Nature in 2010, we pointed out that such trends were a reliable indicator of looming political instability and that they “look set to peak in the years around 2020.” In Ages of Discord, published early in 2016, we showed that America’s “political stress indicator” had turned up sharply in recent years and was on track to send us into the “Turbulent Twenties.”

The Political Stress Index (PSI) combines the three crisis indicators in the Goldstone-Turchin theory: declining living standards, increasing intra-elite competition/conflict and a weakening state. Growing PSI indicates increased likelihood of political violence. The Well-Being Index indicates greater equality, greater elite consensus and a more legitimate state.

This year, the COVID-19 pandemic and the death of George Floyd at the hands of the Minneapolis police have delivered a double-barreled crisis to U.S. politics. America has reacted with a nationwide, months-long series of urban protests. But this explosion of protest is not just the result of this year’s events. The U.S. has weathered epidemics and racial protests before and produced legislation that made the country better as a result.

What is different this decade is that these events are occurring at a time of extreme political polarization, after decades of falling worker’s share in national income, and with entrenched elite opposition to increased spending on public services. These trends have crippled the U.S. government’s ability to mount an effective response to the pandemic, hampered our ability to deliver an inclusive economic relief policy and exacerbated the tensions over racial injustice that boiled over in response to the video of Floyd’s death.

Is the U.S. likely headed for still greater protests and violence? In a word, yes. Inequality and polarization have not been this high since the nineteenth century. . . .

American exceptionalism was founded on cooperation — between the rich and the poor, between the governors and the governed. From the birth of the nation, the unity across economic classes and different regions was a marvel for European observers, such as St. John de Crèvecoeur and Alexis de Tocqueville. This cooperative spirit unraveled in the mid-nineteenth century, leading to the first “Age of Discord” in American history. It was reforged during the New Deal as an unwritten but very real social contract between government, business and workers, leading to another age of prosperity and cooperation in postwar America. But since the 1970s, that contract has unraveled, in favor of a contract between government and business that has underfunded public services but generously rewarded capital gains and corporate profits.

While this new neoliberal [i.e., conservaive, pro-corporate] contract has, in some periods, produced economic growth and gains in employment, growth has generally been slower and far more unequal than it was in the first three postwar decades. In the last twenty years, real median household income has stagnated, while the loss of high-paying blue-collar jobs to technology and globalization has meant a decline in real wages for many workers, especially less educated men.

As a result, American politics has fallen into a pattern that is characteristic of many developing countries, where one portion of the elite seeks to win support from the working classes not by sharing the wealth or by expanding public services and making sacrifices to increase the common good, but by persuading the working classes that they are beset by enemies who hate them (liberal elites, minorities, illegal immigrants) and want to take away what little they have. This pattern builds polarization and distrust and is strongly associated with civil conflict, violence and democratic decline.

At the same time, many liberal elites neglected or failed to remedy such problems as opiate addiction, declining social mobility, homelessness, urban decay, the collapse of unions and declining real wages, instead promising that globalization, environmental regulations and advocacy for neglected minorities would bring sufficient benefits. They thus contributed to growing distrust of government and “experts,” who were increasingly seen as corrupt or useless, thus perpetuating a cycle of deepening government dysfunction.

How can Americans end our current Age of Discord? What we need is a new social contract that will enable us to get past extreme polarization to find consensus, tip the shares of economic growth back toward workers and improve government funding for public health, education and infrastructure.

This sounds like commonplace leftist discourse and a weak response to such extreme conditions. Let us therefore drive home both the urgency of the crisis and the possibility of changing course by looking at two historical cases where countries teetered on the brink of calamity but managed to pull back and forge a new path to progress.

The United Kingdom in the 1820s was coming apart. After defeating Napoleon, the Duke of Wellington became the leader of an elite group that sought to maintain the dominance of the traditional landlord elites. As prime minister and then leader of the House of Lords, Wellington sought to ignore, rather than adjust to, the new realities of the booming cities of Birmingham, Manchester and other burgeoning cities of the fast-growing industrial economy. Meanwhile, the workers of these cities demanded political reforms that would give them a voice in Parliament.

These workers particularly objected to the infamous “Corn Laws,” which, by placing tariffs on imports of foreign grain, kept the costs of food (and hence the profits of English landlords) high and the real wages of workers low. Following a major workers’ protest in Manchester in 1819, which was dispersed with a cavalry charge into the crowd that left an estimated 10 to 20 dead and hundreds injured (the so-called Peterloo massacre), politics in Britain became even more sharply polarized. This became one of the first incidents widely reported by journalists, and indignation spread across the country.

Nonetheless, Wellington not only refused any legal changes, he sought to clamp down on the agitation for voting reforms. New laws were passed to expand police power and block public assemblies; newspapers were closed; protestors and journalists were jailed. Still, popular agitation continued, and there was even an attempt to assassinate several cabinet ministers. The rapid growth of the industrial workforce and the new manufacturing economy produced similar pressures for radical political change across Europe, leading to waves of revolutions in 1830 and 1848. Many in Britain expected a similar outcome, yet the country avoided revolution throughout these years.

The solution was for leaders to accept the Reform campaign, which sought voting reforms that would reduce the power of the landlords and support the new industrial working class. After the growing confrontations of the 1820s, in 1830, Wellington’s Tories lost control of Parliament, and a Whig leader who supported the Reform campaign, Lord Grey, became prime minister. Grey’s initial efforts to pass a Reform bill were frustrated, and Grey threatened to have the King create enough additional Whig peers to force the bill through. The Tories then relented, and in 1832, Parliament passed the first Reform bill, which expanded the franchise, undermined the clientage of the landed elite and gave representation to the residents of the factory cities. Additional Reform bills followed, allowing Britain, despite continued large-scale workers’ movements, to avoid the revolutions that wracked the continent and emerge as the leading economy of Europe.

A century later, it was the United States that was coming apart. In the early 1930s, democracy was retreating in Europe while the U.S. economy had fallen into a depression, with a dust bowl in the Great Plains and millions of industrial workers losing their jobs. Prohibition had heightened cultural conflict and crime, while nativist demagogues (such as radio personality Father Coughlin and Louisiana Governor Huey Long) stirred fear.

Then in 1932, Americans voted for change. Franklin Delano Roosevelt replaced Herbert Hoover as president and undertook a sweeping reform program to restore work and shared prosperity. Labor organizations were strengthened, and public works programs provided jobs for construction workers, craftsmen and artists. The resulting buildings were decorated with monuments to the dignity of labor. It took years to transition to an economy based on mechanization, skilled labor, strong unions and public education, but the result was a country strong enough to fight the rising tide of global fascism and emerge as the world’s leading economy.

The formula in both cases was clear and simple. First, the leader who was trying to preserve the past social order despite economic change and growing violence was replaced by a new leader who was willing to undertake much-needed reforms. Second, while the new leader leveraged his support to force opponents to give in to the necessary changes, there was no radical revolution; violence was eschewed and reforms were carried out within the existing institutional framework.

Third, the reforms were pragmatic. Various solutions were tried, and the new leaders sought to build broad support for reforms, recognizing that national strength depended on forging majority support for change, rather than forcing through measures that would provide narrow factional or ideologically-driven victories. The bottom line in both cases was that adapting to new social and technological realities required having the wealthy endure some sacrifices while the opportunities and fortunes of ordinary working people were supported and strengthened; the result was to raise each nation to unprecedented wealth and power.

To be sure, the path back to a strong, united and inclusive America will not be easy or short. But a clear pathway does exist, involving a shift of leadership, a focus on compromise and responding to the world as it is, rather than trying desperately to hang on to or restore a bygone era.

This has already been, and will continue to be, a violent year in America. . . . It will take heroic efforts to rebuild the political center, to join businesses and workers in partnership and consensus, and to restore fairness in both taxation and public spending. Only if all sides can again recover a stake in our government, no matter which party controls it, can we avoid sliding into a crisis that will undermine our Constitution and pit Americans against each other in a way we have not seen for generations.


Yes, if more of us vote this year, the pendulum can swing and we can set this country on a progressive path.

At Least We Know Death Is a Certainty

Despite being on a news vacation, I heard that The New York Times got copies of some of Txxxx’s tax returns. I read the Times article, but will let a few other Times readers comment.

Ralph from Nebraska:

This stunning report takes some time to read and digest and we will all find numbers that amaze and annoy us. I was once a bankruptcy lawyer and I often had to explain this scenario to clients: If you borrow money and don’t repay the money the IRS sees the money that you didn’t repay as income on which you need to pay taxes. Here’s the number that jumped screaming off of my I Pad: $287,000,000. During the last ten years our President has stiffed his creditors to the tune of $287 million. 

STSI from Chicago:

There is something rotten in our tax system that allows someone like Dxxxx Txxxx to spend years litigating the IRS so that he can pay little or no taxes owed. Dxxxx Txxxx is the poster child for how the US tax code has been exploited and scammed by individuals who use taxpayer money to fund their legal battles with the IRS. Congress needs to address this issue and level the playing field so that every American pays his or her fair share of taxes due.

Ron S. from Los Angeles:

I run two small, moderately profitable businesses. I deduct legitimate business expenses, but I also make monthly estimated tax payments to the IRS, knowing full well if I claim losses year after year I will be audited. That Dxxxx Txxxx cheats the system is not only no surprise, it also shows how the U.S. tax system is set up one way for the rich and another way for everybody else.

B. Reed from Washington DC:

Txxxx is a crook who deserves to be prosecuted. But I wish this was an anomaly because it isn’t. . . . How people can see this stuff and not be radicalized and demand dramatic change is beyond me. . . . 

It’s beyond me too.

By the way, we have an election 36 days from now, in which Dxxxx Txxxx and lots of his Republican enablers are candidates for high office.

Distraction for a Saturday Afternoon (or Sunday)

Rolling Stone, still in business after 52 years, took a poll of 300 people in the music business to create a new “500 Greatest Albums” list. They polled 271 people in 2003 to do the same.

I’ll offer no opinion, except to note that hundreds of people supposedly submitted lists of their Top 50 albums, from which the magazine generated the Top 500. How did Rolling Stone find 300 people willing to make that kind of effort? Did they let their kids or dogs weigh in?

Anyway, it’s interesting that albums by Marvin Gaye and the Beach Boys were the only ones to stay in the Top 10 between 2003 to 2020. The Beach Boys stayed at #2 and Marvin Gaye rose from #6 to #1.

Everything else in 2003’s Top 10 went down, although none of them fell out of the Top 40. 

In the 2020 list, Abbey Road jumped ahead of four Beatles albums from the 2003 list. Three albums on the 2020 list didn’t even make the Top 50 in 2003. Lauryn Hill’s 1998 album went from #312 to #10. That’s quite a jump. (And Rumours, Fleetwood Mac’s 1977 mega-seller, is more popular now than it was in 2003? That’s just weird.)

2003 2020 2020 2003
1 The Beatles, Sgt. Pepper 24 1 Marvin Gaye, What’s Going On 6
2 The Beach Boys, Pet Sounds 2 2 The Beach Boys, Pet Sounds 2
3 The Beatles, Revolver 11 3 Joni Mitchell, Blue 30
4 Bob Dylan, Highway 61 Revisited 18 4 Stevie Wonder, Songs in the Key of Life 57
5 The Beatles, Rubber Soul 35 5 The Beatles, Abbey Road 14
6 Marvin Gaye, What’s Going On 1 6 Nirvana, Nevermind 17
7 The Rolling Stones, Exile on Main St. 14 7 Fleetwood Mac, Rumours 26
8 The Clash, London Calling 16 8 Prince and the Revolution, Purple Rain 72
9 Bob Dylan, Blonde on Blonde 38 9 Bob Dylan, Blood on the Tracks 16
10 The Beatles, The White Album 29 10 Lauryn Hill, The Miseducation of Lauryn Hill 312

Someone kindly made a YouTube playlist for Marvin Gaye’s 1971 album What’s Going On. The title track sure fits 2020:

Making Pet Sounds playlists is a cottage industry. I’d forgotten that I made one comprising stereo versions of the original 13 tracks three years ago. It’s been viewed 400,000 times.

On the other hand, the one I did called “If Pet Sounds Was, God Forbid, an EP”, which only includes four tracks, has been viewed 7 times. That sounds right. 

PS: If enough of us vote for our favorite candidates this year, not our favorite albums, we can damage the Republican Party for decades. Wouldn’t that be wonderful, not just nice?

Why Indeed?

Another in what has turned into a series of selections from Charles Lindblom’s Politics and Markets: The World’s Political-Economic Systems (1976):

A set of unifying beliefs that assert the virtues of the fundamentals of social organization will be found in any stable society. . . . In the market-oriented polyarchies [where there is “rule by the many”], the beliefs show a distinctive character. They are greatly influenced by inequality of wealth and by the existence of a dual set of leaders who enjoy a privileged position in politico-economic organization [that is, government leaders and business leaders]. Many of the unifying beliefs of the society are those beliefs communicated by a favored class to all other classes, with enormous advantage in a grossly unequal competition of ideas.

. . . Deep-seated beliefs and attitudes that persist over time, some people will say, have to be understood as the product of random “spontaneous” social forces. What does that mean? It cannot mean that they arise without cause. Perhaps, then, it means that they arise without deliberate intent. No person or group or government plans them. They are unintended consequences of mutual influences of persons on each other.

Granted. Yet we know that, although people do indeed influence each other’s attitudes in countless unintended ways, they also intend a great deal of control over attitudes, beliefs and volitions. Parents and teachers, for example, teach children — explicitly and through their own behavior as example — the virtues of obedience to authority. In most societies, they also teach children that improvement in their position in life will and ought to depend on their own personal qualities (rather than on an alteration in social structure).

Moreover, many of the unintended influences of people on each other reinforce the intended indoctrinations, as when someone who repeatedly challenges authority makes his friends so uncomfortable that they gradually drop [them]. Much unintended mutual influence among persons is therefore patterned control rather than random, because it reflects a pattern in intended influence, which is itself not random.

Why the particular pattern of intentions that we perceive? Why the emphasis on such a theme as obedience to authority (rather than a skeptical, only conditional, and selective acceptance of it)? Why deference toward the wealthy (that does not even discriminate between earned and inherited wealth)? Why individual responsibility for improvement in the quality of life (rather than social cooperation to improve polity and economy)? Why genialized privilege for the wealthy and powerful (rather than offsetting constraints and responsibilities to balance their advantages in wealth or power)? Why so profound a respect for property as to lead many people to think it immoral to steal a loaf of bread to save one’s family from hunger?

These are not random themes. They confer advantages on persons in the favored social class. How do they come to be “spontaneous”? How do they come to be near universally taught? They have been endlessly communicated to the population — explicitly and through behavior as example — through the church, the media, the schools, the family and the pronouncements of business and government leaders. Since they have been in this way communicated for centuries, they have passed into folklore and common morality, with the result that almost everyone joins in the intended and unintended or “spontaneous” processes by which they are passed on to the young and reinforced for the old [230-231].


Maybe there’s more skepticism about our common beliefs than there was in 1976. If so, such skepticism hasn’t translated into very many progressive government policies. In the US, at least, with a few exceptions, it’s been the reverse. But as skepticism justifiably grows, will our politics lean toward the alternatives Lindblom put in parentheses? I sure hope so.

(A giant blue wave 40 days from now would help.)