Where's Today's Beethoven?

This piece kicks off a short series inspired by this question:

Say that Beethoven was the greatest musician of all time (at least in some particular significant sense - see below for some caveats). Why has there been no one better in the last ~200 years - despite a vastly larger world population, highly democratized technology for writing and producing music, and a higher share of the population with education, basic nutrition, and other preconditions for becoming a great musician? In brief, where's today's Beethoven?

A number of answers might spring to mind. For example, perhaps Beethoven's music isn't greater than Beyonce's is, and it just has an unearned reputation for greatness among critics with various biases and eccentricities. (I personally lean toward thinking this is part of the picture, though I think it's complicated and depends on what "great" means.¹)

But I think the puzzle gets more puzzling when one asks a number of related questions:

• Where's today's Darwin (for life sciences), Ramanujan (for mathematics), Shakespeare (for literature), etc.?
• Fifth-century Athens included three of the most renowned playwrights of all time (Aeschylus, Sophocles and Euripides); two of the most renowned philosophers (Socrates and Plato); and a number of other historically important figures, despite having a population of a few hundred thousand people and an even smaller population of people who could read and write. What would the world look like if we could figure out what happened there, and replicate it across the many cities today with equal or larger populations?
• "Over the past century, we’ve vastly increased the time and money invested in science, but in scientists’ own judgment, we’re producing the most important breakthroughs at a near-constant rate. On a per-dollar or per-person basis, this suggests that science is becoming far less efficient." (Source) Can we get that efficiency back?

I'll be giving more systematic, data-based versions of these sorts of points below. The broad theme is that across a variety of areas in both art and science, we see a form of "innovation stagnation": the best-regarded figures are disproportionately from long ago, and our era seems to "punch below its weight" when considering the rise in population, education, etc. Since the patterns look fairly similar for art and science, and both are forms of innovation, I think it's worth thinking about potential common factors.

Below, I will:

• List the three main hypotheses people offer to answer "Where's Today's Beethoven?": the "golden age" hypothesis (people in the past were better at innovation), the "bad taste" hypothesis (Beethoven and others don't deserve their reputations), and the "innovation as mining" hypothesis (ideas naturally get harder to find over time, and we should expect art and science to keep slowing down by default). Importantly, I think each of these has interesting and not-widely-accepted implications of its own.
• Examine systematic data on trends in innovation in a number of domains, bringing together (a) long-run data on both art and science over hundreds of years and more; (b) recent data on technology and more modern art/entertainment genres (film, rock music, TV shows, video games). I think this is the first piece to look at this broad a set of trends of this form.
• Briefly explain why I favor the "innovation as mining" hypothesis as the main explanation for what we're seeing across the board.
• Do some typical "more research needed" whining. Since any of the three hypotheses has important implications, I think "Where's today's Beethoven?" should be a topic of serious discussion and analysis, but I don't think there is a field consistently dedicated to analyzing it (although there are some excellent one-off analyses out there).

Future pieces will elaborate on the plausibility of the "innovation as mining" hypothesis - and its implications. Those pieces are: How artistic ideas could get harder to find, Why it mattrs if ideas get harder to find, "Civilizational decline" stories I buy, Cost disease and civilizational decline (the latter two are not yet published).

Three hypotheses to answer "Where's Today's Beethoven?"

Say we accept - per the data I'll present below - that we are seeing "innovation stagnation": the best-regarded figures are disproportionately from long ago, and our era seems to "punch below its weight" when considering the rise in population, education, etc. What are the possible explanations?

The "golden age" hypothesis

The "golden age" hypothesis says there are one or more "golden ages" from the past that were superior at producing innovation compared to today. Perhaps understanding and restoring what worked about those "golden ages" would lead to an explosion in creativity today.

If true, this would imply that there should be a lot more effort to study past "golden ages" and how they worked, and how we could restore what they did well (without restoring other things about them, such as overall quality of life).

I generally encounter this hypothesis in informal contexts, with a nostalgic vibe - a sort of pining for the boldness and creativity of the past.²

Interestingly, I've never seen a detailed defense of this hypothesis against the two main alternatives ("bad taste" and "innovation as mining," below). Some of the people who have written the most detailed pieces about "innovation stagnation" seem to believe something like the "golden age" hypothesis - but they seem to say so only in interviews and casual discussions, not their main works.³

As I'll discuss below, I don't think the "golden age" hypothesis fits the evidence we have as well as "innovation as mining." But I don't think that's a slam dunk, and the "golden age" hypothesis seems very important if true.

The "bad taste" hypothesis

The "bad taste" hypothesis says that conventional wisdom on what art and science were "great" is consistently screwed up and biased toward the past.

If true, this means that we're collectively deluded about what scientific breakthroughs were most significant, what art deserves its place in our culture, etc.

This hypothesis is often invoked to explain the "art" side of innovation stagnation, but it's a more awkward fit with the "science" side, and I think a lot of people just have trouble swallowing it when considering music like Beethoven's. I do think it's an important part of the picture, but not the whole story.

The "innovation as mining" hypothesis

The "innovation as mining" hypothesis says that ideas naturally get harder to find over time, in both science and art. So we should expect that it takes more and more effort over time to maintain the same rate of innovation.

This hypothesis is commonly advanced to explain the "science and technology" aspect of innovation stagnation. It's a more awkward fit with the "art" side.

That said, my view is that it is ultimately most of the story for both (and my next post will discuss just how I think it works for art). And this is important, because I think it has a number of underappreciated implications:

• We should expect further "innovation stagnation" by default, unless we can keep growing the number of innovators. As discussed here, population growth and artificial intelligence seem like the most likely ways to be able to sustain high rates of innovation over the long run (centuries or more), though other things might help in the shorter run.
• Hence, our prospects for more innovation in both science and art could depend more on things like population growth, artificial intelligence, and intellectual property law (more on this in a future post) than on creative individuals or even culture.
• Finally, this hypothesis implies that a literal duplicate of Beethoven, transplanted to today's society, would be a lot less impressive. My own best guesses at what Beethoven and Shakespeare duplicates would accomplish today might show up in a future short post that will make lots of people mad.

Data on innovation stagnation

Below, I provide a number of charts looking at the "production of critically acclaimed ideas" over time.

I give details of my data sets, and link to my spreadsheets, in this supplement. Key points to make here are:

• In general, I am using data sets based on aggregating opinions from professional critics. (An exception is the technological innovation data from Are Ideas Getting Harder to Find?) This is because I am trying to answer the "Where's today's Beethoven?" question on its own terms: I want data sets that reflect the basic idea of people like Beethoven and Shakespeare being exceptional. This comports with professional critical opinion, but not necessarily with wider popular opinion (or with my opinion!)
• As such, I think the charts I'm showing should be taken as showing trends in production of critically acclaimed ideas, with all of the biases (including Western bias) that implies, rather than as showing trends in production of "objectively good" ideas. In some cases, the creators of the data sets I'm using believe their data shows the latter; but I don't. Even so, I think falling production of critically acclaimed ideas is a type of "innovation stagnation" that deserves to be examined and questioned, while being open to the idea that the explanation ends up being bad taste.
• I generally chart something like "the number of works/discoveries/people that were acclaimed enough to make the list I'm using, smoothed,⁴ by year." As noted below, I've generally found that attempting to weight by just how acclaimed each one is (e.g., counting #1 as much more significant than #100) doesn't change the picture much; to see this, you can check out the spreadsheets linked from my supplement.
• In this section, I'm keeping my interpretive commentary light. I am mostly just showing charts and explaining what you're looking at, not heavily opining on what it all means. I'll do that in the next section.

Science and art+literature+music, 1400-1950

First, here are the number of especially critically acclaimed figures in art, literature, music, philosophy, and science from 1400-1950. (This data set actually runs from 800 BCE until 1950; my supplement shows that the "critical acclaim scores" over this period are dominated by ancient Greece (which I discuss below) and by the 1400-1950 period in particular countries, and I'm charting the latter here.)

Blue = science, red = art + literature + music

And here is a similar chart, but weighted by how acclaimed each figure is (so Beethoven counts for more than Prokofiev or whoever, even though they're both acclaimed enough to make the list):

A couple of initial observations that will be recurring throughout these charts:

First, as mentioned above, it doesn't matter that much whether we weight by level of acclaim (e.g., count Beethoven about 10x as high as Prokofiev, and Prokofiev 10x higher than some others), or just graph the simpler idea of "How many of the top 100-1000 top people were in this period?" (which treats Beethoven and Prokofiev as equivalent). In general, I will be sticking to the latter throughout the remaining charts, though I chart both in my full spreadsheet (they tend to look similar).

Second: so far, there's no sign of innovation stagnation! Maybe the single greatest musician or artist was a long time ago, but when we are more systematic about it, the total quantity of acclaimed music/art has gone up over time, at least up until 1950. The question is whether it's gone up as much as it should have, given increases in population, education, etc.

So next, let's chart critically acclaimed figures per capita, that is, adjusted for the total population in the countries featured:

This still doesn't clearly look like innovation stagnation - maybe you could say there was a "golden age" in art/lit/music from around 1450-1650, with about 50% greater "productivity" than the following centuries, but meh. And science innovation per capita looks to have gone up over time.

I've created two estimates of "effective population growth," based on things like increases in literacy rates, increases in urbanization, decreases in extreme poverty, and increases in the percentage of people with university degrees. My methods are detailed here. (My two estimates mostly lead to similar conclusions, so I'll only be presenting one of them here, though you can see both in my full spreadsheet.)

So here are the total number of acclaimed figures in science and art+lit+music, adjusted for my "effective population" estimate:

(Ignore the weird left part of the blue line - in those early days, there was a low effective population and a low number of significant figures, which sometimes hit 0, which looks weird on this kind of chart.)

Ahh. Finally, we've charted the decline of civilization!

(It doesn't really matter exactly how the effective population estimate is done in this case - as shown above, per-capita "productivity" in art and science was pretty constant over this time, so any adjustment for growing health/nutrition/education/urbanization will show a decline.)

This dataset ends in 1950. Seeing what happened after that is a bit challenging, but here we go.

Technological innovation, 1930-present

Next are charts on technological innovation since the 1930s or so, from the economics paper Are Ideas Getting Harder to Find? These generally look at some measure of productivity, alongside the estimated "number of researchers" (I take this as a similar concept to my "effective population").

First, overall aggregate total factor productivity growth in the US:

It's not 100% clear how to compare the units in this chart vs. the units in previous charts ("number of acclaimed scientists per year" vs. "growth in total factor productivity each year"),⁵ but the basic idea here is that the "effective population" (number of researchers) is skyrocketing while the growth in total factor productivity is constant - implying, like the previous section, that we're still getting plenty of new ideas each year, but that there's "innovation stagnation" when considering the rising effective population.

The paper also looks at progress in a number of specific areas, such as life expectancy and Moore's Law. The trends tend to be similar across the board; here is an example set of charts about agricultural productivity:

There's more discussion and some additional data at this post from New Things Under the Sun.

20th century film, modern (rock) music, TV shows, video games

What about art+literature+music after 1950?

This one is tricky because of the way that entertainment has "changed shape" throughout the century.

For example:

• My understanding is that visual art (paintings, sculptures, etc.) used to be the obvious thing for a "visual innovator" to do, but now it's an increasingly niche kind of work.
• The closest thing I've found to recent "data on critically acclaimed visual art" is this paper on the "most important works of art of the 20th century," which only lists 8 works of art (6 of them between 1907-1919 - see Table 1).
• 20th-century visual innovators may instead have worked in film, or perhaps TV, or video games, or something else.
• A lot of the demand that "literature" used to meet is also now met by film, TV, and arguably video games.

Music is tough to assess for a similar reason. Mainstream music in the 20th century has mostly not been orchestral; instead it's been the sort of music covered on this list. Some people would call this "rock" or "pop," but others would insist that many of the albums on that list are neither; in any case, there's no credible ranking I've been able to find that considers both Beethoven and Kanye West.

So to take a look at more recent "art," I've created my own data sets based on prominent rankings of top films, music albums, TV shows, and video games (details of my sources are in the supplement).

First let's look at the simple number of top-ranked films, albums, video games and TV shows each year, without any population adjustment:

Films (# in top 1000 released per year, smoothed)

Albums (# in top 1000 released per year, smoothed)

TV shows (# in top 100 started⁶ per year, smoothed)

Video games (# in top 100 released per year, smoothed)

Interestingly, an earlier version of these charts using only the top 100 films and albums had albums picking up just as films were falling off, and then TV and video games picking up just as albums were falling off. That's not quite what we see with my updated charts. But still, here are the four added together:

Films, albums, TV shows, video games: summed % of the top 100-1000 that were released each year (smoothed)

Now for the versions adjusted for "effective population." I think the "effective population" estimates are especially suspect here, so I don't particularly stand behind these charts, but they were the best I could do:

Films (# in top 1000 released per year, smoothed and divided by an "effective population" index)

Albums (# in top 1000 released per year, smoothed and divided by an "effective population" index)

TV shows (# in top 100 that started per year, smoothed and divided by an "effective population" index)

Video games (# in top 100 released per year, smoothed and divided by an "effective population" index)

Films, albums, TV shows, video games: % of the top 100-1000 that were released each year (smoothed and divided by an "effective population" index)

Books: the longest series I have

I wasn't really sure where to put this part, but the only data set I have that is measuring the same thing from 1400 up to the present day is the one I made from Greatest Books dataset:

I think the drop at the end is probably just because more recent books haven't had time to get onto the lists that website is using.

Here's the version adjusted for effective population:

The big peak for fiction specifically around 1600 is heavily driven by Shakespeare - here's the same data for fiction, but excluding him:

Interpretation

The general pattern I'm seeing above is:

• In absolute terms, we seem to have generally flat or rising output in both "critically acclaimed art/entertainment" and "science and technology." (The exceptions are film and modern music; I think different people will have different interpretations of the fact that these decline just before TV and video games rise.⁷)
• In effective-population-adjusted terms, we generally see pretty steady declines after any given area hits its initial peak.

To me, the most natural fit here for both art and science is the "innovation-as-mining" hypothesis. In that hypothesis:

• The basic dynamic is that innovation in a given area is mostly a function of how many people are trying to innovate, but "ideas get harder to find" over time.
• So we should often expect to see the following, which seems to fit the above charts: a given area (literature, film, etc.) gains an initial surge in interest (sometimes due to new things being technologically feasible, sometimes for cultural reasons or because someone demonstrates the ability to accomplish exciting things); this leads to a surge in effort; there's lots of low-hanging fruit due to low amounts of previous effort; so output is very high at first, and output-per-person declines over time.

I think "bad taste" is part of the story too, but I don't think it can explain the patterns in science and technology (or why they are so similar to the patterns in art and entertainment). A separate post goes into more detail on how I see "bad taste" interacting with "innovation as mining."

"Golden age" skepticism

I'm quite skeptical that a "golden age" hypothesis - in the sense that some earlier culture was doing a remarkably good job supporting innovators, and in the sense that copying that culture would lead to more output today - has anything to add here. Some reasons for this:

No special evidential fit. I think the "innovation as mining" hypothesis is a good simple, starting-point guess for what might be going on. Most people find it intuitive that "ideas get harder to find" in science and technology; I think intuitions vary more on art, but I think the same idea basically applies there too, as I argue here.

And I don't see anything in the data above that is way out of line with this hypothesis.

• For example, in most charts, the only "golden age" candidate comes with the first spike in output, with declining "productivity" from there - consistent with the idea that earlier periods generally have an advantage. We see few cases of a late spike that surpasses early spikes, which would suggest a "golden age" whose achievement can't simply be explained by being early.⁸ (Generally, I'd just expect more choppiness if most of the story were "variations in culture" as opposed to "ideas getting harder to find.")
• As discussed in the supplement, I also looked for signs of a "golden place" - some particular country that dramatically outperformed others - and didn't find anything too compelling.
• For the most part, the decline in "productivity" for both art and science looks pretty steady (with exceptions for modern art forms whose invention is recent). You could try to tell a story like "The real golden age was 1400-1500, and it's all been steadily, smoothly downhill since then," but this just doesn't seem intuitively very likely.

No clear mechanism. I hear a lot of informal pining for a "golden age of innovation," but I've heard little in the way of plausible-sounding explanations for what, specifically, past cultures might have done better.

For science and technology, I've occasionally heard speculation that the modern academic system is stifling, and that innovators would be better off if they were independently funded (through their own wealth or a patron's) and free to explore their curiosity. But this doesn't strike me as a good explanation for innovation stagnation:

• I'd guess that there are far more people today (compared to the past), as a percentage of the population, who are financially independent and in a position to freely explore their curiosity. With increasing wealth inequality, there are also far more potential patrons. So for academia to be the culprit, it would need to be drawing in a very large number of people who formerly could and would have freely explored their curiosity, but now choose to stay in academia and play by its rules. This seems far-fetched to me.
• I also note that the scientific breakthroughs we do see in modern times seem to mostly (though not exclusively) come from people with traditional expert credentials. If the "freely explore one's curiosity" model were far superior, I'd expect to see it leading to more, since again, there are plenty of people who can use this model.
• Additionally, this explanation seems particularly ill-suited to explain why art and science seem to have seen the same pattern - I don't see any equivalent of "academia" for musicians or literary writers. (You could argue that TV and film force artists to endure more bureaucracy, as those art forms are expensive to produce. But the "decline" in art predates these formats.)
• This isn't a denial of the ways in which academia can be stifling and dysfunctional. I just don't think the rise of academia is a strong candidate explanation for a fall in per-capita innovation.
• I do think it's probably true that the past had more innovators whose contributions cut across disciplinary lines, and whose fundamental style and manner could be described as "nonconformist freethinker generating concepts" rather than "intellectual worker bee pursuing specific narrow questions."
  • I think this is a function of the "innovation as mining" dynamic: a greater share of the innovations within reach today are suited to be reached by "intellectual worker bee" types, as opposed to "nonconformist freethinker" types, due to the larger amount of prerequisite knowledge one has to absorb in a given area before being in much position to innovate.
  • I think academia does tend to reward "intellectual worker bees," but that this is transparent and that most potential (and financially viable) "nonconformist freethinkers" are staying out.

I've heard even less in the way of plausible-sounding explanations for how, specifically, previous cultures may have facilitated better art.

General suspiciousness about "declinism," the general attitude that society is "losing its way." I feel like I see a lot of bad arguments that the past was better in general (example), and I am inclined to agree with Our World in Data that (for whatever reason) people seem to be naturally biased toward "declinism."

I also suspect that subjective rankings of past accomplishments just tend, for whatever reason, to look overly favorably on the past. To illustrate this, here are charts similar to the charts above, but for well-known subjective rankings of baseball and basketball players:

Baseball players (# in top 100 with career midpoint each year, smoothed)

Basketball players (# in top 96 with career midpoint each year, smoothed)

Disregarding the dropoffs at the end (which I think are just about the lists being made a while ago), these charts look ridiculous to me; there's little question in my mind that the level of play has improved significantly for both sports over time. (Here's a good link making this point for baseball; for basketball I'd encourage just watching videos from different eras, and may post some comparisons in the future.)

My own intuitions. This is the least important point, but I'm sharing it anyway. A lot of comparisons between classic vs. modern art/science are very hard for me to make sense of. I can often at least sympathize with a subjective feeling that the “classic” work feels subjectively more impressive, but this feeling often seems bound up in what I already know about its place in history.⁹ In cases where it seems relatively easier to compare the quality of work, though, it seems to me that modern work is better. For example, quantitative social science seems leaps and bounds better today than in the past, not just in terms of data quality but in terms of clarity and quality of reasoning. I also feel like Shakespeare's comedies are inferior to today's comedies in a pretty clear-cut way, but are acclaimed (and respected more than today's comedies) nonetheless. I recognize there's plenty of room for debate here.

A note on ancient Greece. As discussed in the supplement, ancient Greece (between about 700 BCE and 100 CE) is "off the charts" in terms of how many acclaimed artistic and scientific figures (per capita) it produced. It performs far better on these metrics than any country in Europe (or the US) after 1400, and it outperforms all other countries and periods by even more. Is this evidence that ancient Greece had a special, innovation-conducive culture that could qualify as a "golden age?"

My take: yes and no. My guess is that:

• Ancient Greece is essentially where the basic kind of intellectual activity that generates critically acclaimed work first experienced high demand and popularity. This article by Joel Mokyr gives a sense of what I have in mind by the "basic kind of intellectual activity" - ancient Greece might have been the first civilization to prize certain kinds of "new ideas" (at least, the kind of "new ideas" celebrated by the critics whose judgments are driving the data above) as something worth actively pursuing.
• While ancient Greece produced a lot of critically acclaimed work over the centuries, its interests didn't "catch on": at that time, there wasn't the sort of global consensus we have today about the importance and desirability of this sort of innovation. And eventually demand fizzled, before spiking again hundreds of years later in modern Europe.

Thus, in my view, ancient Greece is best interpreted as an isolated spike in demand and effort at innovation, not a spike in exceptional intelligence or knowhow. And I doubt the level of demand and effort were necessarily very high by modern standards - so in that sense, I doubt that ancient Greece represents a "golden age" in the sense that we'd produce more innovation today if we were more like they were.

Reasons I think ancient Greece's accomplishments are best explained by a spike in demand/effort, not intelligence/knowhow:

• Ancient Greece was also the first country to score highly on "significant figures per million people" metric. (Out of 72 significant figures before the year 400 BCE in the entire data set, 66 were from Ancient Greece.¹⁰)
• Given that ancient Greece was the first home of substantial amounts of critically acclaimed work, it seems unlikely that it was also the best environment for critically acclaimed work, in terms of institutions or incentives or knowhow. By analogy, the first person to work on a puzzle might make the most noteworthy progress on assembling it, but this probably isn't because they are bringing the best techniques to the task: being early is an easy explanation for their high significance, and having the best techniques or abilities is a less likely explanation. (The best techniques seem especially unlikely given that they haven't had a chance to learn from others.)
• When I look at the actual figures from Ancient Greece, it reinforces my feeling that they are more noteworthy for being early than for the intrinsic impressiveness or usefulness of their work. For example, the two highest-rated figures from Ancient Greece are Aristotle (who ranks highly in both philosophy and science) and Hippocrates (medicine).
  • In my view, both of these figures did the sort of theorizing and basic concept formation that was useful near the founding of a discipline, but wouldn't have nearly the same utility if brought to philosophy or medicine today.
  • One could argue that if Aristotle or Hippocrates were transplanted to the present day, they might invent an entirely new field from whole cloth, of comparable significance to philosophy or medicine; I would find this extremely hard to believe, but won't argue the case further here.

More research needed

I've done an awful lot of amateur data wrangling for this piece. I think a more serious, scholarly effort to assess "Where's today's Beethoven?" could make a lot more headway, via things like:

• Better estimates of the "effective population" (how fast is the amount of "effort" at innovation growing?) How much "innovation stagnation" we estimate is very sensitive to this.
• More systematic attempts to assess the significance of different innovations (both in terms of science and art), and look at what that means for the pace of innovation. I would guess that whether we're seeing "innovation stagnation" is pretty sensitive to how exactly this is done; for example, I'd guess that if you look at popular rather than critical opinion, the modern era looks extremely productive at producing art/entertainment.
• More intensive examination of times and places that seem like decent candidates for "golden ages," and hypothesizing about, specifically, what made them unusually productive.

I think this would be worth it, because I think each hypothesized explanation for "Where's today's Beethoven?" has some important potential implications. Later in this series, I'll discuss how the "innovation as mining" hypothesis - which I think explains a lot of what's going on - might change our picture of how to increase innovation.

Next in series: How artistic ideas could get harder to find

Special thanks to Luke Muehlhauser for his feedback on this piece and others in the series, especially w/r/t the state of modern highbrow art and entertainment.

Footnotes