One of the coolest patterns in history is something called "the multiple." It's this spooky phenomenon where someone invents something or makes a new discovery and then, at roughly the same time, someone else invents the same thing or makes the same discovery independent of the first person. Consider:
- Isaac Newton and Gottfried Leibniz independently developed calculus in the 1670s
- Carl Scheele and Joseph Priestley independently discovered oxygen in the 1770s
- Thomas Edison and Joseph Swan independently invented the light bulb in the 1870s
Crazy, right? What a weird bunch of anomalies. Except the multiple isn't an anomaly. It's more like a rule. It's so common that sociologists and economic historians have written amusingly titled papers like "Are Inventions Inevitable?" which show that most of the breakthrough discoveries of the last thousand years can be traced to several disconnected people in different parts of the world.
Nor is the multiple confined to the "simple" kinds of discoveries you can get patents for. The very advent of agriculture is a multiple! Anatomically modern humans have been around for about 200,000 years, and for basically all of that time we've relied on methods like foraging or hunting and gathering to find food and other resources. But about 11,000 years ago, in the virtually simultaneous span of a single millennium, farming independently sprang up in five or six different parts of the world. Here's Matt Ridley in How Innovation Works:
There is no evidence that any of these people got the idea of farming from each other and the particulars of crop and cultivation were different in each case. The wheat farmers of Mesopotamia did not influence the millet farmers of China, let alone the potato farmers of the Andes or the yam farmers of New Guinea.
So what's going on here? Magic? Graham Hancock thinks a lost civilization of advanced humans visited the peoples of different continents and shared techniques like agriculture with them. Now, I like science fiction, but I think there's a better and simpler explanation for the agricultural multiple as well as all the other examples of simultaneous invention that have puzzled scholars over the decades.
To get to the bottom of innovation multiples, you have to understand innovation per se. And to understand innovation, you have to work your way up from first principles.
What is innovation?
Simply put: all new things come from old things. You just have to combine the old things in the right way. As the Roman poet Lucretius wrote in 50 BC:
And how these atoms are arranged makes all the difference —
Their position and formations, and what moves they give and take
From one another, for the selfsame atoms go to make
The heavens and the sea, the land, the rivers and the sun,
The same make crops, trees, animals — but by their combination.
Lucretius predated formal atomic theory by nearly 2,000 years, but he was spot on: When you combine two parts hydrogen atom with one part oxygen atom, an altogether new configuration emerges called water (H₂O). This new water configuration, in turn, becomes a brand-new spare part that nature can combine with all the other spare parts that exist. For example, to create the configuration we call glucose (C₆H₁₂O₆) — a necessary energy source for all life on earth — you have to combine a few parts water with a few parts carbon dioxide.
And voila: in a very broad sense, this act of combining spare parts into new configurations is what we mean by innovation. Not all new configurations are innovations, mind you, since most new things are worthless. So really, an innovation is a useful new configuration. A configuration that, to paraphrase popular science author Steven Johnson, enables jobs to be done that couldn't be done before. 
The adjacent possible
The magic in all of this is that innovation doesn't merely enable. It also compounds enablement. That is, it provides a platform on which to stack second-order innovations, then third-order innovations, then fourth-order innovations, and so on. This is because every new configuration of spare parts is really just a brand-new spare part. And by adding to the sum total of spare parts, you expand the "adjacent possible"  — the total space of possible configurations.
"The strange and beautiful truth about the adjacent possible," writes Steven Johnson:
is that its boundaries grow as you explore those boundaries. Each new combination ushers new combinations into the adjacent possible. Think of it as a house that magically expands with each door you open. You begin in a room with four doors, each leading to a new room that you haven’t visited yet. Those four rooms are the adjacent possible. But once you open one of those doors and stroll into that room, three new doors appear, each leading to a brand-new room that you couldn’t have reached from your original starting point. Keep opening new doors and eventually you’ll have built a palace.
Of course, the reverse is also true. For example, if you don't combine hydrogen and oxygen into water, there's no possibility of glucose. And if there's no possibility of glucose, there's no possibility of life.
With all that in mind, we're ready to solve the problem of the multiple.
The shoulders of giants
Innovation multiples don't just happen. They get made possible by prior events that introduce new spare parts into the environment. When these new spare parts become available, it's largely a matter of time before the brilliant (or merely obsessive) tinkerers of the world start combining them with all the old spare parts and eventually achieve their discoveries.
Let's revisit those multiples I referenced at the start of this essay:
Calculus. Newton and Leibniz independently developed calculus in the 1670s. But only because they'd both been given access to an ancient precursor to calculus called the method of exhaustion. This long-lost method, originally developed in the 5th century BC in Greece, had only recently been rediscovered, and in 1647 the mathematician Bonaventura Cavalieri had formalized it into a much more workable form.
Oxygen. Scheele and Priestley independently discovered oxygen in the 1770s. But only because they'd both been given access to literal new spare parts like the bell jar — a kind of advanced scale — as well as new techniques for heating and separating gases.
Light bulbs. Edison and Swan independently invented the incandescent light bulb in the 1870s. Or really, they invented a usable form of the light bulb. Incandescent lights had been around for a full century by that time, and even light bulbs themselves had been around for a few decades. Only… their filaments would burn out too quickly to be of any practical use to anyone. Edison and Swan's contribution was to play around with different filament materials until they found combinations — mostly carbon — that lasted.
Agriculture. 11–12,000 years ago, humans from different continents spontaneously started farming. But here again, only because a vital new spare part had appeared: an arable climate. The entirety of human history up to that point had taken place during a long ice age called the Pleistocene. Think vast ice sheets over the land, long droughts, dry air. Not very farmable. But the dawn of the modern era made the advent of farming not just possible, but perhaps inevitable.
Look, the people behind all of these innovations were inhumanly smart. Especially Newton. But as Newton himself would famously write in a 1675 letter to his rival Robert Hooke: "If I have seen further it is by standing on the shoulders of Giants."
Well said. Except… Newton didn't say it first. He borrowed the phrase from a French philosopher, according to John of Salisbury:
Bernard of Chartres used to compare us to dwarfs perched on the shoulders of giants. He pointed out that we see more and farther than our predecessors, not because we have keener vision or greater height, but because we are lifted up and borne aloft on their gigantic stature.
Great innovators are great, in other words, not because of their ability to create new things out of nothing, but because of their ability to synthesize the insights around them.
The problem with big innovations
There are two points I hope you've come away with so far. The first is that innovation is really fascinating… in principle. The second is that, in practice, it might just be more trouble than it's worth. At least if we're talking about the sorts of world-changing innovations that win people patents and Nobel Prizes and personal Wikipedia pages.
Let's refer to these big public breakthroughs as "macro innovations." Macro innovations usually explore the frontiers of science, technology, or economics.
Not many people can play the macro innovation game. As a rule with some exceptions, you have to be highly talented, well-resourced, motivated, and lucky to find much success. Why? For one thing, you need access to the particular spare parts that make the next configuration possible. For another, macro innovation is a hyper-competitive and often zero-sum competition. In the sciences, for example, no one cares about the second person who makes a discovery.
But macro innovation isn't the only game in town. We can also leverage the adjacent possible to overcome smaller, more personal challenges like being more productive, tapping into creativity, or managing relationships. Let's call these private breakthroughs "micro innovations." 
High-profile examples include David Allen's Getting Things Done method, a micro innovation in time management, or spaced repetition, a micro innovation in memorization, or K. Anders Ericsson's deliberate practice, a micro innovation in skill acquisition.
But most micro innovations aren't as popular or professional-sounding as these ones. In fact, most don't even have a name. For example, the Pulitzer Prize-winning author John Cheever innovated a work routine where he would get out of bed, put on his only suit, and ride the apartment elevator down to the storage room on the bottom floor. There, he would strip down to his boxer shorts and write until lunchtime.
Unlike macro innovation, micro innovation is a game with broad access and appeal. First, because there's no "problem of multiples" to worry about when you're just trying to solve your own problems. But also because the rewards are immediate, continuous, and personalized to your individual circumstances.
Months ago, I wrote about my personal productivity system. A lot of folks enjoyed the piece and asked me to share more details. And I will. But first, I want to write about the process I used to innovate that system.
So whereas this essay has been about innovation in principle, the next will be about innovation in practice. And it'll begin with the story of how I myself got tangled up in an innovation multiple.
By the way…
The "story model of purpose" is my life philosophy to a) continuously b) make progress on c) problems d) that matter to me. And this newsletter is where I'll discuss topics based on these four themes.
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 Image credit goes to DALL-E 2, which I just got access to! For the curious: the cover image was generated by the prompt "A hand drawn sketch of Thomas Edison in his lab looking disappointedly at his light bulb." The second image was generated by the prompt "A hand drawn sketch of indigenous people farming."
 Here's how Steven Johnson puts it in Where Good Ideas Come From:
There are many ways to measure innovation, but perhaps the most elemental yardstick, at least where technology is concerned, revolves around the job that the technology in question lets you do. All other things being equal, a breakthrough that lets you execute two jobs that were impossible before is twice as innovative as a breakthrough that lets you do only one new thing. By that measure, YouTube was significantly more innovative than HDTV, despite the fact that HDTV was a more complicated technical problem. YouTube let you publish, share, rate, discuss, and watch video more efficiently than ever before. HDTV let you watch more pixels than ever before. But even with all those extra layers of innovation, YouTube went from idea to mass adoption in less than two years.
 The biologist Stuart Kauffman coined the term "adjacent possible" to suggest that one of the ironclad laws of life on earth — as ironclad as the law of entropy is in physics — is to "become as diverse as possible, literally expanding the diversity of what can happen next."
 To be clear, this distinction I'm making between "macro" and "micro" innovations is somewhat arbitrary. The usefulness of the mental model is that when people think of "innovations," they tend to automatically think of the big ones, which I consider to be a huge missed opportunity. Macro innovations are great: they make headlines, mint new celebrities, and often change a lot of lives for the better. But micro innovations offer a self-empowering path for everyday people.