A couple of weeks ago, I tweeted this:
It’s a pretty bold and provocative statement, and its implications are both important and profound. So I figured I’d do a Substack post more fully exploring this.
Exponential Growth is Hard to Understand
Exponential growth is hard for the human mind to comprehend. There’s an old puzzle: put a grain of rice on one square of a chessboard. If you double that amount of rice and put it on an adjacent square, and do that for all 64 (8*8) squares, how much rice would you have after all the squares have been filled?
If you do the relatively simple math, you will find that you have 18,446,744,073,709,551,65 grains of rice. (Eighteen quintillion and change.) Most people don’t understand this intuitively, and if they haven’t heard the puzzle before, will be surprised at the result. If you want to read about this in more depth, Wiki’s entry is a good start.
That’s one form of exponential growth. It’s steady exponential growth, but it’s still exponential growth.
J-Curves: Where Exponential Growth Goes Super
Now consider exponential growth, in which the exponent itself increases over time. That is the flywheel that technology is currently powering. The rates of technological improvements grow, but so too does the rate at which the rate increases.
The implications of this are rather profound, as you may intuit. But if this doesn’t make intuitive sense to you, I can offer up four links which help make this more concrete:
That last link, from the Foresight Institute, helps us understand what’s going on here:
If you think long-term exponential growth is interesting and disruptive, there’s another kind of growth that is even more curious and potentially disruptive. That is faster-than-exponential (superexponential) growth. Unlike exponential growth, where the curve looks the same at every point, superexponential growth has one or more “knees” in the curve, places where growth suddenly switches from a slower to an even faster (or sometimes slower) exponential mode.
This kind of growth has been called “Hockey Stick” or J-curve growth, as, like a capital J, there is a period of low growth, a knee in the curve, and then a period where growth goes almost vertical for a time. Human population growth is a good example of superexponential growth….
Economic growth has been another fascinating example of superexponential growth. Over a few decades, economies look like they are engaged in simple exponential growth. But as we saw with computing technologies, when we look at economic growth over a long enough time period, it appears superexponential….
As with human population earlier, we see the knee of the J-curve of GDP growth in the 1850s, during the Industrial Revolution. From that point forward, GDP growth has looked increasingly vertical, when it is considered on a global scale, and plotted over a very long time period.
But while human population growth started saturating in the 1960s, global economic growth switched to a steeper curve in 1960. From 1950 to 2000, global GDP increased by 800% while human population increased by less than 300%. Even with our recent recession, global economic growth is now even faster than it was in 2000. We have recently seen more than a decade of annual rates of economic growth in some Chinese cities of over 20% per year, and many developing world economies are growing at rates far faster than the 2-3% annual global rate we saw in the mid 20th century.
Will global GDP growth per capita soon saturate, as human population is now doing? On first consideration, it seems reasonable to expect it would. But if such growth is driven primarily by technical productivity, and particularly by nano and info technologies, and if those special technologies remain on fast exponential or superexponential growth modes for the foreseeable future, then economic growth may also remain superexponential for some time to come.
As automation and machine intelligence grow within nano and info technologies, they can increasingly engage in their own technical, economic and intellectual explorations, competitions and economic activity. Such activities may increasingly take over from technical, economic, and intellectual competitions drive by biological humans. As increasingly smart populations of machine minds are added to society in coming decades, we will very likely see a “decoupling” of biological human population and economic growth.
The last two paragraphs of this rather long quote are the most important—and the most profound. Note that nothing here makes any prediction about the success of any given company or startup; these are claims about the economy, broadly construed. So while many companies will fail over the coming decades, and many will succeed, the general trend of economic growth should be one of increasing growth over time. (A lot of people will fallaciously point to a cluster of failed companies and say “See! The economy isn’t growing because these companies failed!”)
Some Real-World Examples of Superexponential Growth in Technology
Let’s focus this discussion a little bit. I’m borrowing heavily from the first link above, Packy McCormick’s newsletter. So the following is taken from him and paraphrased by me.
Companies like Stripe, Plaid, and more recently, Remote, are building API-first software companies. APIs (application programming interfaces) are software which offer services to other pieces of software. The particular APIs that these companies offer allow other companies to build services and apps atop Stripe’s, Plaid’s, and Remote’s infrastructure.
This means that these companies are converting an expense—the tech infrastructure and software that they have built—into a revenue stream. Not only does this arrangement benefit them, because running a paid API is a highly scalable and profitable business model, but it allows other companies to rapidly scale at rates heretofore unknown. This presages the claim from the Foresight Institute, above, that economic growth will decouple from population growth in the future.
And that’s what’s key: technology innovations allow other technology innovations. Leverage creates more leverage. The flywheel spins, only it spins faster with each revolution.
Understand that, and you will understand the profound consequences of growth whose rate itself grows over time.