5. Power Law Growth (L-curves)
Power laws, or L-curves, are another useful growth curve, as they tell us how learning or performance increases in closed systems, temporary environments of fixed complexity. Power laws have similarities to the saturation phase of S-curves, though they are likely each due to different physical mechanisms. In either case, we see declining marginal learning over time.
With a power-law curve, each time cumulative output doubles, learning improves by a fixed percentage (for example, 20%, like Swenson’s law for photovoltaic panel manufacturing). For an individual doing practice trials to learn some new skill or method, or organization or industry of a fixed size learning production, if each of these are capable of a standard output each year, learning or performance will start out very rapid, as it is very easy to double a small batch size at first, but it will increasingly slow. Over time, there’s less new efficiency to be discovered, and less total and marginal learning left to be done to improve performance.
Many manufactured technologies improve their performance over time based on manufacturing experience curves, a type of industry learning curve. As these are power law curves, each time cumulative output volume doubles, value added costs fall by a constant percentage (for example, 10%, 20%, or 30%, as in the figure at right), a rate which will vary by industry and technology. When plotted on a non-log scale (picture left), we see the “L” shape of the L-curve, with declining learning/efficiency improvement over time with each new unit produced.
Manufacturing, human psychological learning, and many other natural processes are subject to these experience curves. Power laws are why startups are such dynamic environments. Everybody is rapidly learning, falling down the steep first section of power law learning curves. But unlike exponential growth, the annual velocity of power law growth must eventually decrease with any fixed technology, as it grows into a market, and these curves become increasingly flat with time.
During the beginning stages of power law growth, and also in the special case where output doubles every year or less, as in any young industry that is rapidly growing to serve a large market by comparison to the entrepreneur’s share, power-law growth can look like exponential growth. In fact, many technology writers commonly refer to this kind of growth as “exponential”, because many people understand exponentials, but far fewer people understand power laws. That convention is a useful shorthand sometimes, but we must remember that exponentials and power laws are two very different animals.
Salim Ismael’s Exponential Organizations, 2014, is one such book. It’s an excellent introduction to accelerating strategies for business, and I highly recommend it to all entrepreneurs. But as happens in all such books today, with our current state of industrial science, its examples and strategies sometimes refer to exponential growth and at other times to power law growth, while treating them all as exponentials, and never distinguishing the difference. As a practical matter however, if we are investing time and energy into any strategy, product, or service, that difference is often quite important, and we need to understand it if we want to really improve innovation, strategy, and action to drive accelerating learning, wealth production, and change.
Again, power law growth is only exponential at the beginning, when learning is new and resources aren’t constrained, or, as we discuss in Chapter 7, if we’re continually moving to new adaptive and technological frontiers, further down in Physical and Virtual Inner Space. In that case, we’re continually resetting the game to the beginning of our learning curve, and our R&D teams have the potential, if they are allowed the freedom and resources and culture, to act like startups again. So if an industry is young, if new technologies and processes are continually involved, or if more people with different skills keep entering the mix, as is common in startups, power-law learning will keep returning to the beginning of its learning curve. In that case, performance gains can look exponential for long periods, and even briefly superexponential (a J-curve) if powerful new technologies, funding, marketing, or adoption processes enter the mix.
We at EDU want to host a research conference on the Science of Performance Curves, including power laws and exponentials, to better understand them from a physical, informational, technical, and complex systems perspective. It is a sad testament to our deficits in scientific foresight today that such a conference doesn’t yet exist anywhere on Earth. No one is studying these curves on a regular basis. There are only a few hundred scientific papers directly on the topic of performance curves. I co-founded the Acceleration Studies Foundation in 2003 primarily to highlight this need. In my view, a substantial philanthropic sponsorship, on the order of $200K or more, will be needed to put on such a conference. A contribution on the order of $1M or more will be needed to fund an academic center at a second tier university devoted to acceleration studies, even more for a first-tier university. If you know any philanthropists with an interest in accelerating change, let me know.
There is also a power-law distribution, another L-curve (picture below), which is not a growth curve but a distribution of features often seen in collectives of natural systems. Power law L-curves have “fat heads” and “long tails” (see picture right), and are the source of the 80/20 rule, or Pareto Principle, the reality that 80% of the popularity, wealth, and power will be concentrated in 20% of the cities, people, products, and activities, while the rest represent the “long tail” of evolutionary diversity. This also gives us the observation that 80% of our desired results often come from just 20% of our strategies (effort).
As we said in Chapter 1, the 80/20 rule seems very likely to be related, at some complex systems level, to the 95/5 rule, the observation that 95% of many complex adaptive systems, including living organisms, are evolutionary, capable of continual creative change, while 5%, to a rough approximation, are a critical set of highly conserved rules, strategies, and processes of development. That 5% guides the system to predictable futures, and like Pareto’s 20%, is of outsized importance to the adaptiveness of the system.
The 80/20 rule tells us that foresighted strategy, focus and satisficing (versus perfectionism) are key! Good books on using power law distributions in business and life include Chris Anderson’s The Long Tail (2008), and Richard Koch’s The 80/20 Principle, 1999. Knowing the basics of both power law distributions (L-curves) and normal distributions (Bell curves) is important for general foresight.