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I’ve been playing this game called Hexcells Infinite. It’s kind of like minesweeper, but with at least a half dozen ways of indicating how many “mines” there are in a given cell. The way play generally progresses is with long pauses of thinking interspersed with fairly rapid clicking once you figure something out because that initial insight cascades to reveal a bunch of nearby “mines”. It’s quite an enjoyable game and if you’re looking for something casual with a playtime of between 5 and 20 minutes I’d recommend it (there are actually three editions: normal, plus and infinite). But that’s not why I bring the game up. I bring it up because the manner in which it plays is an example of a very, very tiny S-curve.

What’s an S-curve? It’s a curve that looks kind of like a flattened “S”, it starts out nearly horizontal, turns up into something that looks exponential and then flattens out again at the top. Just as my hexcells game play starts with not much activity as I think, before going through a burst, then gradually tapering off as I run out of obvious moves. Anywhere positive feedback loops battle with constraints you’ll see S-curves, and they’ve been a topic of frequent discussion recently (at least in my corner of the internet).

As far as that discussion goes, I’m probably somewhat late to the game, but I think thus far people have mostly been focused on smaller S-curves, perhaps not as tiny as the one I experience when playing Hexcells, but fairly small nonetheless. I want to go in the exact opposite direction and focus on the possible existence of very large S-curves. And, in particular, whether we’re near the top of any of those curves.


One of the points which has been made in other spaces is that if you combine a series of S-curves that combination looks very much like exponential growth. For example, take something like Moore’s Law, which is the exponential growth in the number of transistors that can fit in a given space. At first glance this may seem like one curve, but in reality it’s a bunch of S-curves stacked on top of each other.  You might have an S-curve associated with transistors and then another S-curve around advances with integrated circuits. Farther along there’s the S-curve related to various methods of lithography, and cpu architecture. But as each advance followed immediately on the heels of the last one, there was never a time for the Moore’s Law graph to reach the top of any given S-curve and flatten out. Though perhaps that’s finally about to happen.

My point in bringing this up is not to talk about computer chips, but to point out that something similar happened with energy. If you look at a graph of worldwide energy use, you’ll see a similar vaguely exponential curve, but you’ll notice that within that curve you have various smaller S-curves, sources of energy which start off small, grow really fast and then level off. First there was wood, then coal, then oil. And for a long time there was a lot of attention being paid to the inevitable leveling off of oil, or peak oil as it’s commonly known. Though, of course, just like with processors there was every reason to suspect that another S-curve would come along and keep the overall energy curve pointing up. Initially nuclear power seemed very promising as a candidate for this next innovation, but then it mostly stalled. Fortunately or unfortunately, depending on who you ask, something else came along, fracking, and a new curve started. There’s also, of course, renewables, which could easily be a blog post on its own.\

As I mentioned previously in this space energy production has been growing at somewhere north of 2%/year for centuries, basically through the stacking of the S-curves I’ve been talking about. This growth has been fundamental to the world we now live in, and it’s unclear what happens if that growth stops, but it’s probably bad. And when we tie all of the above together there are many reasons to think that we may be facing exactly that possibility. That we have reached some sort of inflection point. For example here are some of the questions I’m pondering:

1- Do we still have to worry about the S-curve of peak oil. Or is it now an S-curve of peak natural gas?

2- As I pointed out, much of progress seems based on maintaining a certain rate of energy growth. What happens if the technology is there, but the political will isn’t? For example with nuclear power, and possibly fracking.

3- Related, if fracking is problematic even without its contribution to greenhouse gas emissions, and nuclear is problematic despite its lack of the same. How does climate change factor into the continued use of certain sources of energy? So far it doesn’t seem to have had much of an impact either way.

4- In the past new technology was implemented as soon as it was feasible, with little regard to public opinion or politics. This is no longer the case. How does this new reality interact with our reliance on continual progress? Or with the diffuse harm that comes from technological innovation? (i.e. it’s one thing to demand 100% renewable energy, it’s quite another thing to actually make that switch.)


I would offer up antibiotics and another example of a big S-curve. One that appears to definitely be plateauing out recently. I would also argue that unlike previous examples it’s less obviously a composite of lots of smaller S-curves. Yes, new antibiotics have been developed (though that process is getting harder and harder) but my impression is that most of the upward slope is entirely due to just having antibiotics available in the first place (i.e. penicillin) and that subsequent classes of antibiotics allowed us to hold our ground, but didn’t bring any big jump in effectiveness. All of which is to say that there is not some metaphorical nuclear power equivalent waiting to save us once antibiotics are no longer effective. We have one tool and we’ve already extracted most of the benefit.

Obviously I am not the first person to point this out, but my broader contention is that we may be reaching the top of a lot of our big S-curves and our effectiveness at dealing with the diminishing effectiveness of antibiotics could be indicative of how we deal with the other S-curves as they plateau out. So far the signs are not encouraging.

Manned Space Exploration

Manned space exploration has been in the news a lot lately. Not only is the 50th anniversary of Apollo 11 coming up next month, but both SpaceX and Blue Origins have announced plans to send humans to Mars. And then of course there’s Trump’s very… interesting(?) tweet from a few days ago:

For all of the money we are spending, NASA should NOT be talking about going to the Moon – We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!

Where does all of this put us as far as an S-curve for the manned exploration of space? I would argue that we’ve already experienced an S-curve, one which plateaued awhile ago. Remember the description of S-curves we started with. It begins with a positive feedback loop. When you’re talking about the Apollo missions this is a little vague, but obviously competition with the Soviets was a big part of it. After an initial burst things taper off as you run into constraints. On that end things are not vague at all, the constraints of manned space exploration are legion, particularly when you’re trying to do it at the government level.

That last bit is key, I would argue that we have run through the governmental S-curve already and that we’re at the beginning of a new S-curve, the manned exploration of space by private entities. In this new stage we’ll see some more innovations (like reusable rockets) but eventually even Musk and Bezos will run out of places where they can economize and improve, and things will reach another plateau. We’ve seen S-curves which stack one after the other and give the impression of continuous exponential growth. This, on the other hand, is an example of two curves with a long gap in between. Also once the current private entity fueled curve plateaus it’s unclear when or in what domain another one will start. And what’s even more uncertain is whether that will happen before or after we have a long-term sustainable presence somewhere other than Earth. My bet would be that it will definitely be before, and that there is no smooth path to the stars, or even Mars.

Scientific method

At last we finally arrive at the S-curve that worries me most of all, the S-curve of scientific discovery. For decades if not centuries it has been more or less an article of faith that scientific progress would continue to increase in essentially an exponential fashion, and indeed by some measures it still is, for example scientific output, measured in terms of scientific papers, doubles every nine years. But are all of those papers just as impactful as Einstein’s On the Electrodynamics of Moving Bodies? Definitely not, meaning that at best the number of scientific papers is a very rough proxy for scientific progress, not a direct measure of it. But even if you disagree, and argue that the ever doubling number of papers means that scientific progress hasn’t slowed down, there is absolutely no law that says that it never will. And many reasons to think that it’s already happening.

Not too long ago I read The Making of the Atomic Bomb by Richard Rhodes. It was just before I started reviewing everything I read, but maybe I’ll go back and pick that one up, because it was truly a great book. One of the things that was striking is how amazingly fruitful the pre-war years were for physics. Everywhere you turned people were uncovering new things, the structure of the atom, the existence of neutrons, the discovery of fission. (George Gamow also noticed this leading him to write the book Thirty Years that Shook Physics). All of this is a classic description of the bottom of the S-curve. As discoveries and scientists feed off one another it produces a positive feedback loop of understanding.

These days, we’ve got far more scientists working on things, publishing, as I mentioned far more papers, but the discoveries of the last 30 years have been much less consequential. All of the laws of physics where things are unchanging and easy to replicate, have largely been uncovered, or will require spending billions of dollars on a new particle collider. It’s pretty clear that all of the places where the scientific method was easy to apply have been mined out. That we have picked all of the low hanging fruit. The S-curve is starting to plateau as we bump up against various constraints

In part this is because much of science has moved on to experiments about human physiology and behavior, where there are numerous constraints. It’s difficult to establish control groups, things aren’t unchanging, and there are vast differences between individuals, meaning that instead of groundbreaking discoveries that shake our understanding of the universe we get small discoveries about how we just have to assume a “power pose” and it will immediately make us more confident. Worse than the smallness of these discoveries is the fact that 50% of the time they fail to replicate (like the research about the power pose). That sounds a lot like a plateau to me.

Tying all of this together, we have this idea that progress is a smooth curve moving ever upward towards a better and better future, and indeed this has been the case for the last few decades and in some cases for the last few centuries, but as I pointed out a couple of times, the bottom of an S-curve is indistinguishable from exponential growth. It’s only as you get farther along that the difference is apparent. And I would argue that we’re finally reaching the stage where it’s clear that most of the things we’ve come to expect from progress aren’t exponential, that they won’t grow forever, and that in fact we’re nearing the top of a lot of S-curves which have been powering civilization for a long time. And as they start to plateau it’s unclear what will happen

This is not to say that progress is over, even if most things should be viewed as an S-curve instead of something that grows exponentially, there are lots of S-curves remaining, and we’re still at the bottom/high growth part of many of them. But it’s unclear how much comfort this should give us. Saying that while we may be close to peak antibiotics, we’re nowhere near peak Facebook, is not particularly reassuring.

Undoubtedly lumping all trends under the heading of an S-curve will turn out to be too crude, some trends will end up being more complicated, and some really will turn out to essentially grow forever. But just as undoubtedly some of the trends that have powered the modern world over the last few hundred years are S-curves, and they will plateau if they haven’t already. How we will deal with these plateaus? These changes in direction? Will the process be smooth and uneventful or catastrophic? For a long time we’ve essentially been able to innovate our way out of the problems we’ve created, but we’re coming to a time when we’ll no longer be able to count on that.

I know that at least some of my readers love nothing more than proving me wrong. Well if you were to look at donations, they also resemble an S-curve. This is a chance to prove me wrong, make it grow exponentially!