Vaclav Smil on Moore’s Law

Posted on Updated on

Over at IEEE Spectrum, Vaclav Smil has an excellent piece demolishing the absurd idea that Moore’s Law is a good general guide for technological progress. I’m sure you’ve heard these ideas that there is a “Moore’s Law” for solar power.

Just recently, we were being told there is a Moore’s Law for fracking. Of course, there is nothing of the sort. But misguided techno-optimists continue to believe it is true, regardless of actual evidence.

As always, Smil provides numbers where others provide assertions


Corn, America’s leading crop, has seen its average yields rising by 2 percent a year since 1950. The efficiency with which steam turbogenerators convert thermal power to electricity generation rose annually by about 1.5 percent during the 20th century; if you instead compare the steam turbogenerators of 1900 with the combined-cycle power plants of 2000 (which mate gas turbines to steam boilers), that annual rate increases to 1.8 percent. Advances in lighting have been more impressive than in any other sector of electricity conversion, but between 1881 and 2014 light efficacy (lumens per watt) rose by just 2.6 percent a year, for indoor lights, and by 3.1 percent for outdoor lighting (topped by the best low-pressure sodium lamps).

The speed of intercontinental travel rose from about 35 kilometers per hour for large ocean liners in 1900 to 885 km/h for the Boeing 707 in 1958, an average rise of 5.6 percent a year. But that speed has remained essentially constant ever since—the Boeing 787 cruises just a few percent faster than the 707. Between 1973 and 2014, the fuel-conversion efficiency of new U.S. passenger cars (even after excluding monstrous SUVs and pickups) rose at an annual rate of just 2.5 percent, from 13.5 to 37 miles per gallon (that’s from 17.4 liters per 100 kilometers to 6.4 L/100 km). And finally, the energy cost of steel (coke, natural gas, electricity), our civilization’s most essential metal, was reduced from about 50 gigajoules to less than 20 per metric ton between 1950 and 2010—that is, an annual rate of about –1.7 percent.

Let’s compare Smil’s array of facts with the assertions from a recent book, The Infinite Resource by Ramez Naam:

The trend in increasing efficiency – of travel, of steel production, of food production, of carbon fiber manufacture, or of anything else – happens so slowly that at times we underestimate it. It’s an exponential process, not a linear one. The amount of carbon fiber you can buy for a dollar has increased at a rate of somewhere around 9% per year. Over a year or two we may not notice it. But in the long term, it works like compound interest. It’s an exponential process. The gains don’t add up year over year. They multiply. Over 40 years of 9% gain, we don’t end up able to buy 360% more carbon fiber per dollar. We end up able to buy 3000% more. Inventor and author Ray Kurzweil has argued that we humans have a tendency to look at exponential gains and over-estimate the short term impacts, while under-estimating the long term impacts. If you’d asked anyone in 1960 or 1970 to predict the food yields, carbon fiber prices, or energy efficiency of lighting in 2010, you’re likely to have gotten answers that tremendously under-estimated the amount of progress we’ve made.

All of the assertions made by Naam here are demonstrable false, as Smil’s numbers show. It’s incredibly easy to claim things are improving exponentially, but it is also incredibly easy to check whether they are improving exponentially. Why is this so difficult in practise?


13 thoughts on “Vaclav Smil on Moore’s Law

    Geek Grandad said:
    March 20, 2015 at 3:43 pm

    Vaclav Smil does not seem to be saying that most of the increases are not exponential, just that the rates are an order of magnitude less than the increases in transistor density. In fact he quotes the increases as a fixed percentage per year (e.g. 2 percent per year increase for corn yield), which implies an exponential increase. You would need to look at the individual curves to see if they were roughly exponential.


    James Galasyn said:
    March 21, 2015 at 1:56 am

    A lot of people use “exponential” growth as shorthand for “supralinear” growth.

    Re Kurzweil, don’t mention his ideas on evolution to real evolutionary biologists; they get annoyed.


    Ramez Naam said:
    March 22, 2015 at 12:37 am

    Robert, as we’ve discussed on twitter, I make no claims that the compound rates for solar price improvement, steel efficiency, or anything else are as great as Moore’s Law. They very clearly are not. I claim only that the progress in these areas does appear to be something like annually compounding. That’s what ‘exponential’ means. (I also don’t claim that these trends will go on forever. In the book I clearly state that all exponentials in nature end. Everything, in the long run, is an S-curve.)

    The numbers Smil reports here in the passage you’ve quoted are compound annual growth rates. That is to say, they’re the growth rates he produced, assuming an exponential process. For instance, a fuel efficiency improvement of 13.5 mpg to 37 mpg between 1973 and 2014, is annual compound improvement of roughly 2.5 percent.

    Clearly that is far less impressive than 40%. It is also less impressive than the 9% improvement I discuss for carbon fiber prices. Yet, similar logic holds. Human intuition is that 41 years of 2.5% growth is roughly 100% improvement. It is actually 175% improvement. That’s the point of this passage – that most of us intuitively underestimate the effects of compounding improvements.

    Finally, perhaps I should have been more careful in popularizing the application of the term “Moore’s Law” in energy. I wasn’t the first to use it in solar, but I may have helped spread it in this blog post at SciAm:

    You’ll note that in the post itself I’m clear to call out that actual rate of price decline – roughly 7% per year – and that eventually this exponential will end. Why, then, did I use the term Moore’s Law? I used it as an analogy – a way to communicate to the reader the potential impact of long term exponential (yes, quite clearly exponential, even if much lower than 40%) price decline.

    Also note that since I wrote that piece, the price decline of solar modules has accelerated quite substantially, easily exceeding what I forecast in 2011.

    Ramez Naam


      Robert Wilson said:
      March 22, 2015 at 9:48 am


      Thanks for the comment.

      Let me restate my disagreement with you.

      You use the word exponentially at to describe processes in this passage of your book. Later on you say, “oh, actually this is really S-shaped”.

      This is simply a mis-use of scientific language. If improvements of efficiency are described by something like a logistic curve, then call it a logistic curve, not an exponential one. This may not excite the techno optimists who have read too much Kurzweil, but it will keep them half informed.

      Many of the processes you claim (with a buried caveat) are exponentially are clearly getting almost as efficient as they can get. Power plants, wind turbines and most industrial processes are pushing the limits. Talk of exponential growth does no one any favours.



        Ramez Naam said:
        March 22, 2015 at 3:09 pm

        Why do I use the word ‘exponential’ if, as you and I agree, these are ultimately S-shaped curves?

        Because for the trends I care most about, we don’t appear to be close to the limits

        You mention power plant efficiencies, wind turbines, and most industrial processes. I’ll agree with you on power plant efficiencies and provisionally the other two.

        But throughout the book, the number one exponential I write most about isn’t efficiency, it’s cost. Specifically the cost of non-carbon energy and energy storage. The trends there are clearly exponential, as I document. And progress depends primarily not on increased efficiency of, say, solar modules, but rather of manufacturing of solar modules and techniques for deploying them. What’s more, there is every indication of significant room to continue the cost trend in solar and energy storage for at least a decade or two to come.

        In wind power, while the efficiency of wind turbines is unlikely to rise much, it similarly matters less than other metrics. If the levelized cost of wind power can be brought down through cheaper wind turbines (or innovations such as high altitude wind) that is the key metric.

        In steel manufacturing – it may indeed approach a minimum point. But steel is not the only structural material available to us. We see it being gradually replaced with aluminum and even carbon fiber (which was the point of the carbon fiber cost trend in the book). From the purpose of the economy, the relevant category isn’t ‘steel’, it’s ‘structural materials that can be used for the purpose steel is used for.’

        In sum, I see some areas where we are close to the limits of efficiency of a particular technology. But I see few areas where the overall trend in cost reduction or in improvement of the overall category is close to saturation. (With the caveat that the future always surprises us, and I’d like to see us take multiple bets to try to avoid being clobbered by one technology path unexpectedly stagnating.)



        Robert Wilson said:
        March 22, 2015 at 3:39 pm


        You seem to just be changing the rules of the game. Instead of accepting that your claim of exponential improvements in efficiency is false, you are just shifting the subject.


      Robert Wilson said:
      March 22, 2015 at 9:53 am

      And Ramez

      I’ve just noticed you putting words into my mouth on Twitter and claiming I don’t understand exponential growth. I guess that it is easier to misrepresent a critique than to actually deal with it. You similarly misrepresent Smil’s numbers to make it seem he is assuming exponential growth. I’ll take you a lot less seriously in future.


        Ramez Naam said:
        March 22, 2015 at 3:25 pm

        I think you mean this tweet:

        I vented some frustration, without naming you. I think that hardly counts as putting words in your mouth. I had no intent of misrepresenting your critique. I was frankly mystified by your choice of passages to compare and contrast, since, as the first commenter noted, they don’t disagree.

        By the way, I went back to look at the book. Towards the end of Chapter 12, where I talk about the exponential price trends in solar and batteries, I have this passage talking about the flattening of exponential curves and concrete concerns. I hardly think this is buried.

        “Yet there are reasons for concern, or at least, not to take these gains for granted. Exponential curves tend to eventually flatten out in nature. History is littered with examples of trends that didn’t continue. For a while in the 1940s, 1950s, and 1960s, you could draw a graph of the maximum speed a human had ever traveled at, rising astronomically as the sound barrier was broken in 1947 up through May 1969, when Apollo 10 carried three astronauts at speeds close to 25,000 miles per hour. At that rate of growth, we should now be able to travel at around 26 million miles per hour. Needless to say, we’re not.

        And there are concrete challenges ahead. Ecologist Vaclav Smil points out that the last energy transition, from wood to fossil fuels, happened at a time when the world used less than 1 terawatt of power. Today we use 17. The sheer scale of the amount of new equipment that must be built and deployed makes the transition from fossil fuels to wind and solar possibly the largest industrial challenge of all time.

        Along the way, we’ll run into numerous problems. Some are on the horizon now. Silicon photovoltaic cells use the rare earth element indium. Thin film cells use the rare earth tellurium. Both are currently in short supply in global markets. Supply will very likely ramp up in response to price, but it’s hard to know how soon. Researchers have also shown that it’s possible to build cells that don’t need rare earths, for example by using carbon nanotubes, but those techniques are new and still extremely costly. How rapidly will they catch up in price?

        The price of other components that go with solar panels is also becoming an issue. While solar cells themselves have generally dropped in price by about 20% per doubling of capacity, the invertors that convert the DC electricity of the solar cells to the AC used throughout the world are decreasing in price at only half the rate. Other parts of the total cost of installing a solar system, including the labor, permitting, and whatever structure the cells are mounted on, are declining in price more slowly than the core technology of solar cells. Can we reduce those prices more quickly?”



        Robert Wilson said:
        March 22, 2015 at 3:32 pm


        Sorry. They do disagree. What you argue in them is totally flat out wrong. There is simple way of finding out if efficiency is increasing exponentially and that is to plot a time series. This shows clearly that steel making, electricity production and travel efficiencies are not improving exponentially.

        You explicitly claim these things are increasing exponentially. They are not.


    Ramez Naam said:
    March 22, 2015 at 4:35 pm

    Yes. In the book, there is a time series of steel making energy cost in the US. I’ve just switched it to a log scale on my computer. From 1970 – 2005, it’s nearly a straight line on that log scale, showing a reduction from more than 52.6 million BTUs per ton of steel produced in the US to 11.4 million BTUs per ton of steel produced in the US.

    That exponential may run out of steam (no pun intended). But it has indeed followed a roughly exponential trend over that time.

    The same is true for the cost of solar power, the cost of lithium-ion battery storage, the energy cost of desalination, the cost of carbon fiber, etc..


      Robert Wilson said:
      March 22, 2015 at 4:49 pm


      The graph in your book about steel is misleading. I think I explained that to you before.

      You lump together primary steel produced using blast furnaces with secondary recycled steel using electric arc furnaces. The only meaningful comparison is of primary steel efficiency in 2005 with primary steel efficiency in 1970. And this does not show exponential improvements at all. Rates of improvement have slowed down. This is well known, except to seekers of perpetual exponential improvements.

      Here are relevant references:


    donough shanahan said:
    March 23, 2015 at 9:04 am

    Steel figures vary. The 20 GJ/t figures probably comes from Siemens. In terms of accuracy, it is not bad according to Bluescope where @ Port Kembla, they reckon on a figure of 26 GJ/t [1]. That is without BOS recovery.

    US EPA give a similar annual rate of energy reduction looking forward. [2]



Comments are closed.