## Introduction

A couple of weeks ago I wrote an article illustrating why even the transition to nuclear energy will not be able to keep up with our energy consumption if such consumption keeps growing at the rate it has been growing since at least the industrial revolution.

I've recently had the opportunity to debate the contents of the article, so I feel that it might be appropriate to clarify some aspects, and delve into some points with more details.

But first of all, a recap.

In the previous article, I make some back-of-the-envelope estimates about for how long it would be possible to keep growing our energy consumptions at an exponential rate (doubling approximately every 30±5 years, i.e. with a rate between 2% and 3% per year) under several (generous) assumptions on our energy productions capabilities.

Exponential Expiration Time (EET) scenarios for nuclear energy assuming a constant growth in energy consumption with rate $k=2%$ per year, starting from the current ${r}_{0}=6\cdot {10}^{5}$ PJ/yr, for different efficiency levels $E$ (in percent) of mass-to-energy conversion (theoretical maximum: $P=90$ PJ/kg), and different amounts of available mass $M$. The EET is computed in years using Bartlett's formula $\left(\frac{1}{k}\right)ln\left(k\frac{R}{{r}_{0}}+1\right)$ and the total amount of energy that can be produced is computed as $R=E\cdot M\cdot P$.
Mass (kg)
$8\cdot {10}^{9}$ $5\cdot {10}^{12}$ $7\cdot {10}^{12}$ $1.2\cdot {10}^{13}$ $1.2\cdot {10}^{17}$ $5\cdot {10}^{17}$ $7\cdot {10}^{17}$ $3\cdot {10}^{22}$ $9\cdot {10}^{22}$ $7\cdot {10}^{23}$ $3\cdot {10}^{27}$ $2\cdot {10}^{30}$ $4\cdot {10}^{42}$
$0.0013%$
$0.13%$
$1%$
$10%$
$100%$
$10×$

Note: the table currently needs JavaScript enabled, because I'm too lazy to copy the data by hand for each of cell. On the other hand, this means that with the same code you can play with the numbers yourself, by changing the numbers in the following form.

(The defaults are for the current tech level and growth rate, using the total mass of the current known uranium reserves and the current nuclear energy production instead of the entire primary global energy consumption, so the EET refers e.g. to a condition in which the fraction of total energy covered by nuclear remains constant, while the total energy consumption grows at the current rate.)

## Point #1: it's not a prediction

The point of the article was not to make a forecast about what will happen.

The only point of the article was to show the upper bounds of the exponential expiration time (EET) of energy sources if energy consumption keeps growing at the rate it's growing.

Specifically because it was an estimation of the upper bound, the longest-term predictions were done under ideal, and absolutely unrealistic, conditions, such as in particular the possibility to convert matter (any matter) to energy with 100% efficiency, which —by our current understanding of the physical world— cannot produce more than 90PJ of energy per kg of mass.

Now, this is obviously unrealistic: even with nuclear (the most efficient form of energy production we know now) we only get five orders of magnitude less than 90PJ/kg. But it's intentionally unrealistic, leaving plenty of room to scientific and technological progress to catch up.

### Objection #0: you can't tell that it's an upper bound

It's obviously quite possible that in the future (even in the near future) we might be able to find a more efficient form of energy production compared to the best we can do now.

However, the possibility of such an energy source being practically exploitable to produce significantly (i.e. orders of magnitude) more than 90PJ/kg is extremely slim. What it would require is:

1. a scientific discovery that invalidates the famous $E=m{c}^{2}$ formula, showing a way to produce orders of magnitude more than 90PJ of energy per kg of mass or equivalent;
2. technological progress to make such scientific discovery exploitable to produce energy with sufficient efficiency that the amount of energy produced is still orders of magnitude more than 90PJ/kg (or equivalent);
3. that such scientific discovery and technological progress happen before we hit the EET of our current energy production methods.

Now, I'm not saying that this is impossible, but the chances of this happening are so low that I can quite safely claim that the estimations to the EET computed with 90PJ/kg are, indeed, the upper bounds to the EET assuming energy consumption keeps growing at the current rate.

### That being said …

So, again, the point of the article was not to try and predict the future, but only to see for how long still we can keep growing at the rate we're growing.

In fact, if a point had to be taken from the article, I would say that the main point should be the final suggestion: that it's better to invest in reducing the growth rate of energy consumption than it is to invest in improving energy production efficiency.

But let's move on to the more solid objections.

## Objection #1: I'm ignoring the benefits of technological progress

One objection I've read is that my calculations don't take into account the benefits in terms of efficiency (both in energy production and in energy consumption) that will come from technological progress.

For energy production, this is actually mostly false: as I mentioned in the previous point, my estimations of the EET are done in such favorable conditions that I leave room for several orders of magnitude of improvements in energy production efficiency (at least up to the quite realistic but ideal limit of 90PJ/kg). Of course, it's not completely impossible that we won't find (before the expiration date!) a means of energy production that allows us to extract, in practice, more than 90PJ/kg. But unless such a very hypothetical method, beyond even our current scientific comprehension, allows to produce several orders of magnitude more than 90PJ/kg, this part of the objection is completely moot. In fact, even with several orders of magnitude more it would be a very weak objection, since each order of magnitude increase in efficiency only buys us around 3 doublings, which at the current rate means around a century.

For energy consumption, the objection is true, in the sense that I do not discuss the possibility for technological progress to improve the efficiency of our energy consumption, i.e. the possibility to waste less of the produced energy, or to do more work with the same amount of energy.

This is true, but again it's intentional, since how the energy consumed is being spent is irrelevant to my point. The only thing that matters is how much, and how quickly this grows.

Now, for the “how much”, the efficiency of the consumption is completely irrelevant. Where it can become relevant is on the growth of the consumption itself. However, finding a more efficient way to use energy doesn't necessarily mean that less energy will be used (in fact, historically this is mostly false).

That being said, even if improvements in efficiency of consumption did lead globally to a decrease in energy consumption growth, it wouldn't invalidate my point. As an objection, this would make sense if my post was an attempt at making a prediction of what would happen. But it's not, so this is not really an objection.

Au contraire, given that —if a point has to be made— the point would actually be that we should concentrate our efforts on reducing energy consumption growth, encouraging such technological progress (and such application of it) is actually exactly what my post aims for, by providing the estimated EET for our civilization if we don't go in that direction.

That being said, I can't say I'm particularly optimistic of this actually happening any time soon: when humanity finds a way to use energy more efficiently, this doesn't usually turn into “doing the same work with less”, but it tends to become instead a “let's do even more work with the same amounts of energy”.

In fact, even when at the individual level this may lead to lower consumptions, this decrease is not reflected globally; on the contrary, the higher efficiency leads to more widespread adoption of the technology, leading to an overall higher consumption: which is exactly why, despite the massive increase in efficiency since the beginning of the industrial era, energy consumption is still growing at a more-or-less constant rate.

## Objection #2: to grow exponentially for that long, we would have taken to the stars

This was the first objection that tried to take issue with the continuing exponential growth. It was an interesting one, but still rather weak. Moreover, albeit in a bit underhanded way, I had already addressed it in the post, pointing out that the entire (estimated) mass of the Milky Way will last less than 5 thousand years if energy consumption keeps growing at this rate.

For comparison, the radius of the Milky Way is estimated to be between 80 thousand and 100 thousand light years: we wold run out of energy long before even being able to visit our galaxy without FTL.

With FTL? Possibly we could visit our galaxy then, but who knows how much energy is consumed by that.

## Objection #3: you can't make predictions that far into the future

(“That far” being either the millenia for the consumption of our solar system and beyond, or even just the few hundred years before we run out of fissile material to fuel nuclear reactors thousands of times more efficient than the ones we own now.)

This objection comes in at least two variants.

One is essentially on the theme of the already-addressed objections #0 or #1 above, the other comes as a variation on the theme that the exponential growth assumption is invalid.

In either case, it's obviously true that I can't make predictions that far into the future. But then again, it's also true that I'm not making predictions, I'm just calculating the EET under the assumption of constant growth.

Of course, if the exponential growth assumption is invalid, then the EET doesn't hold —but that's not because I can't make predictions into the future, it's because the exponential growth assumption is invalid.

And that's actually OK, because the whole point, as I mentioned, is that we should slow down the growth to either get out of the exponential growth altogether, or at least lower the grow rate to something that will allow growth for a much, much longer period.

So let's get to the final objection:

## Objection #4: we will not grow exponentially for long anyway

On one hand, I could dismiss this with a simple “duh”, since the whole point of the previous post is that if we don't do it by our own choice, it will happen anyway, catastrophically, when we get so close to the EET that it will be apparent to all we won't be able to keep going —except that it will then be too late to slow down without a civilization collapse.

It's interesting however to see the forms that this objection can take. Aside from #2 above, and the masked #3, there's a couple of interesting variants of this that deserve a mention.

### Objection #4a: the magnitude of the consumption after a few more doubling is inconceivable

While the wording wasn't exactly that, the basic idea is that if we keep doubling for centuries still, the order of magnitude of the consumption would be so high that we can't even imagine what all that energy would be used for.

And while it's true that we would be hard-pressed to imagine energy consumptions that large, it's not really much of an objection, since this has always been the case. Would anyone have imagined, even just 20 or 30 years ago, that we'd end up air-conditioning the desert?

Ironically, this objection was raised by the same individual that objected to the 90PJ/kg upper limit: so you can imagine us finding a way to produce more energy than that, but not us consuming several orders of magnitude more energy than now?

Honestly, I have fewer problems imagining the latter than the former: flying cars anyone? teletransportation? robots for everything?

### Objection #4b: population and consumptions will stabilize in time

This is an interesting objection, because in the long term it's quite likely to be true. I will call this the “logistic” objection, because the fundamental idea is that population and consumption follow a logistic function, which is essentially the only way to avoid the Malthusian trap of overpopulation (more on this later).

Now, let's accept for the moment that this is indeed mostly likely to be true in the long term. The big question is: how long of a term, and how fast will it stabilize?

There are two primary contributions to the global energy consumption: per-capita consumption, and world population. For the global energy consumption to stabilize, we thus need (1) the world population to stabilize and (2) the per-capita consumption to stabilize.

Both of these things are actually strongly correlated to the quality of life and standards of living, and so far they have exhibited a distinct tendency to “flatten out” while improving: more developed and wealthier nations have both a more stable population (sometimes even exhibiting negative growth, if not for immigration) and a reduced (or, again, slightly negative in some cases) growth in energy consumption per capita (although different countries have settled at different rates). Developing nations, on the other hand, have an energy consumption growth that is much higher than the world average: China and India, for example, that together account for nearly half the world population, both have a primary energy consumption growth rate that is around 5% per year (doubling time: 14 years).

Note that in both my previous and this posts the only real underlying assumption is that we don't want to reduce our standards of living nor quality of life. It's clear that without this assumption the exponential growth hypothesis doesn't hold, since it's quite simple to reduce energy consumptions simply by stopping using energy —and thus renounce all of the things in our life that depend on it. (This is also evident when looking at the global work energy consumption over time, and how it “dips” after each recession.)

Let's take the USA today as reference for “stable” energy consumption per capita, which is about 80MWh or slightly less than 300GJ per person. (By the way, did you know that the USA is not the worst offender in terms of energy use per capita? small nations such as Iceland and Qatar have much higher per-person energy use, currently closer to 200MWh per person, or 720GJ per person; even Norway sits slightly higher than the USA, at over 90MWh per person.)

We can expect global energy consumption to keep growing at least until the whole world reaches a similar per-capita consumption, and considering that the world average per-capita consumption is 20MWh per person, growing at a rate of slightly less than 1% annually on average (doubling time: over 70 years), this will take a century and a half if things keep going at the current rate. In fact, it will take at least 70 years even just to get to, say, German levels (around 40MWh per person per year).

If energy consumption per capita stabilizes, global energy consumption will only grow with population: after the ~2.1% growth rate peak reached in the '60s of the XX century, population growth rate has been on a stable decline, and is currently slightly over 1% per year, projected to drop below 1% halfway through this century —thus earlier, in fact, than the doubling time of the per-capita energy consumption.

With these two pieces of information, we can thus say that —unless something goes catastrophically wrong— the global energy consumption will keep at the current rate at least until the end of the XXI century. What will happen after that? According to those raising the objection, the flattening out of the population growth will only require the maintenance of the standards of living, which will require a constant (if not decreasing thanks to technological progress) amount of energy per year.

But is this actually the case?

In the following sections I will discuss two possible counter-points to the “logistic” objection, at the end of which I will drive the following conclusion: the most likely alternative to exponential growth is not stabilization, but societal collapse, i.e. a profound crisis that will lead to a drastic decrease in quality of life and standards of living for the majority of world population.

## Counter-objection #1: there's no guarantee that the population will stabilize

Let's briefly recap what the Malthusian trap is. The basic idea is that, in a case where resources (e.g. food) are abundant, population grows exponentially. However, if the resources do not grow at the same rate as the population, we soon reach a point where they are not abundant anymore: there are less resources than the population would require, and this leads to the population collapsing (this is the “trap”), until it again drops below the level of scarcity, and the cycle begins again.

This kind of phenomenon has in fact been historically observed, both locally and globally. However, this seems to have stopped happening since the industrial revolution: since the XIX century in particular, population worldwide has instead grown at an ever-increasing pace up to the second half of the 1960s, peaking at around 2.1% per year. The growth rate has since been decreasing, dropping today to about half the peak rate, but still keeping a positive (larger than 1%, in fact) rate.

The observed trend is quite different from what could be expected by Malthus' model. The chief explanation for this has been the accelerating pace of technological progress, that has allowed the avoidance of the Malthusian trap by changing the ways resources are consumed (improving the efficiency of their consumption, accelerating the shift from one source to another as the previous one became scarcer, etc).

Avoiding the Malthusian trap has allowed a different mechanism to take over: the demographic transition from a child-mortality growth limit to an old-age growth limit. In this model, the plateau in population growth depends essentially on the improvement of living conditions that lead to lower child mortality, and a subsequent (and consequent) lowering of fertility (as a larger percentage of children reach adult age). As long as technological progress maintains the resource/population ratio high enough to avoid the Malthusian trap, this demographic transition shifts the age distribution up, as humans lives approach their maximum natural extent and fewer children are born.

This plateau actually contributes to avoiding the Malthusian trap by keeping the population size below the threshold of resource exhaustion.

There's more to it, though.

Looking at the timeframe of the rapid growth in world population, it's interesting to see how the time span of growing growth rate matches pretty well with the period of more revolutionary scientific and technological breakthroughs.

It's possibly a sad state of affairs that since the end of the Cold War technological progress, despite advancing at an incredible pace, has not given us any world-changing breakthroughs: most of the tech we use today is more a refinement of tech that emerged between the interwar period and the end of the Cold War than something completely new and original. (Sad state of affairs because it would hint that wars, be them hot or cold, are a stronger promoter of technological progress than peace.)

In some sense, we've reached a plateau not only in population growth (in the more developed nations), but also in the —allow me the expression— “originality” of technological progress.

Now the question is: when the next significant breakthrough happens, will it come alone, or will it be associated with a renewed increase in population growth rates?

One would be led to answer negatively, since we're already reaching the maximum natural extent of human life, but it's actually quite plausible that we can expect another spike. Some possible scenarios as examples:

1. improved medical knowledge allowing significant age extension, upping e.g. the average age of death by about 50% compared to now; this would lead to another (although smaller) demographic transition to reach the new plateau associated with the longer life expectancy;
2. colonization of the currently uninhabited (or very sparsely inhabited) areas on the planet surface, including both deserts and oceans: again a new spike in population growth;
3. space travel and the colonization of the inner planets (Mars and Venus at least) would lead to a massive spike in population growth (not world population only anymore, but global humanity population growth, of course), something that will go on for several centuries more.

These are just examples, of course, but each and all of them are quite plausible. And together with many others, possibly unthinkable at the moment, they are a hint that we are only one technological breakthrough away from the delay of the population stabilization than we can forecast at the moment.

And with it, of course, the associated growth in energy consumption.

## Counter-objection #2: stable population and quality of life does not imply stable energy consumption

While it is true that most modern, industrial, “Western” societies have reached a largely stable population, quality of life and energy consumption, I posit that the stabilization of the energy consumption is not, in fact, due to the stabilization of the population and their standards of living. In fact, I will further argue that a stable population at our standards of living cannot be maintained without growing energy consumption. Allow me to justify the latter first, and then explain why we have the perception of a locally stable energy consumption where population and standards of living have reached our levels.

As I've already mentioned, the accelerating pace of technological progress has allowed us to avoid the Malthusian trap (so far): humanity has been able to circumvent the resource/population ratio inversion by improving resource utilization and regeneration at a faster pace than population growth. However, the cost of these improvements has always been paid in terms of energy consumption.

Increased crop yields rely on synthetic fertilizers, whose generation is more energy-intensive than natural ones, and on agricultural machinery, whose construction and use is more energy-intensive than traditional human- or animal-based alternatives. Modern distribution networks are likewise more energy-consuming to build, maintain and use than footwork or animal transportation. For raw materials, especially those that are essentially non-renewable, the trap has been avoided by shifting consumption, as they became scarcer, from the “lower-hanging fruits” to materials that are harder to find, extract, create or manipulate, and that would therefore be prohibitive at lower levels of efficiency or energy production.

It's interesting to show the last part (material source transitions) from an example that will probably soon apply to energy production itself: as shown before, the EET of the current estimated uranium in known conventional sources (8 million metric tons) is only 14 years (assuming constant energy consumption growth of 2% per year, and nuclear alone being used for energy production). This means that soon uranium extraction from unconventional sources (especially the sea) will become not only convenient, but in fact the only possible way to keep maintaining our energy requirements —but extracting uranium from the sea is much more expensive, energy-wise, than the conventional methods.

In essence, what the industrial revolution has allowed has been to shift the entire burden of resource management into one single resource (category): energy. This, by the way, is why energy is the only resource I've discussed in the previous post: its EET is the only one that really matters, since expiration of any other resource can be compensated by increasing energy consumption.

For example, it has been said that “water is the oil of the 21st century”: this maxim is intended to mean that (clean, drinkable) water will become so scarce in the near future that it's likely to become as pricey and crucial as oil (as primary energy source) was in the XX century. Water, after all, is an essential resource for human survival and well-being both as a primary resource (drinking) and as secondary resource (e.g. farming), and with its usage growing at an exponential rate (doubling time: around 20 years), some scientists are worried that we'll soon hit its EET.

I'm actually not worried of that happening before we hit the energy EET, because with water like with any other resource we can (and in fact I predict we will) be able to expand our (clean, drinkable) water reserves trading out more energy consumption to reduce water consumption, improve filtering and develop better ways to extract useful water from the sea or the atmosphere.

In other words, as long as we can keep producing energy, humanity is largely unaffected by the Malthusian trap of other resources (or, in yet other words, the only resource that would trigger the Malthusian trap now is energy —and it will happen, as we've discussed in the previous post in this series).

The problem with that is: by avoiding the Malthusian trap, even if population stops increasing, we're already past the Malthusian trap point, meaning we're already consuming resources faster than they can regenerate: and this means that even if population stops growing, we will soon run out of the resources we're using, and we'll need to move to other, more “energetically expensive” resources to replace them. A similar argument holds for the environment: we have triggered a vicious cycle where our standards of living destroys the environment at a rate faster than it can regenerate, and this leads to higher energy consumption to preserve inhabited areas at levels which are more comfortable for humans (open air conditioning in the desert is only the prelude), which in turns accelerates the destruction of the environment, requiring a growing energy consumption to compensate: the “best” recipe for exponential growth.

That being said, it's quite possible (but see below) that the growth rate of energy consumption then (after the world population settles in size and standards of living) will be lower than the one we are experiencing now that the population is growing, and that's a good thing. But the key point is that our current standard of living still requires exponential growth in energy consumption just to be maintained at the present level.

Why then, one may ask, we are not seeing such growth in energy consumption in nations where the population and living standards have largely stabilized?

The answer to this is that what we are observing is a local aspect of a non-local phenomenon: a large part of the energy consumption needed to maintain our standards of living has been externalized, by outsourcing much (if not most) of the manufacturing process and resource extraction to the developing nations.

In other words, the energy consumption growth rate observed in developing nations accounts not only for the growth in size and standards of living of their population, but also for the maintenance of ours —hence energy consumption growth rates of 5% or higher in the face of population growth rates of 3% or lower.

In this situation it's obviously hard to isolate the component in energy consumption growth related to internal factors from the ones related to the burden of the maintenance of “stabilized” nations, but as the developing countries approach our levels of stability and quality of life, and the outsourcing possibilities diminish, we are likely to see a new redistribution (and relocalization) of the energy consumptions that will help characterize the factors. My “gut feeling” (correlating the energy consumption and population growth) is that the baseline (“maintenance-only”) energy consumption growth will remain around 2% (or marginally lower, but most likely not lower than 1%), but we'll have to wait and see.

## And the conclusions?

Even though the estimation of the energy EET was not intended to be a prediction of how things will turn out, it's quite plausible that the current growth rate in energy consumption will continue long enough to get us there, unless either active action is taken to focus research on reducing the energy consumption (growth) needed to maintain our current standards of living or we end up hitting some other snag (before the energy EET) that leads to societal/civilization collapse, with the consequent drastic reduction in energy consumption.

And nuclear still won't save us.