The idiocy of Mars

If you think that we can continue economic growth by simply moving to Mars, you’re a fool.

Many people do not understand that the growth in resource usage by humans will, if not stopped, result in us hitting the limits of what Earth can provide at some point in the fairly near future. Unless we address this problem the result will probably be the collapse of civilisation. Some of the people who think they do understand this problem argue that, well, there is Mars¹: we can just go there and carry on as normal and everything will be fine.

It won’t be, and here’s why.

Growth

We all hear about economic growth in the news. And people like it when it’s some positive number. Growth:

can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy over time. [From Wikipiedia article above.]

What that means is that growth is the rate of change of some measure of the size of an economy. Growth is measured as a percentage increase in the size of the economy per year, which I will call \(g\), so if at some time \(t\) (measured in years) the economy has size \(s(t)\), then \(s(t + 1) = s(t)(1 + g/100)\). That means that if growth is constant over the long term, the size of the economy is increasing exponentially with time:

\[ s(t) = s_0 e^{t/\tau}\quad\text{where $\tau = 1/\ln(1 + g/100)$} \]

And economists are very keen that \(g\) should not drop to zero or, still worse, become negative: they want it to be some long-term constant value.

Rescaling

One possibility is that this measure \(s(t)\) might simply involve rescaling the economy somehow: we think it’s bigger but in fact it’s not. Let’s say that I’m interested in buying aluminium: if, every year, the economy ‘grows’ by \(1 + g/100\), but the price of aluminium also grows by \(1 + g/100\) then I can’t actually buy any more at the end of the year, even though the economy has ‘grown’.

This, in fact, is inflation: the economy hasn’t grown, it’s just been rescaled. Inflation is not what people mean by growth: they mean that you can actually buy more stuff.

Well, if you can buy exponentially more stuff over time there’s a problem, isn’t there? Even economists can see this, I expect.

Hand-waving

So if growth means being able to afford ever more material goods there’s a problem: at some point you’ll run out of stuff. This is awkward for economists who have built entire theories on the idea that growth can continue indefinitely.

Is there a meaning of the term ‘growth’ which doesn’t involve crashing into finite limits or somehow finding an endless source of new material goods? One option that economists push is that we start being able to use the existing raw materials ever more efficiently. That’s fantasy in the medium term because there are hard physical limits on efficiency. Another popular option is that we all somehow fall into a simulation and live ever more complex virtual lives, while the real world carries on without us. That’s almost certainly also fantasy both because, despite endless AI hype, we have no idea how to do that, and because exponential growth in computing power also has hard physical limits²: Moore’s law is only a transient phenonenon.

In these hand-waving cases there’s also a question about what happens to the prices of physical materials. For things to make any sense the prices have to inflate at least as fast as the growth rate, and in fact faster. If, for instance, the price of aluminium remained roughly constant (when corrected for currency inflation), then after some time it would be possible to simply buy all the aluminium in the world and thus hold to ransom anything which is made from it, however efficiently that is done. So that shows that the price of materials must rise at least as fast as growth. In fact it must rise faster than that: given the finite supply of aluminium ore, the real cost of aluminium should represent that, meaning that, even as people become richer, new physical goods must become more expensive and scarce over time.

But there’s no need to speculate: instead let’slook at what actually has happened.

Energy

A good proxy for the processing and consumption of material goods is energy consumption: energy is consumed to do some useful physical work, so it should correlate approximately with the amount of materials being processed in some way. And energy is fungible, so it’s easy to measure. And data on energy usage is available. Tom Murphy’s excellent book, Energy and Human Ambitions on a Finite Planet contains, in section 1.2, this information for the US, sourced from the US Energy Information Administration. He uses this data to derive a rate of growth in US energy usage of about \(3\,\mathrm{\%/y}\) between about 1650 and 2000. So during this period growth in energy usage was approximately exponential and so, it’s pretty safe to say, there was exponential growth in the physical material being used during this period.

So at least until recently (see below) growth meant what it naïvely means: an exponentially increasing rate of material production. This obviously can’t continue on Earth.

Mars

But we can just go to Mars right? Once we’ve used up Earth we can up sticks, move planet, and carry on. It took us thousands of years to use up Earth’s resources, so Mars will buy us thousands more years.

Or so say the innumerate space fantasists.

This kind of claim is so silly it’s hard to know where to start. But let’s just take it at face value. I will assume:

• it is possible to either move huge numbers of humans to Mars or to mine it for raw materials and bring them back to Earth cheaply, using spacecraft driven by some unexplained magic³;
• Mars has the same amount of raw materials as Earth (it doesn’t);
• we can hit the ground running and simply immediately start stripping Mars at the rate Earth was being stripped;
• any other kind of problem I haven’t thought of can be solved by yet more unexplained magic.

So let’s do the maths.

The maths

Let’s assume that we’re using up physical resources at some rate \(r(t)\) which is increasing exponentially:

\[ r(t) = r_0 e^{t/\tau} \]

Where \(r_0\) is the rate at some time \(t = 0\). This can be integrated to get the total resources consumed to some time:

\[ R(t) = R_0 e^{t/\tau}\quad\text{where $R_0 =\tau r_0$} \]

Here \(R_0\) is the total consumption to \(t=0\).

OK, so let’s measure \(t\) in years and assume that the annual growth percentage is \(g\). In other words:

\[ r(t + 1) = \left(1 + \frac{g}{100}\right)r(t) \]

Well

\[ \begin{aligned} r(t + 1) &= r_0e^{(t + 1)/\tau}\\ &= r_0e^{t/\tau}e^{1/\tau}\\ &= e^{1/\tau}r(t) \end{aligned} \]

so we can get \(\tau\) in terms of \(g\):

\[ \tau = \frac{1}{\ln\left(1 + \frac{g}{100}\right)} \]

So, now, how long does it take for the resources consumed to go up by some factor, say \(k\)?

\[ \begin{aligned} k = \frac{R(t + \Delta t)}{R(t)} &= \frac{e^{(t + \Delta t)/\tau}}{e^{t/\tau}}\\ &= e^{\Delta t/\tau} \end{aligned} \]

or

\[ \begin{aligned} \Delta t &= \tau \ln k\\ &= \frac{\ln k}{\ln\left(1 + \frac{g}{100}\right)} &&\text{using $\tau$ from above} \end{aligned} \]

How long does Mars get us?

Let’s assume, as above, that at \(t=0\) we run out of resources on Earth and start mining Mars, and that we start doing it at the same rate that we were stripping Earth, and that Mars has the same amount of material as Earth, and that growth continues as before at a rate I will assume to be \(2\,\mathrm{\%/y}\) (so lower than the measured rate above). When do we run out of resources on Mars? Well, we run out of resources when \(R(t+\Delta t)/R(t) = k = 2\), so when

\[ \begin{aligned} \Delta t &= \frac{\ln 2}{\ln\left(1 + \frac{g}{100}\right)}\\ &\approx 35\,\mathrm{y} \end{aligned} \]

Under entirely unrealistically optimistic assumptions, stripping Mars will maintain growth at \(2\,\mathrm{\%/y}\) for 35 years.

What about Venus? Jupiter?

If we make the same assumptions about Venus and start on that after Mars it gets us a further 20 years and six months. If instead we went to Jupiter, and assuming its resources scale like the ratio of its mass to Earth’s we’d buy about 256 years, which is better, but we’re not going to be able to do that.

So, growth of physical resource usage can not be maintained at \(2\,\mathrm{\%/y}\) for any significant amount of time in the future.

Perhaps good news

The good news here is that data since 2000 does make it look as if the growth in energy usage is slowing down. That means either we’re moving into one of the economists’ handwavy fantasy scenarios (hint: it doesn’t), or that we’re in the early stages of falling off the exponential phase of growth. Assuming that’s true then we’re moving into a world where the models economists have built simply no longer work, and where we can’t endlessly assume we will get richer for ever. It’s perhaps not coincidental that the years since 2010 have seen the rise of a number of extremely unavoury political movements: there will be more of these as there is more competition for increasingly scarce resources and as climate change takes effect, further increasing scarcity and driving migrations on vast scales. The likely outcome, I think, is not a smooth transition to a zero or negative growth world, but something pretty unpleasant: resource wars between major players, extreme racist responses to the migration problem, authoritarianism and fascism.

Some of these processes seem to be well on the way as I write.

Some pictures

Here are plots which show the time to exhaust resources on:

• Mars (about \(35\,\mathrm{y}\)) & then Venus (another \(20.5\,\mathrm{y}\), exhausting both in about \(55\,\mathrm{y}\));
• Jupiter alone (about \(291\,\mathrm{y}\));
• the Sun alone (about \(642\,\mathrm{y}\)).

These assume that available resources scale like mass, and that growth continues at \(2\,\mathrm{\%/y}\). Note that time is the y-axis in these plots: the x-axis is the resource ratio (assumed to be the mass ratio) compared to Earth’s.

Time to exhaust resources on Mars & Venus, growth at 2%/y

Time to exhaust resources on Jupiter, growth at 2%/y

Time to exhaust resources from the Sun, growth at 2%/y