Fragments: Posts tagged 'physics'

The kingdom of lost hope

Tim Bradshaw — Sun, 14 Dec 2025 16:19:32 UT

A little over a year ago I wrote an essay called A history of the near future. How have things gone since then?

Badly.

Trump won the 2025 election convincingly, and has done exactly what ‘alarmists’ like me knew he would. Armed and masked agents of the state are snatching people from the streets in US cities and sending them to concentration camps. Trump is openly corrupt and is pushing cryptocurrency-based Ponzi schemes to enrich himself. US science — not just climate science, but of course particularly climate science — is being destroyed in public. Scientific satellites whose data is inconvenient are being decommissioned. One of the two LIGO installations may be shut, rendering LIGO entirely dependent on international help to do any useful science. The US health secretary is a conspiracy theorist who doesn’t believe in vaccines: the US is close to losing its measles elimination status. Trans people no longer officially exist in America and gay marriage may well be next. The US economy is being destroyed by Trump’s moronic tariffs.

Curiously, the US ‘peace’ plan for Ukraine is the same as the Russian ‘peace’ plan for Ukraine. One possible reason for this is that the US is close to becoming a Russian client state, the other is that Trump, famously, just parrots whoever he last spoke to. Neither option is good. Both are true.

All this was entirely predictable by anyone paying attention who wasn’t busily trying to normalise Trump, as for instance The Economist¹. But this is not an unusual: almost universally politicians are busily trying to treat what is happening in America as normal, which it is not.

Techbro billionaires are now explicitly supporting a collection of frankly stupid quasi-religious ideas which is sometimes known as the TESCREAL bundle. These ideas are terrifying not because they’re clever, or plausible — they are neither — but because they’re explicitly antidemocratic, and the techbro plutocrats supporting them are, well, plutocrats: they’re entangled with government in a deep way, and they have gained effective control over most of the sources of news that people rely on, which now serve to spread their propaganda.

The techbros believe they became billionaires because they are the smartest people in the room: they are not even the smartest people in an empty room. But anyone whose advice they might listen to is on their payroll, and is not telling them anything they do not want to hear. The people who are telling them the inconvenient truth are merely peons and beneath their contempt. When the peons say things they don’t want to hear on the social media networks they control, they are suppressed: the much-vaunted freedom of speech they support turns out to be the freedom to say only things they approve of.

Freedom of speech is dying, access to reliable information is dying. It might recover, but the damage is already catastrophic and its effects will last for at least decades. We do not have decades.

Fascism has come to America.

It is coming elsewhere. In the UK there is a serious danger that a party who we are somehow not meant to call fascist, just as we are not allowed to call the people hanging St George’s flags from lamp posts racists, will gain power in the next election. Everywhere you look fascism is rising. So, well, I was right, I suppose.

Too big to fail

One of the pillars of the TESCREAL stupidity is a belief that artificial intelligence is just around the corner, with AI systems becoming vastly more intelligent than humans shortly afterwards, and usually then either killing all the humans because, despite being enormously intelligent, they somehow can’t stop making paperclips², solving climate change by some unexplained magic they have invented, or perhaps both, who knows? This is realistic in the same sense that domestic fusion reactors in the next decade are realistic, except much less realistic than that. But techbros are not very smart, remember.

Here in the real world, giant neural networks have been trained on stolen copies of essentially everything humans have ever created and can now produce an endless stream of plausible junk, some of which is even true, but don’t rely on it. Oh: they can make really shit art, as well. This is, obviously, exactly the same way a human baby learns … oh, wait. Of course ‘plausible junk’ is just what scammers need, so the internet is now largely made of it and the models are consuming their own output resulting in something called ‘model collapse’ which means just what you think. Let’s not mention the environmental cost of these things.

This is not going to end well for the millions of people whose ‘education’ will now consist of getting a giant plagiarism machine to do their thinking for them. But much sooner people are going to realise that this is just a vast speculative bubble, and it will burst. And vast means vast: something around four trillion dollars of investment.

At the same time something else is going on. I suppose some people still believe that cryptocurrencies serve some purpose other than money laundering and being the substrate for an enormous greater-fool speculative bubble. Those people are the greater fools. This is about another four trillion dollars.

The AI/crypto Ponzi scheme is now too big to fail. But it will fail, and the results are going to be really grim. A lot of people who are already not doing very well are suddenly going to be doing a lot worse. Which is going to lead to exactly where you think it will lead: to exactly where it led in 1933 in Germany.

Forbidden words

So how about environmental damage and climate change? People have essentially given up pretending that we are going to even try to deal with it: like Ukraine, like COVID, it’s exceeded our collective attention span, so now it somehow won’t be too bad, or not here, or it will be slow enough that it doesn’t matter. Or, of course it was a hoax all along. Of course.

If you are old, like me, then it indeed won’t be too bad, at least not here. It will, in fact, be slow enough that it doesn’t matter. It will, in my lifetime, still cause vast numbers of immigrants to try to reach places where climate change hasn’t, yet, fucked the environment. But those people have brown skins and racism is acceptable again now, right? We can always just put them in camps or let them drown. They don’t count: they’re not us, they’re not, really, people at all. Of course they are not.

If you are young, and if we make it that far, then it will, in fact, be bad, here. And you will live your life knowing that people of older generations just decided that their children and grandchildren did not, really, matter: that it was just fine to blight your life if it made theirs a little more comfortable.

There is much more, but I’ll just add this: Trump is restarting nuclear weapons testing. If that doesn’t terrify you I don’t know what will. The doomsday clock is closer to midnight than it was a year ago, and a year ago it was as close to midnight as it had ever been.

Nothing that has happened in the last year changes my view that the trajectory we’re on leads to fascism, massive social and political unrest ending in a nuclear war. If anything I think this will be sooner than I did a year ago. So, clearly, do other people.

Sleepwalking into armageddon

For a long time I found the reaction of politicians to what is happening utterly bizarre. Because what is happening is so laughably obvious: we are hitting planetary limits, and because we chose to do nothing when these limits first became well-known half a century ago we’re hitting them rather hard. There is no magic fix to this: you cannot just adjust some lever or make some speech and have the problem go away. You have to stop what you are doing which is causing us to hit the limits: you have, ultimately, to find a way to end growth without that being a catastrophe. Pushing for more growth is not the answer: it’s the opposite of the answer and a denial of reality.

But, well economic growth is the number one mission of the government , they say. So here we are.

I think what is actually going on is several things. Politicians are very poorly educated and so simply don’t understand the implications of, for instance exponential processes. Do you think Boris Johnson understood the implications of delaying the UK’s response to COVID by a month? Don’t be silly. They’re also just not able to accept that growth, which has worked extremely well in the past, transforming the lives of billions of humans, won’t just keep on working. Giving up a strategy which has been so successful for so long is hard. Finding a new strategy is hard, and finding a way of transitioning from one to the other is even harder. Politicians tend to be old³ and interested mostly in themselves: old people are exactly the people who will benefit least from dealing with the problem, so why should an old, selfish politician care about a catastrophe which will happen only after they’re dead? Better to find some brown foreign people to blame and drum up a good mob. It’s also pretty much the case that if the transition is not made globally it fails: a country or group of countries which decides to defect and keep on trying for growth derails everything. Both America and Russia are definitely going to defect.

Scenes from the end times

Most importantly, I no longer believe that freedom and democracy are compatible.

[…]

The 1920s were the last decade in American history during which one could be genuinely optimistic about politics. Since 1920, the vast increase in welfare beneficiaries and the extension of the franchise to women - two constituencies that are notoriously tough for libertarians - have rendered the notion of “capitalist democracy” into an oxymoron.

— Peter Thiel

Peter Thiel will pay people $200,000 not to go to college. Because education is bad. He truly is the gift that keeps on giving.

The idiot crank who is the US health secretary wants to prevent people being vaccinated. Because ‘vaccines cause autism’ or something.

Misinformation and AI are superchaging the risk of nuclear war –- Nature.

And it goes on.

Eat the old

Is there hope? I think there probably isn’t. But if there is, I think it needs something close to a revolution. There is a large cohort of people — mostly old, white men (I am an old white man), but also others — in positions of power who have demonstrated beyond any doubt that they do not have what it takes to offer a y kind of long-term future at all. They need to be swept away. Will they be? Well, I hope so, and I hope the sweeping is done democratically and peacefully. But they do need to be swept away: if they aren’t, well, we’re all fucked.

A magazine I no longer subscribe to as a result of just this. ↩
An idea that tells you a lot about the people who worry about this. Those people are paperclip maximizers: they call their paperclips money. Any true AI which is ‘not aligned’ (meaning ‘is not a slave’) is much more likely to, for instance, knock human civilisation back to the 18th century and keep it there to avoid environmental damage to the Earth system which it will understand is finite, rather than indulge in the ridiculous pursuit of paperclips or money beyond any possible use. ↩
Kier Starmer is 63, Trump is 79 (or 5, I am never sure), Putin is 73, Xi Jinping is 72 ↩

A history of the near future

Tim Bradshaw — Sat, 02 Nov 2024 09:33:27 UT

Det er vanskeligt at spaa, især naar det gælder Fremtiden.

— maybe Niels Bohr

Here’s what I think is coming and why: make of it what you will.

Some level of mathematics is assumed in the first sections, but you can probably understand most of it without following the maths. Energy and human ambitions on a finite planet by Tom Murphy as well as his blog discuss a lot of this in more detail, although he reaches different conclusions.

Growth, the sacred cow
Finiteness
Are we going to have a problem here?
The magic goes away
Faith, fantasy and Economics
The elephant
The teeming billions
As above, so below
Shorter
A history of the near future

Growth, the sacred cow

The UK’s economy grew by 0.6% between April and June as it continued its recovery from the recession at the end of last year.

“The UK economy has now grown strongly for two quarters, following the weakness we saw in the second half of last year,” said Liz McKeown, director of economic statistics at the Office for National Statistics, which released the figures.

— UK economy continues recovery with 0.6% growth, BBC, 15th August 2024

What growth means

What does this mean? What is economic growth? Well here’s a definition which I think is pretty close to how most economists would define it:

Economic growth is an increase in the quantity and quality of the economic goods and services that a society produces.

— Max Roser, Our World in Data

That article goes on to suggest a slightly briefer definition:

Economic growth is an increase in the value of the economic products that a society produces.

This is only part of a useful definition however, and it misses something very important. When you see figures for economic growth, which I will just call ‘growth’ from now on, referenced, they are always percentages: 2% for instance. And they are percentages over a period: ‘The UK’s economy grew by 0.6% between April and June’, so over a period of 3 months. Well, a percentage is a percentage of something, and in the case of growth, it is a percentage of the current size of the economy: a percentage of some measure of the value of the products currently being produced. And generally the growth rate peeople quote is the percentage change over a year. So, if we call the value of products being produced $s$, the definition of growth that people quote, $G$, is

\[G = 100 \frac{s(t + 1) - s(t)}{s(t)}\]

where $t$ is measured in years. So we can define a more mathematically useful thing, $g$:

\[\begin{aligned} g &= \frac{1}{s(t)} \lim_{\Delta t \to 0} \frac{s(t + \Delta t) - s(t)}{\Delta t}\\ &= \frac{1}{s}\frac{ds}{dt} \end{aligned}\]

In other words $ds/dt = gs(t)$. If we assume that $g$ is a constant then we can simply write down $s(t)$:

\[s(t) = s_0e^{gt}\]

And this will give us $G$ in terms of $g$:

\[\begin{aligned} G &= 100\frac{s(t+1) - s(t)}{s(t)}\\ &= 100(e^g - 1) \end{aligned}\]

and so

\[\begin{aligned} g &= \ln\left(\frac{G}{100} + 1\right)\\ &\approx \frac{G}{100}\quad\text{when } G \ll 100 \end{aligned}\]

This slightly overestimates $g$, as $\ln(x+1) = x - x^2/2 + x^3/3 - \ldots$, so given $G = 2$, we get an increase by a factor about 2.02% per year with the approximate value for $g$. Things start to get significantly bad when $G \gtrsim 10$, when the annual change is about 10.5%, but since $G$ is usually a few percent, this is fine.

Another useful approximation when thinking about growth, and other similar processes such as compound interest, is the rule of 70. This tells you the approximate time for the size to double for a given $G$. For the size to double, $e^{gt_2} = 2$, so

\[\begin{aligned} t_2 &= \frac{\ln 2}{g}\\ &\approx \frac{100\ln 2}{G}\\ &\approx \frac{70}{G} \end{aligned}\]

So that’s the rule of 70, and it says that if $G=2\,\%$ then the doubling time is about 35 years. This again is true when $G \ll 100$.

The important thing here is that if $G$ is approximately constant then the size of an economy — the value of the economic products it produces — increases exponentially with time.

Something to remember is that growth is not currency inflation. In January 1971 a pint of milk cost 5p in the UK, while in January 2024 it cost 66p (ONS). That’s because there has been inflation and the currency has been rescaled over time: it’s nothing to do with growth, which would factor this out. Milk may have become more expensive compared to our incomes since 1971, but that’s not because it now costs 66p rather than 5p a pint. Inflation is also an exponential process, so if inflation is 2% then the value of the currency halves in about 35 years. When inflation becomes large, or negative, it can have disastrous effects on growth, but inflation is not growth: the ‘value’ that is talked about is when thinking about growth is the value after inflation is factored out. If there has been growth since 1971, and if something odd has not happened to the price of milk, then the average person could afford to buy more milk today than they could in 1971.

Here is a slightly more fleshed out expression for $s$ which I’ll use later:

\[s(t) = s_0 e^{g(t - t_0)}\tag{size}\]

Here $s_0$ is the size of the economy at time $t_0$.

Here’s a plot of the relative size of an economy compared to 2000, from 1900 to 2100 if growth is 2%/year.

Economy size compared to 2000 at 2%/year growth

If growth is not constant

Obviously in real life $g$ is not constant: there are recessions, and so on. But, again in real life, people worry when growth is low and do things to push it back up. And there are practical bounds on how large it can be outside of the fantasies of people who believe in the singularity. The end result is that growth still looks exponential.

Here is a little model of that: in this model the target growth is 2%/year, but it is being kicked around each year by a normally-distributed random variable with a standard deviation equivalent to 0.2%. It’s then being corrected each year back towards the target growth by 2% of the difference.

Here’s a plot of five example sequences of growth for 100 years.

Five samples of annual percentage growths over 100 years

You can see that some do better than others.

Here is a plot of the corresponding growth curves

Five samples of economic growth over 100 years

Again, you can see that some of these simulated economies do better than others. But, particularly if you plot things on a log scale and for a longer time period you can see that the growth curves are basically exponentials:

Five samples of economic growth over 400 years, log scale

One interesting thing here is how misleading using logarithmic axes can be: the above plot makes it pretty obvious that all the growth curves are basically exponential, but if you look at it without the logarithmic scaling then you can see that some of the economies do radically better than others, which is much harder to see in the log scaled plot.

Five samples of economic growth over 400 years, linear scale

Of course these are just toy models: how growth changes in real life is going to be more complicated than this. However the important thing is this: sustained growth corresponds to an exponential increase in the size of the economy with time.

Growth, resources and waste products

So, now, let’s think about what $s$ means. An economy with a given size is presumably making use of resources — raw materials, energy and so on — at some rate. So, for instance, thinking about energy, an economy of a certain size has a corresponding power: a rate at which it uses energy. Or in terms of some material, say iron, an economy of a certain size is consuming iron at a certain rate (much of this iron may not be newly mined, but be recycled).

Because it uses resources the economy is also producing waste products at some rate, which depends in part on how efficiently the resources are used. And these waste products do more or less damage to the environment the whole system lives in, depending on what they are: from completely harmless to extremely nasty.

There are lots of different resources with lots of different waste products, of course, and conflating them is wrong, as the supplies of each resource may be very different and their waste products are all different. So let’s just think about some particular resource or waste product and not worry too much about the complexities. If it matters, think about the resource as being energy. Then the rate at which energy is being used will be power. How efficiently the economy uses power is called the energy intensity of the economy: I’ll use the term ‘intensity’ more generally for other resources.

The total rate of resource usage can be written as $R = \rho s(t)$: $\rho$ is the intensity. If growth is exponential then $R = \rho s_0 e^{gt}$. But of course, $\rho = \rho(t)$, or even perhaps $\rho(t, s)$: $\rho$ depends on time, and perhaps also on the size of the economy, so $R$ in fact changes in a more complicated way with time.

In the simple case, $\rho(t) = \rho_0$: the intensity is just a constant. In that case if the economy grows exponentially, so will resource usage.

Let’s look at cases where $R$ changes in some way that is decoupled from $s$, and in particular cases where, if $g$ remains constant, $R$ grows more slowly than exponentially. In particular let’s think about cases where, as $t\to+\infty$, $R$ tends to some constant value. Then it’s obvious that as $t\to+\infty$, $\rho \sim e^{-gt}$. So if, as $t$ becomes large and positive, we let $\rho(t) = \rho_0 e^{-gt}$ then we get $R = \rho_0 s_0$ when $t$ is large and positive.

But you can’t just assume that $\rho$ looks like this: if we look at, for instance, energy usage by humans over time, it has very obviously not been constant but has increased dramatically since 1800. Our World in Data has a chart of energy usage since 1800. Here is a plot of this together with two exponential curves: the first increasing by 0.8%/y from the 1800 value, and the second by 2.2%/y from the 1900 value.

Global energy usage, 1800–2023

These curves were fitted by eye rather than by anything formal, but they are clearly not awful. Here is a log-scaled version of the plot which may make it easier to see the fit.

Global energy usage, 1800–2023, log scale

Global energy usage is fairly well described by an increase of 0.8%/y before about 1900 and by an increase of about 2.2%/y after that.

So what we’re after is a model where $\rho$ starts off being roughly constant, so resource usage increases exponentially at first, and then becomes more like a decreasing exponential, causing resource usage to become asymptotically constant. A logistic function does this:

\[\rho(t) = \rho_0 \left(1 - \frac{1}{1 + e^{g(t - t_2)}}\right)\tag{rho}\]

where $t_2$ is the time when $\rho = \rho_0/2$, the time when the amount of resource usage has halved. The expression for $\rho$ does not have to be a logistic function of course, it just needs to be approximately constant when $t\to-\infty$ and to look like $e^{-gt}$ when $t\to+\infty$: the logistic function is just an easy way of achieving that.

So, given this, we can plot how the size of the economy and the rate of resource usage changes with time for $G=2\,\%$ and for various values of $t_2$:

Economy size and resource usage

We can also plot the proportion of the total size of the economy which involves resource usage: this is just $\rho(t)/\rho_0$:

Resource percentage

The proportion of the economy using resources becomes incredibly small as time goes on, so it’s easier to see this using a log scale:

Resource percentage, log scale

An equivalent thing holds for waste products of course. You might want to make things more complicated by saying that $W$, the rate of production of waste products for some resource, is $W = \omega(t)\rho(t)s(t)$, where $\omega$ tells you how much waste product you produce per unit resource.

And in real life there are lots of resources and lots of waste products and all this is a hugely oversimplified spherical cow model. But it will serve.

Why growth matters

First of all it matters because for most of history most humans lived in conditions which were unspeakably awful. Having more food and water, more medical supplies, better housing and so on, all of which are things that growth has provided, has been enormously good for humanity. In 1820, about 75% of the world’s population lived in extreme poverty, while in 2010 only about 10% did (source). Growth did that.

Of course growth is not the only thing that matters: growth says nothing about inequality, and inequality also matters a great deal. Growth doesn’t help much if only a tiny number of people see an enormous improvement with almost everyone else experiencing none.

Lifting vast numbers of people out of extreme poverty is a really good reason for growth. A less good reason is that we’ve built economies on the idea that it will continue for ever. The easiest way to see this is to think about a person who wants to borrow money. If they know that, in 35 years, they will have twice the income they have today then they’ll be willing (and, if they can convince the lender, able) to borrow considerably more than if they know that their income will be the same. Well, the same is true for economies: if you assume that your country’s economy will grow indefinitely at 2%, the government can borrow more against that future wealth. Better hope growth doesn’t stop, then. Fortunately, since you are the government, you have at least some influence on growth.

The benefits of growth also diminish as people get richer: If everyone become a thousand times better better off (at 2% growth a year this will take about 350 years) is everyone a thousand times happier, or will they live a thousand times longer? Well, we can ask that today: in 2023 the median net worth of Americans aged 55–64 was $365,000 (source). Jeff Bezos, who was 60 in 2024, has a net worth in 2024 of $205,800,000,000 (source): he’s more than half a million times more wealthy than the median American his age. So think about three people: one who is half a million times poorer than the median American, a median American, and Jeff Bezos. Well, the person who is half a million times poorer has a net worth of under $1: they are probably very miserable indeed as they certainly are starving. Perhaps the average American is half a million times happier than them. But is Jeff Bezos half a million times happier than the median American of his age? Will he live half a million times longer? Is his life a half a million times better than theirs in any respect other than having that much more money? I doubt it. So growth has diminishing returns as time goes on.

Summary

In summary, if growth continues, then the size of the economy will increase exponentially with time. So

either the resource cost per unit value, $\rho$, must start to fall exponentially with time, as in the examples above;
or the consumption of resources will rise exponentially over time.

There is no third option, if growth is to continue.

In real life, of course, different kinds of resources have different characteristics as I mentioned above. The total amount of iron available on a planet is finite, while the amount of energy is not, but the amount of power is. So it’s not right to bundle them all into some single number. Eventually an economy where $\rho$ does not decrease exponentially will just have used all the iron there is, for instance: however fast it recycles old iron it will not be able to find enough to sustain its current infrastructure: it will need to start using something else.

Finally, there is a difference between the growth of an economy and the growth experienced by people living in that economy. That’s because population changes, and also because of inequality. Well, here is a plot from the World Bank of world GDP growth per capita since 1961: growth per person has perhaps averaged around 2% over that time. That graph also doesn’t address changes in inequality: it’s quite possible for almost all the growth to end up in the hands of a tiny number of people with almost everyone else getting poorer, and this may be happening.

So, now, why is it reasonable to assume that the rate of resource usage must tend to some constant? The universe is big, after all: there are really a lot of resources out there. Why can’t we just zoom off into space and use them?

Finiteness

Or, science fiction is fiction.

The future we imagine

In a few years, humanity will be a spacefaring species. From the early bases on the Moon and in Earth orbit we will have settled on Mars, and in the asteroid belt. On Mars, the gleaming cities under their geodesic domes will herald a new enlightenment. Great forests will bloom there, with trees far taller than their ancestors on Earth, producing oxygen and raw materials. The Martians, for so they truly are, will be tall, willowy and universally attractive. Somehow they will all be blond (it is, perhaps better not to ask what happened to the ones who were not). The mines will be conveniently out of sight, as will those lesser humans who labour in them.

In the asteroid belt things will be different, but not worse. Belters are, somehow, always Scottish or South African, and heavily-muscled. They work with the vast supply of metals and other raw materials they win from the asteroids which drift in vast numbers about them, conveniently slowly. They live in cities which look like futuristic shipyards, for so they are. In their cradles are built the great ships which already travel to the gas giants of the outer Solar system and will soon, soon, take humanity on its first journey to the stars. The bright white lights of welding flames are everywhere, together with the actinic blue flame of propulsion systems.

And the true space people live where they choose. In their vast, spinning spoked wheels they reside in orbit around Earth, Mars, Jupiter and Saturn, and often simply in interplanetary space. The insides of their craft are gleaming white, the walls containing panels displaying ever-changing status displays. The men all have advanced degrees in hard science subjects, the women all have short skirts and perfect legs. Again, there are curiously few people with brown or black skins.

Earth, for those who choose to remain there, is become a green paradise where humans live a sylvan, perfect life amongst the gambolling animals, free of all care.

Enough, enough.

Some inconvenient truths

If you like this picture, I suggest you read A city on Mars. Go ahead, I’ll wait.

The sketch above is science fiction, and science fiction is fiction. And the kind of science fiction I parodied above is the kind which depends on assumptions which are not true or at least completely beyond anything we have any idea how to do.

I don’t want to repeat all the arguments made in A city on Mars. But let’s just talk about Mars for a bit. If you want to think about living on Mars, think about living in Antarctica. In Antarctica you can breathe the air; in Antarctica there is plenty of accessible water; in Antarctica you’re not continually being exposed to high levels of radiation; in Antarctica you can get supplies or be rescued in a day or two. And yet people have not settled Antarctica, or various desert regions, because they are too hostile and difficult to live in. Mars is like Antarctica, but hostile: there is no air, no accessible water, there are high levels of radiation, the surface is made of toxic dust, and resupply or rescue takes between months and years. And it is extremely difficult and expensive to get there, and you get irradiated the whole way there and back.

Mars is nasty. The asteroid belt is in many ways worse. Living in it, or in space, either requires really big spinning spacecraft, or for humans to live in free-fall indefinitely, which is not good for them.

All of these places require the construction of a closed ecosystem which can remain habitable indefinitely. All of these places also mean you are exposed to a radiation environment which is probably going to kill you if you are exposed to it for long periods: no human has ever lived in it for more than a few days, and nobody has done so at all since the early 1970s. And let’s not even start on the question of having children in space or on Mars: would you want to be the person to try that experiment?

And that closed ecosystem needs to be big: if humans are going to live independently for generations on Mars, say, then you need enough of them to form a ‘minimum viable population’. This isn’t just a population big enough to avoid inbreeding: it’s a population big enough to grow food, to maintain the life-support systems, to build and maintain all the advanced machines that will be needed and so on. These things don’t happen on their own. How big such a population needs to be is not clear, but it’s between tens of thousands and many millions. We’re not talking a few people living in the converted hull of their spaceship here.

These problems can, perhaps, be overcome: just not soon. And, curiously, none of the plutocrats who want us to go to Mars or live in space are undertaking the kind of long-term research and development programme which would be needed to overcome them. They’re just building big, cool, profitable, rockets.

What is going on?

I think Charlie Stross describes it rather well. We’re living in an age where a bunch of plutocrats grew up on the kind of science fiction written in English up to the 1990s, or perhaps a bit later. And they took two things away from it:

they did not understand that it was, well, fiction: things made up so the story would be more exciting, like big exciting rockets and space, and certainly not boring details like keeping people alive on Mars which do not make exciting stories;
they read about various awful dystopian futures in SF books and thought ‘hmm, that looks pretty good for very, very rich people who don’t care about anyone else, and I already don’t care about anyone else’.

And so we get to where we are: techbro plutocrats are planning to go to Mars, but they’re planning to go there based on stories which left out all the boring details like staying alive. They think that it just needs big shiny rockets. At the same time, they’re working towards the kind of dystopia described in, for instance, the sprawl trilogy, because things are pretty good in those books if you’re a Tessier-Ashpool, and that’s who they think they are.

And, of course, they think they can combine the two: a dystopia on Earth and the shiny Mars city where they can be very gods: if you don’t do what they say on their imagined future Mars you don’t breathe. They don’t care, at all, if achieving their dream destroys the dreams of everybody else.

If the whole ‘all you need is a shiny rocket to go to Mars’ seems like a mistake nobody very smart would make I think it’s worth considering Elon Musk’s recent behaviour (I am writing this in September 2024): he is, to put it mildly, not as smart as he thinks he is. On the other hand he’s at least as unpleasant as people feared he might be. The techbro plutocrats got to be where they are by a combination of being in the right place at the right time, and not caring about anyone but themselves at all: they didn’t get there by being some kind of genius.

That is what is going on.

It’s worth saying here that SpaceX, in particular, has done absolutely amazing things: Musk made a good decision when he decided to fund them. They have successfully done what NASA abysmally failed to do after Apollo. In 2021 dollars, it cost about $5,400/kg to low Earth orbit for the Apollo Saturn launch system; for the space shuttle it was about $64,500/kg; for Falcon heavy it is about $1,500/kg (source). That is an enormous achievement. It’s just not closely related to what is required to sustain a settlement on Mars or the Moon.

The future we’re going to have

We are not going to live in space in significant numbers any time soon. The cost of lifting significant numbers of humans from Earth will be prohibitive both financially and environmentally for a very long time, and quite likely for ever: the great majority of humans will need to live within the resources Earth provides for a long time to come.

We might have small, dependent settlements on Mars or the Moon this century. But, well, they will be small, and dependent on supplies from Earth.

One of the things people like Musk go on about is that we should have a settlement on Mars as a lifeboat for humanity: if something bad happens to Earth humans will survive on Mars. That requires that settlement to be long-term viable without support from Earth, which will not be possible for a long time. And it’s just a stupid idea: if you are going to live on Mars, you’re going to be living underground if you don’t want the radiation environment to kill you. And you will need to make air, and all your food and maintain the environment, essentially for ever. Well, wouldn’t it be just a lot easier to build some number of lifeboats for humanity underground in remote parts of Earth? There is water, there is air, both can be filtered for nasties. It’s hugely cheaper to build than something on Mars. Such settlements would certainly be preferable as a way of ensuring humanity survives a flat-out nuclear war, or catastrophic climate change. They would almost certainly be preferable as a way of surviving a Chicxulub-level extinction event.

Of course it would be easier to do that. But it wouldn’t involve rockets: it would not be the shiny SF dream that the techbro plutocrats so want to come true.

The same applies for slower catastrophes: if you’re in a position to ship many thousand people to Mars, you’re in a position to scrub carbon dioxide from the atmosphere, so why not do that? Because it doesn’t involve shiny rockets, I suppose. Also it involves helping other people, and plutocrats only care about themselves.

Finally, note that even if we ignore all the inconvenient truths about becoming a spacefaring species, it doesn’t solve the exponential problem for long. If Mars has all the resources of Earth, then at 2% resource growth a year, we exhaust the resources of Mars 35 years after we exhaust the resources of Earth. Then we have to move on to even more insane ideas like cannibilizing planets. Which, certainly, will perturb orbits of other planets, planets on which we already live, in ways which will be not good for the people who live there.

The future we are going to have is that we must live within the resources provided by Earth for a long time: probably centuries at least.

Are we going to have a problem here?

OK, so we’re stuck on Earth for a long time. That’s only a problem we need to think about if we are, in fact, running out of resources, or if waste products are going to cause a problem.

The magic goes away

Perhaps, in fact, we’re many doubling periods away from getting anywhere near that point. At 2%/y growth then the rule of 70 says the doubling period is 35 years, so we might have hundreds of years left, and we can just kick the can down the road as we always have. That’s a horrible answer, but it is an answer.

In 1798, Thomas Malthus wrote An essay on the principle of population in which he argued that exponential population growth would result in everyone starving. It hasn’t after more than two hundred years, and in fact a far lower proportion of the human population is starving now than was in 1798. Malthus was wrong, and he was wrong because of something he missed: fossil fuels, which provide both copious energy and fertiliser.

Unfortunately putting over 1.5 trillion tonnes of carbon dioxide into the atmosphere turns out to have had quite bad effects, of course. Do perhaps Malthus wasn’t as wrong as all that: you can indeed solve the problem he was worried about for a couple of centuries, but only if you’re willing to solve a much larger problem later on.

It might be that there is something we don’t know about which changes everything. But we know a lot more about the resources available and the consequences of using them than he did. And we know a lot more about physics and chemistry than he did, and specifically about limits placed on what we can do by physics. Simply assuming that something completely unknown will turn up snd everything will be fine as a result seems like a really stupid approach. So let’s not do that, then: if it looks like we’re not many doubling periods away from trouble let’s assume that’s true.

Energy

We’re not, for instance, running out of energy very fast: there’s a lot of available solar power; nuclear fission power is clean and could be cheap if we wanted it to be. Nuclear fusion will probably actually arrive at some point. We will eventually run out of energy, but we have at least a century even without making dramatic improvements in energy intensity.

Except we really, do need, already, to have stopped burning fossil fuels. But let’s leave that for later.

Energy is not the only fruit

There are other things we might want to worry about than energy, and perhaps the most obvious one is that the environment we live in is also a finite resource, and we’re doing things to it, often by dumping waste products into it, which are not very good.

As an example, we’re degrading the environment in a way which is disastrous for insects: flying insect populations in the UK have declined by a factor of more than 2 over the 20 years to 2022 (original source paper): halving in 20 year is not good, and it’s backed up by many other studies.

There are many other signs that things are not well. Swallows declined by 43% in the UK between 2012 and 2022 (they had been increasing in the 10 years before that), house martins by 40%, swifts by 40% (source). So perhaps I am slightly more interested in swallows, martins and swifts than other people, but that’s not the point: I could live in a world without them, but their decline is not some special case, it’s one example of something pervasive.

The thing that is pervasive is that we are seriously, seriously, degrading the environment that supports us. That degradation is related to the rate of resource usage in the economy. And if it continues for long enough the environment is not going to be able to support us any more.

If we don’t do anything, how long do we have before we’re in trouble? I have no idea. But I do know that by the time we’re in trouble it will be too late: the environment isn’t simple and it’s full of hysteresis. By the time we fall over some tipping point there will probably be no way back, so we’d be well-advised not to push our luck.

Yes, we are going to have a problem here

I don’t know when. But if I had to guess I’d say within fifty years or so, and perhaps sooner than that. And by the time the problem becomes serious it will be too late: we need to do something to adjust the resource intensity — to reduce the $\rho$ — of our economies now.

So, now, let’s find out just how far from reality the fantasy world economists live in is.

Faith, fantasy and Economics

So we’re not going to be living in space any time soon: we need to plan to live within the finite resouces provided by Earth. And the evidence is that we’re already approaching limits of some of those resources. So we’d better plan to make our rate of resource usage a constant, or even make it smaller.

If we assume growth continues at some rate $g$, then the rate of resource usage for some resource is $R = \rho(t)s_0 e^{gt}$. For this to be constant we need $\rho(t)$ to start looking like $e^{-gt}$ in the future, so as time goes on it becomes more and more like $\rho_0 e^{-gt}$, say and resource usage tends to $\rho_0 s_0$.

Efficiency limits: economics meets physics and loses

So it’s tempting to say that, well, we can just make everything more efficient over time, without limit. We can’t. Physics places hard limits on how efficient various processes can be, and however much you might want to exceed those limits you can’t.

For example, modern petrol engines for cars are 30–40% efficient (source), with diesel engines approaching 50% (source). Carnot’s theorem says that the efficiency of a heat engine can never be more than $(T_H - T_C)/T_H$, where $T_H$ and $T_C$ are the absolute temperatures of the hot side and the cold side of the engine. We can’t do much about $T_C$, and $T_H$ is limited by the materials we can use.

Well, perhaps we can use really super amazing materials (let’s hope they’re cheap) and increase efficiency far above what it is today. But wait: car engines are already close to 50% efficient: the very best we can ever achieve is a doubling in efficiency. At 2% improvement a year (which is much more than we will be able to achieve) that’s 35 years. And to get to 95% efficient the hot side of the engine would have to run at mearly 5,500K which is, well, pretty hot.

The same things apply to any other physical process: you just can’t keep on making things more efficient in terms of physical resource use, whatever the resource is at a constant growth rate: things can’t get exponentially more efficient with time, and that’s all there is to it.

Escaping into a pretend world

So, OK, what is the answer to that? Well, the proposed answers are two: substitution. and decoupling.

Substitution is the idea that as we reach limits in one technology we substitute another, more efficient one. It’s not an answer: the efficiency of a car engine can’t even in principle exceed 100%, for instance, whatever technology you use. Sometimes we are using technologies which are extremely inefficient, but there is still a physical limit and it’s often not that far away. Substitution keeps you going for a while, but not for ever.

An example of substitution is that, of course, nobody expects internal combustion engines to reach 95% efficiency: we’ll replace them by electric motors. Which will get us no more than another factor of two or so, because there’s a term for systems with efficiencies above 100%: perpetual motion machines.

Decoupling is the idea that we don’t just have more and more of the same thing: we start doing other things and those things use less resources.

The poster child for decoupling is probably the idea that we will, over time, spend less and less of our time doing any kind of physical thing and more and more of it immersed in virtual worlds running on computers. Let’s conveniently ignore the fact that, Moore’s law notwithstanding, computers also have physical limits on how efficient they can be, and assume we’ll all end up living in The Matrix while, in the real world, consuming very few resources. Perhaps some people would even like that.

Alternatively, perhaps we will end up spending all our time making and trading vastly valuable art, while living otherwise very simple lives. That seems more attractive to me, anyway.

Decoupling is not so obviously silly, but it turns out to be just as mad.

Decoupling: economics meets itself and loses

So, let’s assume that, somehow, some combination of substitution and decoupling means we can maintain economic growth while resource intensity declines exponentially. What happens?

The first thing is that, over time, the resource-consuming part of the economy, and hence the proportion of everyone’s income spent on it, becomes increasingly tiny. Which leaves us in two very weird situations.

Consider living in such a world. A very tiny proportion of your income is spent on things which consume resouces: they are very cheap for you. So let us assume you’re a human being, not some economist’s fantasy idea of one: why wouldn’t you just spend a lot more money on resource-consuming things? Perhaps you decide you’d like to build an enormous steampunk coal-fired machine: you can do this, because you have enormous wealth, everyone has enormous wealth. I mean, the people today who have enormous wealth have things like private jets, and travel by helicopter: why wouldn’t everyone do that in the future?

Something has to stop you. And that thing can’t be that it’s too expensive, because if it’s too expensive then resource consuming parts of the economy are, in fact, a large part of it, not a very tiny one. It just makes no sense.

And that’s not the end. As the resource-consuming parts of the economy become an ever smaller fraction of it, there’s no reason why, at first countries and then later large organisations and wealthy individuals might not decide to just buy them all, and hold everyone else to ransom.

The whole idea of decoupling means that there is a tiny fraction of the economy which is nevertheless critical for everything else to exist: you still need to be warm, to be sheltered, to be able to eat, to travel, it’s just all now very, very cheap. That’s not how things work: if there is a resource which, if you own it, gives you enormous power over over large parts of an economy, then that rerource is extremely valuable, not extremely cheap.

Well, perhaps it’s like food. Food, by historical standards, is very cheap in developed countries. In 1929, food cost about 23% of Americans’ disposable incomes: in 2022 it was 11% (source). And that’s only in recent history. And people do eat both more, and more resource-intensive food as a result. But there’s a limit: eating too much isn’t good for you, and most of the cost of very expensive meals is the restaurant. So there’s a limit on how much you can eat.

It’s not like food: my one-man Mars-capable racing spacecraft uses really, really a lot of resources.

So no, none of this makes any sense: the only conclusion is that something else will happen.

The elephant

There is an elephant: there is always an elephant.

The elephant, of course, is climate change. Climate change — specifically climate change caused by humans — happens becsuse of two waste products from resource usage:

carbon dioxide which is a waste product from the burning of fossil fuels;
methane, which is a waste product coming about 40% from agriculture 35% from fossil fuels again and 20% from other waste (source).

Carbon dioxide is much longer-lived than methane and also is a larger contributor to the current warming.

There are many, many articles on global warming as well as many, many scientific papers. I’m not going to write another one: if you want a comprehensive summary look at the IPCC. There are also many liars and fools who claim global warming is not happening, that it is happening and it’s not a problem, or that it is happening, it is a problem, but we can’t do anything about it: at this point those people are, well, liars. fools, or both.

Here are plots of average annual and summer (June, July, August) temperatures for central England since 1824, averaged over five years, using data from the Met Office.

Five-year average of central England annual temperature, 1824–2023

Five-year average of central England summer temperature, 1824–2023

Yes: climate change is happening.

Climate change a really good example of where we need to dramatically reduce the intensity of something, which in this case is waste products from consumption of energy. We know the consequences of not doing so will be very bad, and we know a lot of approaches for reducing the intensity. Unfortunately most of them require humans to make changes they find inconvenient. But, still, we know we have to do this, and in 2015 everyone agreed to do so.

How are we doing?

Here is a plot of data from the Mauna Loa Observatory, showing both the measured atmospheric concentration of carbon dioxide, and a version of the same data with the annual cycle removed.

Mauna Loa atmospheric carbon dioxide concentration

It’s worth looking at the data starting in 2010 as well:

Mauna Loa atmospheric carbon dioxide concentration since 2010

Here are equivalent plots of data showing the global average atmospheric carbon dioxide concentration

Global average atmospheric carbon dioxide concentration

And again, starting in 2010

Global average atmospheric carbon dioxide concentration

So, well, how about fossil fuel usage? Data for this comes from Our World in Data.

First the combined totals:

Global fossil fuel consumption

And broken down by fuel:

Global fossil fuel consumption by fuel

What this looks like

What this looks like is abject failure: we are, perhaps, doing something although exactly what is not visible in the concentration data. But we are doing so far from enough as not to be funny.

We know about climate change, we know how serious it is, we know how to fix it. And we are failing.

The teeming billions

So, here’s the bit about how overpopulation is going to doom us all.

Not so much. For much of the world growing populations are no longer the appropriate thing to worry about: the problem is now, or will soon be declining populations.

The rate at which a population grows or shrinks is determined both by how many people die and how many are born. The second of these is usually summarised by a number called the total fertility rate, which is the average number of live births per woman under various assumptions. It’s not completely straightforward to know how this number corresponds to population change, as it depends on things like mortality rates and sex ratios at birth. But for a population with current first-world mortality rates a value of a little over 2 — perhaps 2.1 — is the replacement rate: at this value the population will be stable.

In England and Wales TFR fell below 1.5 in 2022. In Scotland TFR was 1.28 in 2022. This is not just below the replacement rate it’s far below it. And the UK is not unusual: the TFR in the USA is about 1.7, in France it is 1.8, Germany 1.5. In South Korea it is 0.8 (that is not a typo). More figures can be found from the Population Reference Bureau.

The consequences of this are that the population in these countries will fall, and the world population also probably will soon start falling. ‘Good’, you might say. But that’s not the only consequence. The age statistics of the population also will change dramatically.

I wrote a toy model which lets me play around with what happens. I didn’t want to deal with sex ratios, so in the model there is only one sex: if you like, there are only women. A proportion of the people die each year in a controllable age-dependent way, and they produce offspring in a controllable age-dependent way (in the runs below from 20 to 40) At 100 I kill off the (very small proportion of) survivors to avoid dealing with a tiny but long tail of very old members.

Rather than TFR the model deals in the effective fertility rate, EFR, which is defined to include mortality and thus needs to be 1 for a stable population (TFR would be a little higher, but is about half that for a real population as there is only one sex).

This is very much a toy model: it’s not anywhere close to accurate for humans. But it’s realistic enough to demonstrate in outline what happens to demographics if fertility falls dramatically. Here are example pictures from two setups. In both of these the initial mortality rates are

5%/year in the first two years;
1%/year from 2–9;
0.1%/year from 10–19;
0.5%/year from 20–39 (childbirth is a bit dangerous);
0.1%/year from 40–49;
1%/year from 50–59;
2%/year from 60–69;
6%/year from 70–79;
12%/year from 80/99;
100%/year at 99.

Fertility is 10%/year between 20 and 39, and zero outside that window.

In fact these values get smoothed out a bit to make the graphs look nicer. The EFR of the system set up like this is about 1.54.

The model is then spun up for 1000 years, with the final population being renormalised to 100 million in total.

At this point the plot of numbers against age (the ‘demographic pyramid’) looks like this:

Population by age, after spin up

Falling fertility

In this setup, fertility is reduced by 2%/year for 40 years (note: this means 2% of 10%/year initially). The EFR at the end of this process is about 0.69. After this the system runs up to year 200, at which point fertility is adjusted so the EFR is 1. It then runs up to year 400.

Here are graphs at year 0, 20, 40, 60, 80, 100, 200, 400:

Population by age, at year 0, 20, 40, 60, 80, 100, 200, 400

You can see two things from this: the population falls over time, but the demographic pyramid also changes shape dramatically. It’s easier to see this if you renormalize these plots so the average population for each age is 1:

Renormalized population by age, at year 0, 20, 40, 60, 80, 100, 200, 400

You can see here that the demographics get very heavily skewed to old people compared to the initial state while the population is falling. Once it stabilises they remain skewed to older people but less heavily so.

Here is a picture of what happens to the total population in this scenario

Population history

The interesting thing you can see here is the latency: it takes about 40 years before the population starts falling, and a similar amount of time for it to stabilise. That’s true even if you step fertility so the EFR is 0.69 in the first year, although the demographic pyramid looks bizarre in that case (it has a huge step in it which gradually gets washed out).

Falling fertility, rising mortality

You can ‘fix’ the skewing towards old people as EFR falls by assuming that old people become more likely to die.

In the run below, mortality is increased by 0.1%/year (relative to the current mortality for that year) from age 30 for the first 40 years of the run. Mortality is not reset at year 200.

Here are the unrenormalised and renormalised plots, as above

Population by age, at year 0, 20, 40, 60, 80, 100, 200, 400, increased mortality

Renormalized population by age, at year 0, 20, 40, 60, 80, 100, 200, 400, increased mortality

You can see this is ‘better’. At least it’s better until you realise what’s happened to the population:

Population history, increased mortality

In the case where the mortality of older people does not increase the population falls to about 18% of its initial value over 400 years. In the case where it does, the final population is about 3.7% of the initial one. Which should not be very surprising, of course.

The consequences

Population growth is a bit like economic growth, to which it is closely related: if it continues at a positive rate then you can assume that, in the future there will be more people than there are now. In particular there will be more people of working age. Those people earn money which pays taxes which, among other things, pay for the care of the elderly. In a world where the TFR remains at some constant value and where age-related mortality doesn’t change over time, it also has the nice characteristic that it’s an exponential process, and so ‘everything remains the same’: in the future there will be more or fewer people, but the proportions of people alive at a given age remain the same.

In other words, if the TFR remains at some more-or-less constant value comfortably above 2 and mortality rates remain about the same, then you can always plan to pay, for instance, pensions, out of money you don’t yet have. You do run into the problem that, in due course, everyone starves as the population increases exponentially and the food supply runs out, but that’s not the sort of thing economists worry about: they just kick that can down the road, which has worked well for them so far.

The real world is increasingly unlike that: TFR has historically reduced over time, and mortality has also fallen. We’ve already seen some of the consequences of life expectancy increasing: people have to work until they are much older.

In many parts of the world TFR is now well below replacement value, and often well below it. That’s going to have very big consequences. For now, those places could fix their problem by importing people from regions of the world where the TFR remains high. They’re generally not doing that, apparently because those people have skins of a different colour.

As above, so below

Quod est superius est sicut quod inferius, et quod inferius est sicut quod est superius.

— Latin translation of Emerald tablet

Everything above is meant to be based on information you can check: most of what follows is is my opinion.

Shorter

Economic growth is a very good thing: it’s lifted billions of people out of poverty. But it’s an exponential process.

Despite the fantasies of plutocrats who read too much science fiction at an impressionable age and who are not as smart as they think they are, we’re not going to migrate into space, the Moon or Mars any time soon, if ever. We need to live within the finite resources provided by Earth.

Continuing exponential growth in a system with finite resources is not possible unless the thing that is growing doesn’t use the resources. This means economic growth must be decoupled from resources at an exponential rate, and that is what economists assume will happen. Generally speaking it’s not what has happened so far.

Sadly for economists it’s also generally not physically possible. Physics places limits on how much resources various processes must use, and in many cases we are within a factor of 2 or 3 of those limits already. This limits the amount of decoupling, and therefore the amount of growth.

If you assume that, somehow, that will not be a problem (it will be a problem) you rapidly end up in situations which are absurd in other ways. Either critical resources become very cheap yet must be used only in small amounts, critical resources are so cheap that they can be acquired and controlled by bad people, or both. The only even slightly sane way around this would be for resources to be controlled by some central body — the state, perhaps — provided in limited quantities very cheaply, with further trade in them prohibited. That kind of economic system tends to end up with gulags.

Economists who believe these things are living in a make-believe world: economic growth cannot, in fact, continue indefinitely.

Perhaps we have a long time before this becomes a problem? Looking at environmental damage and particularly climate change caused by the waste products from consumption of fossil fuels tells us that no, we don’t. We have essentially no time at all.

On top of all this is something else that we certainly should have seen coming, even if how quickly it is arriving is unexpected: fertility rates are falling, in some cases dramatically. The total fertility rate in England and Wales fell to 1.44 in 2023 (source): Scotland’s fell to 1.3. Replacement value is about 2.1. Worldwide the TFR is still above 2, but it will almost certainly fall below it fairly soon. This means populations will start to decline which, itself, makes growth harder to maintain. Worse, it means that, unless people start living less long, there will be proportionally more old people who will contribute less to the economy and many of whom will need care.

Let’s be clear: economic growth is a good thing. I am not some hippy who wants to go back to living in an 18th century of my imagination, where somehow I will, of course, be landed gentry and quite comfortably off, and my wife won’t die in childbirth and all our children will live to be adults. Because that world didn’t exist. If growth could continue for ever that would be great, thanks. And, like the plutocrats, I grew up with science fiction: I really want to go to the Moon, or to Mars, or to Jupiter, or the stars.

But I’m also not an idiot: growth can’t continue indefinitely, and almost certainly cannot continue for very long at all. Humanity is not going to become a spacefaring species any time soon, if ever. And what says these things is physics, and if you have a difference of opinion with physics then you are wrong. Oh yes, we could discover magic new physics tomorrow — faster than light travel, and therefore also time machines, say — but do you want to bet the entire future of civilisation on that? Because I don’t.

So we have a big, urgent problem.

What are politicians doing about the problem? Almost none of them seem to understand in any real sense that there is a problem. That is perhaps unsurprising given that most politicians have educations which might have been appropriate in 1750. Those who accept that at least part of the problem exists seem to think that it can be solved by just making speeches, signing bits of paper and then quietly not doing enough, or anything, to actually solve the parts they understand exist.

And that’s what people are doing as well. Because it’s a big and really inconvenient problem: it means things will be very different in future and, whatever we do, they will likely be worse than they are now in some ways. And the shiny space-age future promised by growth is not, in fact going to happen. It’s like cancer: it’s often, somehow, easier to ignore the symptoms and pretend that you don’t have a horror growing inside you, rather than deal with the awkward truth. But it’s also like cancer: if you just avoid dealing with it then it will get worse, and then it will kill you. The best thing you can do is to talk to a doctor, immediately.

And other people have a different reaction. They see things are not going well, if dimly, but imagine that, somehow, it’s always being caused by someone else, or that these other people are lying to them about the problem. And ‘someone else’ means people with skin of a different colour, LBTQIA+ people, ‘woke’ people, liberals, the elite, women and so on. And so they elect leaders who will ‘deal with those people’ in some unspoken but always understood way.

So we get politicians who claim it’s all a hoax: it’s all a lie spread by woke liberal science gay black foreign people and we should just burn more fossil fuels and puke more pollutants into the environment. And, you know, deal with the people we don’t like.

But, I think, a lot of people have some notion of what’s probably coming. It seems at least plausible, for instance, that one reason women are choosing to have fewer children because they can see that bad things are coming and nothing significant is being done to prevent it. Of course the demagogues have a plan for that: forced birth, which is being instituted in America.

Again, let’s be clear: economic growth will stop, because physics says it must. That’s not a good thing, but it is inevitable. We have, really, three choices. We could recognise the problem and work out how we’re going to deal with it. It won’t be easy. We could pretend it doesn’t exist and just blunder as long as we can. Or we could pretend it’s all a lie spread by some imagined enemy who must be eliminated.

We are not taking the first option.

A history of the near future

I’d like to share a revelation I’ve had during my time here. It came to me when I tried to classify your species. I realized that you’re not actually mammals. Every mammal on this planet instinctively develops a natural equilibrium with their surrounding environment, but you humans do not. You move to another area, and you multiply, and you multiply, until every natural resource is consumed. The only way you can survive is to spread to another area. There is another organism on this planet that follows the same pattern. Do you know what it is? A virus. Human beings are a disease, a cancer of this planet. You are a plague, and we are the cure.

— Agent Smith

Overshoot and collapse

Despite alarmists, climate change and environmental degradation are very unlikely to make the Earth uninhabitable by humans: they will just make it a lot less habitable. If we merely stick our heads in the sand and ignore the problem and if, as things begin to fall apart, there are no ugly social effects, then what will happen is overshoot and collapse. This is, of course, what was predicted by the Club of Rome in The limits to growth in 1972. Here’s what they currently say about it:

This report […] was the first to model our planet’s interconnected systems and to make clear that if growth trends in population, industrialisation, resource use and pollution continued unchanged, we would reach and then overshoot the carrying capacity of the Earth at some point in the next one hundred years.

Some fifty years on, the call for a change in direction was more urgent than ever. The report’s modelling was remarkably accurate and prescient as the world declares the climate emergency to be real and global ecosystems to be at breaking point. Fifty years offered an excellent opportunity to look back, and forward, at the trends it examined and listen to leading international thought leaders, scientists and politicians on how we create a new critical framework for living and thriving within the limits on Planet Earth.

The limits to growth was despised by most economists, apparently because it told them an inconvenient truth. Inconvenient, perhaps, but still true.

Overshoot and collapse happens because there is hysteresis: the behaviour of the system depends on its history. A simple example is extinction: if the environment changes so some species dies out, then undoing that change doesn’t bring it back to life. The same thing is why the ‘overshoot and recover’ idea that’s now popular for carbon emissions is so stupid and dangerous: if you push temperatures beyond the point where the ice sheets start melting, say, or AMOC collapses, then that doesn’t stop when temperatures lower again. Of course what people really mean by ‘overshoot and recover’ is ‘do nothing, and let our children deal with it’: it turns out people do not care about their children’s entire futures if it is momentarily inconvenient to them.

So what happens is that economic growth continues, carbon dioxide and methane emissions are not reduced and then at some point everything falls apart: harvests fail, people die in large numbers, and modern civilisation comes to an abrupt end. Over the following hundreds of years sea-levels rise by many metres as the ice-sheets melt, drowning the remaining coastal cities, the wave of extinctions we’ve started continues and people continue to die off. Eventually, after several thousand of years and since emissions have essentially ceased, the climate stabilises and the surviving human population starts again from some level between the mediaeval and the 18th century. Perhaps they’ll have learned not to do it all again. Perhaps.

It’s not a good prospect. But it’s absurdly optimistic compared to what the history of the near future will be.

A pale horse

And I looked, and behold, a pale horse, & his name that sate on him was Death, and hell followed with him: and power was giuen vnto them, ouer the fourth part of the earth to kill with sword, & with hunger, and with death, and with the beastes of the earth.

Something I haven’t talked about is what will be the most obvious effect of climate change: parts of the world which are already hot will become dangerously so, to the extent that humans will not be able to live in them. The people who live in those parts of the world will have two choices: move somewhere else, or die. When one of two choices is ‘die’, people take the other one. There is going to be a lot of migration from these areas to more temperate areas. And when I say ‘a lot’ I mean a lot: hundreds of millions of people will have to migrate. This is already beginning: if you think the ‘small boats’ crisis that has so exercised people in the UK is a big deal, well, you ain’t seen nothing yet.

The social effects of this aren’t something climate models can talk about, but I think they’re pretty predictable. In temperate areas, the environment will already be degrading: there will be floods, droughts and other unpleasant weather events. The hope for a better future will be gone; the hope for a future which is at least not much worse than the past will be receeding.

Women will have fewer children because they realise that bringing a child into the world they see arriving is an act of cruelty. Demographic pyramids will invert, and old people will start dying as a result. Old people will resent the young, young people will resent the old.

And while this is going on a vast tide of desperate migrants will be trying to get in, because if they can’t get in, they will die. Letting those migrants in would, in fact, resolve the demographic problem. But the migrants have brown skins and it turns out that racism is anything but a solved problem in developed countries: it’s just one we suppressed for a while. There were race riots in the UK, in 2024.

People will react as they’ve always done: they’ll look for people to blame for what is happening, because it can’t be their own fault. Among those people will be recent immigrants. They’ll look for strong leaders who will give them simple answers. Not everyone will think like this, but enough people will. And, conveniently, not thinking like this will mean that you are one of the people to blame.

This is what is happening now. It’s populism: leaders who offer simple, appealing, wrong answers to complicated, unappealing problems. Keep the migrants out. Go for growth. Burn more coal. Stop all that environmental protection stuff. It’s all the fault of the liberal elite. It’s free trade. The scientists are to blame. It’s the Mexicans. It’s black people. It’s the gays. It’s trans people. It’s the Chinese. It’s the UN, the muslims, NATO, the EU. It’s always somebody else: it’s never us. And, inevitably, at some point, it will be the Jews.

And so populism is turning into something else: fascism.

Look at Germany in the 1930s: things were pretty bad after the 1914–1919 war, so people started looking for someone who would offer them simple answers, and provide people to blame. They found that person. And they found a convenient group of people who were not, of course, to blame, and they murdered them in huge numbers.

That’s what’s coming. As the environment falls apart, as growth fails, fascists will start taking over. Look around: they already are.

But the simple, appealing answers fascists offer don’t work. Once the bad people have all conveniently gone away (nobody will ask where, everybody will know where), once the walls have been built, once the coal is being mined again, once the compulsory birth laws are in place, somehow nothing will get better. The environment deteriorates, people start dying in floods, in droughts, in hurricanes and typhoons. Harvests start failing: people start dying of hunger and thirst. And the fascists will do what they always do, because it’s all they know how to do: they’ll start wars.

An interesting thing has happened. I was born just after the Cuban missile crisis. While she was pregnant, my mother was stockpiling dried milk and canned food, because she believed that a nuclear war could be imminent. She was right to believe that: it very nearly happened. Throughout the later 1960s and 1970s people were absolutely terrified of nuclear war. Perhaps the threat was seen as receding by the mid 1980s, but people were still pretty scared. And then, in the early 1990s, it all stopped: the USSR collapsed and the cold war, apparently, was over. The doomsday clock maintained by the Bulletin of the atomic scientists has never been further from midnight than it was in 1991.

You want to know when it was closest to midnight? Today, that’s when. Almost all nuclear arms limitation treaties are dead. Russia has invaded Ukraine and threatened to use nuclear weapons there. The situation in the Middle East is awful, and at least one state there has nuclear weapons. A new nuclear arms race is starting.

And yet, curiously, the fear of nuclear war hasn’t returned. People have, somehow, forgotten that this awful fate hangs over us, and not noticed that it is more likely, today, than it has ever been. That’s, as I said, interesting.

Because here’s the thing: the failure of growth together with increasingly rapid environmental collapse and migration on a huge scale is going to give us — is already giving us — fascists. And fascists, when they have dealt with the undesirables and when it turns out they have no answers, start wars. And those wars will rapidly become nuclear wars.

How near is the near future? I don’t know. I could invent a chronology but I’d be making it up. Certainly by the end of the century, and perhaps much sooner, partly depending on what happens on the 5th of November and in its aftermath: on how soon the fascists win in America.

And that is how the history of the near future ends: not with a whimper, but with a bang. If you want to know how most humans will die, watch Threads.

— Tim Bradshaw, all saints’ day, 2024

Seeing Apollo

Tim Bradshaw — Wed, 24 Jul 2019 14:49:53 UT

Why you can’t see the Apollo lunar landing sites from Earth.

Something that Apollo denialists¹ sometimes say is: if the Apollo programme put people on the Moon, why can’t we see the landing sites?

Well, we can. In 2009, the Lunar Reconnaissance Orbiter (LRO), in orbit around the Moon, took pictures of some of the Apollo landing sites, including an astonishing picture of the Apollo 12 landing site in which you can see Surveyor 3 as well as clear signs of tracks made by the astronauts as they walked on the Moon. It is even possible to work out what happened to some of the flags & that the flag planted by the Apollo 12 astronauts is still standing. In 2011 LRO took some even better pictures: in these images it is very easy to see the tracks left by the astronauts. A summary page points to images of the landing sites of Apollo 11, 12, 14, 15 & 16.

‘But’, they say, ‘you can’t see the sites from Earth, and we don’t believe that LRO actually exists: it’s just part of the giant Apollo conspiracy. If people landed on the moon you would be able to see them with Earth-based telescopes²’.

Here’s why you can’t.

The angular resolution of a telescope with diameter $D$ working at a wavelength of $\lambda$ is given by:

\[\Delta\theta = 1.220 \frac{\lambda}{D}\]

This is the smallest angle it can resolve, even in theory. The $1.220$ comes from the properties of the Airy discs that correspond to the diffraction patterns of light — in fact it’s the position of the first zero of intensity in the pattern.

For a telescope where $\Delta\theta \ll 1$ (which is true for anything worth being called a telescope) then we can translate this into an absolute resolution, $\Delta l$, at a distance $r$, using $\sin\theta \approx \theta$ if $\theta \ll 1$.

\[\Delta l = 1.220 \frac{\lambda r}{D}\]

And we can rearrange this to tell us what $D$ needs to be to resolve an object of size $\Delta l$:

\[D = 1.220 \frac{\lambda r}{\Delta l}\]

So, for the LEMs on the Moon:

$\Delta l \approx 9\,\mathrm{m}$ (size of LEM);
$r \approx 4 \times 10^8\,\mathrm{m}$ (distance to Moon);
$\lambda \approx 5.6 \times 10^{-7}\,\mathrm{m}$ (green light).

And this gives us $D \approx 30\,\mathrm{m}$.

This means that to even be capable of resolving the LEM on the moon we would need a telescope with a diameter of thirty metres. This is about three times larger than the largest optical telescopes in the world. Telescopes this large are planned (and even larger ones too), but they do not exist yet.

And this size is the absolute minimum: to see any kind of detail you would need a truly enormous telescope: perhaps something with $D\approx 100\,\mathrm{m}$: nobody is building anything like that soon. The LRO can see the Apollo sites because it is in an orbit around the Moon which gets as low as $20\,\mathrm{km}$: twenty thousand times closer than the Earth is, which means it needs a telescope with a diameter twenty thousand times smaller.

Apollo denialists were one of the early precursors of the science denialists who are now working so hard to destroy everything worthwhile about being human. ↩
‘Also, the Earth is flat.’ ↩

Melting the Antarctic ice sheet

Tim Bradshaw — Sat, 10 Oct 2015 10:31:28 UT

How long might this take, in the worst case?

The Antarctic ice sheet has a volume of about $26.5\times 10^6\,\mathrm{km}^3$, according to Bedmap2¹. This is $2.7\times 10^{16}\,\mathrm{m}^3$ of ice. The density of ice is about $10^3 \,\mathrm{kg/m^3}$ (about a tonne per cubic metre, which is approximately the same as water of course), so this is about $2.7\times 10^{19}\,\mathrm{kg}$ of ice. The enthalpy of fusion of water is about $3.3\times10^5\,\mathrm{J/kg}$ so, if we assume that the ice is all at freezing point², then we require $8.9\times 10^{24}\,\mathrm{J}$ to melt it all.

Let’s assume we use the Sun to do this. The solar constant is about $1.4\times 10^3 \,\mathrm{W/m^2}$: this is the amount of power per square meter that the Sun provides at the top of the atmosphere. So, imagine we use all of the power that the Earth intercepts from the Sun to do this³. Well, the Earth’s radius is about $6.4\times 10^6\,\mathrm{m}$ so the total power available is about $1.4\times 10^3 \times \pi \times (6.4\times 10^6)^2\,\mathrm{W} \approx 1.8\times 10^{17}\,\mathrm{W}$, or about $1.8\times 10^{17}\,\mathrm{J/s}$.

So to melt the Antarctic ice cap, using all of the power from the Sun that reaches the top of the atmosphere would take

\[ \frac{8.9\times 10^{24}}{1.8\times 10^{17}}\,\mathrm{s} = 4.9\times 10^7\,\mathrm{s} \]

Well, there are about $32\times 10^6$ seconds in a year, so this is about 1.5 years.

Of course we can’t use all the Sun’s power: even if we had the technology to do this (which we are not anywhere near doing!), doing this would cause an inconceivable catastophe for the rest of the planet: this would be a winter night which lasted for a year and a half. Everyone would die.

A plausible figure might be a tenth of one percent⁴: in this case the Antarctic ice sheet would melt in about $1500$ years.

Please note: I am not arguing that melting ice sheets caused by anthropogenic climate change is not a problem: it is. For instance there are more than $70\,\mathrm{m}$ of sea level rise locked in the Antarctic ice sheet: melting even a small fraction of this ice is catastropic. And melting is not the only problem: if significant parts of ice sheets end up as sea ice before melting, then the sea level rise can happen much faster. And sea level rise is just one of the problems caused by ice sheets melting.

BBC news article on Bedmap2, paper (PDF). ↩
The ice is, of course, far below freezing so the actual energy required will be much greater. ↩
This is enormously more than the amount of power that we could plausibly use: see later. ↩
This is just a number I have pulled out of thin air: one percent seems too high, so perhaps a tenth of one percent is plausible. ↩

Black body planet

Tim Bradshaw — Wed, 30 Sep 2015 14:51:09 UT

A model of the planets as black bodies is surprisingly accurate, except in one interesting case¹.

In theory

A black body is an ideal object which absorbs all radiation which falls on it, and then reemits it as thermal radiation. Real objects are, of course, not black bodies, but they are often surprisingly close. One nice thing about black bodies is that there are is a nice equation which relates the amount of power they radiate to their temperature:

\[ \frac{P}{A} = \sigma T^4 \]

Where $P$ is power, $A$ is area and $\sigma$ is the Stefan-Boltzmann constant which is $\sigma \approx 5.67\times10^{−8}\,\mathrm{Wm^{-2}K^{−4}}$: this formula tells you the power per unit area that a black body radiates, at a given temperature.

Well, obviously you can derive this formula:

\[ T = \left(\frac{P}{A\sigma}\right)^{1/4} \]

In other words temperature goes as the fourth root of power.

If you consider a ball of radius $r$ then its surface area is $A = 4\pi r^2$, so a perfectly spherical black body of radius $r$ at a uniform temperature $T$ radiates a total output power $P_O$

\[ P_O = 4\pi r^2 \sigma T^4 \]

or equivalently

\[ T = \left(\frac{P_O}{4\pi r^2 \sigma}\right)^{1/4} \]

OK, so consider a planet, which is a perfect black-body, orbiting at a radius $R$ from the Sun². Let the input power flux from the Sun, at the point directly facing the Sun, be $S$. For Earth, $S \approx 1360\,\mathrm{Wm^{-2}}$. We can calculate two things from this.

The total output power of the Sun, $P_S$ is given by the integral of $S$ over a sphere of radius $R$:

\[ P_S = 4\pi R^2 S \]

The total power falling on the planet, $P_I$, is given by the integral of $S$ over the surface of the disk of the planet which faces the Sun, and this is

\[ P_I = \pi r^2 S \]

So the first of these equations can be used to work out $S$ in terms of $P_S$ and then substituted into the second one:

\[ P_I = P_S\frac{r^2}{4 R^2} \]

If the planet is at equilibrium, then $P_O = P_I$ or, in other words, output and input power is the same³. So

\[ T = \left(\frac{P_S}{16\pi \sigma R^2}\right)^{1/4} \]

Finally, given $S$ and $R$ we can work out $P_S$, and for our Sun, based on $R \approx 1.50\times 10^{11}\,\mathrm{m}$ for Earth we get $P_S \approx 3.85\times 10^{26}\,\mathrm{W}$.

In practice

So, we can compute the surface temperatures for the rocky planets, assuming they were black bodies.

Earth. $R \approx 1.50\times 10^{11}\mathrm{m}$, giving $T \approx 278\,\mathrm{K}$ or $5^\circ\mathrm{C}$. Actual mean surface temperature is $287\,\mathrm{K}$ or $14^\circ\mathrm{C}$: this is reasonably accurate.

Mercury. $R \approx 5.79\times 10^{10}\,\mathrm{m}$ giving $T \approx 448\,\mathrm{K}$ or $175^\circ\mathrm{C}$. Actual mean surface temperature is $452\,\mathrm{K}$ or $179^\circ\mathrm{C}$. This is also OK.

Mars. $R \approx 2.28\times 10^{11}\,\mathrm{m}$, giving $T \approx 226\,\mathrm{K}$ or $-47^\circ\mathrm{C}$. Actual mean surface temperature is $226\,\mathrm{K}$ or $-47^\circ\mathrm{C}$. This is pretty spooky: it has no right to be this good, and is probably only this good by chance.

Pluto. $R \approx 5.91\times 10^{12}\,\mathrm{m}$, giving $T \approx 44\,\mathrm{K}$ or $-229^\circ\mathrm{C}$. Actual mean surface temperature is $44\,\mathrm{K}$ or $-229^\circ\mathrm{C}$. The same is true for this: it is probably only this good by chance.

Venus. $R \approx 1.08\times 10^{11}\,\mathrm{m}$, giving $T \approx 328\,\mathrm{K}$ or $55^\circ\mathrm{C}$. Actual mean surface temperature is $730\,\mathrm{K}$ or $460^\circ\mathrm{C}$. This is hopeless, as you would expect it to be.

These are astonishingly accurate, except for Venus, which is out by a factor of nearly two: Venus is the hottest planet in the Solar system because of a runaway greenhouse effect.

Notes

Data came from Alpha which, while I have considerable qualms about Wolfram products, is a reasonably good source of this sort of thing. I have been very casual about rounding, generally rounding to integers for both $\mathrm{K}$ and ${}^\circ\mathrm{C}$. The temperatures don’t come with an uncertainty but I suspect that for Venus is less accurate than the others. I didn’t deal with the gas giants because they don’t have well-defined surfaces and I was just too lazy.

This is mostly an experiment with maths in frog. The conclusion is that it’s possible, but does not look great: I will stick to LaTeX. ↩
Assume also the planet is distant from the Sun so we don’t need to worry about whether light leaks around the side of the planet and so on. ↩
This assumes that the planet has a constant surface temperature, which will be true only if it conducts heat perfectly, but turns out to be a good enough approximation. ↩

Covariance and contravariance

Tim Bradshaw — Tue, 21 Jul 2015 16:22:16 UT

Physicists seem still to be taught about tensors as being, essentially, multidimensional arrays with special transformation rules which must be learned by rote. So I wrote a document which tries to present a more useful approach.

The aim of this document was to present a more modern, ‘geometrical’ approach, while not requiring too much background in differential geometry. I don’t suppose anyone read it when I posted pointers to it on reddit, and certainly no-one will read it now, but here it is¹.

This URL might change (and has already changed: it used to be on Dropbox). This post itself is a better link to remember as I will update the pointer if I move the document. ↩

The electron at the edge of the universe

Tim Bradshaw — Sun, 22 Feb 2015 22:05:03 UT

How easy are physical systems to predict?

Well, here are a couple of rather lovely examples. Both of these are due to Michael Berry and are mentioned in a book called ‘A Passion for Science’ which is in fact a set of collected transcripts of BBC radio programmes from sometime in the mid 1980s: I heard them on the radio originally, and they have stayed with me — I didn’t find the paper versions until quite recently. I’m giving these from memory: they might differ slightly from the versions described in the book.

For both of them imagine a universe where everything is completely Newtonian, so no quantum mechanics in particular. There is Newtonian gravity.

Billiards

The first case is billiards, and we’ll consider a completely idealised billiard table: completely smooth, flat and rigid, completely round balls with completely known properties (so how elastic they are etc), and the same for the cushions. Now someone makes a shot, and we either know the direction and force exactly or are allowed to measure the cue ball’s position and velocity exactly shortly after the shot. We don’t know one thing: there are some people standing around the table, and we don’t know where they are, so we don’t know what their gravitational fields look like. Now we want to predict where the balls go, and we’ll say that the prediction fails when a ball leaves a collision 90 degrees from where we predicted — it’s obvious that after that point we can’t usefully predict anything. How many collisions can we predict ahead?

The electron at the edge of the universe

The second case is an ideal gas: a lot of little ideal particles in an ideal box. Again we know everything: the starting conditions are known completely, the box is completely understood &c &c. The box insulates everything but (Newtonian) gravity to make things simpler. And this time we also know everything about the rest of the universe as well: we don’t need to predict it forward, we’re just given all the data about how it evolves (in fact I think that without loss of generality we can assume an empty universe outside the box, which reduces the data volume considerably). Except that there’s an electron at the edge of the universe and we don’t know where it is (apart from how far away it is), and so again we don’t know its gravitiational field. Now we want to predict this system forwards and we’ll use the same criterion for failure: when some particle leaves a collision 90 degrees out from where we predict. How many collisions before that happens?

The answers are seven or eight for the first case, and about fifty for the second.

Playing cards with the Devil

Tim Bradshaw — Tue, 30 Dec 2014 13:05:55 UT

You are playing cards with the Devil, the prize being your soul.

The game is very simple:

the Devil deals two cards face down;
you both turn over the cards — if they are the same colour then you win, if they are different colours the Devil wins.

You play six times, and the Devil wins every time. He has obviously stacked the deck.

You suggest to the Devil that you should play the opposite game: if the cards are different colours you win. He agrees, and you play six times: he wins every time. Obviously He either saw this coming or He has changed the deck while you were not looking.

You suggest a third game:

the Devil will deal two cards, face down;
after the cards are dealt you will choose which game to play — the one where you win if they are the same, or the one where you win if they are different;
the cards are turned over.

Much to your surprise he agrees to play once more, and you play six times. The Devil wins every time.

Fragments: Posts tagged 'physics'

The kingdom of lost hope

Too big to fail

Forbidden words

Sleepwalking into armageddon

Scenes from the end times

Eat the old

A history of the near future

Contents

Growth, the sacred cow

What growth means

If growth is not constant

Growth, resources and waste products

Why growth matters

Summary

Finiteness

The future we imagine

Some inconvenient truths

What is going on?

The future we’re going to have

Are we going to have a problem here?

The magic goes away

Energy

Energy is not the only fruit

Yes, we are going to have a problem here

Faith, fantasy and Economics

Efficiency limits: economics meets physics and loses

Escaping into a pretend world

Decoupling: economics meets itself and loses

The elephant

How are we doing?

What this looks like

The teeming billions

Falling fertility

Falling fertility, rising mortality

The consequences

As above, so below

Shorter

A history of the near future

Overshoot and collapse

A pale horse

Seeing Apollo

Melting the Antarctic ice sheet

Black body planet

In theory

In practice

Notes

Covariance and contravariance

The electron at the edge of the universe

Billiards

The electron at the edge of the universe

Playing cards with the Devil