Bad moon rising

I fear rivers over flowin', I hear the voice of rage and ruin

This Substack is called Logging The World, and newer subscribers may not know why. The key word is log, as in logarithms and log scales, because even after a pandemic gave a horrifying demonstration of it, I still don’t believe enough people understand exponential growth and what it can mean - and not just for the spread of diseases.

Indeed, I’m worried that the UK media, politicians and civil servants are too often stuck thinking in a linear (“add the same amount on each year”) mode, when the key issues of our time, including the energy transition, drone warfare, pensions and AI, tend to operate in an exponential (“multiply by the same amount each year”) way.

So here’s a couple of quick questions for you to ponder:

1. If installed battery capacity grows by 68% each year, what percentage of the batteries that we’ll have by 2035 will be in place by 2030?

2. If the cost of batteries falls by 20% in real terms each year, and we have a fixed sum to spend on them, when should we buy batteries to cause the greatest total CO2 reduction by 2035?

Tracking exponentials

Neither of the answers are immediately obvious, but they aren’t hard to work out (see below). But given the story of the pandemic, are we confident that the right people are thinking in this way? I got a reputation as a Twitter log scale obsessive, but looking back, it seems crazy that as late as 1st October 2020 I could publish a piece in The Spectator simply by correctly arguing that exponential COVID growth in the North West put us on a slow but inevitable path towards intolerable pressures on the healthcare system:

On 26 August, the number of hospitalised Covid patients in the region reached a low of 77. Five weeks later, this number has grown to 612 – an eightfold increase. While this is much lower than the 2,890 reached on 13 April, another eightfold increase would see it far exceed that first-wave peak. The arithmetic of epidemic growth means that such a further increase, perhaps over a similar timescale, cannot be ruled out – and could even be regarded as the expected outcome. Given constraints on NHS capacity, heightened by regular winter flu admissions, I believe this is a risk we need to take seriously.

Of course, pandemics are relatively easy to predict, because there are well-understood toy mathematical models which can give good approximations to their likely evolution, at least for a few weeks at a time. However, we can also observe empirically from phenomena such as Moore’s Law that technological progress also tends to exhibit exponential growth, and so we should be thinking in these terms here too.

So to answer the questions I posed previously, using sophisticated mathematical tools (Microsoft Excel) we can see that:

If battery capacity grows by 68% per year, then at the start of 2030 we will have 13.4 times as much capacity as we do now, and by 2035 that will be 179 times. So the amount of storage we’d have in 2030 is 7.5% of what we’ll have by 2035¹. I’m pessimistic about the prospects for long-term energy storage being available by the arbitrary 2030 deadline we’ve chosen to shackle ourselves to, but as a result of this exponential trajectory it’s much more plausible to me that we’ll get there in the end. But has this kind of thinking been factored into the 2030 target, or is it just a round number which sounds good on a political leaflet?

It’s a slightly more complicated sum to model CO2 reduction if battery cost drops by 20% per year.²

We have to calculate the cost of a system, and see that the number of systems we can buy grows exponentially as a result. Since the effect of a system is multiplied by the number of years it is in action, we need to multiply the “systems” column by the “years” column to see that the sweet spot is batteries coming online in 2030 or 2031, but that even as late as 2032 wouldn’t be the end of the world.

Of course, this is a toy model that doesn’t capture any number of effects, but it’s still worth knowing that the “best time to act is now” mantra may not necessarily apply in an exponential world. But when you read Kate Bingham’s reflections on the vaccine process at the COVID inquiry

how confident are you that even this simple level of thinking is embedded into our decision making?

Hidden figures

However, these can perhaps be thought of as warmup problems. These were examples where the exponential growth was openly on display, but there are subtler situations of hidden exponential growth which can be potentially disastrous.

Think about the start of the omicron wave in December 2021. Of course, we were lucky in the end because the severity of the variant was so much lower, but by extrapolating toy models it was possible to predict that its much faster speed of spread put us on the way to sudden explosive growth in COVID cases.

Indeed, by carefully tracking the percentage of cases that were omicron, it was possible to predict more or less to the day when case numbers would really take off. The key thing to understand is that if you have something which makes up a tiny share but is growing exponentially fast, then eventually it will hit a point where it starts to dominate, and the overall number will start to grow in an exponential kind of way.

So the question I’d like to ask is: what if we are at a “December 2021 omicron” moment for AI?

Of course, there’s a huge amount of hype in the area, and we can still argue about the extent to which AI is genuinely creative rather than just mimicking patterns it has observed. But equally, it’s been remarkable how in two years we’ve gone from laughing about pictures with the wrong number of fingers to seeing AI operating at an International Mathematical Olympiad silver medal level.

Even if these systems can’t be creative in a true sense, if they can carry out routine writing and comprehension tasks at scale then it’s going to have an extremely dramatic effect on a lot of white collar jobs - take the legal profession for example - and I’m not sure we’re ready for that. But these social changes are out of the scope of this Substack, and other people can give a better answer to what it might mean.

But to circle back to one of my topics here lately, what does it mean for energy requirements? If I do a little bit of digging, I can see that the UK’s reference scenario (see Annex E here) is that energy demand³ will be essentially flat up until 2050, or perhaps rising slightly.

However, if we look at Ireland for example, just like the omicron scenario the electricity taken up by data centres seems like it has been on an exponential kind of trajectory, taking up an ever-increasing share of the total demand:

So I think a reasonable question to ask is, since it’s going to be tough to even (mostly) meet constant-ish energy demand by 2030 using renewables, if we really are in a world of exponentially growing AI capability and demand, how are we going to cope with that? Are we really sure the UK demand curve is going to look so flat, and not like the “hidden exponential growth” omicron one?

As Sam Bowman points out, other places seem to be operating on a very different set of assumptions:

The US State of Georgia is planning for 36.5 GW of new demand in the next decade, inc 19.9 GW in the next four years. That is more than half the entire UK's peak demand of 61.1 GW, just to be *added* in a decade, for a state of 11 million people.

If the cost of solar power is falling exponentially (log scale, straightish line!) much faster than other modes of generation, it seems hard not to conclude that solar will win out globally:

Of course, that’s not really a great option for an often-cloudy island quite a long way north. When the electricity bill is a huge fraction of the overall cost, how is it going to be internationally competitive for the UK to host a lot of wind-powered data centres, when they could be built in sunny Spain instead?

This needn’t be the end of the world for us. Just like Douglas Adams’s Deep Thought, if a system spends a long time churning through an intricate calculation only to spit out a short answer, then there’s no reason that the programmer needs to be located close to it to gain the benefit.

In fairness, the UK’s AI strategy does acknowledge some of this. Even if we can’t be the leader in hosting data centres, we can still play a large role in developing AI ideas, which may even be of greater value. Of course I should declare an interest here, but it seems plausible to me that the international strength of UK universities can still mean we are well positioned in this respect.

However, I’m still not convinced that we are ready to act at the necessary speed in this exponential world. Do we need to wait for a white paper “later this year” to tell us that £20-25k in fees and healthcare charges for the winner of a Global Talent Visa⁴ to bring their family of four to the UK for five years might be cutting off our nose to spite our faces? What powers will the “AI Energy Council” have to ensure we meet our energy demands fast enough?

Maybe there are good answers to all these questions. Maybe it will all be OK. But it’s sometime hard not to think we are stuck trying to think about exponential problems with a linear mindset.

Note: if you found this interesting, please do share it on the platform of your choice. I’m still not on Bluesky whatever anyone tells me, but I’m finding Twitter less and less appealing. However, I’ve been extremely heartened to see more and more of my Twitter mutuals and others showing up here with Substacks of their own, so as usual I’d encourage you to take a look at potential follows from my recommendations list which continues to grow, and help build the community here.

1. If you prefer you can think about this as 1/(1.68)^5.

2. 20% may be somewhat optimistic, but similar calculations would apply for other numbers.

3. The units here are Mtoe: megatonnes of oil equivalent, or how many million tonnes of oil we’d have to burn if that was the only game in town.

4. Such applicants are prescreened and approved by bodies such as the Royal Society and the Royal Academy of Engineering. About 12,000 people qualified in the first 3 years of the scheme. We’re not making a lot of money off these fees, in the grand scheme of things.