How geoengineering could save us from climate disaster; Have we broken mathematics?; Why exercise reduces cancer risk

0:28This episode is brought to you by Google Chrome. Dr Rowan Hooper. And I'm Dr Penny Sarchet. On today's show we investigate the number that could destroy mathematics and we discover a reason why exercise is linked with positive outcomes in cancer. We've known for a long time that there's a link but we haven't known exactly why. But we're going to start with geoengineering. Yeah there was a conference last week in Exeter, it was the Global Tipping Points Conference and there was a study at the meeting there that suggested that if we want to avoid irreversible world-changing tipping points, and if we don't stop putting CO2 into the atmosphere, then we should start altering the atmosphere to slow down heating.

1:09In other words, we should do geoengineering. Right. So this is a model that looks specifically at this crucial ocean current we've discussed on the podcast before, the AMOC or the Atlantic Meridional Overturning Circulation. It carries heat from the tropics to Europe. And if the AMOC collapses, and we're probably talking next century here, maybe a bit earlier, if the AMOC collapses, there could be rapid sea level rise in North America, severe drops in temperatures in Northern Europe, and serious disruption to monsoons across Asia. Big, big effects. And the small matter of a total collapse in agriculture in Northern Europe, much of Europe.

1:48So a total disaster. Yeah. Can't be allowed to happen. If the AMOC does turn off, there's no turning it back on again. Even if we did somehow suddenly get to, you know, back down to under 1.5 degrees of warming. So that's why it's a tipping point. That's why people say we should do everything we can to avoid it. It is geoengineering is hugely controversial. There's lots of reasons why we're going to get into that and not least that it could be used as a weapon in war so that's what we're getting into today but at this exeter meeting there were about 200 delegates they put out a statement calling for action from policymakers and especially global leaders attending cop 30 in brazil the climate summit later and the statement said these world leaders must take immediate action to prevent devastating tipping points like amok and here's part of the statement I just want to read out.

2:42The window for preventing these cascading climate dynamics is rapidly closing, demanding immediate, unprecedented action from policymakers worldwide and especially from leaders at COP30. This is a human rights and planetary health imperative and ultimately a matter of survival. So strong words but of course there have been many strong statements from scientists before and we're yet to see that sort of unprecedented political action that's needed. So what else can we do? There is, of course, geoengineering. These are ideas along the lines of adding particles to the atmosphere, for instance, these kind of big projects that could limit warming.

3:20And as you said, it's hugely controversial. Michael LePage was at the Tipping Points meeting in Exeter. Michael, I gather geoengineering was one of the ideas they were discussing there. It was, and as you're saying, very, very controversial. sure so because of the risk there are some climate scientists who don't even want to research this and in fact at one of the sessions that was focused on geoengineering there was one attendee refused to even go to it at all so that's out of principle out of principle not going yeah interesting and we're going to come on to those dangers shortly um but shall we start with what are the potential benefits can geoengineering really help us prevent these scary tipping points So yes, geoengineering potentially can prevent these tipping points, but there is a big catch.

4:04Now, one of the talks at the meeting was about what would happen if we injected sort of aerosols into the stratosphere to reflect sunlight, specifically to prevent the risk of the collapse of the AMOC current. So in practical terms, that would mean having planes flying around in the stratosphere and releasing these particles, and then they reflect the sunlight and they cool things down. It's the same as what happens if a volcano erupts. anyway so according to a model by claudia vieners at utrecht university in the netherlands that would if we didn't do this and we carried on pumping co2 into the atmosphere the strength of the amok would decline by more than half but if we do this geoengineering we could largely maintain amok at the current strength even if we're still emitting co2 this is doing enough geoengineering to keep the temperature around 1.5 degrees celsius and in fact she said that in her scenarios geoengineering worked better at preserving AMOC than simply reducing emissions fast.

5:03So it actually geoengineering was more effective at preserving AMOC than sort of reducing climate emissions in this particular model. So obviously there's a strong case. That sounds like a strong case to do it. But I don't think I've heard a case made before saying that we've got to the point where geoengineering is more effective than emissions reduction. yeah it's this one model and uh obviously um it's for this one purpose of maintaining the amok we don't know what the other consequences would be necessarily so of course there are also huge uncertainties about how amok is going to behave and we don't know that one model is necessarily going to tell us to sort of represent that very well so there are huge uncertainties we can't take this as it's definitely going to work and you did say that there's a big catch to this as well Yes.

5:52So the catch is we need to do it soon. So Vienna's also looked at what would happen if we did geoengineering, but we didn't start until 2080. So you'd wait until 2080 and then you'd start pumping out the sulfate aerosols and try and get the global temperature down to 1.5. By that time, you've already got a lot of weakening of the AMOC. And what she found is there's no recovery at all. That's exactly what you're saying. It's a tipping point. You don't expect that it's an irreversible change. You don't expect there to be recovery. but this model is showing exactly that. So if we delay geoengineering too long, we can't prevent these tipping points because they'll already be happening.

6:29Okay, let's dig into some of the challenges a bit more because I do think we're sometimes guilty of sort of just airily saying, oh, we'll do geoengineering later on and sort this out. But, you know, this is just one study. We're nowhere near ready for this. No, and I think there are lots of problems, But I think the biggest one is that in order to do this successfully, it would take very close international cooperation. In fact, there was another talk at a conference where Steve Garner from the University of Washington said, this is the greatest governance challenge that humanity has ever faced.

7:06And potentially, this would have to be global coordination for centuries, because it's kind of long term big projects. And it's kind of hard to have faith that everyone's going to muck along and do the same thing. together. I guess one of the questions is this issue of termination shock. So for example, we could start geoengineering and then stop when CO2 levels are still too high. And then we might see suddenly rapid warming on a scale where, you know, a more gradual change would have been easier to adapt to. Exactly. In fact, we may be going through a kind of mini termination shock at the moment.

7:42There are quite a lot of talks at the conference about the effect of all the sort of sulfate pollution that we've been pumping out for the past few decades and now we're cleaning it up and there's growing evidence that a lot of the rapid warming of the past decade past two decades is due to this cleaning up of the sulfate pollution so it's been like a form of geoengineering that we're suddenly taking away and now we're getting this very rapid warming in response of course if we carried on pumping co2 into the atmosphere and use geoengineering to compensate for that we'll get an even bigger leap in warming in the future.

8:14And that's that's a big danger. This is why it's so important that we have political agreement to make geoengineering work, we need to carry it on for a long, long time. And it also needs to be coordinated. So for instance, say, one country decided to go alone, and you sort of just did geoengineering in the northern hemisphere, well, then what you could do is shift the rain, the tropical rainfall zone could be shifted in one direction or another. And that would obviously have huge consequences for agriculture. So there are these big dangers. And in fact, we could even end up with climate wars.

8:48Imagine, for instance, that China decides to go alone, and it's sort of geoengineering to suit itself. And the US decides the kind of geoengineering that China is doing is bad for it. So it starts geoengineering in a different way. And then you have these sort of conflicting things going on. And geoengineering actually being used as a weapon to sort of fight a global battle. I mean, the CIA have said for years that they've identified climate as a huge factor in conflicts around the world. But that's over things like water or, you know, food, territory, the traditional resources you need. But using geoengineering itself as a weapon in war, like, I mean, you have to think that with the way things are, It's a real, it's a plausible scenario.

9:35What if, let's just sort of be optimistic, forcibly, grittily optimistic, supposing we could get a political agreement broadly, when could we start doing this thing? Yeah, unfortunately that still doesn't solve the problem because we're just at such an early stage of researching this and there are some really serious dangers. So for instance, one of the talks at the conference was by someone called Jim Haywood, and he's been looking at something called marine cloud brightening. So this is where you sort of release sulfates at sort of near sea level, and it makes the clouds whiter and they reflect more heat.

10:15Now, he did one experiment where he found that if you release these sulfates in certain parts of the world, it produces this mega La Nina effect that is so strong. Doesn't sound good. No, it's so strong, it actually changes the air pressure over the Pacific Ocean so much that it raises sea level by more than global warming would up to that point. Wow, yeah. So he actually said, this is inverse terraforming. This is making the Earth look like another planet. So that is something we really don't want to be doing. And of course, the point of that research is to identify the dangers and make sure we don't ever do this.

10:53But we're just at such an early stage of doing this. so we can't yet sort of say oh we know enough to avoid this. To give another example one of the things researchers are starting to do for climate sort of forecasts they're starting to use these very high resolution models that we now use for weather and they're starting to apply those to climate and they find in some cases these high resolution models are showing dangers that didn't show up in the lower resolution models but no one's applied these to geoengineering yet Jim Haywood told me after one of the talks. So we're not nearly at a point where we can say, this is what we should do, and this is how we should do it.

11:31And we could be confident that this is going to work and produce the desired effects. So we're in this really difficult situation, then that if we're going to do it, we need to start doing it really soon to avoid these tipping points and the sort of scary outcomes if things like the AMOC collapse. But we can't actually start doing it soon, because there's still so much that we don't know about it scientifically and the political sort of framework for doing it properly isn't there either. Absolutely. It's a catch-22. So I asked Claudia Wieners about this, the woman who presented that model, and she talked about walking the line over researching it and governing geoengineering.

12:10And here she is. The biggest issue with SRM is maybe not so much physical side effects or imperfections, but the political risks that come with it, distraction from mitigation, and also just because SRM is relatively cheap, it could well be that one actor or small group of actors says, we are going to do it, even if the rest of the world doesn't like it. Maybe this could lead to conflict, or even if it doesn't lead to conflict, it would still be unfair in the sense of not consulting everybody in a fair manner. What if someone makes a stupid kind of decision because maybe they don't care so much about really solving certain climate issues, but they just want the prestige of being seen as the powerful actor who is the guardian of the climate.

12:54So all these political problems you can't solve by climate modeling. But what is the solution to this? Because it's starting to feel like this could be the way we go, that a powerful actor will just take it upon themselves to do something. I don't think there's anyone who really has a solution. I mean, of course, what you would want is that there's some kind of globally legitimized representative body that takes input from everyone, including poor countries and marginalized people within the countries, taking their interests into account and then come up with a fair compromise of what to do. The question is how to make sure that happens.

13:37I still think that it's better to have discussion about SRM, including what it can do, but also very much what it cannot do and what are the dangers, rather to pushing it under the rug. Because suppose that this political bad scenario would happen, that someone says we're going to do it or we want to do it, then at least I hope that if that happens, we live in a world where we roughly know what can work and what can't. I think that the demon is out of the bottle. So SRM has already, it's not known by everyone on the street, but it's known by sufficiently many people that if something bad happens, let's say a huge heat wave in India, like in the Ministry of the Future novel, people will come up saying, oh yeah, there's SRM.

14:22Once we implement it, it works pretty quickly. So maybe now the time has come to do it. And I'd rather than hope that enough people have information about what kind of implementations could be a decent idea and what are terribly horrible. So that at least you have good arguments if this actor will try to do it in the wrong way. But what I'm saying, like spreading the information, being open and transparent about it, sharing research, collaborating scientifically, all this is great, but all this is in no means a guarantee that this will be handled wise in a political way, especially seeing how the world is headed now.

14:56So SRM research, with the political situation now, is getting more dangerous, but not SRM research, like not doing the research, also getting more dangerous because we are not going to the good direction with mitigation. So it's really a huge dilemma, this whole SAI thing. And even if it's physically, maybe if you had an intelligent, benevolent, globally fair governance body to administer this, then probably using it from what we now know would be physically a good idea. But politically, in the real world, it's far more doubtful whether it's a good idea. Now, I mentioned that statement that world leaders put out from the Tipping Points Conference.

15:39And in that statement, they go on about how we need to trigger positive tipping points in economies and societies. And what they want to do is basically generate self-propelling changes in technology and in behaviour to get us towards zero emissions. And there's two things to say about that. The first is in the UK, we've got this independent committee called the Office for Budget Responsibility, the OBR. And yesterday or a couple of days ago, it produced a report finding that achieving net zero will be cheaper, much cheaper for the UK government than we previously thought. And the economic damages of climate change are far more severe than the costs of net zero.

16:22It's the sort of thing we have been saying before, but this is from the OBR. and you know with the cost of solar especially coming down so fast that's the sort of self-propelling positive tipping point changing technology that they're talking about that we need. Yeah and we're really seeing that at the moment the cost of solar power is falling so fast renewable energy in general but especially solar. It is absolutely stunning. So this is a great way of thinking about it right if you think of a coal-fired power station its capacity is a gigawatt of power and that capacity of solar panels is now going up around the world every 15 hours.

16:58Every 15 hours. Yeah, so the growth in renewable energy is unlike the growth of any power source we've ever seen before, including the Industrial Revolution. It's like we're at the start of the Industrial Revolution, except this time it's clean and this time it's bigger. And you mentioned positive tipping points earlier. Yeah, and we are actually working on a special podcast episode about positive tipping points. So coming soonish.

17:51What does it mean to talk about the edge of mathematics? That's the precipice we're going to walk along today as mathematicians close in on a number so large that it brings us to the limit of what is knowable in modern mathematics. Get ready, guys. So this story starts with the legendary figures of Alan Turing and Kurt Gödel and it takes us to a number that makes the number of all particles in the universe look puny by comparison. Yeah, this is starting to blow my mind already, this story. We're going to find out if we've broken mathematics. Yes. It is a lot to get your head around. So we're going to be guided by the steady hand of Jacob Aaron.

18:29Jacob, this is about something called Busy Beaver Numbers. And that's a deceptive title, isn't it? Because it makes it sound like it's something simple that we're going to understand. And kind of cute and childish. So can you gently take us through it? Yeah. So there is a sort of a childish and playful element to it that I'll get to. But really, as you say, this story starts with Alan Turing in the 1930s, who showed that any computer algorithm can be mimicked by imagining a simple Turing machine that reads and writes the zeros and ones of information on an infinitely long tape following a series of instructions that are called states.

19:06And a more complex algorithm requires more states to execute. so for every number of possible states say five states or 100 states there are finitely many corresponding turing machines but the big question is how long it takes a turing machine to execute its algorithm to work through the states and this is something that mathematicians have wrestled with for some time and this is where the busy beaver comes in the busy beaver number is defined as the Turing machine with the longest possible runtime for a particular number of states. So you can kind of think of it as a link between the complexity of the algorithm and how long it takes to run.

19:51What's interesting about the Busy Beaver number is it grows extraordinarily quickly. So Busy Beaver 1 or BB1 is just 1, BB2 is 6, and then the fifth Busy Beaver number is 47 176 ,870. Oh, God. Now, if you want to know what the value for the next Busy Beaver number is, the sixth, we don't actually know. People are still working to attempt to discover it. And actually, there's this whole online community that sort of enjoys this challenge. They call it the Busy Beaver Challenge. And they were actually the ones to find the value for the fifth Busy Beaver number in 2024, putting an end to a 40-year search.

20:35and they've now turned their eye to the next one. And a member of this community known as MXDYS has discovered that it must be at least as big as a number that I'm really going to struggle to describe, but I will attempt to. So how can a number be so large that you can't explain it? Can't you just put N to the power of X or the other way around or use a Greek symbol or something? Yeah, like, and how can it be that? I mean, I remember once scrolling through this web page of Pi to a billion places. For some reason, I just scrolled through it. Can it be written down physically? How do you help us out here, Jake?

21:20Well, Pi is, of course, infinite. So we can never fully write it down. But even these numbers that we're talking about go far beyond a billion digits. A billion would be easy to describe. So the easiest way I find to think about this is to think about the number of atoms there are in the universe, which we estimate to be 10 to the power of 80. It's a very, very large number. This is one followed by 80 zeros. That's something we're supposed to be able to. OK, that's the simple thing. That's the simple thing. Just have the entire universe in your mind, 10 to the 80, and then we'll go from there.

21:5710 to the 80 is an operation called exponentiation. That's what happens when we're raising one number to the power of another. But BB6 requires us to go beyond exponentiation. And we're now doing tetration, which is iterated exponentiation. So while 2 to the power of 3 is 8, two tetrated to three is two raised to the power of two to the power of two which is equal to 16 so that's not too difficult but two tetrated to five is a number with almost 20 000 digits wow so far beyond the number of atoms in the universe okay so we are okay we're getting we're getting quite big yeah that number is actually quite small yeah when compared to bb6 though So remarkably, MXDYS has shown that BB6 is at least two tetrated to the two, tetrated to the two to the nine.

23:00So this is this tower of iterated tetration. And that's the best I can do. I can't compare it to anything that's even remotely familiar. It's absolutely ludicrous. Yeah, I mean, there's nowhere to go with this. is there. It's a vastness that's incomprehensible. I know this is the least of it, but I didn't even know you could go beyond exponentiation. No, no idea. Mathematicians will always find a way to go beyond. Yeah, just do it to itself more times. Much of this work to find the busy beaver BB numbers is done in a sort of community, amateur mathematical endeavour sort of way. I've seen this term around busy bee virology.

23:44I love that. Yeah, so I don't know, there's just something about the strangeness, this idea of you're sort of exploring the unknown and they have sort of various ways of finding these Turing machines that help you map out these numbers with sort of obscure bits of code. And so, yeah, it's, you know, it's not the most fun thing in the world, but for these guys, you know, they really, really enjoy it. Okay, let's talk about how it's broken maths, or we're on the edge of maths. And what does it even mean to have this whole region of mathematics that you may not be able to interrogate? Yeah, like, isn't this just pointless?

24:22Like, what does it really sort of... I'm really sorry, guys, out there. But like, what does this tell us rather than just, hey, look, we can generate massive numbers? So to understand that, we need to dive into the very foundations of mathematics, which is called ZFC theory. And you can think of this as kind of an agreed rulebook of how to do maths, the logical assumptions that underpin the modern way of doing mathematics. But the dirty secret, and we've known this for almost a century, is that there is a fatal flaw within these foundations. As you mentioned, Penny Kirk-Gerdl, he showed that the rules of ZFC cannot themselves be used to prove that ZFC is free of contradictions.

25:08And so what that means is that essentially there are some questions that are unknowable within this framework of mathematics. You simply cannot say whether they are true or not. So this is what kind of serves as the edge of mathematics. And what's fascinating is that the busy beaver numbers are sort of a measuring stick that show how close we are to reaching this strange edge. For example, we don't know what the value of BB 643 is and that's going to be a number so huge that it makes BB 6 look tiny I literally have no idea how you would even begin to start expressing it despite that and despite not knowing what the value of that that figure is mathematicians have proved that BB 643 would transcend ZFC, it would break the rules of mathematics as we know them.

26:06Now, you could essentially fix this problem by saying, okay, we'll add BB 643 to the rules of mathematics. But the question is, when does that threshold happen between BB 6 and BB 643? We don't yet know. Next week, can we break another discipline? Biology? Let's not. We need that one. We do need masks.

26:34It's really become clear that the microbiome plays a big part in many aspects of our health. But this week, there's news of one health outcome it influences that I found surprising. Exercise and cancer survival rates. Yeah, so let's go into that because we know that exercise improves cancer survival. But what has that got to do with the microbiome? Well, I think it's probably quite well known at this point that exercise being fit makes you less likely to get cancer in the first place. But it's also been known for a little while that exercise seems to be linked to improved outcomes if you do get cancer.

27:07And some of the statistics we see around that, it might just be, for example, exercise helps deal with some of the side effects you get with cancer treatment. or say it's kind of knock-on effects if it's good for your heart it means that you're not going to survive cancer only to die of heart disease a few years later which you know in cancer is more common the older you get so that that's a factor in these studies but this new study suggests a more direct effect that exercise may have on tumor growth and it is mediated by the microbiome okay and so is that through somehow the effect on inflammation or the immune system because we know there's that link.

27:45Yes, so immune system seems to be key here. And it all starts in mouse experiments, but I promise it does get to humans. So a team in Pittsburgh gave aggressive melanomas to two groups of mice, some were sedentary, and the others had been on a four week exercise regime. And as Avery Hurt wrote for us this week, they found as expected that the mice who'd exercised had smaller tumours and better survival rates. However, that effect was not seen when they did this in exercising mice who'd been given either antibiotics or had been kept in a germ-free environment. All right so that's we classically see this in microbiome studies don't we that you raise mice in a sterile environment so they're able to look at the effect of microbes on yeah or what happens if you don't have microbes and so the fact that they didn't see this protective effect in sterile mice or mice who'd basically had their microbes nuked by antibiotics suggests that you need those microbes to have this protective effect that they were seeing and then the team went on to identify a molecule called formate that's made by bacteria and increases in the body when we exercise.