What We Cannot Know

THE POLITICS OF CHAOS

Bob May is currently practising what he preaches. Or perhaps I should say Lord May of Oxford, as I was corrected by a man in a top hat who greeted me at the door to the peers’ entrance of the House of Lords. May has in recent years combined his scientific endeavours with energetic political activism. He now sits as a cross-party member of the House of Lords, which is where I popped in for lunch to find out how he was doing in his mission to alert politicians to the impact of chaotic systems on society.

Ushered through the peers’ entrance to the Lords by the man in the top hat and policemen with machine guns, I found May waiting for me on the other side of metal detectors and X-ray machines. May has no truck with all these formal titles and in his earthy Australian manner still insists on being called Bob. ‘I’m afraid I messed up and already ate lunch but I’ll come and eat cake while you get some lunch.’ As I ate fish he consumed an enormous piece of House of Lords chocolate cake. At 79, May is as energetic and engaged as ever and was rushing off after his second lunch to a select committee discussing the impact of a new rail link between London and the northwest of England.

Before joining the Lords, May was chief scientific adviser both to John Major’s Conservative government and then subsequently to Tony Blair’s Labour government. I wondered how tricky a balancing act such a political position is for a man who generally is not scared to tell it like it is.

‘At the interview I was told that there would be occasions where I would be called upon to defend the decisions of a minister and how would I feel about that? I said that I would never under any circumstances deny a fact. On the other hand, I’m fairly good at the kind of debating competition where you’re given a topic and according to a flip of a coin you’ve got to argue for either side of the debate. So I said I’d be happy explaining why the minister’s choice was arrived at. I simply wouldn’t agree to endorse it if it wasn’t right.’

A typical mathematical response. Set up the minister’s axioms and then demonstrate the proof that led to the conclusion. A judgement-free approach. That’s not to say that May isn’t opinionated and prepared to give his own views on the subject at hand.

I was curious how governments deal with the problems that chaos theory creates for anyone trying to make policy decisions. How do politicians cope with the challenges of predicting or manipulating the future, given that we can have only partial knowledge of the systems being analysed?

‘I think that’s rather a flattering account of what goes on here. With some notable exceptions it’s mostly a bunch of very egotistical people, very ambitious people, who are primarily interested in their own careers.’

What about May personally? What impact did the discoveries he’d made have on his view of science’s role in society?

‘It was weird. It was the end of the Newtonian dream. When I was a graduate student it was thought that with better and better computer power we would get better and better weather predictions because we knew the equations and we could make more realistic models of the Earth.’

But May is cautious not to let the climate change deniers use chaos theory as a way to undermine the debate.

‘Not believing in climate change because you can’t trust weather reports is a bit like saying that because you can’t tell when the next wave is going to break on Bondi beach you don’t believe in tides.’

May likes to quote a passage from Tom Stoppard’s play Arcadia to illustrate the strange tension that exists between the power of science to know some things with extraordinary accuracy and chaos theory, which denies us knowledge of many parts of the natural world. One of the protagonists, Valentine, declares:

We’re better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it’ll rain on auntie’s garden party three Sundays from now.

May jokes that his most-cited works are not the high-profile academic papers he’s published in prestigious scientific journals like Nature, but the programme notes he wrote for Stoppard’s play when it was first staged at the National Theatre in London. ‘It makes a mockery of all these citation indexes as a way of measuring the impact of scientific research.’

THE HUMAN EQUATION

So what are the big open questions of science that May would like to know the answer to? Consciousness? An infinite universe?

‘I think I’d look at it in a less grand way, so I’d look at it more in terms of the things I am working on at the moment. Largely by accident I’ve been drawn into questions about banking.’

That was a surprise. The question of creating a stable banking system seemed very parochial, but May has recently been applying his models of the spread of infectious diseases and the dynamics of ecological food webs to understanding the banking crisis of 2008. Working with Andrew Haldane at the Bank of England, he has been considering the financial network as if it were an ecosystem. Their research has revealed how financial instruments intended to optimize returns to individual institutions with seemingly minimal risk can nonetheless cause instability in the system as a whole.

May believes that the problem isn’t necessarily the mechanics of the market itself. It’s the way small things in the market are amplified and perverted by the way humans interact with them. For him the most worrying thing about the banking mess is getting a better handle on this contagious spreading of worry.

‘The challenge is: how do you put human behaviour into the model? I don’t think human psychology is mathematizable. Here we are throwing dice with our future. But if you’re trying to predict the throw of the dice then you want to know the circumstance of who owns the dice.’

That was something I hadn’t taken into account in my attempts to predict the outcome of my casino dice. Perhaps I need to factor in who sold me my dice in the first place.

‘I think many of the major problems facing society are outside the realm of science and mathematics. It’s the behavioural sciences that are the ones we are going to have to depend on to save us.’

Looking round the canteen at the House of Lords, you could see the sheer range and complexity of human behaviour at work. It makes the challenge of mathematizing even the interactions in this tiny microcosm of the human population nigh impossible. As the French historian Fernand Braudel explained in a lecture on history he gave to his fellow inmates in a German prison camp near Lübeck during the Second World War: ‘An incredible number of dice, always rolling, dominate and determine each individual existence.’ Although each individual die is unpredictable, there are still patterns that emerge in the long-range behaviour of many throws of the dice. In Braudel’s view this is what makes the study of history possible. ‘History is indeed “a poor little conjectural science” when it selects individuals as its objects … but much more rational in its procedure and results when it examines groups and repetitions.’

But May believes that understanding the history and origins of the collection of dice that make up the whole human race is not as straightforward as Braudel makes out. For example, it’s not at all clear that we can unpick how we got to this point in our evolutionary journey.

‘I’ll tell you one of the questions that I think is a particularly interesting one: trying to understand our evolutionary trajectory as humans on our planet. Is the trajectory we seem to be on what happens on all or most planets, or is it the result of earlier fluctuations in the chaos which took us on this trajectory rather than another. Will we ever know enough to be able to ask whether the disaster we seem to be heading for is inevitable or whether there are lots of other planets where people are more like Mr Spock, less emotional, less colourful, but much more detached and analytical.’

Until we discover other inhabited planets and can study their trajectories, it’s difficult to assess whether evolution inevitably leads to mismanaged ecosystems based on just one dataset called Earth.

‘The question of whether where we’re heading is something that happens to all inhabited planets or whether there are other planets where it doesn’t happen is something I think we’ll never know.’

And with that May polished off the last few crumbs of his chocolate cake and plunged back into the chaos of the select committees and petty politics of Westminster.

May’s last point relates to the challenge that chaos theory poses for knowing something about the past as much as the future. At least with the future we can wait and see what the outcome of chaotic equations produces. But trying to work backwards and understand what state our planet was in to produce the present is equally if not more challenging. The past even more than the future is probably something we can never truly know.

LIFE: A CHANCE THROW OF THE DICE?

May’s pioneering research explored the dynamics of a population as it went from season to season. But what determines which animals survive and which die before reproducing? According to Darwin, this is simply down to a lucky roll of the evolutionary dice.

The model of the evolution of life on Earth is based on the idea that once you have organisms with DNA, then the offspring of these organisms share the DNA of their parent organisms. But parts of the genetic code in the DNA can undergo random mutations. These are essentially down to the chance throw of the evolutionary dice. But there is a second important strand to Darwin’s proposal, which is the idea of natural selection.

Some of those random changes will give the offspring an increased chance of survival, while other changes will result in a disadvantage. The point of evolution by natural selection is that it is more likely that the advantageous change will survive long enough to reproduce.

Suppose, for example, that I start with a population of giraffes that have short necks. The environment of the giraffes changes such that there is more food in the trees, so that any giraffe born with a longer neck is going to have a better chance of survival. Let’s suppose that I throw my Vegas dice to determine the chance of a mutation for each giraffe born in the next generation following this environmental change. A roll of a 1, 2, 3, 4 or 5 condemns the giraffe to a neck of the same size or shorter, while a throw of a 6 corresponds to a chance mutation which causes a longer neck. The lucky longer-necked giraffes get the food and the shorter-necked giraffes don’t survive to reproduce. So it is just the longer-necked giraffes that get the chance to pass on their DNA.

In the next generation the same thing happens. Roll a 1, 2, 3, 4 or 5 on the dice and the giraffe doesn’t grow any taller than its parents. But another 6 grows the giraffe a bit more. The taller giraffes survive again. The environment favours the giraffes that have thrown a 6. Each generation ends up a bit taller than the last generation until there comes a point where it is no longer an advantage to grow any further.

It’s the combination of chance and natural selection that results in us seeing more giraffes with ancestors that all threw 6s. In retrospect it looks like amazing chance that you see so many 6s in a row. But the point is that you don’t see any of the other rolls of the dice because they don’t survive. What looks like a rigged game is just the result of the combination of chance and natural selection. There is no design or fixing at work. The run of consecutive 6s isn’t a lucky streak but is actually the only thing we would expect to see from such a model.

It’s a beautifully simple model, but, given the complexity of the changes in the environment and the range of mutations that can occur, this simple model can produce extraordinary complexity, which is borne out by the sheer variety of species that exist on Earth. One of the reasons I never really fell in love with biology is that there seemed to be no way to explain why we got cats and zebras out of this evolutionary model and not some other strange selection of animals. It all seemed so arbitrary. So random. But is that really fair?

There is an interesting debate going on in evolutionary biology about how much chance there is in the outcomes we are seeing. If we rewound the story of life on Earth to some point in the past and threw the dice again, would we see very similar animals appearing or could we get something completely different? It is the question that May raised at the end of our lunch.

It does appear that some parts of evolution seem inevitable. It is striking that throughout evolutionary history the eye evolved independently 50 to 100 times. This is strong evidence for the fact that the different rolls of the dice that have occurred across different species seem to have produced species with eyes regardless of what is going on around them. Lots of other examples illustrate how some features, if they are advantageous, seem to rise to the top of the evolutionary swamp. This is illustrated every time you see the same feature appearing more than once in different parts of the animal kingdom. Echolocation, for example, is used by dolphins and bats, but they evolved this trait independently at very different points on the evolutionary tree.

But it isn’t clear how far these outcomes are guaranteed by the model. If there is life on another planet, will it look anything like the life that has evolved here on Earth? This is one of the big open questions in evolutionary biology. As difficult as it may be to answer, I don’t believe it qualifies as something we can never know. It may remain something we will never know, but there is nothing by its nature that makes it unanswerable.

WHERE DID WE COME FROM?

Are there other great unsolved questions of evolutionary biology that might be contenders for things we can never know? For example, why, 542 million years ago, at the beginning of the Cambrian period, was there an explosion of diversity of life on Earth? Before this moment life consisted of single cells that collected into colonies. But over the next 25 million years, a relatively short period on the scale of evolution, there is a rapid diversification of multicellular life that ends up resembling the diversity that we see today. An explanation for this exceptionally fast pace of evolution is still missing. This is in part due to lack of data from that period. Can we ever recover that data, or could this always remain a mystery?

Chaos theory is usually a limiting factor in what we can know about the future. But it can also imply limits on what we can know about the past. We see the results, but deducing the cause means running the equations backwards. Without complete data the same principle applies backwards as forwards. We might find ourselves at two very divergent starting points which can explain very similar outcomes. But we’ll never know which of those origins was ours.

One of the big mysteries in evolutionary biology is how life got going in the first place. The game of life may favour runs of 6s on the roll of the evolutionary dice, but how did the game itself evolve? Estimates have been made for the chances of everything lining up to produce molecules that replicate themselves. In some models of the origins of life it is equivalent to nature having to throw 36 dice and get them all to land on 6. For some this is proof of needing a designer to rig the game. But this is to misunderstand the huge timescale that we are working on.

Miracles do happen … given enough time. Indeed, it would be more striking if we didn’t get these strange anomalies happening. The point is that the anamolies often stick out. They get noticed, while the less exciting rolls of the dice get ignored.

The lottery is a perfect test bed for the occurrence of miracles in a random process. On 6 September 2009 the following six numbers were the winning numbers in the Bulgarian state lottery:

4, 15, 23, 24, 35, 42

Four days later the same six numbers came up again. Incredible, you might think. The government in Bulgaria certainly thought so and ordered an immediate investigation into the possibility of corruption. But what the Bulgarian government failed to take into account is that each week, across the planet, different lotteries are being run. They have been running for decades. If you do the mathematics, it would be more surprising not to see such a seemingly anomalous result.

The same principle applies to the conditions for producing self-replicating molecules in the primeval soup that made up the Earth before life emerged. Mix together plenty of hydrogen, water, carbon dioxide and some other organic gases and subject them to lightning strikes and electromagnetic radiation and already experiments in the lab show the emergence of organic material found only in living things. No one has managed to spontaneously generate anything as extraordinary as DNA in the lab. The chances of that are very small.

But that’s the point, because given the billion billion or so possible planets available in the universe on which to try out this experiment, together with the billion or so years to let the experiment run, it would be more striking if that outside chance of creating something like DNA didn’t happen. Keep rolling 36 dice on a billion billion different planets for a billion years and you’d probably get one roll with all 36 dice showing 6. Once you have a self-replicating molecule it has the means to propagate itself, so you only need to get lucky once to kick off evolution.

Our problem as humans, when it comes to appreciating the chance of a miracle such as life occurring, is that we have not evolved minds able to navigate very large numbers. Probability is therefore something we have little intuition for.

THE FRACTAL TREE OF LIFE

But it’s not only the mathematics of probability that is at work in evolution. The evolutionary tree itself has an interesting quality that is similar to the shapes that appear in chaos theory, a quality known as fractal.

The fractal evolutionary tree.

The evolutionary tree is a picture of the evolution of life on Earth. Making your way through the tree corresponds to a movement through time. Each time the tree branches, this represents the evolution of a new species. If a branch terminates, this means the extinction of that species. The nature of the tree is such that the overall shape seems to be repeated on smaller and smaller scales. This is the characteristic feature of a shape mathematicians call a fractal. If you zoom in on a small part of the tree it looks remarkably like the large-scale structure of the tree. This self-similarity means that it is very difficult to tell at what scale we are looking at the tree. This is the classic characteristic of a fractal.

Fractals are generally the geometric signature of a chaotic system, so it is suggestive of chaotic dynamics at work in evolution: the small changes in the genetic code that can result in huge changes in the outcome of evolution. This model isn’t necessarily a challenge to the idea of convergence, as there can still be points in chaotic systems towards which the model tends to evolve. Such points are called attractors. But it certainly questions whether if you reran evolution it would look anything like what we’ve got on Earth today. The evolutionary biologist Stephen Jay Gould has contended that if you were to rerun the tape of life that you would get very different results. This is what you would expect from a chaotic system. Just as with the weather, very small changes in the initial conditions can result in a dramatically different outcome.

Gould also introduced the idea of punctuated equilibria, which captures the fact that species seem to remain stable for long periods and then undergo what appears to be quite rapid evolutionary change. This has also been shown to be a feature of chaotic systems. The implications of chaos at work in evolution are that many of the questions of evolutionary biology could well fall under the umbrella of things we cannot know because of their connections to the mathematics of chaos.

For example, will we ever know whether humans were destined to evolve from the current model of evolution? An analysis of DNA in different animals has given us exceptional insights into the way animals have evolved in the past. The fossil record, although incomplete in places, has also given us a way to know our origins. But given the time scales involved in evolution it is impossible to experiment and rerun the tape of life evolving on Earth and see if something different could have happened. As soon as we find life on other planets (if we do), this will give us new sample sets to analyse. But until then all is not lost. Just as the MET office doesn’t have to run real weather to make predictions, computer models can illustrate different possible outcomes of the mechanism of evolution, speeding up time. But the model will only be as good as the hypotheses we have made on the model. If we’ve got the model wrong, it won’t tell us what is really happening in nature.