Martin Novak

Martin Nowak

Mathematical Biologist

'I think it is a more rational position to actually believe in God than not to believe in God. I find not believing in God slightly irrational.'

FULL INTERVIEW 27 min

The mathematics of cooperation

'As soon as I saw the pattern, I thought there’s something great here, but I don’t fully understand it and I don’t fully understand the implications. But the sheer beauty of it made it clear there was something amazing.'

Transcript

THE MATHEMATICS OF COOPERATION

MN: So here we have a sea of co-operators in blue and a single defector.

David: Tell me what you mean by co-operator and defector.

MN: A co-operator is somebody who pays a cost to help somebody else. So, for example, I pay a certain cost and you have a benefit. That’s cooperation.

David: Okay.

MN: And a defector does not do that. A defector does nothing: does not pay the cost, refuses to pay the cost, but also does not distribute benefit.

Ard: The defector’s selfish.

David: Is it selfish?

MN: Defectors are selfish and the co-operator does something very strange. The co-operator…

David: More generous?

MN: They’re generous, but kind of generous to a competitor, because everybody here is a competitor to everybody else. And the co-operator helps a competitor. It reduces its own potential in order to augment the potential of somebody else.

David: Which you wouldn’t expect natural selection to allow.

MN: Yes, natural selection should basically make sure those co-operators who do this strange thing, they get wiped out.

David: Yeah.

MN: We would expect them to get wiped out. Okay.

David: So what happens?

MN: Yeah, let us start the game. And we see, yes, these defectors, they are spreading, you know. So the colours that we are observing here are: red are defectors and blue are co-operators, and yellow and green are changing sides.

So yellow is now a new defector: it was a co-operator before. And green is a new co-operator: it was a defector before. We see the pattern is spreading. A kind of symmetry is being maintained here because they are deterministic of the rules, and the initial symmetry is never broken. But the amazing thing is these co-operators, they are persistent. They just refuse to get wiped out and they survive in those clusters. And if you watch very carefully, you see the clusters, they are actually growing until they collide with other clusters, and then they’re shrinking, and then they grow.

David: But they never go out of business.

MN: But they never get out of business. And the amazing thing is the average abundance of co-operators in this pattern is very close to 12log2-8.

David: What does that mean?

Ard: It’s close to constant.

MN: It converges to a constant which is approximately 31%, and this is a mathematical curiosity.

Ard: Natural selection would say the co-operators would get wiped out, because they are paying a cost to help their competitors. And yet it’s not happening. So why?

MN: The reason why it’s not happening is because the co-operators form clusters and in those clusters of co-operators, they actually get a high payoff. They have a high fitness.

David: So they do better?

MN: They do better than the defectors that are surrounded by other defectors. So we always have to ask, on the edge between a co-operator and defector cluster, who is actually winning?

MN: Because the co-operator, even though sitting on the edge, is still getting all the help from other co-operators inside, but a defector is, sort of, getting no help from his defectors. And therefore the co-operators form these clusters that can persist and can even grow in the presence of defectors.

Ard: So this is a bit like, if I’m with my neighbours and we help each other, then we’ll, in the end, be better off than the neighbours one block down who don’t help one another.

MN: Yes, that’s right. So the neighbours that help each other, they form a community that is cooperative, and the neighbours who don’t help each other, they form a community that is defective. And the first can prosper and the other one will kind of perish.

David: Is this, sort of, an addition to the rule of competition in natural selection. Is this a natural law of cooperation?

MN: I think the very interesting observation is the following: going back to first principles, natural selection favours defectors over co-operators. Yet we have cooperation in nature, and we need to find a reason why there is cooperation in nature. And thousands of papers have been written on that topic, actually, and I have been trying to classify all those different propositions into five mechanisms.

And what we’re seeing here is one of those five mechanisms, for the evolution of cooperation, that I call spatial selection.

The other four are… The most important mechanisms for humans, in my opinion, are indirect reciprocity and direct reciprocity. Direct reciprocity is the fundamental idea that we have repeated interaction between two people: I help you, you help me.

And indirect reciprocity is where there’s a repeated interaction in the group: I help you, somebody will help me. I help you, I gain the reputation of a helpful person and I receive help.

Spatial selection, that’s the third mechanism.

The fourth mechanism is group selection. Groups of co-operators out-compete other groups.

And the last one is kin selection: you help relatives. So J.B.S. Haldane said, ‘I will jump into the river to save two brothers or eight cousins.’

Ard: And these five, you call them laws or principles? What would you call them?

MN: They are mechanisms for the evolution of cooperation. So a mechanism is an interaction structure.

David: And this is a different part of nature from… We’re always taught in school of nature red in tooth and claw. This isn’t that, is it?

MN: I would say nature red in tooth and claw is the first, simple, interpretation of Darwinian selection, of Darwinian evolution, and this is now the add-on. I think this is the modern view. And the modern view is somehow also the one that I’ve wanted to promote over the last twenty years: that cooperation is a fundamental principal of the living world, of evolution. And cooperation is necessary whenever evolution makes a step to a higher level of organisation. So whenever evolutions leads from a simple level of organisation to a higher level of organisation, cooperation is essentially involved. And this is the emergence of the first cell; the emergence of eukaryotic cells that have actually organised inside; the emergence of multi-cell organisms, of social insects and of human society.

Ard: So these principles are what explain how very complex societies or organisms arose from evolution?

MN: I think that’s the fundamental step. So I call cooperation an architect, a master architect of complexity.

Ard: And without cooperation, this wouldn’t happen?

MN: I would expect that without cooperation, it is very likely that you would be stuck on a certain level of organisation. So, for example, just a world of single cell bacteria.

David: So, it’s really a very creative…?

MN: I think this is what makes evolution creative.

David: Yes. If you just had competition, then you would just repeat versions of whatever simple thing you started with.

MN: Yes, I think so. And also, competition would lead to the most selfish, to the most successful type dominating.

David: Ah.

MN: Everything would also be more impoverished.

David: So this is going to give you a richer kind of…?

MN: Yes, that is what I definitely, what I…

Ard: And more beautiful?

MN: Yes, more beautiful.

David: When you first had the idea, did you realise then what effect it would have on your life, or how powerful an idea it has become? Was it clear, or was it something you felt like you were just, sort of, exploring?

MN: As soon as I saw the pattern, I thought there’s something great here, but I don’t fully understand it and I don’t fully understand the implications. But the sheer beauty of it made it clear there was something amazing.

Ard: Something true?

MN: Something true.

Ard: You think the beauty of it told you there was something true about it?

MN: Something true. Something extremely relevant, yes, because this beauty emerged from that game in a completely simple way.

Ard: And was that a surprising emergence?

MN: Yeah, once we had it, you know, one could explain it, but when I set out I wouldn’t have expected something like this.

Competition and cooperation in evolution

‘Competition and cooperation are always totally locked together. There’s never the pure form of cooperation, like the utopia, this is never there. Cooperation is never fully stable.'

Transcript

COMPETITION AND COOPERATION in evolution

Ard: Some people of faith would be very nervous that you could explain altruistic behaviour by the laws of nature. What would you say?

MN: That they give a mathematical explanation for why these actions can actually be the ones preferred by natural selection, that’s very good.

Ard: Yeah.

MN: And I’m not nervous, but curiously, long ago, when Newton had the mathematical description of gravity, he asked himself briefly the question, you know, by having a mathematical description of gravity, do I take away from God? Does this take away from God? And he made the remark ‘Hypotheses non fingo’ – I make no hypothesis as to why there is gravity. This could as well be the action of God. So just by having a mathematical description of gravity, it doesn’t take away God as a reason for why there is gravity.

Ard: And the same is true for…

MN: For anything we could learn about the living world: for natural selection, for the mathematical description of natural selection.

David: What was the view of moral behaviour before your work, about whether people could cooperate; whether nature could generate cooperative behaviour?

MN: I think in the realm of evolutionary biology the idea really is that natural selection favours selfishness: that natural selection would promote defectors over co-operators. And, therefore, it is actually difficult to explain the emergence of cooperation. And that was realised as a problem, already, by Darwin: in some sense, he actually said, ‘If you would find a trait in a species that is just there for the benefit of another species, that would invalidate my theory,’ something like that.

David: So he knew it was a problem?

MN: He might have sensed it. Not having had access to the mathematical description of evolution, I would argue that his understanding was partial. But now our understanding is very rigorous, very quantitative.

So natural selection favours defectors over co-operators. That is now the starting point. But now we realise that cooperation is abundant in nature and is kind of needed to explain complex life. So, we have to ask the question, why is it that sometimes natural selection favours cooperation?

David: Yes, because the simple view of natural selection would be…

MN: It won’t.

David: That it can’t.

MN: Yes, and so, then, that is where the mechanisms for the evolution of cooperation come into play, and mechanisms and interaction structure in the population, such that natural selection sees the advantage of cooperation – favours co-operators over defectors.

David: In your work it’s very evident that two are, sort of, locked together. Would you describe that relation like that?

MN: Competition and cooperation are always totally locked together, yes, intertwined. There’s always competition, and there’s sometimes cooperation: competition and cooperation. There’s never the pure form of cooperation, like the utopia. This is never there. Cooperation is never fully stable.

David: And it’s dynamic? It’s constantly switching?

MN: It is dynamic, always changing. Cooperation is never fully stable. Cooperation always gets destroyed, and then you have to worry, ‘How do I rebuild cooperation once it’s destroyed?’

Ard: So, do you think that is also a metaphor for ourselves, our own lives?

MN: Yes, very much so. Theirs is like the cycles, you know, of cooperation and defection, of like friendship and loss of friendship.

Ard: And then it brings me to another question. I’ve heard you speak about the various evolutionary transitions from no life to life, etc. How important do you think the emergence of language was?

MN: So, I consider language the most interesting thing that happened in the last 600 million years.

Ard: Okay.

MN: So 600 million years ago, you know, it was the evolution of complex multi-cellularity on Earth.

Ard: Animals.

MN: Yes, gave rise to animals

Ard: Plants

MN: Plants, the nervous system, the immune system. But ever since then, what was the greatest thing that happened? Arguably human language, because it leads to a new mode of evolution.

Ard: Okay.

MN: So before human language, evolution is almost exclusively limited to genetic evolution. So the information that is being transferred from one generation to the next is coded in genetic structures. But with humans, we have both genetic evolution and cultural evolution: a linguistic evolution, so we can actually have an evolutionary process where one person has an idea and then talks about it and others sort of copy that idea so the idea spreads in the population.

Ard: And why is that such an important… Why do you consider it the most important thing in the last 600 million years?

MN: Because it leads to a new mode of evolution – to a very fast way of evolution. So humans, in a much, much faster time scale, discover, invent all sorts of new things: they don’t have to wait for a new idea to fix that genetic evolution.

Ard: Because new ideas are much more powerful because of language?

MN: Language is a vehicle to transmit, to replicate new ideas in an unlimited fashion.

Ard: And if we now think about cooperation, does language… is that a big step, is that important for cooperation?

MN: Yes, very much. Language is very important for cooperation. Once we go to the mechanism of indirect reciprocity, which I think was a key mechanism for humans, because we have to be able to talk to each other about others.

Ard: So, you think language has hugely changed our ability to cooperate?

MN: Yes, language gives us access to use all five mechanisms, and, in particular, indirect reciprocity, in an unlimited way. So animals without language can still use indirect reciprocity but they have to observe… They have to observe something directly, but humans can talk about things.

David: I just wanted to ask you, when we were sitting here, that you suggested that the cooperative side of natural selection was the side that was responsible for making things, making leaps of… I was going to say leaps forward, but to make things more complex.

MN: Yeah, I believe…

David: Why? Why is that? Why do you think that is?

MN: I think natural selection, competition, gives you better adaptation on a certain level of organisation. But then to move from one level of organisation to a higher level of organisation, so for example from single-cellular organism to multi-cellular organism, cooperation is involved. Even the emergence of human language is somehow based on cooperation, because the two people who want to share some information by communication, they want to do so because they are already in a cooperative relationship.

David: So that cooperative force is more creative in its…

MN: I believe cooperation is the master architect of the complexity of biological life that we see around us.

A rational god

‘I think it is a more rational position to actually believe in God than not to believe in God. I find not believing in God slightly irrational.’

Transcript

A RATIONAL GOD

Ard: Now, one of the things in this film is I believe in God – I’m a scientist – but David is an atheist. So, do you think David is irrational?

MN: I think it is a more rational position to actually believe in God than not to believe in God. I find not believing in God slightly irrational.

David: Why?

MN: Because it’s a very… it is a very intolerant position, because in some sense you would have to say I know that in all reality there is no God. How can you possibly know that? I find that very difficult.

David: Hmm, no, I wouldn’t say that. I mean, I would just say, I don’t believe in Him because He hasn’t spoken to me. I feel no reason, no need to. I don’t say I know He doesn’t exist, because I don’t.

MN: Yeah, then you’re not really an atheist.

David: Okay, well, what am I then?

MN: An athe… hmm, something like on the edge of agnostic. You know, something on… I also believe that agnostic is, sort of, you’re either on one side or the other side, but a real atheist sort of knows that God doesn’t exist.

David: No, I don’t know that. How could I?

Ard: But there are people who say, in fact scientists who say, that if you are a scientist, you have to be an atheist.

MN: Yeah, I don’t think that that is not at all necessary. So I think the…

Ard: Do you think it’s a rational thing to say?

MN: No, it’s totally irrational to actually say this. So science is not making an argument for atheism at all, you know. In my opinion that would be a misinterpretation of science. Science is neutral with respect to theism or atheism, and it is only the interpretation of science. Scientific atheism is, for me, a kind of religion. It’s a metaphysical choice that has actually nothing to do with science.

Ard: But do you think, the average person in the public, in the street… what do they think? How do they think about science and…?

MN: I think it is unfortunately presented to the public, also in the US, as if you have to make a choice. But there is no need for such a choice. Well-formulated theology is fully compatible with any scientific investigation and no scientific result that has ever been produced, that could ever be produced, would actually be at variance with well-formulated theology.

Ard: And so if you… but a lot of people think these things are in competition with each other. Do you think that’s a dangerous thing or…?

MN: I think it is sad, because it is both… Religion, if used properly, is for me very similar to philosophy: philosophy is something very beautiful. There is no need to make a choice between philosophy and science. There is no need to make a choice between religion and science, if that religion is properly formulated, if that science is properly formulated.

Ard: But you think it’s actually more rational to believe there is a god than there isn’t?

MN: You have to say, for me, the reason to believe in God is really very philosophical and also mathematical, if you like. So you have to ask yourself the primary question for Christians: why is there something? Why is there something? So I was sitting in the pub with my good Hungarian friend Dieper Antell [?] and then he looks up at me, and he says, ‘It is very strange that there is something.’ He’s a physicist. ‘It would be more normal if there was nothing.’

Ard: No, I agree.

MN: And I like that. It’s a beautiful statement coming from a physicist. So I said to him, ’So do you believe in God?’ And he said, ‘Oh, absolutely not. Absolutely not.’ He’s like too pessimistic. But it was… This is a very interesting way to put it: why is there something? And so, then, I believe in a universe that makes sense. I find this idea of logos very attractive, you know, going back to Plato. Things make sense out there. There’s the wisdom to study that which makes sense. There’s the language to talk about it. Where does this sense come from, you know?

David: But, see, I would agree with that. I wouldn’t say that if you don’t believe in God then you also say, then things don’t make sense. I think the universe makes sense. My particular small world makes sense, and when I look at the universe, I say this is a universe full of meaning. And my interest is, is the universe a meaningful place – a place that makes sense?

MN: Yes.

David: And then the difference is, I don’t feel the personal need to say, well that must be underwritten by God, and I think Ard does.

Ard: But that’s because I think we both agree on what the universe is like, but then I would ask you, but why is the universe that way?

Mathematics, goodness and God

‘It leads us basically to the question where does goodness come from?’ ‘And where does it come from Martin?’ 'From God.'

Transcript

MATHEMATICS, GOODNESS AND GOD

David: Do you think mathematics… I mean, you are a mathematician… is it something we are making up?

MN: I believe…

David: Or something we are discovering?

Ard: Or do you think evolution created mathematics?

MN: I think mathematicians unveil eternal truth, you know, that exists independent of evolution. So you have something like prime numbers, numbers, they are just principles that exist. So, for me, the material world is an instantiation of fundamental principles.

David: Right. But if I’ve got those, then surely I don’t need God. I mean, in other words, there are these truths and they are the things which make the world the way it is, and they’re there before I thought about them, so I’m discovering them…

MN: But those fundamental principles, these eternal fundamental principles, for me, that is God.

David: Ah, okay.

Ard: Okay, here’s a question: if someone says to you, ‘Well mathematics is really science,’ what would you say?

MN: No. Mathematicians can make statements that are independent of any particular universe.

Ard: So give me an example.

MN: Well, some properties of prime numbers.

Ard: Okay.

MN: There are infinitely many prime numbers.

Ard: And so these are true, they don’t need scientific experiments to…

MN: Yeah, they don’t need any particular universe to be instantiated to make them true.

Ard: And do you think there’s a parallel between these mathematical truths, which don’t need scientific proof, and theological truths or philosophical truths?

MN: Yes, very much, philosophical ways…

Ard: Or theological truths.

MN: So, for me, philosophy and theology, that’s very close, and the most convincing way to think about theology is always the philosophical one.

Ard: And so do you think that if something, just like mathematics, is true independent of scientific experiments, something like that could be true for philosophical truths or theological truths?

MN: Yes…

David: Or moral truths.

Ard: Or moral truths.

MN: Yes, definitely. So, for example, when Andrew Wiles proved Fermat’s last theorem, then it doesn’t need a scientific experiment to confirm it: it was just, this is now true.

Ard: Yeah. And could there also be, then, moral truths, for example, or other theological truths that are true the way Fermat’s last theorem is true?

MN: Yeah, again, you have to ask yourself, what is the meaning of goodness and where does goodness come from? And I would agree with Plato, that goodness is a form – is the highest form: it’s the form that illuminates all other forms, because all other forms that exist, it’s good that they exist.

Ard: And so goodness is something that exists independent of us?

MN: As the highest form, yes.

Ard: As the highest form. That’s really interesting.

David: If you see these truths as being out there, then when we think of them, the way a lot of people think is that, ‘I’m making this up,’ or ‘I’ve grasped it.’ If they’re there, then it’s more of an encounter, isn’t it? That you’re encountering something.

MN: So Socrates and Plato, they asked themselves, what is learning? And they came to the conclusion that all learning is only remembering.

David: In the sense that there is something there that was waiting for you.

MN: Yeah, in some sense. And also Augustine asks the question, actually, how do these concepts that you understand enter your brain? So if he understands the sense of touch, the sense of smell, the sense of seeing, of hearing, and there’s a certain concept, you know.

David: Okay.

MN: And he then says, for that concept, maybe love, maybe goodness, it doesn’t come to you through any of those senses.

David: And where does it come from Martin?

MN: From God.

Ard: From God.

MN: From the fundamental principles. It’s like from the fundamental principles.

Ard: Martin and I agree.

David: Yeah, I know, I’m feeling in the minority. I don’t think I got mine from God, but I don’t know.

Ard: I think.. I think you did.

David: I know you do.

Life, meaning and God

‘The complete opposite of Platonistic view in philosophy would be nihilism, but then nothing has any meaning, and I don’t understand the usefulness of that position.’

Transcript

Life, meaning and God

David: You’ve used the phrase several times, that something should make sense. Is that important to you in your view of the world or science, that it… that you think things should make sense in addition to just being factually correct?

MN: Yes, I believe that the actual understanding in science is always there when we have a mathematical description of it. So mathematics is somehow a rigorous language, it’s a mysteriously rigorous, efficient language of science that if we have a mathematical description of something, we understand it. If we don’t have a mathematical description, we are just talking around at a level which is less precise.

David: But how does that link up with this idea of meaning and making sense? Because there are scientists who said to me, ‘Look, with science we find the rules that make the world work, but they don’t have any meaning, and so there is no meaning.’

And then here you a mathematician that works at Harvard, who freely uses the word meaning. Why is that?

MN: I think the rules that make up the world, they have a meaning. I don’t understand what it says to have no meaning.

Ard: Yeah. What do you mean, they have no meaning? I don’t understand that either.

David: Well, I don’t, but they said it to me. I mean, I suppose they’re just saying, ‘Look, meaning is… We think things mean things. You think… human beings, we attribute meaning to things, but there is no meaning. There is just one thing that causes another thing that causes another thing, and it’s all meaningless.

Ard: Ah, is what you’re saying maybe this: you’re saying once we’ve come up with a mechanistic system, then that is it.

David: Yes.

Ard: The story ends there.

David: Yes, precisely, and that therefore the universe doesn’t have a meaning.

MN: So, for example, you discover a formula that explains something and then you explain your formula to me, and then I understand your formula, so the meaning of your formula is transmitted to me. If there was no meaning, that conversation wouldn’t have any meaning.

David: Yeah.

MN: So, for me, like the complete opposite of a Platonistic view in philosophy would be nihilism, but then nothing has any meaning, and I don’t understand the usefulness of that position, because then there’s no need for any kind of conversation.

Ard: But some scientists would argue that is what science is telling us.

MN: I don’t… I think science doesn’t make a statement one way or the other about those two philosophical positions. So, for me, the philosophy, the perspective, the world view, is something that you have to choose. And then, once you have chosen this, you can argue with somebody else about it and we can compare our world views, and we can see whether your world view is consistent. As long as your world is consistent with what we can measure scientifically and can understand mathematically, and mine is also, then this method cannot allow us to choose.

David: Right, so you do have the world view first. It’s not that science will give you the correct world view?

MN: Exactly. I think science is not an objective, ultimate description of reality. It is like something that emerges at the interface of the human brain that asks questions, certain kinds of questions, and nature that gives answers.

David: Yes, but that view which is often promulgated by science: we are totally objective and we come with no assumptions…

MN: Yeah. You can prove…

David: You’re saying that that is just not right?

MN: Yeah, you can prove mathematically that this is inconsistent.

Ard: Okay. Which is quite a strong way of saying it’s wrong.

David: It’s a posh way of saying that’s wrong.

Martin Nowak 

Martin A. Nowak is Professor of Biology and Mathematics at Harvard University and Director of the Program for Evolutionary Dynamics where he works on the mathematical description of evolutionary processes, including the evolution of cooperation and human language, as well as the dynamics of virus infections and human cancer. Born and educated in Austria, he has made many seminal contributions to mathematical biology. His books include: Virus Dynamics (2000); Evolutionary Dynamics (2006); Supercooperators (2011).

Quotes from the interview


Competition and cooperation are always totally locked together, yes, intertwined. There’s, sort of, always competition, and there’s sometime cooperation: competition and cooperation. There’s never the pure form of cooperation, like the utopia. This is never there. Cooperation is never fully stable.’
Ard: So, now, one of the things in this film is, I believe in God. I’m a scientist. But David is an atheist. So, do you think David is irrational?
Martin:I think it is a more rational position to actually believe in God than not to believe in God. I find not believing in God slightly irrational.
Science is not making an argument for atheism at all. In my opinion, that would be a misinterpretation of science. Science is neutral with respect to theism or atheism.
Scientific atheism is, for me, a kind of religion. It’s a metaphysical choice that has actually nothing to do with science.

MARTIN NOWAK FULL INTERVIEW TRANSCRIPT

THE MATHEMATICS OF COOPERATION

MN: So here we have a sea of co-operators in blue and a single defector.

David: Tell me what you mean by co-operator and defector.

MN: A co-operator is somebody who pays a cost to help somebody else. So, for example, I pay a certain cost and you have a benefit. That’s cooperation.

David: Okay.

MN: And a defector does not do that. A defector does nothing: does not pay the cost, refuses to pay the cost, but also does not distribute benefit.

Ard: The defector’s selfish.

David: Is it selfish?

MN: Defectors are selfish and the co-operator does something very strange. The co-operator…

David: More generous?

MN: They’re generous, but kind of generous to a competitor, because everybody here is a competitor to everybody else. And the co-operator helps a competitor. It reduces its own potential in order to augment the potential of somebody else.

David: Which you wouldn’t expect natural selection to allow.

MN: Yes, natural selection should basically make sure those co-operators who do this strange thing, they get wiped out.

David: Yeah.

MN: We would expect them to get wiped out. Okay.

David: So what happens?

MN: Yeah, let us start the game. And we see, yes, these defectors, they are spreading, you know. So the colours that we are observing here are: red are defectors and blue are co-operators, and yellow and green are changing sides.

So yellow is now a new defector: it was a co-operator before. And green is a new co-operator: it was a defector before. We see the pattern is spreading. A kind of symmetry is being maintained here because they are deterministic of the rules, and the initial symmetry is never broken. But the amazing thing is these co-operators, they are persistent. They just refuse to get wiped out and they survive in those clusters. And if you watch very carefully, you see the clusters, they are actually growing until they collide with other clusters, and then they’re shrinking, and then they grow.

David: But they never go out of business.

MN: But they never get out of business. And the amazing thing is the average abundance of co-operators in this pattern is very close to 12log 2-8.

David: What does that mean?

Ard: It’s close to constant.

MN: It converges to a constant which is approximately 31%, and this is a mathematical curiosity.

Ard: Natural selection would say the co-operators would get wiped out, because they are paying a cost to help their competitors. And yet it’s not happening. So why?

MN: The reason why it’s not happening is because the co-operators form clusters and in those clusters of co-operators, they actually get a high payoff. They have a high fitness.

David: So they do better?

MN: They do better than the defectors that are surrounded by other defectors. So we always have to ask, on the edge between a co-operator and defector cluster, who is actually winning?

MN: Because the co-operator, even though sitting on the edge, is still getting all the help from other co-operators inside, but a defector is, sort of, getting no help from his defectors. And therefore the co-operators form these clusters that can persist and can even grow in the presence of defectors.

Ard: So this is a bit like, if I’m with my neighbours and we help each other, then we’ll, in the end, be better off than the neighbours one block down who don’t help one another.

MN: Yes, that’s right. So the neighbours that help each other, they form a community that is cooperative, and the neighbours who don’t help each other, they form a community that is defective. And the first can prosper and the other one will kind of perish.

David: Is this, sort of, an addition to the rule of competition in natural selection. Is this a natural law of cooperation?

MN: I think the very interesting observation is the following: going back to first principles, natural selection favours defectors over co-operators. Yet we have cooperation in nature, and we need to find a reason why there is cooperation in nature. And thousands of papers have been written on that topic, actually, and I have been trying to classify all those different propositions into five mechanisms.

And what we’re seeing here is one of those five mechanisms, for the evolution of cooperation, that I call spatial selection.

The other four are… The most important mechanisms for humans, in my opinion, are indirect reciprocity and direct reciprocity. Direct reciprocity is the fundamental idea that we have repeated interaction between two people: I help you, you help me.

And indirect reciprocity is where there’s a repeated interaction in the group: I help you, somebody will help me. I help you, I gain the reputation of a helpful person and I receive help.

Spatial selection, that’s the third mechanism.

The fourth mechanism is group selection. Groups of co-operators out-compete other groups.

And the last one is kin selection: you help relatives. So J.B.S. Haldane said, ‘I will jump into the river to save two brothers or eight cousins.’

Ard: And these five, you call them laws or principles? What would you call them?

MN: They are mechanisms for the evolution of cooperation. So a mechanism is an interaction structure.

David: And this is a different part of nature from… We’re always taught in school of nature red in tooth and claw. This isn’t that, is it?

MN: I would say nature red in tooth and claw is the first, simple, interpretation of Darwinian selection, of Darwinian evolution, and this is now the add-on. I think this is the modern view. And the modern view is somehow also the one that I’ve wanted to promote over the last twenty years: that cooperation is a fundamental principal of the living world, of evolution. And cooperation is necessary whenever evolution makes a step to a higher level of organisation. So whenever evolutions leads from a simple level of organisation to a higher level of organisation, cooperation is essentially involved. And this is the emergence of the first cell; the emergence of eukaryotic cells that have actually organised inside; the emergence of multi-cell organisms, of social insects and of human society.

Ard: So these principles are what explain how very complex societies or organisms arose from evolution?

MN: I think that’s the fundamental step. So I call cooperation an architect, a master architect of complexity.

Ard: And without cooperation, this wouldn’t happen?

MN: I would expect that without cooperation, it is very likely that you would be stuck on a certain level of organisation. So, for example, just a world of single cell bacteria.

David: So, it’s really a very creative…?

MN: I think this is what makes evolution creative.

David: Yes. If you just had competition, then you would just repeat versions of whatever simple thing you started with.

MN: Yes, I think so. And also, competition would lead to the most selfish, to the most successful type dominating.

David: Ah.

MN: Everything would also be more impoverished.

David: So this is going to give you a richer kind of…?

MN: Yes, that is what I definitely, what I…

Ard: And more beautiful?

MN: Yes, more beautiful.

David: When you first had the idea, did you realise then what effect it would have on your life, or how powerful an idea it has become? Was it clear, or was it something you felt like you were just, sort of, exploring?

MN: As soon as I saw the pattern, I thought there’s something great here, but I don’t fully understand it and I don’t fully understand the implications. But the sheer beauty of it made it clear there was something amazing.

Ard: Something true?

MN: Something true.

Ard: You think the beauty of it told you there was something true about it?

MN: Something true. Something extremely relevant, yes, because this beauty emerged from that game in a completely simple way.

Ard: And was that a surprising emergence?

MN: Yeah, once we had it, you know, one could explain it, but when I set out I wouldn’t have expected something like this.

 

7.56 – COMPETITION AND COOPERATION IN evolution

Ard: Some people of faith would be very nervous that you could explain altruistic behaviour by the laws of nature. What would you say?

MN: That they give a mathematical explanation for why these actions can actually be the ones preferred by natural selection, that’s very good.

Ard: Yeah.

MN: And I’m not nervous, but curiously, long ago, when Newton had the mathematical description of gravity, he asked himself briefly the question, you know, by having a mathematical description of gravity, do I take away from God? Does this take away from God? And he made the remark ‘Hypotheses non fingo’ – I make no hypothesis as to why there is gravity. This could as well be the action of God. So just by having a mathematical description of gravity, it doesn’t take away God as a reason for why there is gravity.

Ard: And the same is true for…

MN: For anything we could learn about the living world: for natural selection, for the mathematical description of natural selection.

David: What was the view of moral behaviour before your work, about whether people could cooperate; whether nature could generate cooperative behaviour?

MN: I think in the realm of evolutionary biology the idea really is that natural selection favours selfishness: that natural selection would promote defectors over co-operators. And, therefore, it is actually difficult to explain the emergence of cooperation. And that was realised as a problem, already, by Darwin: in some sense, he actually said, ‘If you would find a trait in a species that is just there for the benefit of another species, that would invalidate my theory,’ something like that.

David: So he knew it was a problem?

MN: He might have sensed it. Not having had access to the mathematical description of evolution, I would argue that his understanding was partial. But now our understanding is very rigorous, very quantitative.

So natural selection favours defectors over co-operators. That is now the starting point. But now we realise that cooperation is abundant in nature and is kind of needed to explain complex life. So, we have to ask the question, why is it that sometimes natural selection favours cooperation?

David: Yes, because the simple view of natural selection would be…

MN: It won’t.

David: That it can’t.

MN: Yes, and so, then, that is where the mechanisms for the evolution of cooperation come into play, and mechanisms and interaction structure in the population, such that natural selection sees the advantage of cooperation – favours co-operators over defectors.

David: In your work it’s very evident that two are, sort of, locked together. Would you describe that relation like that?

MN: Competition and cooperation are always totally locked together, yes, intertwined. There’s always competition, and there’s sometimes cooperation: competition and cooperation. There’s never the pure form of cooperation, like the utopia. This is never there. Cooperation is never fully stable.

David: And it’s dynamic? It’s constantly switching?

MN: It is dynamic, always changing. Cooperation is never fully stable. Cooperation always gets destroyed, and then you have to worry, ‘How do I rebuild cooperation once it’s destroyed?’

Ard: So, do you think that is also a metaphor for ourselves, our own lives?

MN: Yes, very much so. Theirs is like the cycles, you know, of cooperation and defection, of like friendship and loss of friendship.

Ard: And then it brings me to another question. I’ve heard you speak about the various evolutionary transitions from no life to life, etc. How important do you think the emergence of language was?

MN: So, I consider language the most interesting thing that happened in the last 600 million years.

Ard: Okay.

MN: So 600 million years ago, you know, it was the evolution of complex multi-cellularity on Earth.

Ard: Animals.

MN: Yes, gave rise to animals

Ard: Plants

MN: Plants, the nervous system, the immune system. But ever since then, what was the greatest thing that happened? Arguably human language, because it leads to a new mode of evolution.

Ard: Okay.

MN: So before human language, evolution is almost exclusively limited to genetic evolution. So the information that is being transferred from one generation to the next is coded in genetic structures. But with humans, we have both genetic evolution and cultural evolution: a linguistic evolution, so we can actually have an evolutionary process where one person has an idea and then talks about it and others sort of copy that idea so the idea spreads in the population.

Ard: And why is that such an important… Why do you consider it the most important thing in the last 600 million years?

MN: Because it leads to a new mode of evolution – to a very fast way of evolution. So humans, in a much, much faster time scale, discover, invent all sorts of new things: they don’t have to wait for a new idea to fix that genetic evolution.

Ard: Because new ideas are much more powerful because of language?

MN: Language is a vehicle to transmit, to replicate new ideas in an unlimited fashion.

Ard: And if we now think about cooperation, does language… is that a big step, is that important for cooperation?

MN: Yes, very much. Language is very important for cooperation. Once we go to the mechanism of indirect reciprocity, which I think was a key mechanism for humans, because we have to be able to talk to each other about others.

Ard: So, you think language has hugely changed our ability to cooperate?

MN: Yes, language gives us access to use all five mechanisms, and, in particular, indirect reciprocity, in an unlimited way. So animals without language can still use indirect reciprocity but they have to observe… They have to observe something directly, but humans can talk about things.

David: I just wanted to ask you, when we were sitting here, that you suggested that the cooperative side of natural selection was the side that was responsible for making things, making leaps of… I was going to say leaps forward, but to make things more complex.

MN: Yeah, I believe…

David: Why? Why is that? Why do you think that is?

MN: I think natural selection, competition, gives you better adaptation on a certain level of organisation. But then to move from one level of organisation to a higher level of organisation, so for example from single-cellular organism to multi-cellular organism, cooperation is involved. Even the emergence of human language is somehow based on cooperation, because the two people who want to share some information by communication, they want to do so because they are already in a cooperative relationship.

David: So that cooperative force is more creative in its…

MN: I believe cooperation is the master architect of the complexity of biological life that we see around us.

14:53 – A RATIONAL GOD

Ard: Now, one of the things in this film is I believe in God – I’m a scientist – but David is an atheist. So, do you think David is irrational?

MN: I think it is a more rational position to actually believe in God than not to believe in God. I find not believing in God slightly irrational.

David: Why?

MN: Because it’s a very… it is a very intolerant position, because in some sense you would have to say I know that in all reality there is no God. How can you possibly know that? I find that very difficult.

David: Hmm, no, I wouldn’t say that. I mean, I would just say, I don’t believe in Him because He hasn’t spoken to me. I feel no reason, no need to. I don’t say I know He doesn’t exist, because I don’t.

MN: Yeah, then you’re not really an atheist.

David: Okay, well, what am I then?

MN: An athe… hmm, something like on the edge of agnostic. You know, something on… I also believe that agnostic is, sort of, you’re either on one side or the other side, but a real atheist sort of knows that God doesn’t exist.

David: No, I don’t know that. How could I?

Ard: But there are people who say, in fact scientists who say, that if you are a scientist, you have to be an atheist.

MN: Yeah, I don’t think that that is not at all necessary. So I think the…

Ard: Do you think it’s a rational thing to say?

MN: No, it’s totally irrational to actually say this. So science is not making an argument for atheism at all, you know. In my opinion that would be a misinterpretation of science. Science is neutral with respect to theism or atheism, and it is only the interpretation of science. Scientific atheism is, for me, a kind of religion. It’s a metaphysical choice that has actually nothing to do with science.

Ard: But do you think, the average person in the public, in the street… what do they think? How do they think about science and…?

MN: I think it is unfortunately presented to the public, also in the US, as if you have to make a choice. But there is no need for such a choice. Well-formulated theology is fully compatible with any scientific investigation and no scientific result that has ever been produced, that could ever be produced, would actually be at variance with well-formulated theology.

Ard: And so if you… but a lot of people think these things are in competition with each other. Do you think that’s a dangerous thing or…?

MN: I think it is sad, because it is both… Religion, if used properly, is for me very similar to philosophy: philosophy is something very beautiful. There is no need to make a choice between philosophy and science. There is no need to make a choice between religion and science, if that religion is properly formulated, if that science is properly formulated.

Ard: But you think it’s actually more rational to believe there is a god than there isn’t?

MN: You have to say, for me, the reason to believe in God is really very philosophical and also mathematical, if you like. So you have to ask yourself the primary question for Christians: why is there something? Why is there something? So I was sitting in the pub with my good Hungarian friend Dieper Antell [?] and then he looks up at me, and he says, ‘It is very strange that there is something.’ He’s a physicist. ‘It would be more normal if there was nothing.’

Ard: No, I agree.

MN: And I like that. It’s a beautiful statement coming from a physicist. So I said to him, ’So do you believe in God?’ And he said, ‘Oh, absolutely not. Absolutely not.’ He’s like too pessimistic. But it was… This is a very interesting way to put it: why is there something? And so, then, I believe in a universe that makes sense. I find this idea of logos very attractive, you know, going back to Plato. Things make sense out there. There’s the wisdom to study that which makes sense. There’s the language to talk about it. Where does this sense come from, you know?

David: But, see, I would agree with that. I wouldn’t say that if you don’t believe in God then you also say, then things don’t make sense. I think the universe makes sense. My particular small world makes sense, and when I look at the universe, I say this is a universe full of meaning. And my interest is, is the universe a meaningful place – a place that makes sense?

MN: Yes.

David: And then the difference is, I don’t feel the personal need to say, well that must be underwritten by God, and I think Ard does.

Ard: But that’s because I think we both agree on what the universe is like, but then I would ask you, but why is the universe that way?

 

19:30 – MATHEMATICS, GOODNESS AND GOD

David: Do you think mathematics… I mean, you are a mathematician… is it something we are making up?

MN: I believe…

David: Or something we are discovering?

Ard: Or do you think evolution created mathematics?

MN: I think mathematicians unveil eternal truth, you know, that exists independent of evolution. So you have something like prime numbers, numbers, they are just principles that exist. So, for me, the material world is an instantiation of fundamental principles.

David: Right. But if I’ve got those, then surely I don’t need God. I mean, in other words, there are these truths and they are the things which make the world the way it is, and they’re there before I thought about them, so I’m discovering them…

MN: But those fundamental principles, these eternal fundamental principles, for me, that is God.

David: Ah, okay.

Ard: Okay, here’s a question: if someone says to you, ‘Well mathematics is really science,’ what would you say?

MN: No. Mathematicians can make statements that are independent of any particular universe.

Ard: So give me an example.

MN: Well, some properties of prime numbers.

Ard: Okay.

MN: There are infinitely many prime numbers.

Ard: And so these are true, they don’t need scientific experiments to…

MN: Yeah, they don’t need any particular universe to be instantiated to make them true.

Ard: And do you think there’s a parallel between these mathematical truths, which don’t need scientific proof, and theological truths or philosophical truths?

MN: Yes, very much, philosophical ways…

Ard: Or theological truths.

MN: So, for me, philosophy and theology, that’s very close, and the most convincing way to think about theology is always the philosophical one.

Ard: And so do you think that if something, just like mathematics, is true independent of scientific experiments, something like that could be true for philosophical truths or theological truths?

MN: Yes…

David: Or moral truths.

Ard: Or moral truths.

MN: Yes, definitely. So, for example, when Andrew Wiles proved Fermat’s last theorem, then it doesn’t need a scientific experiment to confirm it: it was just, this is now true.

Ard: Yeah. And could there also be, then, moral truths, for example, or other theological truths that are true the way Fermat’s last theorem is true?

MN: Yeah, again, you have to ask yourself, what is the meaning of goodness and where does goodness come from? And I would agree with Plato, that goodness is a form – is the highest form: it’s the form that illuminates all other forms, because all other forms that exist, it’s good that they exist.

Ard: And so goodness is something that exists independent of us?

MN: As the highest form, yes.

Ard: As the highest form. That’s really interesting.

David: If you see these truths as being out there, then when we think of them, the way a lot of people think is that, ‘I’m making this up,’ or ‘I’ve grasped it.’ If they’re there, then it’s more of an encounter, isn’t it? That you’re encountering something.

MN: So Socrates and Plato, they asked themselves, what is learning? And they came to the conclusion that all learning is only remembering.

David: In the sense that there is something there that was waiting for you.

MN: Yeah, in some sense. And also Augustine asks the question, actually, how do these concepts that you understand enter your brain? So if he understands the sense of touch, the sense of smell, the sense of seeing, of hearing, and there’s a certain concept, you know.

David: Okay.

MN: And he then says, for that concept, maybe love, maybe goodness, it doesn’t come to you through any of those senses.

David: And where does it come from Martin?

MN: From God.

Ard: From God.

MN: From the fundamental principles. It’s like from the fundamental principles.

Ard: Martin and I agree.

David: Yeah, I know, I’m feeling in the minority. I don’t think I got mine from God, but I don’t know.

Ard: I think.. I think you did.

David: I know you do.

 

23:19 – Life, meaning and God

David: You’ve used the phrase several times, that something should make sense. Is that important to you in your view of the world or science, that it… that you think things should make sense in addition to just being factually correct?

MN: Yes, I believe that the actual understanding in science is always there when we have a mathematical description of it. So mathematics is somehow a rigorous language, it’s a mysteriously rigorous, efficient language of science that if we have a mathematical description of something, we understand it. If we don’t have a mathematical description, we are just talking around at a level which is less precise.

David: But how does that link up with this idea of meaning and making sense? Because there are scientists who said to me, ‘Look, with science we find the rules that make the world work, but they don’t have any meaning, and so there is no meaning.’

And then here you a mathematician that works at Harvard, who freely uses the word meaning. Why is that?

MN: I think the rules that make up the world, they have a meaning. I don’t understand what it says to have no meaning.

Ard: Yeah. What do you mean, they have no meaning? I don’t understand that either.

David: Well, I don’t, but they said it to me. I mean, I suppose they’re just saying, ‘Look, meaning is… We think things mean things. You think… human beings, we attribute meaning to things, but there is no meaning. There is just one thing that causes another thing that causes another thing, and it’s all meaningless.

Ard: Ah, is what you’re saying maybe this: you’re saying once we’ve come up with a mechanistic system, then that is it.

David: Yes.

Ard: The story ends there.

David: Yes, precisely, and that therefore the universe doesn’t have a meaning.

MN: So, for example, you discover a formula that explains something and then you explain your formula to me, and then I understand your formula, so the meaning of your formula is transmitted to me. If there was no meaning, that conversation wouldn’t have any meaning.

David: Yeah.

MN: So, for me, like the complete opposite of a Platonistic view in philosophy would be nihilism, but then nothing has any meaning, and I don’t understand the usefulness of that position, because then there’s no need for any kind of conversation.

Ard: But some scientists would argue that is what science is telling us.

MN: I don’t… I think science doesn’t make a statement one way or the other about those two philosophical positions. So, for me, the philosophy, the perspective, the world view, is something that you have to choose. And then, once you have chosen this, you can argue with somebody else about it and we can compare our world views, and we can see whether your world view is consistent. As long as your world is consistent with what we can measure scientifically and can understand mathematically, and mine is also, then this method cannot allow us to choose.

David: Right, so you do have the world view first. It’s not that science will give you the correct world view?

MN: Exactly. I think science is not an objective, ultimate description of reality. It is like something that emerges at the interface of the human brain that asks questions, certain kinds of questions, and nature that gives answers.

David: Yes, but that view which is often promulgated by science: we are totally objective and we come with no assumptions…

MN: Yeah. You can prove…

David: You’re saying that that is just not right?

MN: Yeah, you can prove mathematically that this is inconsistent.

Ard: Okay. Which is quite a strong way of saying it’s wrong.

David: It’s a posh way of saying that’s wrong.

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