The limits of knowledge
What, if any, are the limits to knowledge?
Ard: I wanted to ask a question that I read on your blog recently. You talked about how colour is perceived, and this has to do, partially, with the way our brains are structured. So the structure to our brains allows us to see colour in certain ways, and then there’s also a structure to our brain that allows us to perceive mathematics in certain ways. And that’s clearly evolved over time.
SZ: Yes, well, look, I think we have to go a step back and ask, what is the function of the brain? Now, there are a lot of functions which you can impute to the brain – individual functions: seeing, hearing, working out solutions, acting and so on. But there is one primordial, overall function, which is to acquire knowledge about the world. Now, here is the most important philosophical question of all: to obtain that knowledge, you have to stabilise the world. You cannot obtain that knowledge unless you can stabilise it. Now, in colour vision, what does stabilising it mean? It means that you have to get rid of all the continual changes in the wavelength anti-composition of the light coming from surfaces. You have to discard these and assign a constant colour to a surface.
David: When you say ‘stabilising reality or the colour’, what do you mean by that?
SZ: Well, I’ll give you an example. If we look at green leaves in a park, we see these green leaves as green, at noon on a cloudy day or a sunny day. If you look at them at dawn or at dusk, you’ll still see them as green. If you were to measure the amount of red, green and blue light reflected from these leaves in these different conditions, you find vast differences, and indeed, at dawn and at dusk, they’ll reflect more red light.
Now, how does the brain stabilise the world so that you can see it only as green? It takes the amount of red, green and blue light reflected from that leaf, and the amount of red, green and blue light reflected from the surround. It takes those ratios – those ratios never change.
So whatever amount of green light this leaf is reflecting, the surround will always reflect less, because it’s got lower efficiency. And whatever amount of red light it’s reflecting, the surround will always reflect more because it’s got a higher efficiency. Now, there is no physical law which says that these ratios should be taken. It’s the brain’s law – it’s the brain’s way of stabilising the world in terms of colour.
David: So that we can always say, ‘Oh, that’s a leaf because it’s green’?
SZ: Yes, you can identify something by its colour, absolutely.
David: So, in some ways, we’re not making reality up, but we are imposing a, sort of, slightly artificial order on it.
SZ: No, no, no, no you are making reality up, in a way. The only reality that you can experience is what the brain allows you to experience. Now supposing that you did not have this ratio-taking mechanism in the brain, what will happen? Sometimes that leaf would appear red, sometimes it would appear green, sometimes it would appear blue, sometimes yellow. Then you would no longer be able to recognise it by its colour because you’ve not stabilised the world.
David: Which would be bad news if you fed on green leaves!
SZ: This would be bad news if you fed on green leaves, indeed. It would be very bad news.
David: If you got to a certain time of day and say, ‘My God, there’s not a leaf in sight!’
SZ: Yes, yes, so I think that this is another fundamental issue, which is that there is a reality out there and that we represent that reality, and we take part in constructing that reality. Our brain, through its laws, takes part in constructing that reality. And here in comes stabilising the world: the brain is able to stabilise that world, and acquire knowledge about it, and that’s the only way it can do it.
David: When you talk about stabilising the world, what struck me was that the brain must get a certain pleasure from doing that, because it makes sense of it, as you were saying.
SZ: Yes, yes.
David: And in some way, what you’re doing in science, at a sort of cognitive level, is you’re doing that same thing. You’re saying, here’s all of the confusion of the world, and I will stabilise it by saying, well, underneath this, there are these stable rules that allow me to understand all of it.
SZ: All these mathematical formulations which tell you about the structure of the universe are also an attempt, at a highly cognitive level, to acquire knowledge about the world. I mean, it would be correct, would it not, to say that the description of the structure of the universe is an attempt to acquire knowledge about it.
Ard: Yeah, that’s right.
SZ: Now, there are situations in which there are contradictions. For example, you know, the well-known optical illusion: the bi-stable figures.
David: Oh, the young woman/old woman or the duck/rabbit
SZ: Yes, duck/rabbit, that sort of thing, which you can illustrate. Now, there is no solution to this… there is no certainty as to which solution is the valid one, because there isn’t a valid solution. So what the brain does is very simple, it makes both solutions valid, but only one has the conscious state at any given moment: you cannot see them both. And what does the brain do when you’ve got the laws of gravitation conflicting with the laws of quantum mechanics? It treats them separately. So, it’s again using the same strategy of saying, look, they are both correct, but not at the same time.
Ard: So something which is very surprising about the laws of mathematics is that somehow our brain has evolved in order to understand these laws, apparently, but then it turns out these laws are deeply engrained in the universe. So why did our brains…?
SZ: Well, our brains have evolved in the universe, and they… This is not an easy question to answer, and I just do not know the direct link between the structure of the universe and the structure of mathematical formulae which reveal that structure of the universe. But what is evident is that there is a certain logical deductive system, which by the way is applicable in as much in mathematics as it is in the humanities, and to obtain… to stabilise the world, to obtain the knowledge, you have to obey that logical deductive system.
Ard: Do you think that suggests that that logical system might somehow be in the universe before our brains arrived?
SZ: I wouldn’t dare stick my neck out as much as that. But I would say that it is through that logical system that you derive knowledge about the universe, and hence the reality you create, and the reality that you know, is based on that system, and because that system is similar in most humans, you get this similar, kind of, reality. Now, yes, there are big differences – a Buddhist maybe thinking of things in different terms — but if you look at it very carefully, it boils down to essentially the same thing.
I’m not saying there’s no physical reality out there. I’m not saying there isn’t a universe. I’m not saying the Earth isn't round. I’m not saying any of these things. All I’m saying is that to obtain knowledge about that, we do it through our brain, and we use our brains’ mathematical, logical system to obtain that knowledge.
Now, it would be, to me, extremely interesting about certain kinds of knowledge which are not directly observable, such as the Big Bang, such as black holes, such as the fact the universe was a billionth of the size of an atom before the Big Bang. These are not directly observable by us: these are deductions arrived at by mathematical formulations.
I’m very interested to learn, and I’ve got no strong position on that, if a totally different logical system would have arrived at the same conclusion. Now, if it does, then my argument is completely null and void, on the other hand, if it does not, then you’ve got to concede that a significant part of our knowledge is based on the structure and functioning of our brains.
David: So it’s whether the lens that we look through reflects what’s out there, or somehow distorts it? Whether we look through a glass darkly or clearly?
SZ: Yes, yes, yes.
David: Why do they want this Grand Unified Theory?
MG: I think it has a little bit to do with Occam’s razor: the idea that you want to look for the simplest explanation for everything, if possible. And if you look at nature, nature is complex: it’s very diversified. But perhaps we’re looking at nature with the wrong glasses. If you put the right glasses on, you would see that all that we see as different is really a manifestation of this single force, and so that’s Grand Unification.
David: Sounds awfully religious to me.
MG: It does, doesn’t it? Sounds like monotheism.
David: Yeah. Sounds like God in a white coat.
MG: That’s exactly what I think. I think that even though I’ve worshipped unification for many, many years in my career, I’m not like that anymore – I’ve sort of moved away.
David: Why not? What happened?
MG: Because I don’t see the point.
David: Wait a minute… What happened to you that you used to see the point, and then now you don’t? That’s a bit of a change.
MG: Yeah. So, what happened to me was that I was a full-fledged Platonist before that: I really believed in symmetry as beauty and beauty as truth.
MG: And so what could be more beautiful and true than to have an all-encompassing theory of nature, where all different forces are really a manifestation of a single force. And you would say, everything came from the Big Bang; everything was one in the beginning, so there must have been a single force explaining all of that. It’s very compelling. I mean, we’ve had 3,000 years of monotheistic thinking, and so we are kind of biased to look for one explanation – these absolute explanations.
My whole career as a scientist has been within the expectation of unification, because I was young in the 70s, but I was doing my PhD in the 80s, and through this whole time we were, like, ‘Okay, come on, come on!’ and ‘Where is it?’
Ard: Soon it will come.
MG: Yeah, soon it will come. It’s next year. And what we’ve been seeing is it has not. So you have two choices here: one is it doesn’t matter that it’s not coming, because it’s there, and it’s just a matter of time before we find it. Faith – you know, there is faith in science, obviously. And the other one is let’s listen to nature. It’s trying to tell us something, and let’s pick it up. And what are the consequences of that?
So I came up with a solution to this dilemma which is the following – at least I’m happy with it; I don't know if everybody else is, but I’m happy with it – it’s that the most that we can expect to achieve as humans, in terms of understanding nature, is a simplified theory that could encompass everything as we know it now.
So it might be possible to have a unified theory of what we know now, but it is a fundamental mistake to call that theory a Final Theory of Everything because that goes completely against the spirit of science.
You know, science moves through a progression of ideas. We invent new tools, we find new things, and so who is to tell that we get this theory, ten years from now, the beautiful theory of everything, and then 150 years from now this new machine finds another force of nature? ‘Oops! That’s not part of our scheme. Now what do we do?’
So you have to encompass that. And there is no fundamental reason why knowledge should be final. Because the way we acquire information from nature is through experiments, through tools, and every tool has a limit. You can see that far, you can probe that small, but there is a limit to how far we can see.
Ard: So are you saying that maybe nature’s like an onion. You keep unravelling one bit and then there’s another bit beneath it and another one beneath it, and we shouldn’t ever say that we’ve gotten to the end?
MG: Right. I like to say that knowledge is like an island.
Ard: Oka, like an island? Okay.
MG: Yeah, knowledge is like an island. What we know of the world fits in an island. This island moves out, and sometimes it goes back in when we retreat. We say, ‘Oh, we understood that. No, no, we don’t understand that.’ So we go back. But as any good island, it’s surrounded by what I call the ocean of the unknown.
As this island of knowledge grows, so do the shores of our ignorance, because the perimeter of the island, which is the exposure to what we don’t know, grows as well. Because as you discover more about nature, you become equipped to ask questions you couldn’t even have anticipated before.
There is always going to be other things to find out, which I find… Some people think, ‘Oh, that’s so depressing. What’s the point?’
And to me that’s exactly the opposite. The point is there is always going to be something to find out. That’s exciting, you know. That is like we are always going to be able to be in awe and confused and trying to figure things out.
David: I like that, because one of the things that worried me listening to Frank and others is… I got this feeling that what they wanted was to get their Theory of Everything, where they’d have… We talked about a T-shirt – we’d have all the rules on it and that would be it. From that, everything in the universe would fall out. And I got the feeling that it meant that as we got closer to knowing this Theory of Everything that the universe just got quite boring.
It would just become a machine where I understood it all, and it would just be a glorified watch.
MG: Yeah, absolutely. I’m completely like that. I think it would be a sad day, the day that humanity declared it understood everything about the world. A sad day, because without the mystery we wouldn’t create any more, and that, to me, is just an awful thing.
The dream that we can figure everything out at a very fundamental level, to me, is just a fallacy. I think that just does not make sense. It doesn’t make sense from a philosophical perspective either because it’s based on an absolute, which is there is the possibility of knowing everything exists. And having an absolute is sort of like you can’t contrast that with anything else. You say, ‘the Theory of Everything is this,’ and then you say, ‘Well, how do you know it?’
‘Well, because we know all there is to know.’ And that is wrong: we do not know all there is to know, and we cannot know all there is to know. And to me that opens up this whole freedom of the surprises that come from the unknown.
David: Do you buy into the notion that some people… We’re going to talk to George Ellis about emergence, and I hinted at it there, that when the universe began, presumably there were the rules of physics, but there was no rule of natural selection. It just wasn’t here, but now it is, which seems to me that if you’ve been really quick, if you’d been a physicist around at the beginning and you worked really quickly, you could have understood all the rules of the universe, then life would have come along, and you wouldn’t know everything, because the universe had made itself up a bit. It was now more than it was and had an extra rule. Surely, if it can do it once, who are we to say it’s not going to do it again?
David: So this notion that we could find all the rules and that would be it seems to me you’ve found all the rules up to now.
MG: I think that’s exactly right.
David: Or is that just rubbish?
MG: No, that’s perfect. And I would say you can divide the history of the universe into four ages: the Physical Age, which is from the Big Bang to the first stars – up to that point, there was no chemistry. And then you call it the Chemical Age, which is when the first stars burn and create the periodic table of elements.
David: So that’s something new already.
MG: That’s something completely new. Then you have the Biological Age, which is when some of these chemicals self-organised to create life. And then after the Biological Age there was the Cognitive Age, which is when some of these living creatures became so sophisticated that they were able to ask questions such as the ones we’ve been talking about.
So these are the four ages, and we don’t know if that’s all there is to know. And they all have different laws. There is no way out, you know. There are fundamental limits to how we can understand what’s going on. It doesn’t matter how sophisticated you are, you still have to follow the laws of thermodynamics. There’s only so much information you can process. There’s always going to be noise in your system, and so there is always going to be some loss of information. And so ultimate knowledge, to me, is just another name for God.
Ard: Okay. And so you think these people, even though they are often arguing against God, are actually doing it in a kind of religious way? They’ve got a new kind of god, which is the god which will explain everything.
MG: Yes, they are trying to make human knowledge into the new God.
MG: And, of course, that horrifies a lot of people, because humans are not supposed to be gods. We mess everything up. And so we should understand our limitations and go back to being humble about how we think about creation and about who we are, before we jump into this incredible notion that we can know everything.
Ard: I wanted to ask you something else. You wrote, ‘We have a compelling need to lend form to the universe without destroying its mystery.’ Do you think we can destroy its mystery by science?
SG: No. I think that science only… well, again we’re talking about that religious… I think we’re talking about the same thing: that sentiment of wonder, and awe, and terror. And I think, for me, one of the greatest moments of making peace with science was to realise that rather than taking away the mystery, it added to the mystery, only in the sense of that experience.
I’m calling mystery the sense of that experience, not a lack of clarity about what’s going on. But when you understand something, in all its clarity, that adds to the experience. Maybe I shouldn’t call it mystery.
Ard: No, I think that people sort of think that mystery is only about things we don’t understand. In fact, religious people sometimes think that in order for them to have God in science, they have to have bits they don’t understand, but I think that’s just the wrong way of thinking about it.
I think part of what makes science so beautiful, or that sense of the beauty of science being close to the sense of terror, is that you do see something more clearly and it’s very beautiful, but it seems to point to something beyond itself, and that’s what generates that sense of being at a precipice, where you think it’s beautiful, but it’s also actually making the mystery more. There’s more of a mystery rather than less of a mystery, even though…
SG: It intensifies the mystery.
Ard: It intensifies the mystery, even though you understand it better. And that sounds a bit fluffy, but…
David: No! Surely not, Ard!
Ard: I was accusing him of being fluffy.
David: All the time!
Ard: But I think if as a scientist you have that experience, and you do understand something, actually it intensifies the mystery.
David: Why did you say ‘I made peace with science’? When did you have to make peace with it? What do you mean?
SG: Well, I suppose… I don't know. I never thought I’d say that, but…
David: Well, you did.
SG: .You made me say it; or it came out. So what does that mean? Maybe at some point I was a bit suspicious of science. I thought, maybe, it would take away from my appreciation of the universe.
David: The sort of picking-the-butterfly-apart effect.
SG: Yes, exactly. So while I was fascinated by what I was learning, perhaps part of me feared that once it was all explained, it would get rather dull.
So it was hugely reassuring to me that when I understood something, that it actually created in me the same sentiments, the same emotions emerged as when I didn’t fully understand something and simply wanted to take delight in it.
It gave me a better understanding of what mystery – which I think is a very basic emotion, almost – was actually all about. So that must be why I said ‘I made peace with science.’
David: Is mystery aligned with meaning? With thinking this means something? That it makes sense of it?
SG: Well I suppose what I think we’re both trying to say is that there is no contradiction between making sense of it… between finding meaning and preserving mystery.
Ard: It reminds me of a quote by Henri Poincaré, a very famous French mathematical physicist, who says, ‘A scientist does not just only study science because it’s useful; he studies it because it’s beautiful. And if nature were not beautiful, it would not be worth studying, and life would not be worth living.’
It’s very French. But I think there’s something about ‘you study it because it’s beautiful’. And if it weren’t beautiful it wouldn’t be worth doing.
David: Yes. And you’ve already defined beauty as being, at least in part, that sense of it pointing forwards, beyond itself, as you would say. So that when we say nature has to be beautiful, and if it wasn’t I wouldn’t study it, it’s another way of saying, if it wasn’t always expanding, pointing to new things that it might generate. Because I think, sometimes, and maybe it’s us in the media, the popularisers, we give this impression that there’s a big mystery. But don’t worry, there’s an army of people in white coats who are clearing up the mystery, like clearing up the knick-knacks in a room. And before you know it, it’ll all be squared away like a Prussian dining room and…
SG: That’s a particular aspect of science, and what scientists do, practitioners of science do. But then there is also the exhilarating part of understanding the universe, which, for me, is what drew me to science.
David: A friend of mine’s a mathematician, Greg Chaitin. He described, I think, what you’re talking about. He said, for him, he would have small ideas: just a small idea, like sitting on your chair. Then, he said, he had certain huge ideas, and for him it was like climbing up a mountain. And the exciting thing was not just getting to the top of the mountain, but from there he could see a whole range of mountains out in the distance, which he hadn’t been to, obviously, but suddenly he realised they were there. Is that the same sort of thing?
SG: Yes. For me that’s definitely how it works. A lot of my work is built on an idea and a model that I came up with 20 years ago. And I remember that moment of watching it do something I didn’t expect it to do, which is on a computer screen. I’d written down some simple equations, and I expected it to behave in a particular way, and it didn’t. And it showed me something that then became the basis of pretty much what I do in science.
David: How did it feel?
SG: It felt amazing! It really did. And this was in the day when you could actually watch the computer simulation happening, because computers were very slow 20 years ago, and so I did actually watch this simulation.
David: So what were you actually seeing? I’m just fascinated.
SG: I wanted to see how populations of pathogens would evolve under selection from host immunity: by host, I mean us. So when a malaria parasite enters my body, I will, of course, mount immune responses to this parasite. So parasite populations evolve under this selection pressure. What’s interesting about a lot of parasite populations is that they seem to exist as these, sort of, discrete tribes ‒ different strains ‒ and this is the mystery, because there’s no reason why they should be doing that.
And what this model showed me is how, under selection pressure from host immunity, these populations would self-organise into these discrete tribes, simply in order to avoid competing with each other.
David: And nobody knew that before?
SG: Nobody had done that before.
David: And it’s not what you were expecting?
SG: No, it wasn’t. I thought they’d be a big mush, and that we’d have to think of ways in which we’d have to impose structure. So, at a fundamental level, I was setting something up where I expected there to be huge mush, and then we’d have to come up with ways to impose structure, and instead the structure emerged on its own. So that was fun; that was great.
Ard: That’s amazing.
SG: It was quite a moment.
Ard: It must have been amazing to see.
SG: It was. And so what I’ve been doing since then is trying to validate that. So I’m interested, obviously, in whether this is truth, in the sense of being a useful metaphor, or a useful framework for understanding what happens in infectious diseases, because it does have practical implications.
So that’s what I’ve been doing for the last 20 years: trying to validate that theory.
Ard: Yesterday we talked to Marcelo Gleiser and he talked about the idea of knowledge like an island. So as you grow… an island in a sea of ignorance. So as knowledge grows, so does the size of the border that you have of the ignorance that you see. So as you get more and more knowledge, you also see more and more ignorance.
GC: That’s a very nice image. Also people don’t like talking about what they don’t know. They like talking about what they know. I’m the other way around. I prefer thinking about what I don’t know.
Certainty is bad because it’s uncreative. It means you know already – you don’t need to think any more about it. Well it’s also totally uncreative in mathematics. The idea of Hilbert was to ensure certainty He thought it was possible: he thought the possibility of doing this is what it meant to say that mathematics was black or white, that mathematical truth is more solid than any empirical truth. And it’s wonderful that mathematics refuted this.
You know, Gödel’s Incompleteness Theorem is suppressed. The mathematics community doesn’t want to take it into account, because they view it as a tremendously pessimistic, horrible fact that you can’t have a ‘theory of everything’ for mathematics, and that mathematics doesn’t give absolute truth. I think this is absolutely wonderful. The viewpoint is wrong. What Gödel’s Theorem is about… it’s not a negative theorem, it’s a positive theorem. It’s about creativity. It’s the first step in the direction of a mathematical theory of creativity – of saying that math is not a closed system, it’s an open system, just like biology. And this is totally liberating and we should all celebrate…. celebrate this fact rather than bemoaning it, beating our breast, ‘Oh my God. What happened to absolute truth in mathematics?’ Well, what happened was that absolute truth was a closed system. It was a prison: the notion of a formal theory that would give you absolute certainty.
Ard: A theory of everything.
GC: A theory of everything. Yes, a formalisation of all of mathematics in one finite set of axioms. This would have been horrifying.
Let’s say that they have this computer program which can decide if mathematical assertions are true or false.
Well, what good is it to know whether something is true or false? You want to understand what’s happening, right?
David: The why rather than the…
GC: The why, exactly. You want to be convinced emotionally that something is true. That’s why new questions are important, because what counts is not the mathematics we know – the science we know is uninteresting – it’s what we don’t know that’s interesting.
Unfortunately universities spend all their time filling your head with what’s known, but that’s totally trivial. What’s interesting is what we don’t know. That’s what all the courses should be about, so that maybe the students can come up with new ideas before they’ve been brainwashed with the current paradigms. That would be the university I would create, you know, which only would talk about what we don’t know because what we know is really very uninteresting.