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A Top Mathematician Dives Into the Mysteries of Time, Chaos, and Consciousness

A Top Mathematician Dives Into the Mysteries of Time, Chaos, and Consciousness

Marcus du Sautoy is the Charles Simonyi Professor for the Public Understanding of Science at Oxford University. A Fellow of the Royal Society, he has received the Berwick Prize, given to Britain’s most outstanding young mathematician. He recently joined Heleo’s Jeremy Price to discuss chaos theory, relativity, and other mind-bending ideas from his latest book, The Great Unknown: Seven Journeys to the Frontiers of Science.

This conversation has been edited and condensed. To view the full conversation, click the video below.

Jeremy: Often in science, we focus on the things we know. You want to focus on the things that we don’t know, the areas of science where we’re coming up against our own ignorance. Tell me a little bit more about the idea behind this book.

Marcus: It was kind of inspired by this crazy title that I have, the Professor for the Public Understanding of Science. It’s such a grand sounding title, and everyone expects I must know the whole of science, and here I am to explain it to you all. Certainly no one scientist can know it all, but it got me thinking about the question of whether science might, at some point, be able to answer all the big questions about the universe. We’ve been discovering so many things over the last decade, [that] I think it’s fueled this expectation [of] “Yeah, maybe we could know it all.” I thought it would be interesting to come from the other end, and look at what might always be beyond the ability of science to know.

Jeremy: One of my favorite quotes from the book is, “The desire to know is as important as the drive to reproduce.” That’s something we can all connect to, because everybody is curious about something. And the way that you frame that [turns] curiosity into this biological drive. Maybe it’s no accident that we talk about a “hunger” for knowledge or a “thirst” for knowledge, right?

Marcus: Yes. I think that those who weren’t curious did not survive. It is the thing that has helped us to evolve as a species. The more that we know, the more we are able to adapt to and change our environments. As we go into an uncertain future, it’s the knowledge we have, the data, the patterns from the past, [that allow us] to see we are heading for a difficult time if we don’t do something, for example, about the climate.

I was fascinated to discover that the word “to know” is actually one of only a hundred or so words that have a translation across all languages. Even the word “to eat” doesn’t have a universal translation across all languages, but “to know” seems to be something we all know about.

Jeremy: Maybe talking about knowledge is more important than talking about food.

Marcus: It’s food for the brain, which I hope this book is.

Jeremy: Let’s talk about the book itself. I was so happy you started off with chaos theory, because when I was 16 years old, my pre-calculus teacher encouraged me to read this book by James Gleick on chaos theory, [which] literally changed the way that I see the world. For the uninitiated, what is chaos theory?

“Those who weren’t curious did not survive. It is the thing that has helped us to evolve as a species.”

Marcus: Well it’s very close to what my own subject of mathematics is about, which is trying to spot patterns in data from the past to [help] you predict what’s going to happen in the future. Let’s suppose we are in a deterministic world. Does that mean we can know the future? It turns out, not necessarily.

Post-Newton, with the Laws of Motion and calculus, we felt like we had the tools to know the universe into the future. You know the universe now, you run the equations, and it will tell you what’s going to happen in the future. The feeling was, “Well, you’re never going to have a complete description for the present, but perhaps we have an incredibly good approximation. We run the equations, and we should get a very good approximation of the future.”

Chaos theory shows us that isn’t a well-founded theory. A very small error in the present can explode through these equations to a completely different prediction for the future. This is something people might have heard of called “the butterfly effect,” that a [predicted] sunny day can turn into a hurricane just because of a little change in the wind speed that a butterfly has caused. [That’s] why the weather is so hard to predict beyond, say, seven days, because of the sensitivity to these small changes. This places limitations on how much we can use the equations of mathematics to make predictions into the future.

That’s not to say we can’t use these equations in some circumstances; we’ve used them to land a spaceship on the side of a comet. [But] I’ve seen chaos theory used to question the climate science that we are heading for bad times if we don’t do something. [They] say, “Look, it’s so sensitive! How can you know it won’t suddenly sort itself out in the future?” One has to recognize that there are things which we do know about. Trying to use chaos theory to question climate science is like saying, “Okay, I can’t predict when the waves are going to crash on the beach, so I don’t [believe in] tides.” The small-scale structure of waves is inherently chaotic, [but] the tides are very predictable.

Jeremy: In [another] chapter, you dive into Einstein’s special and general theories of relativity. This in particular felt stranger than fiction to me… Contrary to one of our most basic assumptions about the universe, it seems that time is actually this very slippery, flexible concept. Can you tell us a little bit more about that?

Marcus: The story of relativity is absolutely staggering. Going back to Newton again, Newton thought that space and time were absolute, that if you set clocks across the universe, they would keep going in sync. Einstein’s thought experiments revealed that actually, time can go [at] different rates according to how you’re moving with respect to other things keeping time.


My favorite example is the twins paradox, [although] it’s not actually a paradox. It’s a story about two twins.

Suppose they are called Magaly and Ina. I send Ina out on a spaceship, which accelerates away from Earth for 10 years, then decelerates and accelerates back again [toward] Earth. Her clock will be going slower due to this acceleration and deceleration, so much so that her body is aging at a slower rate. So when she returns, although [Ina] has only seen 10 years go by, [her sister] Magaly will have aged 80 years.

Jeremy: Wow.

Marcus: Have you seen Interstellar?

Jeremy: Yeah.

Marcus: Interstellar is a wonderful film which really chews on this idea. Einstein showed that acceleration is equivalent to gravity, so if you go near a very high gravitational force, like a black hole or a very dense planet, your clock is going to slow down, whilst other clocks will keep on running. [In Interstellar] they talk about the expense of going near a very massive object because they are going to be spending time, in a way. Their relatives back home will be aging, and they’re worried about that.

Another example is the GPS. The atomic clocks on satellites are going at different rates because they have less gravity than we do on Earth. And if we didn’t take into account Einstein’s discovery that time could flow at different rates according to where you are gravitationally, your GPS wouldn’t work.

Jeremy: These big, spacey concepts can seem like interesting but very abstract things, so to tie it into something concrete and practical like that is incredibly helpful. I also wanted to ask you a question about your chapter on consciousness.

Marcus: Another biggie.

“If you cut the brain in two, so you’ve got two independent networks, that raises the question, ‘Are there now two consciousnesses inside the body?’”

Jeremy: One of my favorite stories from this chapter is something that I encountered in my psychology studies back in college. It was about split-brain patients. I remember reading that [for] people [with] intense seizures, as a last resort, doctors will sometimes go in and sever the connection between the left and right hemispheres of the brain. So when they’re done, the person can be an almost entirely normal, functioning human being, it’s just that the two sides of their brain are no longer communicating with each other.

As you chronicle in the book, this leads to different parts of the body being controlled by completely separate entities. There’s actually some evidence to suggest that maybe there are now two different consciousnesses living inside the person’s head. Can you clarify that a bit?

Marcus: Absolutely. In the beginning, people were trying to look for consciousness somewhere in the brain, in the same way that our language centers are located in two different places, one to articulate language, one to understand language. The thought was that maybe consciousness is somewhere in the brain, but now we’re beginning to believe it’s more a property of the way the brain is networked together. That means that if you cut the brain in two, so you’ve got two independent networks, that raises the question, “Are there now two consciousnesses inside the body?”

The left side of the brain controls the right hand side of the body. Now the left side of the brain is where the language center is. If there are two consciousnesses, this is the consciousness that can express itself through language. The right side of the brain doesn’t have access to language, so this one is very frustrated. There’s evidence of a [split-brain] patient who beats herself up with her left hand controlled by the right side the brain because it is so frustrated at not being able to articulate itself.

Jeremy: Wow.

Marcus: Even more crazy experiments: you have a screen, and you’re allowed to put your hand through the screen, and you can feel how many objects there are on the other side. So when the patient puts her right hand through, that’s connected to the left side of the brain, it can feel how many objects there are and articulate, “Ah, I can feel six stones.” Then the experimenter puts a different number of stones and the person puts their left hand through. But now, when asked how many stones are there, the brain that has language doesn’t know. But if you [say], “Put up fingers to indicate [the number of stones],” the right side [of the brain] can do that.

Certainly, there is separated activity going on. The challenge is, are those genuinely two different consciousnesses? Or is the right side of the brain just doing automatic things [without] a sense of self that the language side is able to produce?

It reveals the challenge of trying to identify, “Well is that conscious? Or is it just acting in a zombie way which appears to replicate consciousness?” Can we ever know? That’s one of the big unknowns, the hard problem of consciousness. Philosophers say this is the problem that science really cannot completely answer.

“What gets me up in the morning to wrestle with problems is the fact that I don’t know the answer. That’s what excites me.”

Jeremy: You talk about how, when you explain an event like a tea kettle boiling, you can either say, “Oh, it’s boiling because of all these molecules bouncing around,” or you can say, “Well, it’s boiling because I wanted a cup of tea.” It’s these two complementary ways of explaining the world around us: a mathematical understanding and a more experiential one. To you, how do these two things fit together?

Marcus: You picked up a really important theme in the book, which is [that] even if you believe in a reductionist view of the universe, [in which] everything comes down to maths, that’s not always the best language to navigate the challenge you’ve got. There’s a hierarchy of language that we’ve built up through the sciences and beyond, [and] you have to choose the right language.

This is why, for example, biologists and mathematicians have often found it hard to talk to each other, because they deal in very different systems and languages. I’m a mathematician, I deal in very precise and exact consequences. [But] if you try to understand birds migrating, quantum physics isn’t the right language for that.

Jeremy: Right, right. I have one last question. I’m a big fan of this Buddhist philosopher named Alan Watts. He talks about this concept of “yūgen,” this kind of relishing [and appreciating] of the unknown. It’s an experience of something that you can almost grasp, but it’s always going to be just past what you can fully understand.

Throughout this book, you talk about how as a mathematician who’s very interested in science, you have this desire to almost know it all. [But] this is a book about unknowns. So when Alan Watts talks about his idea of yūgen, is there a place for that in your worldview, or would you just know it all if you could?

Marcus: There is totally a place [for that]. In fact, it’s the lifeblood of being a scientist. What gets me up in the morning to wrestle with problems is the fact that I don’t know the answer. That’s what excites me.

So we have a very strange relationship with the unknown. There’s a point in the book [when] I interview Melissa Franklin, Professor of Physics at Harvard. She said, “If you had a button that you could press and know everything, would you press it?” My first thought was, “Yeah, sure, ’cause I want to know!”

But then… would that be fun? You still want things that you can’t know in order to keep wanting to go on.

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