Is Science Dying? (Patreon)

[This is a transcript of the video.]

Is science coming to an end? I’ve been thinking about this a lot recently. This may sound like old Sabine has finally gone completely crazy. Fair enough. But I believe my worries aren’t quite as crazy as they sound. Though I guess that’s exactly what a crazy person would say, wouldn’t they.

Crazy or not, I think it’s worth discussing: Why might science end, and is it happening? That’s what we’ll talk about today.

In 1996, John Horgan wrote a book called “The End of Science” in which he made a case that science has come to a halt and isn’t going to start moving again. It made him, not so surprisingly, enemy number one of scientists, because it’s not funny to have the end of your profession prophesied in a bestselling book if your income comes mostly from the taxes of people who buy those books.

But Horgan isn’t one to back down. In 2016, 20 years after the book was first published, he wrote a new preface saying that for all he can see, he was right.

Horgan’s claim wasn’t that we’d stop doing science, but rather, in his own words, “that there would be no great “revelations or revolutions” any more, no insights into nature as cataclysmic as heliocentrism, evolution, quantum mechanics, relativity, or the big bang.”

And he has indeed been right, hasn’t he? Just look at physics. All the big questions that were unanswered 40 years ago, are still unanswered today. We still don’t know what dark matter is, how to quantize gravity, or how the universe started. And it’s true in all other scientific disciplines too, we still don’t know how life began, what consciousness is, how to become immortal, and we still don’t know why socks disappear in washing machines.  

I have a weekly science news show and a science newsletter, and it might seem like I’d be the last person in the world to agree with Horgan, but I think he has a point.

He wasn’t even the first to raise the issue. I came across this first in a book by John Barrow called “Impossibility”. Barrow had a logically very compelling argument. He said, knowledge about the laws of nature is either finite or it isn’t. And we’ll either find out all there is to know, or we won’t.

If the knowledge is infinite and we’re really good at figuring it out, science will go on forever. But if the knowledge is either finite, or we have a finite capacity for figuring it out, we’ll reach a limit. We have no way of knowing what we don’t know, so it’s a real possibility that science will end, the question is just when.

There is some ambiguity here on who or what “we” means. Maybe you and I aren’t going to figure out all of science, certainly not if we keep spending all our time on YouTube. But “we” might mean a new kind of species that humans evolve into. Or humans with brain implants, or humans with the help of artificial intelligence, or maybe we’ll carry around spare brains in backpacks. But regardless of how we might expand our minds, there’d still remain the question whether we can indefinitely expand our knowledge, or whether there is a limit.

Horgan’s claim is stronger Barrow’s. Barrow just said science could end. Horgan says we’ve reached the end already. According to Horgan, the discovery of the laws of nature was a temporary phase in human development and it’s over. Just like the exploration of earth’s surface, or that of human anatomy. There is a time when the big discoveries happen. Then, that time ends.

This isn’t to say that cartography or the study of the human body is finished, and neither is the further study of nature in other areas. NASA for example is making more and more precise measurements of the surface of Earth by scanning it with lasers, measuring even the height and depth of forests and the minute changes in gravitational pull from varying surface density. But no one’s going to discover a new continent.

And we’re continuing to explore the human body, finding new way to fix things, like bridging damaged nerves. But no one’s going to find an extra brain underneath the left kneecap. The age of big discovery in those areas is over for good.

And this raises the question: will the same thing happen with science in its entirety? Was the discovery of new natural laws just a phase in our history that’s passed? I think it’s a possibility that we need to seriously consider.

But most scientists, I think, dismiss Horgan’s worries. And to be fair, physicists in particular have good reasons to dismiss the “end of science”. That’s because physics has a lot of big open problems that we know require a solution. Like, what’s with all those observations that are usually at’tributed to dark matter. Is it some kind of particle that we haven’t yet detected? Or do we misunderstand gravity? Our current theories can’t explain it, yet it’s happening out there.

And there is the missing quantization of gravity, that is the incompatibility between Einstein’s General Relativity and Quantum Physics. The easiest way to see that there has to be some solution to this is that we just don’t know what the gravitational field of a particle is when it’s in two places at once. Einstein’s theory can’t handle that.

And what’s with the measurement problem in quantum mechanics? Sooner or later, we’ll need a solution to that, something that tells us just exactly when a device has the right properties to act as detector.

Horgan thinks we’ll never answer these questions. Now, I have worked on all those topics, and I think they are solvable with currently existing mathematics and technology. But maybe he’s right and I am wrong.

That said, there’s another reason why I don’t think we’re anywhere close to reaching the end of science, and it’s nothing to do with physics. It’s a research area that Horgan cheerfully dismissed as “chaoplexity”, the study of chaos and complexity. That’s the whole story with the butterfly effect and self-organized adaptive systems and all that.

Chaos and complexity were big buzzwords in the 1980s and it’s true that not much came out of it. So you might say, ha, Horgan’s right. Maybe, but I think the reason that this research didn’t get very far is that we haven’t developed the mathematics for it. And there are big breakthroughs waiting to happen once we have the maths in place.

You see, I’d say that physics uses the most sophisticated maths of all the science. But if you look at it from a birds-eye-perspective it’s really rudimentary. We only know how to solve certain types of equations, so-called linear differential equations. But most of the interesting phenomena in nature, like chaos and complexity, require non-linear equations. And we don’t have a good method of solving those.

Believe it or not, but the best tried and tested method to solve non-linear differential equations is guessing a solution and then checking that it’s correct. Sometimes it works, sometimes it doesn’t.

Now we can put non-linear differential equations on a computer and that’s what we do for example in general relativity. The non-linear equations in this case are einstein’s field equations. They are non-linear differential equations for the metric tensor, that’s this g. You can’t see it very well in this form, but this R here, that’s a sum over components of the curvature tensor. And the curvature tensor contains sums over products of the metric and its derivatives. So it’s non-linear. It’s a rally nasty set of equations.

We can put them on a computer but there’s a catch. Computers use a finite resolution, a grid basically, and discrete steps in time. Yes, you can use an adaptive mesh and other fancy things, but no matter what you do, computer simulations always rely on the idea that you can ignore details on small scales.

The trouble is, for non-linear equations you can’t do that. It’s what the butterfly effect is all about. It’s a small change, the flap of a tiny butterfly, that has huge consequences like a tornado in Texas.

So, yes, we can put Einstein’s equations on a computer, but strictly speaking we don’t know that what we’re doing is correct. It’s a similar problem with climate models. Yeah, I know one ought not talk about the shortcomings of climate models, but I think we should. Climate models for the atmosphere and oceans ultimately solve the Navier-Stokes equation. That’s a non-linear differential equation and we don’t understand how to solve it, not really. You don’t need to take my word for it it’s one of the 10 Millenium Problems in mathematics.

Some people, but not you I’m sure, might want to spin what I just said into a story saying Sabine thinks climate models are all wrong. This is not what I said. I said climate models are struggling with some things, and incorporating what happens on short scales is one of those things. Climate scientists have developed tools to deal with that, for example by adding random fluctuations on the short scales. And that’s good from the perspective of developing a predictive model. But from the perspective of mathematical understanding, it’s extremely unsatisfactory.

But back to the end of science. We’re missing the maths to deal with non-linear systems, systems that display chaos, systems that develop complexity. We don’t even have a proper definition for complexity. It’s probably THE biggest gap in science right now and it’s the major reason I think science is nowhere near ending. We’re missing a law of nature that explains how and under what circumstances complexity arises.

There have been a couple of attempts at it, curiously enough just a few weeks ago several papers appeared who had a go at it. They’re all based on the idea of finding a way to quantify the growth of complexity.

So far I don’t find any of those new laws of nature terribly convincing, but then again my idea of a ‘complex problem is saying no to a dinner invitation, so maybe I’m not the right person to ask.

But for the purpose of today’s video, it isn’t all that relevant whether any of those proposed new complexity laws is right, the relevant point is that there quite plausibly is such a law, scientists are on it, and if they found it, that’d be real big deal. Think of all the cases where understanding chaos and complexity would have an impact. The stock market, nuclear fusion, society by large, the origin of life, saying no to dinner invitations. It’s all about the growth of complexity.

This is why I dare to say we’ve barely begun with science. We’ve done quite well in the microscopic and macroscopic regime. Particle physics and cosmology, yeah, it’s worked fine because both are mathematically simple. But look at things like biological systems, life, consciousness, society and politics, we don’t have the maths.

Ok, so there are almost certainly new laws of nature left to discover in the mesoscopic range, when complexity and chaos come into play, and quite possibly artificial intelligence is going to help us discover them. But I think we might be reaching the end of science nevertheless.

Here's why. Think back of Barrow’s argument. There are two reasons why science can end. It may be because there’s nothing more to discover. And I just told you why I think that’s not the case. But there’s another reason. There may be natural laws left to discover, we’re just too dumb to figure them out.

I don’t mean that we’re too dumb in the technical sense that we can’t work out the maths, or develop a computer program to do it for us. I think we’re too dumb to organize scientific research so that scientists can efficiently work towards those solutions. And ironically the reason we don’t manage to smartly organize science that is that we don’t understand complex systems in the first place. So it becomes a chicken and egg problem. We don’t understand complexity because scientific research is a complex system that we’d need to understand complexity.

Okay, you might say, I’ve followed you so far, kind of. But why does it even matter? It matters because we put a lot of faith in scientific and technological progress to fix the problems we’ve got ourselves into. Climate change, pandemics, overpopulation, poverty, the threat of nuclear war. All too often we believe that more science and better technologies will come to our help. But well what if they don’t? Then we’re in deep shit.

So is science finished? It might be if we don’t pay enough attention to keeping it alive.