Fallible Animals Episode 4: Intro to Constructor Theory

Below is the transcript of episode 4 of my podcast, Fallible Animals. The original audio can be found on YouTube, Anchor, Spotify, and iTunes.

Hello! Good morning, good afternoon, good night. Whatever time you’re listening to this recording, I hope you’re doing well. This is Logan Chipkin, and you’re listening to the Fallible Animals podcast. Today we’re going to switch gears and not talk about critical rationalism, which we did in episodes 2 and 3, but instead talk about constructor theory, which is our deepest theory in physics, and as far as I’m concerned, it’s our first Theory of Everyhing. I haven’t seen it characterized as a Theory of Everything very much, but I’m pretty sure it is a Theory of Everything, and maybe by the end of this episode, you will agree with me.

As with most of our deepest theories in physics and elsewhere, constructor theory’s beauty is in its simplicity. That’s not to say that the details wouldn’t take effort to understand, but its not some impenetrable labrynth of mathematics and jargon. You don’t have to be an expert in physics or epistemology or anything else to understand the ideas behind and within constructor theory.

By the way, that’s true in general. Don’t let people tell you that you need a degree or credential, or to have taken a class, to understand something. If you’re interested in some idea or topic, just go learn it. It’s 2019! You have the accumulated knowledge of our entire civilization at your fingertips.

Back to constructor theory. It’s hard to know where to start, but I suppose I’ll just start with a little historical background. I mentioned last episode that Isaac Newton’s theory, which was humanity’s first universal theory, took the form of ‘initial conditions plus laws of motion’. Newton’s theory, also called classical mechanics, allows you to predict the future position and momentum of an object as long as you know all of the forces acting on that object, and its current position and momentum. Let’s call its current position and momentum the object’s — or system’s — initial conditions. By the way, in classical mechanics, an object’s momentum is equal to the object’s mass times its velocity, for the record.

Now, we can imagine recording an object’s position and momentum at some time. Let that state be the initial state, or initial conditions, of the system (these are interchangeable terms). And again, if we know the force(s) acting on an object across time, the equations of classical mechanics allow us to predict the object’s state, which is, again, its position and momentum, at later instants of time.

And this theory worked. Its ability to make successful predictions about the motions of objects ranging in size from a pebble to a star was literally awe-inspiring. Such an ability to successfully predict became a standard for good scientific theories.

Later in the 1800s, the theory of electromagnetism, while explaning a different class of phenomena than did Newton’s theory, also took the form of ‘initial conditions plus laws of motion’. In this case, the motion of charged particles, such as electrons, could be predicted if one knew the forces acting on them, and again, their initial state.

Even with the advent of general relativity and quantum mechanics in the 20th century, this paradigm reigned supreme. Although what was meant by a system was no longer necessarily a system’s position and momentum, and the laws of motion necessarily described changes of these attributes, the theories were still cast in terms of trajectories over time. Even in the notoriously weird quantum mechanics, something called a wavefunction evolved predictably over time, given particular laws of motion of that wavefunction.

So theories were thought to be all about what happens in the world. To reiterate, given some state of the world at any given time, a successful theory, it was thought, should predict (or retrodict) the state of the world at some other time. That a theory should take the form of ‘initial conditions plus laws of motion’ is what David Deutsch, the founder of constructor theory, calls the ‘prevailing conception’. In this prevailing conception, a theory provides equations of motion that predict what will happen to some system, given some current state, or initial conditions, of this system. Whether this system is a ball rolling down a hill, or the entire universe itself, or a quantum wave function, the prevailing conception is all about predicting what will happen to the system in question.

But some of our deepest explanations simply don’t conform to this prevailing conception. Consider evolution by natural selection, or the epistemology that we spent the last two episodes talking about, critical rationalism.

Think about the latest form of Darwin’s theory, which is called the Neo-Darwinian Synthesis. This also includes Richard Dawkins’ model of the selfish gene, in which genes are the fundamental unit of biological evolution. Very briefly, genes compete with alternative versions of themselves — also called variants, or alleles — and those genes that are most fit for the environment will propagate more of themselves over time into future generations. I’m speaking in a very hand-wavy fashion about biological evolution because that’s not our focus today, but I just wanted you to notice that Darwin’s theory is all about explaining how the design that we see in the biosphere, this exquisite order that’s all around us, emerged without a Designer. Noticee that this has nothing to do with initial conditions of a system and laws of motion and some sort of equation that can predict the futre state from a previous state. There’s no equation that we can write down that predicts from bacteria several billion years ago, eventually humans will emerge. That’s not the point nor the explanatory power of Darwin’s theory.

Similarly, in critical rationalism, we’re explaining the growth of knowledge — that we guess as to the truth of the matter, and then we criticize that guess, along with all of its rivals. The details of this process — or many of them, anyway — we talked about in the last two episodes. And maybe I convinced you that critical rationalism is our best theory of knowledge, or maybe I didn’t, but the point is that this, too, simply does not take the form of an initial condition of a system plus laws of motion. Again, there’s no equation we can write down that allows us to say, ‘OK, given an initial state of knowledge, this equation lets us predict our future state of knowledge.” That’s actually contradictory for a host of other reasons that we won’t get into now.

But the point is that some of our deepest theories of Reality do not confrom to the prevailing conception. And if Reality is unified and comprehensible as most scientists fully expect it to be, then there has to be a way of formally unifying those theories that do conform to the prevailing conception, such as the ones I’d mentioned earlier, with these other thoeries that simply cannot be put in terms that the prevailing conception can handle, such as evolution by natural selection, critical rationalism, and computation.

One might rebut at this point by saying, “Why not just look for a theory that does conform to the prevailing conception, but that’s even deeper than our other theories in physics, so that we can predict the future state of the world at any poitn in time?” Even if we found such a theory, that theory still wouldn’t explain all of the other phenomena that we observe at higher levels. Such a theory would be reductionism of the highest order. Even if we had such a theory, by definition it would only allow us to predict the trajectories of microscopic objects. And so even if we were to, say, run a simulation of this theory on some computer, we would still have to creatively notice higher-level phenomena, and then explain those, and so we’d just be back to square one.

And finally, it’s important to remember that prediction is not explanation. In fact, prediction is just a way to criticize our explanations in the way rendering them falsifiable, as we talked about last episode.

So if our worldview if ever going to encompass both the wildly successful theories that do conform to the prevailing conception, as well as all of our theories that explain higher level phenomena — such as evolution by natural selection, computation, and epistemology — then we need some new theory, one that provides a language in which we can express all of the theories in the prevailing conception, as well as our other theories. This theory, it turns out, is constructor theory.

One more thing before we get into constructor theory itself. There are a host of principles that most scientists working today accept, but that are only implicit and cannot be expressed in any of the prevailing conception’s theories. For example, the principle of testability itself — that a theory must be falsifiable. Until constructor theory, people just took that as a methodological rule, or a rule of how science ought to be done. But constructor theory naturally and elegantly makes this principle explicit. Another example is a principle that seems to hold true but that the prevailing conception has no room for is the so-called Turing Principle, which we haven’t talked about yet. It basically states that it’s possible to build a computer that can simulate any physical process. It’s a way of stating in precise terms the computability of nature.

Anyway, these two principles, along with others, have no place in the prevailing conception, because they’re not about initial conditions and predicting the future state of a system. In fact, they’re about what’s physically possible and what’s impossible.

This leads us to the governing idea of constructor theory — that is, all of the laws of physics can be expressed in terms of which transformations are possible and which transformations are impossible, and why.

So while theories that conform to the prevailing conception will tell you the trajectory of the state of a system according to some laws of motion and given some initial state of a system, constructor theory tells you which trajectories are possible in principle according to that theory, which are impossible, and why. While in the prevailing conception, what matters is what will happen, given some initial state of a system and laws of motion, constructor theory is all about what can be caused to happen in principle, and so what actually happens is only an emergent consequence of what can possibly happen.

As a brief example, in Einstein’s famous theory of special relativity, no object with mass can travel faster than the speed of light. And so in the prevailing conception, you have some object and its initial velocity, and the equations of special relativity can tell us the object’s velocity at any future point in time. In those equations, it turns out to be impossible for the object’s velocity to ever exceed the speed of light in a vacuum.

In constructor theoretic terms, we can say that the object’s velocity cannot be transformed into a velocity that’s greater than the speed of light, or, equivalently, that transforming an object’s speed into a speed that’s greater than the speed of light in a vacuum is an impossible task.

In that example, we don’t get much purchase by switching to constructor theoretic terms, because the prevailing conception already has a handle on the phenomenon at hand. But what about questions that we can ask about other aspects of Reality? For example, under what conditions is life possible, in principle? That certainly can’t be answered by the prevailing conception. How about — what resources are required to build a universal computer — a computer that can simulate any other computer? There’s no way we can answer these questions in terms of initial conditions plus laws of motion, but we might be able to answer them in terms of possible and impossible transformations. For example, maybe it’s impossible for life to emerge in the absence of a genetic code, or any other sort of code. Maybe that can be shown under constructor theory. Maybe constructor theory can also show exactly under what conditions a universal computer can be built.

There are all sorts of questions that one can ask once one understands the power of constructor theory that the prevailing conception simply can’t account for. And notice that constructor theory brings in counterfactuals into fundamental physics. In other words, what’s fundamental is not what actually happens, but rather what could’ve been caused to happen. So what’s interesting about, say, a computer, is not that it runs a particular program, but that it could be caused to run other programs.

And since constructor theory can just as well account for theories in the prevailing conception, as I had briefly shown with my special relativity example, we see that the prevailing conception is really just a limiting case that allows for classes of phenomena that do conform to an ‘initial condition plus laws of motion’ kind of theory. Constructor theory allows for a much wider class of phenomena, including those that are unpredictable in principle, those that require counterfactuals to explain, and those that can’t be explained by resorting to a reductionist framework, in which we explain greater things, or bigger things, or more complex things, in terms of their contituent parts. All of this is possible because of the singe genius idea that all of the laws of physics can be expressed in terms of transformations that are possible and transformations that are impossible, and why.

I think I’ll stop there because I understand that this is a radical idea and probably seems weird to a lot of you. I really didn’t even go into the details of the theory at all, which I would love to do, but I know I promised that I’d return to critical rationalism, so I’ll leave it up to you. What would you guys prefer we explore next episode? Do you want to go deeper into constructor theory, or do you want to go back to critical rationalism?

Let me know. Contact me on Twitter @ChipkinLogan, or email me through the address on my website, www.loganchipkin.com. And if you enjoyed this episode, pleasing consider sharing. I look forward to geetting these ideas out there.

Thank you, and have a great rest of your day.