Hello, my name is Logan Chipkin, and you’re listening to the Fallible Animals podcast. Last episode we motivated and introduced constructor theory, which is our deepest theory in physics and, in my opinion, the first-ever Theory of Everything.
Today, we’ll continue our introduction to the theory by discussing the conceptual tools that are used by the theory. All of our best theories employ particular conceptual tools in order to explain the relevant phenomena. For example, the neo-Darwinian Synthesis, in explaining the biosphere, employs concepts such as genes, natural selection, mutations, organisms, and many more. Newton’s theory of classical mechanics also employs tools such as momentum, force, gravity, and so on.
I’d like to introduce the conceptual tools that are used by constructor theory. These include the constructor, substrates, tasks, and attributes. We’ll look at a few examples to introduce these concepts.
Imagine you had a Frappuccino machine, or a latte machine, or something like that. Any sort of machine that outputs a particular beverage, given the proper input. Let’s say you provide a Frappuccino machine with coffee beans and milk. Once you give the machine these inputs, it’ll output the Frappuccino drink. In this example, the Frappuccino machine is a constructor. That is, it takes an input, in this case, coffee beans and milk, and it delivers an output, which, in this case, is a Frappuccino drink. Also, and importantly, this machine is capable of repeating this process, or causing more than one of these transformations of raw materials into a final beverage. The Frappuccino machine retains its ability to create a Frappuccino given coffee beans and milk, even after it causes one such transformation.
A constructor is defined as any entity that can cause a particular transformation of input to output, and retains its ability to do so.
To take a more fundamental example, and one that David Deutsch talks about in his foundational paper, consider a chemical catalyst. If you have two molecules, A and B, it may be that they would only chemical combine in the presence of a chemical catalyst. Here, the catalyst may cause chemicals A and B to form a final chemical, C. This catalyst must retain its ability to cause another such transformation, even after the first one. Another way of thinking about this is that during the transformation that the catalyst causes, the catalyst does not undergo any transformation itself, but rather, only causes the transformation of the inputs.
And so a constructor does not undergo any change during a transformation; it only causes the transformation of something, which we’ve been calling the input, into something else, which we’ve been calling the output.
So you can really think of any constructor as just a generalized version of a chemical catalyst. To reiterate, a constructor is any entity that causes a transformation of some input into some output while retaining its ability to do so again.
The thing that’s presented to the constructor is what David Deutsch calls the input substrate. And the output would be the output substrate. So, the substrate is the thing that’s being transformed.
We can now say that constructor theory is all about explaining which transformations of which substrates are possible, and which are impossible, and why.
Another concept in constructor theory is that of an attribute. This roughly corresponds with the colloquial definition of an attribute, and it’s basically the thing about a substrate that’s being transformed in a transformation. For example, if you have an apple-cutting machine such that when you present it with an apple, the machine reliably cuts the apple into six pieces. And so the attribute of the apple that’s changing in this transformation is the number of pieces of the apple. The input substrate is the apple, which initially consists of one piece, and then it undergoes a transformation caused by the apple-cutting machine to become an apple of six pieces. So the attribute that’s being changed, once again, is the number of apple pieces.
Another example would be if you had a machine that, say, faced with an empty water bottle and a reservoir of water, it automatically fills the water bottle until it has 2 grams of water in it. Probably, there are such machines, or similar machines, in many factories around the world. But in any case, here we have essentially two input substrates — the water reservoir and the empty water bottle — and the machine transforms them in a few different ways, but one of which is that it changes their attribute of mass. This means that, because the water reservoir’s mass decreases by 2 grams, and the water bottle’s mass increases by 2 grams (water is transferred from the former to the latter), we can say that the attribute of mass is tranformed for each substrate when presented to the machine (the constructor).
Finally, these things I keep calling transformations are really just called tasks in constructor theory.
And so, constructor theory can be understood to be about explaining which tasks are possible, and which tasks are impossible, and why.
To summarize, in constructor theory, a constructor, when faced with a particular substrate, causes a particular transformation of that substrate, which means that at least one of the substrate’s attributes is changed. This entire process of having a substrate change at least one of its attributes is called a task. And constructor theory is all about expressing the laws of physics in terms of possible and impossible tasks.
Now that we better understand constructor theory, let’s review some of the philosophical problems that it immediately solves.
One is the problem of causation. As David Deutsch writes in the foundational paper on constructor theory, the philosopher David Hume, in 1739, argued that we can never observe causation, and so can never find evidence that causation is real. Now, if you listened to the previous episodes in which we talked about critical rationalism and how the scientific method really works, you can probably detect one or a few errors in that way of thinking. But in any case, constructor theory immediately solves this conundrum by showing that, if causation is to mean anything, then surely it means which tasks are possible and which are impossible in the presence of some constructor. In other words, a constructor causes some transformation to occur.
Constructor theory is incompatible with the assertion that science is a collection of facts or a collection of data points. You’ll never observe an impossible task, almost by definition — it literally can’t happen. And yet, such impossible transformations are implicated as fundamental in our deepest theory in physics.
Another philosophical problem that’s immediately solved in constructor theory is to define knowledge in physical terms. We’ve actually hinted at this in previous episodes, but now we can state exactly what knowledge is in constructor theoretic terms. If you think back to Copernicus’s heliocentric theory — that the Earth revolves around the Sun, and not vice versa — this theory has survived all sorts of criticism, and errors in recording and transmission, and everything else. It’s survived for centuries at this point. As I said in a previous episode, this heliocentric model is not confined to the history books, but rather, confined to the science textbooks. And so this is information that travels from brains to paper to audio podcasts to all sorts of media that can carry information.
Remember the definition of a constructor — it is anything that can cause a particular transformation and retains its ability to do so again. This information about the heliocentric thoery is really the only thing that survives all of its transformations. Copernicus certainly isn’t around anymore. And the people who are transmitting this information come and go, so they can’t count as the constructors. Even the other information-carrying media to which the information is transmitted are temporary. The books that once held the theory may not be around anymore, and the podcasts that talk about it could be extinguished at any time. But the knowledge of this theory yet survives.
So we may elegantly define knowledge as a constructor — throughout the millions or probably billions of transformations of blank pieces of paper and minds that hadn’t heard of the theory into pieces of paper with the theory written on it and minds that understand the theory, the only thing that remains constant is the theory itself. So this information, this theory, is knowledge — that is, information that causes its own construction.
Knowledge is a constructor that, once instantiated, causes itself to remain so. Another feature of knowledge is that not only is it a constructor, but it’s also often the output substrate of those transformations for which knowledge is a constructor.
When we think about all of the possible tasks, or transformations, for which the laws of nature allow, the vast majority of these do not occur spontaneously in Nature (‘spontaneously’, by the way, can be understood to mean ‘in the absence of a constructor’). So while here on Earth, things have been created such as cars, and hospitals, and Frappuccino machines, none of these transformations occur spontaneously in the Universe. In fact, seen in this light, most of the Universe is kind of boring. Sure, we have black holes, and stars, and solar systems, but these compose an infinitesimally small fraction of all entities that can possibly be created.
Most of the things that can be created, or transformed from other things, only occur in the presence of knowledge. For example, a car is only ever createed via the transformation of metals and other raw materials when a person with the knowledge of how to create such a car is present. So while a reductionist framework would insist that particles, and spacetime, and quantum wavefunctions are fundamental — and indeed they are — in a constructor theoretic framework, it is impossible to avoid the fundamental role that knowledge plays in our understanding of Reality.
We can then ask, “What is the entity that can hold knowledge, and create new knowledge?” And the answer is, people. But we’ll hold off on that point for another episode.
I was going to go into scientific problems that constructor theory has already solved, and future problems that the theory may solve, but, as seems to be a habit, I think I’m going to stop here. I’ve given you enough to chew on.
I do want to talk a little bit about the so-called universal constructor. If we think about all of the possible transformations that can be caused in accordance with the laws of physics, constructor theory allows us to ask, “Is it possible to build a machine that is capable of causing any conceivable transformation?”
Such a machine would be the ultimate technology. You could present the machine with any input substrate, and it could transform it into any output substrate that is allowed by the laws of physics. As far as I know, there is no law of physics that forbids the creation of such a machine, and so, one research program for constructor theory or another theory would be to show how such a machine could be built, and why it’s possible.
Alright, that’s enough for now. Next time, I’d like to get into David Deutch’s so-called momentous dichotomy that also emerges naturally from constructor theory, the difference between laws and principles that constructor theory provides for in exact terms, and some of the problems in science that constructor theory has already solved in the domains of information theory and biology.
Thank you very much for listening to the Fallible Animals podcast. You can follow me on Twitter @ChipkinLogan, and you can find some of my previous articles at www.loganchipkin.com. If you enjoyed this podcast, please consider sharing. I look forward to getting these ideas out there.
Thank you, and have a great rest of your day.