# Formulating Science in Terms of Possible and Impossible Tasks[1]

David and I have been working on this together for the past three years, and we’ve been applying it to many different problems. So far, the two completed parts of our trying out constructor theory to see whether it can solve problems are: a fundamental theory of information within physics1; and the constructor theory of life2, which applies this new theory of information to a fundamental problem that's at the boundary between physics and biology, and has to do with how certain features of living things, such as the ability to self-reproduce very accurately, are compatible with the laws of physics as we know them.

In these two cases, you can see how switching to this new mode of explanation allows one to change the perspective and address the problems in a much more effective way. These are two examples where switching to this new mode of explanation makes all the difference.

Take information, for example. Information is something we use in our everyday speaking; also we use it in physics a lot. For instance, we assume that information has certain properties, e.g. that it can be copied from one physical system to another. So far, we did not have a fundamental theory telling us what are the regularities in nature that allow the existence of information in this sense. But whenever we talk about information we refer to those regularities. We assume, for example, that the laws of physics allow copy processes. In constructor theory you can express these regularities, and this is what our theory does. Our way of incorporating information in fundamental physics is by formulating what are these regularities in nature that allow the existence of information.

To see how switching to formulating science in terms of possible and impossible tasks is crucial to solving this problem, consider what happens when you try to express precisely that something contains information. The fact that something contains information has to do with the property that you can swap that thing with something different. It is what philosophers call a "counterfactual property" of the object. It has to do with what tasks you can perform on the object; e.g., that you can swap it with something else.

If you think of a flag, it brings information only if you can swap it with a flag of a different color and you can signal with the two flags. This idea was not expressible in terms of initial conditions and laws of motion, but it can be expressed in terms of possible and impossible tasks and as an intrinsic property of the flag, of the object. This is an example of how switching to this mode of explanation can address a fundamental problem in physics.

Then there is this other issue: we have been talking about classical information, but we know that there’s something more, what we have been calling "quantum information." It’s very interesting that in this constructor theory of information, you can relate in an exact way the notion of quantum information to that of classical information. In constructor theory, you have a unifying framework where you can describe both and this is very promising.

For instance, we have been searching for realizing the universal quantum computer for a long time now. One of the reasons why we have not yet succeeded in finding a way to implement that is that we do not have a good understanding of how quantum information is related to classical information. We did not have, for example, an exact expression for that. Now, if we have a theory where we can talk, in a unified way, about quantum information and classical information and there is a way of relating the two exactly, there is the potential of understanding better what are the properties of the universal quantum computer that we want to realize in the lab. This could inform the search for the universal quantum computer.

Physically instantiated information is also very central to life in the universe, and this is the other example of how constructor theory can address certain problems that have been considered resilient problems for long.

If you consider something like a bacterium, physicists have been particularly impressed by the fact that it is capable of performing tasks to a very high accuracy, retaining the property of doing so again—this is very much like a car factory, for instance; but the bacterium does this via another property, that is to say it can construct a new instance of itself. And that is a property that is very specific to life as we know it.

One might ask whether such entities like bacteria, that are fundamental to biology, are compatible with the laws of physics as we know them, or whether they require something more than those laws of physics. The laws of physics—quantum physics and general relativity—refer only to elementary things like quarks, atoms, and so forth. They do not contain self-reproducers, let alone accurate ones.

In fact, Wigner—one of the pioneers of quantum theory—had this problem, and he proposed an argument according to which we should complement the laws of physics with some new, designed ones to accommodate properties like accurate self-reproduction in living cells. If you apply the tools of constructor theory to this question: is an accurate self-reproducer, like bacterium, possible under the laws of physics as we know them—laws of physics that do not contain the design of biological adaptations? Not only do you see that Wigner’s reasoning was misled by using the prevailing conception of fundamental physics, but you also see that constructor theory, in which the idea of something being possible or impossible is a natural statement, can address the problem very effectively. You can also use the theory of information that I was describing before to tackle and solve the issue.

It turns out that yes, what the bacterium does is compatible with laws that don’t contain its design. The only requirement on the laws of physics for that to be possible is that they allow for information in the exact, constructor-theoretic sense that I was saying before: that they allow those interactions, copying like interactions, to be possible. But these are copying-like interactions that are not designed for a bacterium to undergo self-reproduction—very non-specific interactions, elementary ones.

The key to the way a bacterium performs its own self-reproduction (under laws that do not contain the design of biological adaptations) is the same as the key to the way, say, a car factory constructs a car. In both cases there is a recipe—a bit of information—that has the ability of directing a construction process, of causing a task to be performed because it contains the knowledge about how to perform it by following elementary, non-specific steps. In the case of the bacterium, it is the DNA sequence of the bacterium and, in the case of the car factory, it is the sequence of elementary steps to assemble a car out of elementary components.

This particular kind of information, this recipe, can also have an exact characterization in constructor theory, as knowledge: it is information that can act as a constructor—i.e., an object that can cause transformations and retain the property of causing them again. All these elements that I just mentioned—information, knowledge—are emergent things that, in the prevailing conception of fundamental physics, would not have a natural expression because you would have to talk about many atoms undergoing certain complicated transformation in some phase space; while in constructor theory, they are natural objects. They are the very elements by which the theory expresses itself. These are examples of how constructor theory brings in conceptual 'devices' that are new to physics, so that it can address problems that have been not solved so far. That's very promising.

What are the fundamental ideas of the prevailing conception of fundamental physics that would be impacted by constructor theory? The first thing to say is that constructor theory accommodates those things that the prevailing conception has been handling very well, so it’s a proposal to go beyond that, but not to contradict it. Yet it also has a radically different perspective on things because, as I said, in the prevailing conception, the fundamental objects are the laws of motion and the initial conditions of our universe. In constructor theory, on the other hand, the fundamental objects are transformations that are possible/impossible, and the explanation of why they are possible/impossible. It turns out that, under our laws of physics, in order for any transformation to be achieved, knowledge must be brought about in order to make a certain transformation performable to higher and higher accuracy. Knowledge, which is a 'causal' kind of information—information with a causal power that has the ability of remaining instantiated in physical systems—is a highly emergent object and it cannot be handled in the prevailing conception of fundamental physics, while in constructor theory it becomes one of the central objects. It becomes fundamental because it’s the way accurate transformations can be performed in a world where the laws of physics are simple and do not contain any design of those transformations. Here is an example of a change in perspective, and also an interesting take on the idea that humans are knowledge-creating systems. One of the ways knowledge can come into the world is by natural selection out of no knowledge. Another way is by humans creating it.

It turns out that in the constructor theoretic view, humans, as knowledge creating systems, are quite central to fundamental physics in an objective, non-anthropocentric, way. This is a very deep change in perspective. One of the ideas that will be dropped if constructor theory turns out to be effective is that the only fundamental entities in physics are laws of motion and initial conditions. In order for physics to accommodate more of physical reality, there needs to be a switch to this new mode of explanation, which accepts that scientific explanation is more than just predictions. Predictions will be supplemented with statements about what tasks are possible, what are impossible and why.

One question might be how do you test constructor theory? Well, constructor theory has a status that is that of underlying theories like quantum theory, general relativity, and possibly others, maybe better ones. It's more fundamental than those and it underlies them, and the way it does so is by being a theory of principles. It expresses statements that are a bit like the principle of conservation of energy, statements that constrain theories, so some theories are just incompatible with constructor theory, with its principles.

As I said, constructor theory informs the experiments not in a direct way because it doesn’t make predictions directly, but it provides principles. Just like you would go about testing certain principles such as the conservation of energy, you can in fact indirectly test constructor theory by testing the theories that obey it.

One way it could be tested is this. Take one particular principle of constructor theory, for instance, that of the interpretability of information, that has to do with the very fact that information can be copied. That principle might imply that there must exist certain particles, which we do not know yet about, but they are necessitated for this principle to be obeyed by our best current fundamental theories. This would be a way in which constructor theory could be tested because then you could test whether or not such particles could exist. In other words, more generally, the way you test constructor theory is just the way in which you test principles.

Yes, it is a meta-level. The proposal is that science also contains that meta-level and the principles of physics such as the principle of thermodynamics and some of the constructor theory principles, are part of fundamental physics because there is a way of testing them and because they inform discoveries of future theories, too. Future theories must obey those principles, so that is how they are part of science.

Constructor theory is quite radical, so one might wonder what are the ideas in the established way of doing physics that are threatened by constructor theory. "Threatening" existing ideas is too extreme: rather, one criticises them. I see what constructor theory brings about more like a supplement, or an improvement. But if you want to consider what are the ideas that constructor theory would possibly replace if it turns out to be effective, as I said, there is a tendency to consider physics as applying to a narrow set of things—particles and elementary interactions and so forth—regarding a scientific explanation as valid only if it is expressed via predictions. This is one of the reasons why part of the scientific community still has problems with interpreting quantum theory, for instance. It is also part of the reason why Darwin’s Theory of Evolution, for example, is not considered by some scientists as a satisfactory scientific explanation—because it does not predict the existence of elephants at time t in the universe—yet, it does explain how they come about from simple initial things.

If constructor theory turns out to work, this narrow view of physics will have to be dropped. This is something that reductionists are not very happy about. That is why it is quite a challenge for David and me to show that there are scientific problems that can be addressed by constructor theory, without resorting to predictions.

For example, in regard to this whole issue of what it means for information to be part of fundamental physics: we have just come up with this proposal that what it means is that there are interactions and regularities in nature which allow the existence of information in the world. A way to go about in expressing those is by using constructor theory. It turns out to be the only effective way because these properties of nature, that we are conjecturing, are counter-factual properties, and they must be expressed in terms of possible and impossible tasks rather than in terms of predictions.

Another example is the mode of explanation of Darwin’s theory. In Darwin’s Theory of Evolution you do explain the existence of the appearance of design in the world without the existence of a designer – i.e., without the existence of any intentional design process. But you do not do so by predicting the existence of such entities, because if you could predict them, say with some probability, that might mean that, in fact, you have merely discovered design in the laws of physics. What you do is to explain how it is possible that they can arise in our world given the underlying, no-design, laws of physics.

That is a different perspective—the constructor theoretic way of explaining things. Von Neumann, when thinking about self-reproduction—he pioneered the idea that self-reproduction must occur in two steps: by first copying what we call now the DNA sequence coding for the organism, and then by executing the recipe that is inside the DNA to construct a new instance of the organism—did not use the mode of explanation by predictions in order to explain this. He used a computational model to simulate this process. He had an understanding that this was a fundamentally different question from one that you would answer by only making predictions.

The bottom line is there is a whole set of issues, scientific questions, that cannot be answered by predicting things only. One of the proposals that are implicit in what David and I are doing is that it is necessary for physics to tackle those questions. And therefore it is essential to go about and search for different ways of addressing problems in fundamental physics. Constructor theory is a proposal for that.

We are also planning to apply constructor theory to other problems in fundamental physics. One is this problem of how to make sense of probabilities in fundamental physics. Probabilities have been a hard concept to pin down and they are fundamental to a certain way of looking at quantum physics. Yet, quantum physics is, fundamentally, a deterministic theory. One question is how does one connect the testing of quantum theory, which one way or another relies on the idea of probabilities, with the fundamentally deterministic structure of quantum theory? This question has been tackled in different ways but there is still a controversy about that, and we are hoping to apply constructor theory to this issue in order to sort it out.

There is also this interesting object that is called a universal constructor, which is something that can perform all tasks that are permitted by the laws of physics. It is a bit like the generalization of the universal computer, but it does not perform only computational tasks but also tasks on physical systems. The question is, is it possible given the laws of physics that we know, and what is its minimal instantiation? Is it very small or what? Those are questions that we are thinking about as those to which constructor theory might make a difference.

Constructor theory was initially conceived as a generalization of quantum computing. It turned out to be much more than that, but there is some very promising trait of this theory of information that we have constructed which could be applied to understanding issues such as: what is the thing that makes a quantum computer as powerful as it is? There is a controversy about this issue: Is it entanglement? What sort of entanglement? There is also a difficulty at the moment in expressing what entanglement means in terms of information-theoretic concepts. Precisely because we have related exactly the properties of quantum information to those of classical information, in the constructor theory of information, there will be a possibility to address these questions on a more solid ground.

More generally, we are searching for a quantum computer in too undirected a way. We do not have a sophisticated theory about what to search for and what are the features of quantum physics that we need in order to power the quantum computer. Of course, we know how the quantum computer works, but that is different from knowing what are the features of the quantum system that you must get "right" in your lab in order for it to work as a quantum computer.

My guess is that the reason why we have not yet managed to find a viable realization of a universal quantum computer is that we are lacking this broader, more encompassing view of how quantum information works. In a way, constructor theory is working towards improving on that.

As I said, it is a radical idea, and we would like to make it understood by the scientific community. We would like to apply it to problems that have not been solved so far, and show, by doing this, that it works. At the moment people are just saying "It might work, let’s see…"

We are hoping to persuade the scientific community that this is a worthwhile approach by showing that it can solve problems that could not be solved before. That is what we’re up to now.

The theory is still in its first stage, so the short-term plan is to apply it to as many problems as possible and show that it can make a difference. There are interesting questions relating to for instance the origin of life, to the question of fine-tuning of the laws of physics that could be benefitting from a constructor theoretic approach. We have had some interesting comments from other groups in the world working on these things, such as Paul Davies's group, saying that constructor theory seems very promising in this regard. If it turns out to be working, then more and more people will be using it. That is what we are hoping for.

I have had an unconventional path in physics. I am a theoretical physicist—a quantum physicist. I studied in Turin; I got my master’s there, in physical engineering. Then I moved to Oxford for the DPhil (i.e., PhD) in quantum computing with Artur Ekert and that is where I met David—during my DPhil. We started collaborating on constructor theory, and since the collaboration was very fruitful we decided to extend it after the DPhil—so here I am. I am now working on constructor theory together with David.

We are hoping that this will be fruitful and that we will be capable of delivering this new theory of fundamental physics.

[1] D. Deutsch, C. Marletto, "Constructor Theory of Information [2]"

[2] C. Marletto, "Constructor Theory of Life [3]"