I’ve recently completed a review of Constructor Theory for FQXi with my colleagues Chiara Marletto and David Deutsch (you can read it here arXiv:2606.07352). It was great to work together on this exciting topic and our adventure is something I’d like to tell you more about here.

But first, I should explain the word “kibitzer” (unless, of course, you are familiar with this particular Yiddish slang). I’ve learnt it from my Serbian grandfather, who taught me how to play chess when I was 4. I think my chess ability is more or less at the same level now as it was back then – I am basically a “patzer”, which is yet another Yiddish slang word for you to learn (meaning, a bad chess player).

Photo by Hassan Pasha on Unsplash

Anyway, a kibitzer is a spectator on a game like chess who usually offers uninvited advice to the players. Serbia – the country where I was born and grew up – is full of passionate kibitzers of all sorts of games and, for our purposes here, the game is that of Constructors and Chiara and David are its main players. That, of course, makes me a kibitzer. So here is what I’ve observed so far in their game of constructors (packaged together with the uninvited advice I’ve frequently offered).

A while back, David had the idea that universal computers (i.e., computers that can compute anything that is computable) ought to reflect the underlying laws of physics. Universal classical computers (suggested by Alan Turing) could not perform all computations because the laws of classical physics are not the ultimate laws of our universe. So David wrote a couple of papers back in the early eighties on how to define universal quantum computers. And, fast forward 4 decades, there is now a race to make the world’s first universal quantum computer (illustrating, among other things, the impact one can make with a single great idea).

In the meantime, however, David realised that, while universal quantum computers may well be able to compute anything that can be computed, they might not be able to execute any transformation that is allowed by the laws of quantum physics. For instance, computers (even the quantum ones) cannot reproduce. It is for this reason that von Neumann suggested the idea of constructors, which he thought of as robots that are capable of maintaining themselves by monitoring the degradation of their own parts and scanning the environment for replacement components. Von Neumann imagined they could be sent to colonise Mars, an idea that may still be realised in the future.

But, David thought that we should make the concept of constructors even more general. How about defining them as machines that can facilitate any transformation that is allowed as far as the fundamental laws of physics are concerned? What kind of rules, other than the laws of physics, would such a machine obey? Here is where Chiara comes in, whose PhD thesis (Oxford 2013) was exactly on outlining such rules for constructors. Clearly, constructors should conform to the conservation laws we believe to be ubiquitous and exact. For instance, energy conservation; constructors ought not be able to violate it. Also, their actions should be local, in the same sense as any field theory is: no spooky action at a distance is allowed; i.e., a constructor on Mars should not be able to instantaneously affect things on Earth.

Chiara then defined information in terms of what is copiable. Superinformation contains different information media, which, taken together, no longer constitute information. Quantum information is one example of superinformation, since both position and momentum are individually copiable, but together they are subject to Heisenberg’s uncertainty principle. Chiara and I have recently been speculating that Einstein’s gravity, too, might be thought of as superinformation. But more on this in another blog.

There are three things I like about constructors. The first is that they might help us bridge the gap between physics and biology. How did the inanimate matter become alive? While computers can simulate some processes akin to what happens in biology, they themselves are clearly not alive. Among other things, they lack purposefulness and intentionality. Clearly, a more sophisticated concept is needed, and constructors might just be it. This too is a work in progress. Secondly, even as servants of humans, constructors are much more powerful than computers. By definition, they can construct anything that is not prohibited by the laws of physics. They are like 3D printers. Imagine just pressing a button and your personal constructor makes you a burger, or a house, or a car. How much easier could life become with such a powerful tool?

Ok, so constructors can colonise Mars and make you a burger. But the third reason for studying them is still the most magical for me. Could it be that constructors can offer us a way of unifying the whole of physics? Maybe the ultimate laws of physics are to do with what constructors can and cannot do. Both David and Chiara have been driven by this vision (have a look at Chiara’s great book “The Science of Can and Can’t”) and this is where Yours Truly comes in as a kibitzer.

There is a version of the second law of thermodynamics due to the mathematician Constantin Caratheodory. It says that in the neighbourhood of every allowed thermodynamical state of a given system, there are states which cannot be accessed by adiabatic means. Adiabatic is the name for a transformation that does not allow any energy to be exchanged with the environment of that system. So, if I give you a bottle of beer (the system) and I ask you to cool it down while not allowing you to put it in the fridge (the environment), you will find the task impossible. While steering the beer could always heat it up, there is no mechanical action you can perform to make it chilly (I know, it’s too bad).

Now, wouldn’t it be nice if we could generalise the “no chilling of the beer by mechanical means” principle to capture the whole of physics? I think it would be, and moreover, that it is possible. My suggestion? The ultimate laws of physics are such that in the vicinity of every possible task (i.e., a task that the laws themselves permit) lie tasks that are impossible (i.e., those that are prohibited). The intuition behind this is really Einstein’s, who said that the more prohibitive the better as far as the laws of physics are concerned. So the most prohibitive laws ought to be the ultimate, according to this logic. The snag is that I don’t know how to implement this principle to get to the ultimate laws, but it’s definitely a work in progress. And I am sure that something interesting will come out of it, especially when players like David and Chiara are involved in the game.