David Deutsch, Constructor Theory and the nature of information

David Deutsch is proposing a very interesting conceptual shift in how we understand the nature of a physical theory.   It’s an idea he has for “generalizing the quantum theory of computation to cover not just computation but all physical processes.”  The theory in question he calls Constructor Theory.  A video of Deutsch outlining the ideas (as well as the accompanying written text) were provided by Edge.org last October.

Constructor Theory rests on the nature of information is understood.  According to Deutsch,

There’s a notorious problem with defining information within physics, namely that on the one hand information is purely abstract, and the original theory of computation as developed by Alan Turing and others regarded computers and the information they manipulate purely abstractly as mathematical objects. Many mathematicians to this day don’t realize that information is physical and that there is no such thing as an abstract computer. Only a physical object can compute things…information has to be a physical quantity. And yet, information is independent of the physical object that it resides in.

That information is physical, yet independent of the physical object in which it resides, is one of the cornerstones of the theory.  Deutsch makes the point:

I’m speaking to you now: Information starts as some kind of electrochemical signals in my brain, and then it gets converted into other signals in my nerves and then into sound waves and then into the vibrations of a microphone, mechanical vibrations, then into electricity and so on, and presumably will eventually go on the Internet. This something has been instantiated in radically different physical objects that obey different laws of physics. Yet in order to describe this process you have to refer to the thing that has remained unchanged throughout the process, which is only the information rather than any obviously physical thing like energy or momentum.

The way to get this substrate independence of information is to refer it to a level of physics that is below and more fundamental than things like laws of motion, that we have been used thinking of as near the lowest, most fundamental level of physics. Constructor theory is that deeper level of physics, physical laws and physical systems, more fundamental than the existing prevailing conception of what physics is (namely particles and waves and space and time and an initial state and laws of motion that describe the evolution of that initial state).

The theory works on yet another level of abstraction, (and a familiar mathematical idea) transformations.

The new thing, which I think is the key to the fact that constructor theory delivers new content, was that the laws of constructor theory are not about an initial state, laws of motion, final state or anything like that. They are just about which transformations are possible and which are impossible…When they’re possible, you’ll be able to do them in lots of different ways usually. When they’re impossible, that will always be because some law of physics forbids them, and that is why, as Karl Popper said, the content of a physical theory, of any scientific theory, is in what it forbids and also in how it explains what it forbids.

The laws of Constructor Theory are expressed with an algebra.

The first item on the agenda then is to set up a constructor theoretic algebra that’s an algebra in which you can do two things. One is to express any other scientific theory in terms of what transformations can or cannot be performed. The analog in the prevailing formulation of physics would be something like differential equations, but in constructor theory it will be an algebra. And then to use that algebra also to express the laws of constructor theory, which won’t be expressed in terms of subsidiary theories. They will just make assertions about subsidiary theories.
Chiara Marletto (a student I’m working with) and I are working on that algebra. It’s a conceptual jolt to think in terms of it rather than in the terms that have been traditional in physics for the last few decades. We try and think what it means, find contradictions between different strands of thought about what it means, realize that the algebra and the expressions that we write in the algebra doesn’t quite make sense, change the algebra, see what that means and so on. It’s a process of doing math, doing algebra by working out things, interleaved with trying to understand what those things mean. This rather mirrors how the pioneers of quantum theory developed their theory too.  (emphasis added)
…one of the formulations of quantum theory, namely matrix mechanics as invented by Heisenberg and others, isn’t based on the differential equation paradigm but is more algebraic and it, in fact, is another thing that can be seen as a precursor of constructor theory.

Deutsch acknowledges that, while promising, the effort is new and if it turns out to be wrong, “Then we would have to learn the lesson of how it turned out to be wrong.”  At the end of last year, Deutsch authored a paper that may be found here.

One of the things I most enjoy about David Deutsch is how he expresses his own captivation with how we have come to know things that lie far outside the range of our experience.  In this particular talk he says the following:

One of the central philosophical motivations for why I do fundamental physics is that I’m interested in what the world is like; that is, not just the world of our observations, what we see, but the invisible world, the invisible processes and objects that bring about the visible. Because the visible is only the tiny, superficial and parochial sheen on top of the real reality, and the amazing thing about the world and our place in it is that we can discover the real reality.
We can discover what is at the center of stars even though we’ve never been there. We can find out that those cold, tiny objects in the sky that we call stars are actually million-kilometer, white, hot, gaseous spheres. They don’t look like that. They look like cold dots, but we know different. We know that the invisible reality is there giving rise to our visible perceptions. (emphasis, again, my own)

I think the significance of this was failed to be appreciated by Arnold Trehub, a psychologist at the University of Massachusetts, Amherst and author of The Cognitive Brain. He contributed this critique of Deutsch’s ideas:

Deutsch is to be commended for pointing out that information necessarily involves electrochemical signals in his brain. But the greatest volume of information signaling in his brain is not a part of his conscious experience. It is only after unconsciously selected mini-patterns of preconscious neuronal activity are projected in proper spatio-temporal register into his brain’s perspectival representation of his surrounding space that they become part of his conscious experience of the world around him as well as his conceptions of possible worlds. The physics that he knows and strives to advance exists in this domain of neuronal activity.
We are each born with a system of brain mechanisms that constitute the full scope of our occurrent phenomenal universe. The neuronal structure and dynamics of this cognitive brain system actually construct the world of our experience. But the brain mechanisms that give us this world are evolutionary adaptations selected to better enable us to survive and thrive on our uncertain earth. When David Deutsch regards science as an enterprise for discovering what the world is really like, he seems to be seeking ultimate truths. How can we possibly know the ultimate nature of the world when the cognitive brain, the best tool we have, is a pragmatic and opportunist organ? It seems to me that science, like the brain that conceives it, is a pragmatic enterprise. We may seek to know what the world is really like, but what the world is really like, within the purview of science, is always provisional.

The provisional nature of knowledge is understood.  But the constructive action of the brain is by no means being ignored in Deutsch’s ideas.  The projection of that preconscious neuronal activity may be one of the things Deutsch’s method is meant to capture.  That “volume of information signaling” in the brain, that is not a part of his conscious experience, may be the very thing for which mathematics compensates.  Science (particularly the mathematical side of science) at the very least , suggests that the brain is terribly underestimated when it is characterized as “a pragmatic and opportunist organ.”   The more interesting question would be how is mathematics and science contributing to the brain’s construction of its world.
David Deutsch does a remarkable job of integrating specialized disciplines. In The Fabric of Reality there are four fundamental aspects of reality represented by quantum physics, the theory of evolution, the theory of computation and the theory of knowledge.  This new effort follows the path he seems to want to clear.




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