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FQXI ARTICLE

May 20, 2022

The Math of Consciousness: Q&A with Kobi Kremnitzer

A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

FQXi Awardees: Kobi Kremnitzer

March 29, 2022

Credit: agsandrew, Shutterstock

Kremnitzer’s career pivoted when he discovered a theory that seeks to describe the mathematical structure of consciousness. Now, with the help of an FQXi grant of over $195,000, he’s applying his mathematical training to try and decipher the twin mysteries of conscious experience and the boundary between the quantum and classical world.

I’ve been meditating to some extent for many years. My practice has become more regular in recent years because of Reginald Ray and his somatic approach to meditation. From a certain perspective meditation is a deep empirical study of the mind and of awareness and consciousness. This is one of the reasons I am interested in this practice.

It is one of the biggest open problems in science. Understanding consciousness would help us to understand who we are and what we are.

About ten years ago, I learned about integrated information theory, which describes consciousness as the result of information traveling between different parts of a system. The more interconnected the parts, the more conscious the system. It’s a wonderful, really revolutionary theory. I’m not sure if it’s the right theory or not, or if it covers all aspects of consciousness, but what amazed me as a mathematician is that there’s a precise mathematical theory, with precise definitions of what consciousness is and what experience is.

It’s not just enough to

say what something is,

but you really also

have to say what it does.

If you don’t, it’s not a

scientific theory because

you can never test it.

say what something is,

but you really also

have to say what it does.

If you don’t, it’s not a

scientific theory because

you can never test it.

- Kobi Kremnitzer

There’s an idea that somehow consciousness causes the collapse of the wavefunction, but, at least as far as I could see, it was never rigorously understood what this really could mean, partly because there was just no definition of what consciousness is. So we used the mathematics behind integrated information theory to build a model describing how consciousness could collapse the wavefunction.

I think it’s really important to emphasize that with any scientific theory, it’s not just enough to say what something is, but you really also have to say what it does. If you don’t, it’s not a scientific theory because you can never test it. This is currently a big problem with many models of consciousness.

On the one hand, integrated information theory was revolutionary in the sense that it gave a rigorous mathematical model of what consciousness is, but there’s a missing step: how does it interact with the rest of physics, biology and chemistry? We want our theory to be testable and scientifically falsifiable.

So we’re looking at how integrated information might interact with the quantum world. It may act as a guide that encourages the wavefunction to collapse. There are predictions that this interaction with the wavefunction can emit extra heat not predicted by current physics. There are physicists trying to do very refined measurements of quantum systems to see if this theory is correct.

Kobi Kremnitzer

University of Oxford

It’s all about the rate of collapse. In very small systems—maybe containing a few atoms—the rate of collapse is very slow. The bigger the system gets, the more probable collapse becomes. Traditionally, it’s the increasing mass of the system that’s said to trigger collapse. However, we propose replacing the mass of the system by a measure of integrated information. Levels of consciousness are exactly given by this measure too, so the idea is that the more conscious a system is, the faster the rate of collapse it sees.

Not just humans. Bringing in any observer with high levels of integrated information will do it. Perhaps a cat, a computer or even a thermostat. You can play around with the parameters of the theory and how sensitive it is to the levels of integrated information. Even the the system itself may play a role.

If this type of model

is right, then large

quantum computers

will never work.

is right, then large

quantum computers

will never work.

- Kobi Kremnitzer

It will have high enough levels of quantum integrated information or consciousness so the collapse will happen very quickly. So the system will be conscious all the time and there will essentially be no quantum effects.

A lot of mathematicians are starting to think about how to model consciousness. Clearly, though, this is a very interdisciplinary area. We already have a network within Oxford University that brings together mathematicians, physicists, neuroscientists, experimental psychologists, and philosophers to think about problems and apply for grants together to advance the study of consciousness. There is also a new international association and we will soon have our third international conference Models of Consciousness 2022 in Stanford, California.

We’re now looking for funding to turn this into a formal center with post-docs and professorships associated with it. There are a lot of young, really smart people working on this and we want to have many of them in one place leading this new and exciting area in mathematics.

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THOMAS HOWARD RAY wrote on May 12, 2022

Kobi,

You write as if information accumulates like physical grains of sand that form an Avalanche model (Per Bak). I beg to be corrected on this.

Can you reconcile your model with a model of quantum mechanics that doesn't collapse (Everett, e.g.)?

Kobi,

You write as if information accumulates like physical grains of sand that form an Avalanche model (Per Bak). I beg to be corrected on this.

Can you reconcile your model with a model of quantum mechanics that doesn't collapse (Everett, e.g.)?

THOMAS HOWARD RAY wrote on May 12, 2022

Nicholas,

Indeed. This sums up pretty much what I had in mind when I showed that the 3-dimension limit is equal to the 4-dimension horizon. research paper

I don't agree with the non-separability of 3 dimensions, though. Obviously, 3 dimensions decomposes into (2,1).

Your idea can be easily corrected, though -- 3 dimensions decompose into 2, which gives us the complex plane, the structure for 2-dimension analysis, and including the real line (1 dimension). Is 1 dimension...

Nicholas,

Indeed. This sums up pretty much what I had in mind when I showed that the 3-dimension limit is equal to the 4-dimension horizon. research paper

I don't agree with the non-separability of 3 dimensions, though. Obviously, 3 dimensions decomposes into (2,1).

Your idea can be easily corrected, though -- 3 dimensions decompose into 2, which gives us the complex plane, the structure for 2-dimension analysis, and including the real line (1 dimension). Is 1 dimension...

STEVE DUFOURNY wrote on May 7, 2022

develop because we see nothing there , you wrote this in 2007 but we see no development of the ideas, try to be concrete , we are not on facebook, you tell nothing, you develop nothing, nor in physics, nor in maths, nor in philosophy, we don t know what you tell, we don t know if you have a general model, or a general theory, you tell just some words without real menaing , sorry but it is true

develop because we see nothing there , you wrote this in 2007 but we see no development of the ideas, try to be concrete , we are not on facebook, you tell nothing, you develop nothing, nor in physics, nor in maths, nor in philosophy, we don t know what you tell, we don t know if you have a general model, or a general theory, you tell just some words without real menaing , sorry but it is true

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