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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.

February 7, 2023

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.
by Colin Stuart
FQXi Awardees: Kobi Kremnitzer
March 29, 2022
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Credit: agsandrew, Shutterstock
Kobi Kremnitzer, from the University of Oxford, is a pure mathematician by training, usually interested in how to combine methods from algebra and geometry and apply them to mathematical physics. Yet as someone who meditates, he’s always been interested in ideas around consciousness.

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.

When and why did you start meditating?

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.

Tell us more about your interest in consciousness—it’s not a field of study you’d immediately associate with a pure mathematician.

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.

And you’ve been specifically working on how this might apply to the measurement problem in quantum 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.
- Kobi Kremnitzer
Yes. A quantum system can be described by a wavefunction that encodes all possible states the system can be in. When you measure a quantum system the wavefunction collapses. At least that’s the standard approach to quantum physics, but what causes it to collapse?

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.

Is this theory testable?

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
What can this model tell us about the obvious divide between the multi-state quantum world, in which particles can be in two or more places simultaneously, and our classical, everyday experience of objects always in one place?

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.

What counts as a conscious observer in this case?

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.

And you think that last point could have potential knock-on effects for quantum computers?

If this type of model
is right, then large
quantum computers
will never work.
- Kobi Kremnitzer
If this type of model is right, then large quantum computers will never work. A big enough quantum computer would probably have enough integrated information to just collapse itself. You could still do basic quantum calculations, though, like factorizing large numbers. A quantum computer made of 200 qubits would be enough to do that, but would still have low enough levels of integrated information not to collapse itself.

In the case where a quantum computer collapses itself—because it has a large degree of integrated information—would it have been ’conscious’ before collapse? And what about after collapse?

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.

Tell us more about the new center you’re planning, to bring researchers together to better understand this field.

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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Recent Comments

I play guitar and piano, let s imagine that this consciousness is a specific partition of music and that to be conscious so the music must be precise and must have a number specific of instruments , piano, guitar, violons..... and that these instruments are the systems that I explained generally speaking, so actually we play with one or 2 or 3 or 4 maximum instruments and furthermore without a chief orchestra. So lets imagine that we have considered all the sciences and systems, and so that we...

It is this which seems important, this generality of systems more our unknowns more the philosophy. The majority of models, they just focus on one topic and after try with details to create a model explaining this consciousness, that seems odd frankly because all must be considered. The mathematics alone or the thermodynamics alone , or the neurosciences alone, or the computings, or the quantum mechanics alone, or the cognistive sciences alone or even in mixing one or 2 or 3 topics , it is not...

It seems essential to not focus on one topic , I have remarked that the majority of models are not general, they consider mainly the neuro sciences with a little bit of physics, or after it is the computing with the informations, or thje maths with a little bit of philosophy, or the cognistice sciences and some philosophy, but they never try to unify all the sciences with the computing more a deeper philosophy and more deeper ideas for the quantum computing and more deeper fields , in fact at my...

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