Physicists like to think they can explain everything, and that, of course, includes human consciousness. And so in the last few decades they’ve set out to demystify the brain by throwing math at the problem. Last year, I attended a workshop on the mathematics of consciousness in Oxford. Back then, when we still met other people in real life, remember that?
I find it to be a really interesting development that physicists take on consciousness, and so, today I want to talk a little about ideas for how consciousness can be described mathematically, how that’s going so far, and what we can hope to learn from it in the future.
The currently most popular mathematical approach to consciousness is integrated information theory, IIT for short. It was put forward by a neurologist, Giulio Tononi, in two thousand and four.
In IIT, each system is assigned a number, that’s big Phi, which is the “integrated information” and supposedly a measure of consciousness. The better a system is at distributing information while it’s processing the information, the larger Phi. A system that’s fragmented and has many parts that calculate in isolation may process lots of information, but this information is not “integrated”, so Phi is small.
For example, a digital camera has millions of light receptors. It processes large amounts of information. But the parts of the system don’t work much together, so Phi is small. The human brain on the other hand is very well connected and neural impulses constantly travel from one part to another. So Phi is large. At least that’s the idea. But IIT has its problems.
One problem with IIT is that computing Phi is ridiculously time consuming. The calculation requires that you divide up the system which you are evaluating in any possible way and then calculate the connections between the parts. This takes up an enormous amount of computing power. Estimates show that even for the brain of a worm, with only three hundred synapses, calculating Phi would take several billion years. This is why measurements of Phi that have actually been done in the human brain have used incredibly simplified definitions of integrated information.
Do these simplified definitions at least correlate with consciousness? Well, some studies have claimed they do. Then again others have claimed they don’t. The magazine New Scientist for example interviewed Daniel Bor from the University of Cambridge and reports:
“Phi should decrease when you go to sleep or are sedated via a general anesthetic, for instance, but work in Bor’s lab has shown that it doesn’t. “It either goes up or stays the same,” he says.”I contacted Bor and his group, but they wouldn’t come forward with evidence to back up this claim. I do not actually doubt it’s correct, but I do find it somewhat peculiar they’d make such a statements to a journalist and then not provide evidence for it.
Yet another problem for IIT is, as the computer scientist Scott Aaronson pointed out, that one can think of rather trivial systems, that solve some mathematical problem, which distribute information during the calculation in such a way that Phi becomes very large. This demonstrates that Phi in general says nothing about consciousness, and in my opinion this just kills the idea.
Nevertheless, integrated information theory was much discussed at the Oxford workshop. Another topic that received a lot of attention is the idea by Roger Penrose and Stuart Hamaroff that consciousness arises from quantum effects in the human brain, not in synapses, but in microtubules. What the heck are microtubules? Microtubules are tiny tubes made of proteins that are present in most cells, including neurons. According to Penrose and Hameroff, in the brain these microtubules can enter coherent quantum states, which collapse every once in a while, and consciousness is created in that collapse.
Most physicists, me included, are not terribly excited about this idea because it’s generally hard to create coherent quantum states of fairly large molecules, and it doesn’t help if you put the molecules into a warm and wiggly environment like the human brain. For the Penrose and Hamaroff conjecture to work, the quantum states would have to survive at least a microsecond or so. But the physicist Max Tegmark has estimated that they would last more like a femtosecond, that’s only ten to the minus fifteen seconds.
Penrose and Hameroff are not the only ones who pursue the idea that quantum mechanics has something to do with consciousness. The climate physicist Tim Palmer also thinks there is something to it, though he is more concerned with the origins of creativity specifically than with consciousness in general.
According to Palmer, quantum fluctuations in the human brain create noise, and that noise is essential for human creativity, because it can help us when a deterministic, analytical approach gets stuck. He believes the sensitivity to quantum fluctuations developed in the human brain because that’s the most energy-efficient way of solving problems, but it only becomes possible once you have small and thin neurons, of the types you find in the human brain. Therefore, palmer has argued that low-energy transistors which operate probabilistically rather than deterministically, might help us develop artificial intelligent that’s actually intelligent.
Another talk that I thought was interesting at the Oxford workshop was that by Ramon Erra. One of the leading hypothesis for how cognitive processing works is that it uses the synchronization of neural activity in different regions of the brain to integrate information. But Erra points out that during an epileptic seizure, different parts of the brain are highly synchronized.
In this figure, for example, you see the correlations between the measured activity of hundred fifty or so brain sites. Red is correlated, blue is uncorrelated. On the left is the brain during a normal conscious phase, on the right is a seizure. So, clearly too much synchronization is not a good thing. Erra has therefore proposed that a measure of consciousness could be the entropy in the correlation matrix of the synchronization. Which is low both for highly uncorrelated and highly correlated states, but large in the middle, where you expect consciousness.
However, I worry that this theory has the same problem as integrated information theory, which is that there may be very simple systems that you do not expect to be conscious but that nevertheless score highly on this simple measure of synchronization.
One final talk that I would like to mention is that by Jonathan Mason. He asks us to imagine a stack of compact disks, and a disk player that doesn’t know which order to read out the bits on a compact disk. For the first disk, you then can always find a readout order that will result in a particular bit sequence, that could correspond, for example, to your favorite song.
But if you then use that same readout order for the next disk, you most likely just get noise, which means there is very little information in the signal. So if you have no idea how to read out information from the disks, what would you do? You’d look for a readout process that maximizes the information, or minimizes the entropy, for the readout result for all of the disks. Mason argues that the brain uses a similar principle of entropy minimization to make sense of information.
Personally, I think all of these approaches are way too simple to be correct. In the best case, they’re first steps on a long way. But as they say, every journey starts with a first step, and I certainly hope that in the next decades we will learn more about just what it takes to create consciousness. This might not only allow us to create artificial consciousness and help us tell when patients who can't communicate are conscious, it might also help us allow to make sense of the unconscious part of our thoughts so that we can become more conscious of them.
You can find recordings of all the talks at the workshop, right here on YouTube, please check the info below the video for references.
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