Tononi conceives of consciousness as information: bits that are encoded not in the states of individual neurons, but in the complex networking of neurons, which link together in the brain into larger and larger ensembles. Tononi argues that this special “integrated information” corresponds to the unified, integrated state that we experience as subjective awareness. Integrated information theory has gained prominence in the last few years, even as debates have ensued about whether it is an accurate and sufficient proxy for consciousness. But when Hoel first got to Madison in 2010, only the two of them were working on it there.

Tononi tasked Hoel with exploring the general mathematical relationship between scales and information. The scientists later focused on how the amount of integrated information in a neural network changes as you move up the hierarchy of spatiotemporal scales, looking at links between larger and larger groups of neurons. They hoped to figure out which ensemble size might be associated with maximum integrated information — and thus, possibly, with conscious thoughts and decisions. Hoel taught himself information theory and plunged into the philosophical debates around consciousness, reductionism and causation. John Maniaci/UW Health/Quanta Magazine

Tononi tasked Hoel with exploring the general mathematical relationship between scales and information. The scientists later focused on how the amount of integrated information in a neural network changes as you move up the hierarchy of spatiotemporal scales, looking at links between larger and larger groups of neurons. They hoped to figure out which ensemble size might be associated with maximum integrated information—and thus, possibly, with conscious thoughts and decisions. Hoel taught himself information theory and plunged into the philosophical debates around consciousness, reductionism and causation.

Hoel soon saw that understanding how consciousness emerges at macro scales would require a way of quantifying the causal power of brain states. He realized, he said, that “the best measure of causation is in bits.” He also read the works of the computer scientist and philosopher Judea Pearl, who developed a logical language for studying causal relationships in the 1990s called causal calculus. With Albantakis and Tononi, Hoel formalized a measure of causal power called “effective information,” which indicates how effectively a particular state influences the future state of a system. (Effective information can be used to help calculate integrated information, but it is simpler and more general and, as a measure of causal power, does not rely on Tononi’s other ideas about consciousness.)

The researchers showed that in simple models of neural networks, the amount of effective information increases as you coarse-grain over the neurons in the network—that is, treat groups of them as single units. The possible states of these interlinked units form a causal structure, where transitions between states can be mathematically modeled using so-called Markov chains. At a certain macroscopic scale, effective information peaks: This is the scale at which states of the system have the most causal power, predicting future states in the most reliable, effective manner. Coarse-grain further, and you start to lose important details about the system’s causal structure. Tononi and colleagues hypothesize that the scale of peak causation should correspond, in the brain, to the scale of conscious decisions; based on brain imaging studies, Albantakis guesses that this might happen at the scale of neuronal microcolumns, which consist of around 100 neurons.

"Causation is what you need to give structure to the universe." Larissa Albantakis

Causal emergence is possible, Hoel explained, because of the randomness and redundancy that plagues the base scale of neurons. As a simple example, he said to imagine a network consisting of two groups of 10 neurons each. Each neuron in group A is linked to several neurons in group B, and when a neuron in group A fires, it usually causes one of the B neurons to fire as well. Exactly which linked neuron fires is unpredictable. If, say, the state of group A is {1,0,0,1,1,1,0,1,1,0}, where 1s and 0s represent neurons that do and don’t fire, respectively, the resulting state of group B can have myriad possible combinations of 1s and 0s. On average, six neurons in group B will fire, but which six is nearly random; the micro state is hopelessly indeterministic. Now, imagine that we coarse-grain over the system, so that this time, we group all the A neurons together and simply count the total number that fire. The state of group A is {6}. This state is highly likely to lead to the state of group B also being {6}. The macro state is more reliable and effective; calculations show it has more effective information.

A real-world example cements the point. “Our life is very noisy,” Hoel said. “If you just give me your atomic state, it may be totally impossible to guess where your future [atomic] state will be in 12 hours. Try running that forward; there’s going to be so much noise, you’d have no idea. Now give a psychological description, or a physiological one: Where are you going to be in 12 hours?” he said (it was mid-day). “You’re going to be asleep—easy. So these higher-level relationships are the things that seem reliable. That would be a super simple example of causal emergence.”