(2017-06-01) New Math Untangles The Mysterious Nature Of Causality

New Math Untangles the Mysterious Nature of Causality. IN HIS 1890 opus, The Principles of Psychology, William James invoked Romeo and Juliet... Erik Hoel, a 29-year-old theoretical neuroscientist and writer, quoted the passage in a recent essay in which he laid out his new mathematical explanation of how consciousness and agency arise.

The existence of agents—beings with intentions and goal-oriented behavior—has long seemed profoundly at odds with the reductionist assumption that all behavior arises from mechanistic interactions between particles.

Hoel’s theory, called “causal emergence,” roundly rejects this reductionist assumption.

Using the mathematical language of information theory, Hoel and his collaborators claim to show that new causes — things that produce effects — can emerge at macroscopic scales

Macroscopic states, such as desires or beliefs, “are not just shorthand for the real causes,” explained Simon DeDeo, an information theorist and cognitive scientist at Carnegie Mellon University and the Santa Fe Institute who is not involved in the work, “but it’s actually a description of the real causes, and a more fine-grained description would actually miss those causes.”

Hoel and collaborators have been developing the mathematics behind their idea since 2013. In a May paper in the journal Entropy, Hoel placed causal emergence on a firmer theoretical footing by showing that macro scales gain causal power in exactly the same way, mathematically, that error-correcting codes increase the amount of information that can be sent over information channels.

The work on causal emergence is not yet widely known among physicists, who for centuries have taken a reductionist view of nature and largely avoided further philosophical thinking on the matter. But at the interfaces between physics, biology, information theory and philosophy, where puzzles crop up, the new ideas have generated excitement.

Their ultimate usefulness in explaining the world and its mysteries — including consciousness, other kinds of emergence, and the relationships between the micro and macro levels of reality — will come down to whether Hoel has nailed the notoriously tricky notion of causation: Namely, what’s a cause?

“Famously, Aristotle had a half-dozen notions of causes,” DeDeo said. “We as scientists have rejected all of them except things being in literal contact, touching and pushing.”

The true causes, to a physicist, are the fundamental forces acting between particles

In this view, causes and effects become hard to predict from first principles only when there are too many variables to track.

But it’s almost always easier to discuss causes and effects in terms of macroscopic entities

For graduate school, he went to Madison, Wisconsin, to work with Giulio Tononi — the only person at the time, in Hoel’s view, who had a truly scientific theory of consciousness. Tononi conceives of consciousness as information: bits that are encoded not in the states of individual neurons, but in the complex networking of neurons

Integrated information theory has gained prominence in the last few years

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

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

At a certain macroscopic scale, effective information peaks

Coarse-grain further, and you start to lose important details about the system’s causal structure.

Albantakis guesses that this might happen at the scale of neuronal microcolumns, which consist of around 100 neurons.

In addition to conscious agents, Hoel says this might pick out the natural scales of rocks, tsunamis, planets and all other objects that we normally notice in the world.

Brain-imaging experiments are being planned in Madison and New York, where Hoel has joined the lab of the Columbia neuroscientist Rafael Yuste.

Hoel’s ideas do not impress Scott Aaronson, a theoretical computer scientist at the University of Texas, Austin. He says causal emergence isn’t radical in its basic premise. After reading Hoel’s recent essay for the Foundational Questions Institute, “Agent Above, Atom Below” (the one that featured Romeo and Juliet), Aaronson said, “It was hard for me to find anything in the essay that the world’s most orthodox reductionist would disagree with

Hoel says his arguments go further than Aaronson acknowledges in showing that “higher scales have provably more information and causal influence than their underlying ones. It’s the ‘provably’ part that’s hard and is directly opposite to most reductionist thinking.”

Hoel and his collaborators aim to show that higher-level causes — as well as agents and other macroscopic things — ontologically exist. The distinction relates to one that the philosopher David Chalmers makes about consciousness: There’s the “easy problem” of how neural circuitry gives rise to complex behaviors, and the “hard problem,” which asks, essentially, what distinguishes conscious beings from lifeless automatons.

The criticism that hits Hoel and Albantakis the hardest is one physicists sometimes make upon hearing the idea: They assert that noise, the driving force behind causal emergence, doesn’t really exist; noise is just what physicists call all the stuff that their models leave out.