Into the Woods

...Or, the Integro-Differential theory of consciousness. Perhaps you would suspect from this that this theory has something to do with the calculus of Leibniz and Newton. So far as I can tell, that's not it at all. Instead, Koch and collaborators have constructed - claim to have constructed - a theory of consciousness that depends on the degree of differentiation and integration of a complex system. A sample:

Integrated information theory introduces a precise measure capturing the extent of consciousness called Φ, or phi (and pronounced “fi”). Expressed in bits, Φ quantifies the reduction of uncertainty that occurs in a system, above and beyond the information generated independently by its parts, when that system enters a particular state. (Remember, information is the reduction of uncertainty.) The parts— the modules— of the system account for as much nonintegrated, independent information as possible. Thus, if all of the individual chunks of the brain taken in isolation already account for much of the information, little further integration has occurred. Φ measures how much the network, in its current state, is synergistic, the extent to which the system is more than the sum of its parts. Thus, Φ can also be considered to be a measure of the holism of the network.

Koch, Christof. Consciousness: Confessions of a Romantic Reductionist (MIT Press) (p. 127). The MIT Press. Kindle Edition.

I have no idea what the heck that means. My first reaction was that Koch had taken all those Paul Allen $ and invested them in magic mushrooms. Even if I could figure out what the reduction of uncertainty of the system is when I think about Britney Spears or Homer's "wine dark sea," how does that number connect with consciousness?

Koch adds:

Integrated information theory makes a number of predictions. One of the more counterintuitive, and therefore powerful, ones is that integrated information arises from causal interactions within the system. When those interactions can’t take place anymore, even though the actual state of the system remains unchanged, Φ shrinks.

Koch, Christof. Consciousness: Confessions of a Romantic Reductionist (MIT Press) (p. 127). The MIT Press. Kindle Edition.


The state of any physical system can be mapped onto a shape in this fantastically multidimensional qualia space. Its surfaces are facets. The technical term for this shape is polytope, but I prefer the more poetic crystal. A nervous network in any one particular state has an associated shape in qualia space; it is made out of informational relationships. If the network transitions to a different state, the crystal changes, reflecting the informational relationships among the parts of the network. Each conscious experience is fully and completely described by its associated crystal, and each state feels different because each crystal is utterly unique. The crystal for seeing red is in some unique geometric way different from the one associated with seeing green. And the topology of color experiences will be different from that for seeing movement or smelling fish.

Koch, Christof. Consciousness: Confessions of a Romantic Reductionist (MIT Press) (p. 130). The MIT Press. Kindle Edition.

I hope you found that at least as illuminating as I did.


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