“I think I see the point,” said J. “The information generated by the whole above and beyond its parts— call it integrated information— is what distinguishes Ishmael from a camera. Does this seem right, Alturi?”
“What would be right?” exclaimed Alturi, who was busy grounding the tobacco out with his heel. “Is it right that a distribution of system states, if it cannot be factorized into a product of distributions of its parts, is not reducible? Of course, but SO what? What’s special about this? There are all kind of things that cannot be factorized, that cannot split without a loss, but why would any of this matter for consciousness? Besides, there are many ways to divide a system into parts, of factorizing distributions, and you will get a different answer depending how you cut it into pieces.”
“True,” said J. “If integrated information has something to do with consciousness, it should not change depending how you divide a system into parts. Isn’t it so, Galileo?”
The crucial cut, said Galileo, is the minimum cut, the cruelest cut of all— the cut through a system’s weakest link, the cut that divides it into its strongest parts— those that generate as much information as possible by themselves, leaving as little as possible for the whole.
“Excellent,” said J. “Integrated information is the information generated by a system above its parts, where the parts are those that, taken independently, generate the most information. Now that we have a definition, we need a symbol for it.”
“If you need a symbol, it should be Φ,” said Alturi. “That is the symbol of the golden ratio— the right way of dividing something into parts. And the minimum cut, which reveals how much information is integrated information, is the right way of dividing a system into parts, is it not? You should call it Φ.”
That would be interesting, said Galileo. After all, the golden ratio was studied by a fellow Pisan, the good old Φibonacci.
“It is better than that,” said J. “Φ is like Φenomenology, like experience, which is what consciousness is.”
Better than that, said Galileo. Φ has an I, for information, and an O, a circle, for integration. Let’s call it Φ, then.
“Splendid,” said Alturi. “Now that you have your quantity and your symbol, let’s see what follows. Clearly, every time some elements interact, you’ll have some integrated information: a whole that does not reduce to its parts. Then, if integrated information has something to do with consciousness, as you seem to think, what follows is quite simple: it follows that consciousness is like an onion.
“Take me and the neurons in my brain. Somewhere inside my brain there is me, of course, but I am not alone. If you peel me away, neuron by neuron, you’ll find other me, millions of me, each lacking some part, but all conscious to some extent. I am just the most conscious of my many me, but those diminished selves would be right in claiming their own rights, except that I don’t hear them, but they are along for the ride. “
Then take my body. No doubt my body, too, is made of interacting parts, a whole that cannot be reduced to its parts— either physically or informationally— in fact the brain itself is just one of those parts. So the body, too, is yet another consciousness, an even larger onion than I thought I was. Its Φ may be much less than mine— its minimum cut quite weak, say across my neck— but it, too, is carrying on its own limited existence. A multiplication of selves, a proliferation, of which I know nothing at all, and they know nothing of me.