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Integrated information theory is an attempt to quantify consciousness and attach numbers to it.
In essence, yes. IIT proposes a quantity called "phi" that measures information and integration. According to the theory, it is identical to the amount consciousness associated with a system.
This allows you to quickly find a post-hoc explanation for certain facts we already know about consciousness. The cerebellum, the tiny brain at the back of our heads, doesn't seem to have much to say with consciousness. This is just an empirical fact. The cerebellum does not seem to be involved in any way. It still contains three-quarters all of the neurons in the brain. Why isn't the cerebellum involved in this? There are many possible reasons. However, the IIT explanation is convincing. The wiring of the cerebellum is not suitable for co-expressed information or integration. Instead, the cortex is and cortex is closely related to consciousness.
IIT's claims of integrated information being consciousness, or that the two are connected, is what I find less promising. This stance makes it nearly impossible to measure any nontrivial systems. This implies that consciousness can be found in all systems.
Karl Friston's free-energy principle is also fascinating to you.
The simplest way to express the free-energy principle is, I believe, this: Let's consider living systems as a cell or organism. Living systems are independent from their environment. For example, I don't just melt into mush on my floor. It's an active process. I put energy in and maintain my boundaries with the outside world.
This means that out of all possible combinations of my components, there is only a small number of states I can remain in. For example, my body temperature remains within a narrow range of temperatures which is why I am still alive. How can I achieve this? How can an organism achieve this? It must reduce the uncertainty in the states it is located. I must actively resist the second law thermodynamics so that I don't dissipate to all types of states.
Although the free-energy principle does not directly address consciousness, it is a theory that helps us understand how and why our brains function. It also links back to the notion of consciousness and life being closely related. The idea is that the brain uses predictive models to regulate body temperature and more generally keep the body alive. It's very useful to be capable of predicting how something will behave. My book argues that our conscious experiences are a result of these predictive models, which stem from the fundamental biological imperative to live.
You discuss in your book how things become less mysterious when we understand the science behind them. And you wonder if the mystery surrounding consciousness might disappear more in the same way as the mystery around heat.
Although there may be another connection between consciousness, life and consciousness, it is not literal. Historical records show that there was a commonality between the mysteries of heat and life, but in different ways.
Let's start with heat. The philosopher and historian of science Hasok Chang wrote Inventing Temperature many years ago. Before then, I didn't realize how complex and intricate the story of temperature and heat was. In the 17th century, attempts to understand heat relied on methods to measure heat and coolness in order to create a temperature scale and other things such as thermometers. How do you make a thermometer that is reliable and stable until you have a reference point, a temperature level? How do you make a temperature scale before you have a reliable thermometer. This was a chicken-and egg problem, which was very problematic at the time. It was eventually managed. People slowly but surely built reliable thermometers.
The story of heat was made possible by the scientific measurement. People had previously wondered if heat was something that flows between objects. It is not. In this instance, heat is the molecular energy of atoms and molecules within a substance. This is heat.
The reality of life is quite different. It doesn't matter how alive something feels; nobody can measure it. People still wondered what the essence or meaning of life was. It isn't just one thing that unlocks life. Life is a collection of related properties, which are used in different ways by different organisms. There is homeostasis and reproduction. There is metabolism. There are gray areas in life. These are things we consider to be alive. The suspicion that there was still a lan vital, some kind of vitalistic resonance, to explain this, vanished when we accounted for all its varied properties. It was not solved.