Consciousness is also mathematics – 01/25/2024 – Fundamental Science

I remember that after some mischief my mother would always say: “Edgardzinho, please put your hand on your conscience!”. When my sense of humor (or level of courage) allowed it, I would retort: ​​”But where is the conscience?” The question is provocative, of course. But the surprising thing is that similar questions are formulated by different scientists, in different disciplines. The surprise? Consciousness is also mathematics!

A theory of consciousness is motivated by several questions. For example, why is it easier to associate the color gray with the color black than with the color yellow? Or why is it that when we see lightning we expect to hear thunder?

Note that there are questions about consciousness that concern the way the brain establishes relationships (lightning and thunder) through different senses (sight and hearing). And there are other very interesting questions as well. One of them relates consciousness to the volume of brain activity. During the REM phase of sleep (REM is the acronym for rapid eye movement), for example, we are not conscious, although intense brain activity occurs. Another issue involves the structure necessary for an organism to develop consciousness. Does a newborn have consciousness? Still along these lines, is it possible for a computer to develop consciousness? These two classes of questions have been examined in the literature using rigorous mathematical models.

The theory associated with the first class of questions (lightning and thunder) focuses on the structure of the brain. Here, consciousness is a snapshot of brain activity at a given moment. And this photograph needs to be interpreted in light of relationships between distinct regions of the brain. Let’s compare two distinct states of the brain. For example, when I see a photograph of Caetano Veloso and hear them say “Armênia” or “London”.

In both cases, my brain has similar states, as the areas responsible for vision and hearing are active. However, my library of information generates different relationships between the two sets of stimuli and, from the point of view of consciousness, I obtain different results. When I see the photograph and hear the word Armenia I think of the album “Very”, which I listened to countless times while walking around the capital, Yerevan, in 2018. When I hear the word London when seeing the same photo, I think of the concept of exile.

An explanation for such disparate consciousnesses is proposed by British scientist Jonathan Mason. The brain chooses how to relate the two information – visual and auditory – weighing the minimization of a cost! In fact, given a set of stimuli, the brain minimizes the amount of information necessary to interpret it in light of the available references (erudition, experiences or something similar).

Consciousness is nothing more than the result of this process. And this cost is not just any measure, but rather a measure of the disorganization of the system. In other words, a form of entropy. Similar to the measure introduced by Claude Shannon when founding information theory. In the case that interests us, we see that consciousness depends on the brain’s store of experiences – which says something about consciousness in newborns, for example.

The theory based on entropy minimization is inductive. That is, it starts with a concrete object (the brain and its structures), and proposes a model. Another way of looking at the problem is deductive: we think in the abstract and imagine that consciousness is linked to some structure. The human brain would be just one of the structures in which it occurs. And we start with axioms and postulates – as did Euclid, who gave us the axiom of parallel lines. Using logic, we manipulate the axioms and postulates and draw conclusions. And as the theory operates without presupposing the brain as the place of consciousness, consciousness can happen in any system.

The integrated information theory of consciousness (IIT) performs this deductive exercise. Among the axioms on which IIT is based are existence (consciousness exists), composition (experience is made up of different information) and exclusion (at each instant of time, only one experience occurs). The postulates are about the mechanisms that make experience viable, such as our senses; Among them is the existence of mechanisms and their composition: elementary mechanisms combine into more complex ones (such as the human body).

Remember that IIT does not assume the brain and operates on a more abstract level. As a consequence, she presents more general conclusions. One is that inactive systems (e.g. a patient in a coma) can have consciousness. Another interesting consequence is that two neurons are enough to produce consciousness. Or rather, one signal transmitter and one receiver are enough to produce consciousness. A possible corollary is the viability of artificial consciousness.

A serious risk in the theoretical treatment of anything is simplification, which, when being exaggeratedly reductive, can remove the beauty of the phenomenon that enchanted us in the first place. In the case of a mathematical theory that tries to explain how we perceive the world, we are aware that this risk does not arise.

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Edgard Pimentel is a professor at the Department of Mathematics at the University of Coimbra and a researcher at CMUC.

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