To pretend or to realize: The mathematical theories of our perception of the world

Art by Julia Jabur

By Edgard Pimentel

“Little Edgard, put your hand on your conscience!” my mother would scold after some mischief. When feeling particularly bold, I’d fire back, “Show me where my conscience is!” It was a childish provocation, but surprisingly, scientists from various fields ask similar questions. Surprisingly, consciousness is also mathematics!

Theories of consciousness emerge from several questions. For instance, why is it easier to associate gray with black than yellow? Or why do we expect the sound of thunder to follow a flash of lightning flash?

Notice how questions about consciousness include how the brain links different sensory inputs, like the expectation of hearing thunder after seeing lightning. Others delve deeper, questioning how consciousness relates to brain activity levels. For instance, during REM (rapid eye movement) sleep, there is intense brain activity, yet we lack conscious awareness. More fundamentally, knowing what brain structure is required to develop consciousness is important. Does a newborn baby have it? Could a computer achieve it? Scientists explore these two classes of questions using rigorous mathematical models.

The theory behind the first class of questions (lightning and thunder) focuses on the brain’s structure. Consciousness is seen as a snapshot of brain activity at a given moment. Understanding this snapshot means recognizing the complex relationships between different brain regions. For example, let’s compare the brain’s state when looking at a photograph of Caetano Veloso to hearing people say “Armenia” or “London.”

While the areas of my brain responsible for sight and hearing remain active for both scenarios, my internal information library creates vastly different associations. When I saw Caetano Veloso’s photo and heard “Armenia,” my mind jumped to the album “Muito,” which I listened to repeatedly while walking around Armenia’s capital, Yerevan, in 2018. However, “London” paired with the same photo evokes the concept of exile.

British scientist Jonathan Mason suggests that cost minimization is the key to understanding our seemingly disparate perceptions. His theory proposes that the brain seeks to interpret a set of stimuli most efficiently. It utilizes available cues, such as knowledge and experience, to minimize the information processing needed.

Consciousness is nothing more than the result of this cost-minimizing process. Here, cost isn’t measured simply but calculated as the disorganization or entropy of the system.  This concept parallels the measure introduced by Claude Shannon in the founding of information theory. Through this lens, consciousness becomes highly dependent on the brain’s store of experience, a concept that has implications for our understanding of consciousness in newborns, for example.

The theory of entropy minimization is inductive. It analyzes a concrete object, the brain, and proposes a model based on its structure.  A contrary approach is deductive.  It starts with an abstract concept of consciousness and postulates a structure in which it might occur. The human brain is then simply a potential structure. Instead of concrete observation, this approach relies on axioms and postulates, like Euclid’s parallel lines.  Conclusions are drawn through logical manipulation.  Because this theory isn’t tied to the brain, it opens up the possibility of consciousness in any system that meets the postulated criteria.

The Integrated Information Theory of Consciousness (IIT) takes a deductive approach.  Its axioms include basic assumptions about consciousness: existence (it, consciousness, exists), composition (it is composed of distinct informational parts), and exclusion (there is only one experience at a time).  Postulates deal with the mechanisms that make experience possible, such as the existence and composition of the senses (i.e., elementary mechanisms form complex ones like the human body).

IIT operates at an abstract level, independent of the traditional focus on the brain. This allows for broader conclusions, including the possibility that consciousness could exist in inactive systems such as comatose patients. The theory also suggests that minimal consciousness could arise from as few as two neurons – a transmitter and a receiver.  This raises the possibility of developing artificial consciousness.

An inherent risk of theoretical treatments is oversimplification, which can rob a phenomenon of the very beauty and complexity that first fascinated us. Fortunately, a mathematical theory that seeks to explain our understanding of the world remains safe from this pitfall.

This text was originally publicated on Serrapilheira’s Ciência Fundamental blog on Folha de S.Paulo