Using AI to Quantify the Unconscious: A Mathematical and Neuroscientific Reconciliation of Freud's Incomplete Legacy

by Paulo Camara

I decided to use Artificial Intelligence to explore whether it was possible to resolve something outside the technological or mathematical field, just as I did with the example of prime numbers.

To address one of Sigmund Freud's incomplete ideas using the most cutting-edge tools available today, let's focus on his early 20th-century concept of the “dynamic unconscious.” Freud proposed that the unconscious mind was a psychological force influencing our behavior, thoughts, and emotions, but he lacked the scientific means to measure or quantify this influence directly. He relied on clinical observations and subjective interpretations to support his theories.

With advances in neuroscience and artificial intelligence, we can now attempt to measure the unconscious in a way Freud could never have imagined. One of the most promising approaches for resolving Freud's incomplete idea is the use of functional neuroimaging techniques like fMRI (functional Magnetic Resonance Imaging) and MEG (Magnetoencephalography), combined with mathematical modeling of neural networks.

The Innovative Proposal: "Quantifying the Unconscious"

Freud believed that the unconscious stored repressed memories and desires that indirectly shaped our behavior. With today’s tools, we can measure patterns of brain activation when people are exposed to stimuli they consciously ignore, but that unconsciously influence their behavior. Studies using fMRI have shown that brain regions like the amygdala and prefrontal cortex can be activated by subliminal stimuli (images or sounds presented below the threshold of conscious perception), suggesting measurable unconscious activity.

The concept of the dynamic unconscious could be represented by mathematical models inspired by artificial neural networks. Just as artificial neural networks “learn” patterns from large data sets, the human unconscious can be modeled as a network that processes information unconsciously, linking patterns and influencing decisions and behaviors without passing through conscious awareness. This approach could finally provide a scientific and mathematical framework for Freud’s notion.

Mathematical Example: Modeling the Unconscious

One possible way to model the unconscious would be through a deep convolutional neural network that mimics layers of unconscious processing. We can use deep learning algorithms to detect brain activation patterns corresponding to repressed memories or desires. These algorithms can be trained to identify when an external stimulus activates unconscious processes by comparing observed brain responses with behavioral patterns, forming a robust data set for the unconscious mind.

If we represent the unconscious as a mathematical function, we could approximate it with a nonlinear neural network, as follows:

Contextualizing with Freud: The Mathematics of Repression

Freud believed that repression (the process of burying memories and desires) was one of the ego's primary defense mechanisms. Repression could be mathematically modeled as the diminishing of synaptic weight of a memory in a neural network, preventing the memory from being easily accessed. However, repressed memories don’t disappear; they remain in the network, ready to influence behavior indirectly. We can model this repression as a reduction in the coefficients , lowering the accessibility of the repressed content but not eliminating its influence.

Practical Applications and Timeframe

In practical terms, this approach has already begun to be explored in fields like computational psychology and applied neuroscience. Recent studies in 2023 and 2024, which combined fMRI with machine learning, have already succeeded in predicting, with good accuracy, what decisions people would make based on stimuli they consciously ignored.

Freud, working in the early 20th century (1890-1939), didn’t have access to these mathematical and technological tools. He was limited to clinical methods and dream analysis. However, with today’s tools, we can scientifically validate his theory of the dynamic unconscious, demonstrating that he was correct in suggesting that unconscious processes shape behavior — and we can now quantify those processes.

This resolution represents a convergence between Freudian psychoanalysis and modern neuroscience, something unimaginable in Freud’s time, but now possible thanks to the mathematical and technological advancements of the 21st century. Now I let you explore this!!!