Math May Fill In Where Language Falls Short

Sometimes words aren't enough to describe our experiences, but mathematical advancement could help us fill in the gaps.

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For centuries, we’ve dissected, reduced, and labeled everything we can about our shared external world and reality. Now, we’ve reached a new era of shifting our focus inward to our internal experiences. We’re also beginning to combine subjects to learn how the pieces work together.

Today’s topic is a prime example because we’re about to venture to a place where philosophy and mathematics, two seemingly opposite branches of knowledge, come together to help explain one of humanity’s greatest struggles — describing our internal experiences to others. But also that such ineffability may not be a flaw but an evolutionary feature of consciousness.

The Ineffability of Language

Words are powerful, yet those words also fall short of fully capturing just how powerful words are. I could tell you that words can change the hearts and minds of individuals and nations. Words influence the course of history. They can heal and harm. Yet, words alone are sometimes not enough to capture the richness or depth of words' power.

Similarly, words and language are imperfect tools for communicating our internal experiences — an ancient observation shared by philosophers, poets, and spiritual practitioners. Some things — our emotions, deep thoughts, inner Truths, and more — can feel indescribable. That our internal experiences are ineffable or bigger than words can describe.

After centuries of words falling short, recent advancements in AI, animal studies, neuroscience, meditation, and psychedelics are reigniting interest in consciousness research. Now, scientists are discovering new ways of potentially evolving beyond words in describing our experiences.

A World Beyond Words

Some people, myself included, believe Mathematics is the language of Nature, but mathematician and physicist Johannes Kleiner takes it a step further in his paper, published by Consciousness and Cognition in March 2024. Kleiner hopes that what he calls the “structural turn in consciousness science” can show that math may succeed where words fall short. He explained to Oshan Jarow of Vox:

“My view is that mathematical language is a way for us to climb out of the boundaries that evolution has set for our cognitive systems. Hopefully, [mathematical] structure is like a little hack to get around some of the private nature of consciousness.”

For instance, Jarow says we could write a poem about our feelings after getting splashed in the face while walking on the side of the road by a car driving by. However, a mathematical structure could develop an interactive 3D model of the experience, including how the various sensations relate — such as the fury of watching the car drive off, the smell of wet concrete, and the trickle of dirty water running down your face.

Beyond conveying our literal experiences, such mathematical approaches could expand the entire research field revolving around consciousness by offering new ways to test predictions. One such structural idea, Integrated Information Theory, suggests consciousness can be measured using mathematics. In a practical sense, IIT is already being used to better predict consciousness levels in coma patients, among other things.

As fascinating as mathematical structures are and the potential they hold, Mica Xu Ji, a former postdoctoral fellow at the Mila AI Institute in Quebec, Canada, uses the structural approach differently. In her paper, recently published in Neuroscience of Consciousness, Ji argues that ineffability isn’t a flaw but a feature that evolution cooked into consciousness.

New Research