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When is it better to think without words?

Henrik Karlsson challenges a foundational assumption of the modern knowledge economy: that writing is the primary engine of thought. In a world obsessed with documenting every insight, Karlsson argues that the most profound cognitive work often happens in a wordless, high-dimensional space that language can actually obstruct. This is not merely a philosophical musing but a practical guide for anyone struggling to solve complex problems, suggesting that our reliance on text may be blunting our deepest intuitions.

The Paradox of Wordless Processing

Karlsson anchors his exploration in the work of French mathematician Jacques Hadamard, who discovered that top-tier problem solvers rarely think in sentences. "Thoughts die the moment they are embodied in words," Karlsson quotes Schopenhauer, setting a provocative tone for the essay. He details how these mathematicians described their mental landscape not as a stream of consciousness, but as "vibrations in their hands, nonsense words in their ears, or blurry shapes in their heads." This distinction is crucial; it suggests that the brain's most powerful processing engine operates on a different frequency than our linguistic centers.

When is it better to think without words?

The author posits that this wordless state allows for a "tensely focused" mode of thinking where the brain can run a parallelized search for solutions without the drag of sequential logic. Karlsson speculates that these experts manage to keep both the default mode network, responsible for mind-wandering, and the executive control network, responsible for focus, active simultaneously. "Perhaps this allows them to do a sort of subconscious, in-the-shower-type processing, while still maintaining enough conscious focus to ensure the thoughts don't drift away from the problem and its constraints," he writes. This framing offers a compelling biological explanation for the "sudden illumination" that often strikes when we step away from a task.

"If we can avoid the compression step, and do the manipulations directly in the high-dimensional, non-linguistic, conceptual space, we can move much faster."

Critics might argue that this description romanticizes a cognitive style that is inaccessible to most people without decades of specialized training. For the average professional, attempting to think without words could easily devolve into confusion rather than clarity. However, Karlsson acknowledges this limitation, noting that for most, "our thoughts are riddled with contradictions and holes that we often don't notice unless we try to write them down."

The Heavy Baggage of Language

The essay pivots to the specific friction between language and complex reasoning. Karlsson argues that words are "laborious" because they force a high-dimensional web of associations into a low-dimensional, sequential string. He cites James Joyce to illustrate the immense effort required to compress thought: "I don't know in which order to put them…" This compression is not just slow; it can be deceptive. The author warns that writing forces a "false precision" onto ideas that are still fluid, leading us to accept "credible nonsense" simply because it looks respectable on a page.

This is where the argument becomes most relevant to the modern reader. We are trained to believe that if we can't articulate it, we don't understand it. Karlsson flips this, suggesting that premature articulation can actually stall deep thinking. He notes that Hadamard's subjects were "afraid of the false precision writing forces onto thinking," preferring to keep their thoughts "accurately vague" until they were ready to be solidified. This is a vital insight for leaders and strategists who often feel pressured to draft memos or presentations before their mental models are fully formed.

The Necessary Arch of Masonry

Despite the power of wordless thought, Karlsson does not advocate for abandoning writing. Instead, he reframes it as a structural necessity rather than a generative one. He uses a metaphor from mathematician William Hamilton, comparing deep thinking to tunneling through a sandbank. "Without these subsidiaries, neither process could be carried on beyond its rudimentary commencement," Karlsson writes, referring to language as the masonry that secures the tunnel.

The essay concludes that writing serves as a "relay result"—a way to offload stabilized thoughts from working memory so the mind can tackle the next layer of complexity. Karlsson suggests that the most effective thinkers use writing not to generate ideas, but to capture and validate the insights that emerged from their wordless processing. "Good writing tends to come from an attempt to capture in words something you understand wordlessly," he asserts. This distinction transforms writing from a tool of discovery into a tool of verification, a shift that could fundamentally change how we approach problem-solving.

"Writing forces precision, which can fool us into locking in details we have no reason to lock in, but written notes (or drawings) are a necessary aid when thinking long chains of thoughts."

Bottom Line

Karlsson's most compelling contribution is the redefinition of writing as a stabilizing force rather than a generative one, offering a sophisticated counter-narrative to the "write to think" dogma. The argument's greatest vulnerability lies in its reliance on the exceptional cognitive abilities of elite mathematicians, which may not translate easily to the messy, interdisciplinary problems faced by most professionals. Readers should take away the permission to embrace ambiguity and silence in their work, using language only when the mental architecture is ready to bear its weight.

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When is it better to think without words?

by Henrik Karlsson · · Read full article

Portrait of a Man with Glasses I, Francis Bacon, 1963.

This essay can be read as a complement to last year’s “How to think in writing.”

Thoughts die the moment they are embodied in words.—Schopenhauer

1..

In the 1940s, when the French mathematician Jacques Hadamard asked good mathematicians how they came up with solutions to hard problems, they nearly universally answered that they didn’t think in words; neither did they think in images or equations. Rather, what passed through the mathematicians as they struggled with problems were such things as vibrations in their hands, nonsense words in their ears, or blurry shapes in their heads.1

Hadamard, who had the same types of experiences, wrote in The Psychology of Invention in the Mathematical Field that this mode of thinking was distinct from daydreaming, and that most people, though they often think wordlessly, have never experienced the kind of processing that the mathematicians did.

When I read this, in December 2024, all sorts of questions arose in me. First of all, what does it even mean? Do they not think in words and equations at all? And secondly, how do I square this with my personal experience, which is that whenever I write what I think about a subject, it always turns out that my thoughts do not hold up on paper? No matter how confident I am in my thoughts, they reveal themselves on the page as little but logical holes, contradictions, and non sequiturs.

I recognize myself when Paul Graham writes:

The reason I’ve spent so long establishing [that writing helps you refine your thinking] is that it leads to another [point] that many people will find shocking. If writing down your ideas always makes them more precise and more complete, then no one who hasn’t written about a topic has fully formed ideas about it. And someone who never writes has no fully formed ideas about anything nontrivial.

How come Hadamard’s colleagues are able to have productive thoughts, working in their heads, without words, sometimes, for days on end?

Tense subconscious processing.

Hadamard’s book is most famous for its detailed discussion of what Henri Poincaré called the “sudden illumination”—the moment when the solution to a problem emerges “in the shower” unexpectedly after a long period of unconscious incubation.

The hypothesis here is that if you work hard on a problem, you soak your subconscious with it. Wrestling with a ...