From Monet to Sonnet: The Story of the Three Claudes and Information Theory

Three Claudes, a century and a half, and one shared question: when we communicate something, what exactly are we transmitting?

I · 1872 — A Painting That Scandalizes

In April 1874, in the studio of the photographer Nadar in Paris, a group of painters rejected by the official Salon mounts an exhibition of their own. Among the works hangs a harbor wrapped in mist: barely a few silhouettes of cranes and masts, grey-violet water and, in the middle, an orange sun reduced to a disc and three brushstrokes of reflection. Claude Monet had painted it two years earlier from a window in Le Havre and titled it, almost reluctantly, Impression, soleil levant.

The critic Louis Leroy turned the title into mockery: this was not painting, it was an “impression,” an unfinished sketch. The insult backfired spectacularly: the mocked adopted it as their banner, and Impressionism came to name the first great rupture of modern art.

What Leroy failed to see is that the lack of finish was not laziness but thesis. Monet was not painting the harbor of Le Havre: he was painting the experience of looking at the harbor of Le Havre at one specific instant of light and atmosphere. The object receded into the background; what was transmitted was the perception. Loose brushstrokes, pure colors juxtaposed without mixing on the palette, and a radical wager: that it would be the viewer’s eye that recomposed the image.

II · 1948 — A Paper That Decomposes Everything

Seventy-six years later, another Claude publishes in the Bell System Technical Journal an article with an equally modest title: A Mathematical Theory of Communication. Claude Shannon is 32 years old, works at Bell Labs, and is no newcomer: his 1937 master’s thesis had already connected Boolean algebra to electrical circuits, laying the logical foundation of all digital computing. But it is this foundational 1948 paper that inaugurates, in one stroke, an entire discipline: information theory.

Shannon does several things at once there. He defines the bit as the elementary unit of information. He introduces entropy as a measure of a source’s uncertainty: how much “surprise” each symbol it emits contains, on average. He proves that every channel has a maximum capacity, and that below it reliable transmission is possible even in the presence of noise, thanks to redundancy: extra information that lets the receiver reconstruct a damaged message.

And he does something more — the truly radical move: he separates information from meaning. The theory does not care whether the message is a poem, a photograph, or teletype noise; it only cares about its probabilistic structure. That renunciation, which struck some contemporaries as an amputation, is precisely what made the theory universal. Text, voice, image, music, DNA: everything fits in the same framework.

III · Inverse Symmetry — Two Renunciations in Mirror

The temptation is to say that Monet and Shannon did “the same thing” in different fields. That is not quite right, and the nuance is what makes it interesting. Shannon removes meaning to gain universality: any message, reduced to signal. Monet removes literalness to gain subjectivity: any object, reduced to impression. They are opposite moves that converge on the same revelation: the essence of communication is not where we thought it was. Not in the solemn content of the message, nor in the faithful detail of the object, but in the structure of what travels between sender and receiver.

From there, the echoes multiply. Decomposition: Monet dissolves light into patches of color; Shannon dissolves any message into bits. Noise as protagonist: in the Gare Saint-Lazare series, Monet literally paints steam, smoke and fog — the disturbances of the visual channel — as the central subject of the painting, six decades before Shannon formalized noise mathematically. And reconstruction at the receiver: the brain completes the impressionist image from fragments, just as a decoder exploits redundancy to correct errors.

The series carry the rhyme further. Rouen Cathedral painted more than thirty times, the haystacks at dawn and at dusk: the same subject passing through changing conditions of light. A constant message across variable channels. There is no need to force the analogy; it is enough to let it resonate.

An objection, anticipated. The punctilious reader will say that the “correct” painter for this story is Seurat, not Monet: pointillism truly does decompose the image into discrete units of pure color, almost pixels avant la lettre, and with scientific color theory behind it. That is true, and if the link were only discretization, Seurat would win. But the deep link is not technical; it is conceptual: the question of what is transmitted. And that question is opened by Monet, with perception as protagonist and the series as experiment. (That he also happens to be named Claude is not an argument. But it doesn’t hurt either.)

We should also avoid anachronism: Monet did not “anticipate” information theory, nor was he doing science without knowing it. What happened is more sober and more beautiful: two people, from opposite ends of culture, probed the same territory — the distance between what there is, what is sent, and what is received.

IV · 1948 → 2026 — From Entropy to Language Models

Here the thread stops being metaphor and becomes documentable genealogy. In the 1948 paper itself, Shannon includes an experiment that is astonishing to read today: he generates artificial text by approximating English in stages. First random letters; then letters according to their real frequencies; then letter pairs; then words chained according to which word tends to follow which. Each approximation “sounds” more English than the last. In 1951 he refines the idea in Prediction and Entropy of Printed English, using people as predictors to estimate that English contains, given enough context, about one bit of information per letter.

Read that slowly: predicting the next symbol from the previous ones, and measuring performance in terms of entropy. That is, conceptually, a language model. Seventy-five years later, a large language model does exactly that at planetary scale: it is trained by minimizing cross-entropy — a loss function defined directly on Shannon’s framework — and evaluated with perplexity, which is literally two raised to the entropy. The mathematics that scores the most advanced AI systems of 2026 came out of that paper.

And there is a second, more material debt. Without information theory there is no compression — JPEG, MP3, ZIP — no error-correcting codes, no reliable digital communication. Which is to say: no internet, and without the internet there are no massive corpora on which these models are trained. Shannon did not merely inspire generative AI; he built the conceptual infrastructure that makes it possible twice over.

V · Coda — The Third Claude

In 2023, Anthropic named its language model Claude, in homage — so the story goes — to Claude Shannon. The third Claude of this story is thus a direct descendant of the second. And it bears a kinship with the first that deserves careful phrasing.

A generative model does not reproduce the world: it produces a statistical impression of it, plausible rather than literal. It does not store the texts it was trained on; it stores their distribution, and composes from it. The difference from the painter is essential and should not be papered over: Monet chose what to omit, with intention and craft; a model chooses nothing — it optimizes. But the rhyme lies elsewhere: in how we react. “It’s just token prediction,” people say of the model today, with the same gesture with which Leroy said “they’re just blotches” in 1874. In both cases, the objection describes the mechanism correctly and gets the conclusion wrong: from simple units — blotches, bits, tokens — something emerges that the receiver perceives as image, as meaning.

Perhaps that is the shared inheritance of the three Claudes: having forced us, each in their own way, to distinguish between the object and its impression, between meaning and its signal. And having left us the question open, as it remains: when something reaches us — a sunrise, a message, a generated response — what exactly have we received?

Main references: Shannon, “A Mathematical Theory of Communication” (Bell System Technical Journal, 1948) · Shannon, “Prediction and Entropy of Printed English” (1951) · Monet, “Impression, soleil levant” (1872, Musée Marmottan).