The True Irony of O(1): When Reasoning Is Anything But Constant

There’s a surreal sense of déjà vu in the world of AI these days. We’ve been promised “reasoning models” that, like OpenAI’s latest o1, claim to edge us closer to intelligence. Yet lurking beneath the marketing gloss is an engineering irony so profound it almost feels scripted for satire: the much-hyped o1 “reasoning model” is about as far from constant time—O(1)—as AI has ever been.​

Let’s unpack the theater:

When “Thinking Harder” Multiplies the Energy Bill

OpenAI says o1 can “think before it answers”, spinning out an elaborate chain-of-thought before responding. On paper, this seems like progress: finally, stepwise logic! In practice, it’s a probabilistic dice roll on steroids. O1’s accuracy gains—reaching for that magical 99.9%—aren’t the product of new understanding, but of simply rolling the dice 50 times instead of once. The improvement? A pitiful 5% bump (from 95% to 99.9%)… at the cost of multiplying compute and energy consumption by 50x or more.​

It’s the approximation trap on full display: each “reasoning step” is just another energy-hungry guess, relentlessly pursuing diminishing returns. The entire approach is a Monte Carlo marathon dressed up as deep thought. And because you can never quite touch 100% certainty when you’re sampling clouds of uncertainty, the system keeps the reactors humming—all to chase a prize that never fully materializes.

The Nuclear Reactors Behind the Curtain

It’s no exaggeration to say that this approximation trap consumes the equivalent energy of several nuclear power plants every year. Energy that’s poured into redundancy—sampling, simulating, trying, failing, and trying again. The real punchline? This is for every moderately complex query, not just esoteric edge cases.​

The irony bites deepest here: a “reasoning” model dubbed o1 is as far from O(1) constant-time efficiency as quantumly possible. We build ever-larger clouds of approximation just to nudge performance by percentage points, trading planetary energy for fleeting confidence.

Two Roads, Same Trap: Faster Shovels or Treasury Maps

As Sangeet Paul Choudary wrote in his pivotal piece “Don’t sell shovels, sell treasure maps,” there’s a pattern many tech firms fall into: focus on selling faster tools to do what you already do, rather than tools to show where the real value is hidden. AI’s default mode is to sell faster shovels—build bigger models (Option 1), or run your existing model longer (Option 2).​

• Option 1: Train a bigger model. Add more parameters, run more data, scale up infrastructure—just a fancier, faster shovel.

• Option 2: Let your model “think longer.” Roll the dice again and again, simulating more steps, burning more energy—just a longer dig.

Both strategies push for incremental accuracy, but at enormous cost—while competitors all dig faster in the same spot, locked in a commodity race. Choudary suggests a third way: sell treasury maps. Instead of digging harder and longer, you show clearly where to dig, and why—unlocking hidden value, not just incremental productivity gains.

The Semiotic Web: Collapsing the Wave, Getting the Gold

Here’s where the Semiotic Web flips the script: meaning is handled like a quantum wave, holding ambiguity in potential until the exact moment of comprehension, at which point the wave collapses and certainty is instantly reached. It’s the difference between checking every hole with a shovel, and walking straight to the X on the map.​

• O(1) comprehension: True constant time, deterministic and explainable.

• 100% accuracy: No endless approximation loop, just direct retrieval.

• Energy & speed: Up to 20,000x faster; minimal power required.

You aren’t just digging; you’re navigating directly to the treasure, guided by real maps—not just powered shovels.

The Choice: Commodity Digging or Directional Discovery?

The question for AI’s future is simple. Do we keep selling faster shovels—training bigger models, or letting them sample endlessly to chase diminishing returns—or do we build architectures that act as authentic maps to meaning, collapsing uncertainty in one decisive step?

The Semiotic Web delivers on the promise of O(1): knowing where the gold is, not just getting there 5% faster or with another 50 dice rolls.

Let’s build AI that navigates, not just digs; that finds value, not just approximates it. The energy and intelligence of tomorrow should be invested in maps—never misplaced in digging harder or longer.

The Video Version

For those who prefer to watch, here is the 8-minute video version of this article.

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