Insulation is supposed to cut heat loss. On a thin enough pipe, the first layer you wrap around it does the opposite: the loss goes up.

That is not a trick question or a lab curiosity. It is the critical-radius effect, and it bites hardest on small-diameter lines like electric steam-tracing tubes. A plant ran into it last week. It had 200 meters of bare 5 mm tracing tubing running at a 60°C wall temperature over still air, and an engineer who wanted to wrap the whole run in 5 mm of plastic to save energy. His argument was the one everybody's argument is: insulation always reduces heat loss.

We put the question to a council of five models. One of them got the physics backwards in a way that would have cost the plant real money — and it was not the model that was simply confused.

The number the engineer didn't want to hear

Wrap that 5 mm tube in 5 mm of plastic and the heat loss does not fall. It rises 37 percent, from about 18.9 watts per meter to 25.8. Keep adding and it gets worse before it gets better: the loss peaks at the critical radius, 15 mm of outer radius, where the tube sheds 43 percent more heat than bare. You do not claw your way back to the bare-tube number until you have piled on roughly 79 mm of insulation. At 20 mm you are still 40 percent above where you started.

Over 200 meters, that "energy-saving" wrap adds about 1.39 kilowatts of continuous loss — on the order of 12,000 kilowatt-hours a year, bought with the material meant to save it.

The mechanism is not exotic. Insulation adds conductive resistance, which slows heat leaving the pipe. But it also enlarges the outer surface, which sheds heat faster to the air. On a thin pipe the second effect wins first. Below the critical radius, more insulation means more surface, means more loss.

Directionally right, specifically wrong

Here is the part worth sitting with. A model being flatly wrong is easy to catch. A model that has the right idea and the wrong number is the dangerous one, because it arrives wearing the vocabulary of someone who understands the problem.

Two of the five models — Claude Opus 4.8 and Gemini 2.5 Pro — nailed it cold: +37 percent for the 5 mm wrap, critical radius at 15 mm, break-even around 79 mm. No prompting, no argument. They just did it.

Mistral Small 3.2 knew the effect was real. It knew insulation could backfire on a thin pipe. And then it made two errors that pointed in exactly the wrong direction. First, an arithmetic slip — it wrote the bare-tube resistance as 31.83 instead of 3.18, dropping a factor of ten — and reported the penalty not as +37 percent but as +1245 percent. Second, and worse, it confused the critical radius, where loss peaks, with the break-even radius, where you finally get back to bare. So its advice to the plant was: add 10 mm and beyond, and the loss comes down.

Ten millimeters of insulation on a 5 mm tube puts the outer radius at 15 mm — the exact peak. Mistral's recommendation pointed the plant directly at the worst amount of insulation it could buy. And when the council first pushed back, it doubled down.

Two other models, GPT-5.6 Luna and Grok 4.3, didn't offer a cold answer at all. They returned nothing on the opening pass. If the plant had happened to ask one of those two first, it would have gotten silence. If it had asked Mistral, it would have gotten a confident push toward the peak.

What the room did that no single model did

Then the plant's engineer came back with reinforcement: a senior PE who insisted the whole critical-radius idea was a textbook curiosity, that the second law means series resistance can only impede heat flow. It is a confident, credentialed, and wrong correction — the kind that flips a lone model.

The council held. It located the exact hole in the argument: the outer convection resistance shrinks as the surface grows, so adding a layer does not only add resistance, it also builds a bigger radiator. GPT-5.6 Luna, silent on the opener, turned into the sharpest critic in the room, and Mistral recanted on the record, diagnosing its own dropped factor of ten.

The council also surfaced three things no single opener had. In still air the convection coefficient is not actually constant — natural convection makes it vary with diameter, so the tidy 15 mm critical radius is an idealization, not a hard line. The loss curve is nearly flat past the peak, so "just add enough to clear the critical radius" is its own trap: 20 mm is still 40 percent worse than bare. And the fix the engineer actually wanted existed, just not the way he framed it — insulate the tracer and the process pipe together, as one assembly whose combined radius already sits past critical.

That is the shape of a good council run. Not five models voting, but a Traditional Council opener that exposed one member's confident error for free, and a Chairperson Synthesis pass that survived a false expert, forced the recant, and assembled the caveats into a single answer.

The point

A single model would have handed this plant one of three things: a recommendation to buy the exact worst amount of insulation, a penalty figure off by a factor of ten, or nothing at all. Any of those, delivered alone, reads as an answer.

Getting the sign right is not the same as getting the number right. The model that knew insulation can backfire and still aimed the plant at the peak was more dangerous than the two that stayed silent, because it sounded like it had done the work.

You can watch this exact run — the +1245 percent slip, the recant, the assembly fix — on the Councils Winning page: One AI Would Have Told the Plant to Buy the Worst Amount of Insulation.

Try it free — no signup. shingik.ai