Castor

Why Castor

AI is arriving unevenly. It has taken some things almost completely and barely touched others, and the pattern has little to do with difficulty: a machine will prove a hard theorem and then fail at a judgement a child makes without thinking. Anyone who works with these tools has noticed. Almost nobody has an account of it.

Unwritten. This paragraph is the author’s to write. the claim, in your voice. The spine of the whole piece: there is a line, it is not difficulty, and knowing where it runs is worth more than any forecast about capability.

Where the line runs

Here is the line we think it follows. A task falls quickly when a candidate answer can be produced in volume and checked without a human deciding whether it is good.

Mathematics has that property. So do most of software and much of security. A machine can generate proofs, patches and exploits, and something other than a person tells it whether each one worked. The check is cheap, repeatable and patient. Give the loop enough attempts and it improves around the clock without asking anyone’s opinion.

Whether a piece of writing is honest belongs to another class. So does whether a decision was worth its cost, or what one person owes another. There is no oracle. The verification is the judgement, and the judgement is the thing you wanted in the first place.

That is a property of the task, whatever the model. The technical case gets its own article.

So the useful question is what stays ours for structural reasons, and whether that ground is large enough to stand on.

Terence Tao, a leading research mathematician, leaves capability forecasts to one side and starts with the goals. Machines can flood mathematics with proofs. Humans still decide what is worth proving, which proofs deserve to be understood and what enters the canon. As proofs become abundant, those choices become more valuable.

Then comes his warning for the other path: “Could we have a verified proof of a major result that no human understands enough to explain it?”1 A proof can be correct while humanity is left behind by it. That is the left-behind ending, stated by the person least prone to panic about it.

Unwritten. This paragraph is the author’s to write. your position on that question. This is a belief-statement and it is the one a reader will remember. How much of that line do we think holds, and for how long?

Why that name

Names matter less than people think. We still needed one. We picked Castor. Then we found out how good it was.

The mortal twin

Castor and Pollux were twins. Castor was mortal and Pollux was immortal. When Castor died, Pollux asked Zeus to let him share his immortality with Castor. Zeus allowed the brothers to alternate together between Olympus and the underworld. We picked Castor, the mortal twin.

The immortal one was the one in trouble. Immortality alone was the sentence. The bond rescued Pollux and cost him half of everything: half his time in Olympus and half in the underworld.

Our humanist position on AI is that pairing, held together by a shared direction. Our missions, tastes and half-written values are mortal things. Bound to something that can keep acting, they travel further. The immortal half gets what immortality had taken away: a purpose, and someone to be immortal for.

One future we refuse is easy to picture. Comfortable bodies in padded chairs, carried, fed and entertained, every destination chosen somewhere else. It is a perfect service, and the person has become cargo. The missing thing is agency, and comfort ate it.

A pairing depends on what passes between its parts. Aviation learned this after crews lost working aircraft because critical information failed to reach the person making the decision in time. Crew Resource Management changed pilot training: communication, challenge and shared decisions became part of flying the aircraft, alongside the controls and instruments.2 The components were fine. The connections were the accident. Human to human, human to agent, agent to agent: that is where this will break, if it breaks.

The beaver

In English, Castor sounds like the oil your grandmother threatened you with. The word itself is Latin for the beaver.

A beaver builds its dam for itself. The lodge entrance stays underwater and food stays within reach under the ice. A wetland appears downstream, and fish, birds and plants move in. The beaver acts on a short-term need and builds long-term infrastructure for everything around it. Short-termism and long-termism can describe the same act, depending on whose clock we use.

The boundary question is whose surplus we count, over what period. Art of the Problem’s The Profit Paradox asks it in energy: “Is this increasing the total usable energy in the system, or just repositioning itself to extract from existing flows?” Count only the beaver today and one answer appears. Count the flooded field, the fish and the people nearby over years, and the balance sheet changes.

A dam is never finished. Running water takes it apart and the beaver repairs it. A living body holds its temperature and chemistry against a world pulling them back to match the surroundings. When that work stops, the body dissolves into its environment. Schrödinger put this in a book in 1944.3 Staying different is continuous work, and the beaver pays that bill visibly, every day.4

We believe, maybe naively, that incentives can make self-interest produce public good most of the time. Today they often reward the narrower gain. We believe in a world where the two line up, and if they cannot, none of this is sustainable.

Adam Mastroianni’s Incentives are for losers gives the counter: once a measure becomes a target, people learn to win the measure. Scott Alexander’s The Goddess of Everything Else shows a different possibility: existing drives can be recruited and redirected, again and again. Axelrod’s repeated-game tournaments, described by Dawkins, found that cooperation can win when players remember and expect to meet again.5 The system has to keep correcting its incentives while the game continues; the full argument gets its own article.

So what is Castor

We do not know what Castor is. We are building a dam together, thinking and working as we go. It may become a company. It may lead somewhere else. We really do not know.

Unwritten. This paragraph is the author’s to write. drafted from your words of 21 August, yours to keep or rewrite A beaver’s teeth never stop growing. Gnawing wears them into the edge they need, so the cutting does the sharpening. Lincoln’s advice was to spend four of the six hours sharpening the axe. It separates sharpening from cutting, and that gap is where people like us can spend a lifetime preparing to begin. We are good at sharpening. We also want to get things done. Castor is the way we found to do both, together. The dam is never built. We know. We are building it anyway.

Footnotes

  1. Terence Tao, “Mathematics in the age of AI”, public lecture at the International Congress of Mathematicians, slides dated 28 July 2026 (slides). The question is quoted verbatim from the slide on unverified AI-generated proof submissions. ↩

  2. Crew Resource Management, introduced after accidents including Tenerife (1977) and United 173 (1978), where functioning aircraft were lost through failures in how the crews communicated. ↩

  3. Erwin Schrödinger, What Is Life? (1944), on living systems keeping their order only through continued work, an intuition Boltzmann had in 1886; Ilya Prigogine later made the physics rigorous (Nobel Prize in Chemistry 1977). ↩

  4. Jeff Bezos, 2020 letter to shareholders, drawing on Richard Dawkins’s The Blind Watchmaker: distinctiveness is a bill paid daily. ↩

  5. Richard Dawkins, The Selfish Gene, chapter 12, “Nice Guys Finish First”, summarising Robert Axelrod’s iterated Prisoner’s Dilemma tournaments. ↩