The Belt Equation

In 1961 the astronomer Frank Drake wrote the Drake Equation on a blackboard at the Green Bank radio observatory in West Virginia to organize a meeting about whether any other civilization in the galaxy was sending signals we could detect. The number of detectable civilizations, he proposed, is the product of seven factors: the rate at which stars form, the fraction of stars with planets, and so on down to how long a civilization stays detectable once it starts. Nobody at the meeting knew most of the values, and nobody does now. What the equation did was turn one unanswerable question into seven arguable ones, so that people who disagreed could say exactly where.

The same move works on any question that is too big to answer and too important to leave as a feeling. The one I have carried for most of my life is whether the solar system will open up while I am alive to see it, and not as a place a few astronauts visit, but as a place people go to work, the way The Expanse imagines it. That is the series of science-fiction novels by James S. A. Corey, and the television show made from them, set a few centuries out in a solar system that humans have settled but not left: there are mines in the asteroids, a shipping economy between them, crews rotating out and home again, and a population far enough from Earth that Earth has stopped being home. Asked as one big question, will that world arrive in my lifetime or not, it has no answer, only a feeling attached to it, hopeful on some days and foolish on others, and a feeling never changes what you do on any given day. Drake’s equation suggests a different way to ask it. Instead of one unanswerable question about whether that solar system arrives in a lifetime, write down what would have to be true for it to arrive, and then, since the question is mine, what would have to be true for me in particular to be out there when it does.

So that is what I did. I call the result the Belt Equation, after the Belters, the people in The Expanse who were born and work out in the asteroid belt, and the question it is built to answer is this: what is the probability that, before I die, I get to live and work in a solar system where human industry reaches beyond Earth and Mars? It is a product of factors like Drake’s Equation, eight of them, and under each factor sits a tree of concrete events with a probability on every one. I set it up to answer for myself, at forty, in my current career, under several different possible lifespans, and to track how the prediction moves as the science and the money and the politics behind it change over the years. If I live to about 2071, which is roughly the life expectancy for a man my age, the prediction as of September 25, 2026, is 0.5 percent. That figure and everything under it sits on a website called The Belt Equation. There you can open the full tree of events and follow any branch down to the criterion and reasoning behind it, and you can put your own numbers in, your birth year, the lifespan you are betting on, the route you would take in and your own odds of taking it, and see what the equation says for you under whatever scenario you want to look at. The site also watches the news. Every week it scans for developments in science, technology, and politics that bear on any event in the tree, and records what they moved, so that over time you can see the latest developments changing the equation rather than reading one fixed number.

A forecast of half a percent about your own life is a strange thing to publish, and the rest of this essay explains why it is worth publishing anyway.

The Eight Links in the Chain

The equation splits the question into eight factors:

1. The window. I am alive on the date in question.
2. Launch. Getting mass into orbit becomes cheap enough for everything else to follow.
3. Energy. There is real power generated off Earth, enough to run industry rather than a small outpost.
4. Drive. Ships get fast enough that the outer solar system becomes a place people go to work.
5. Biology. Human bodies hold up, and eventually reproduce, in low gravity and deep-space radiation.
6. Motive. There is an economic reason for large numbers of people to be out there at all.
7. Regime. The politics let a multi-decade build survive elections, recessions, and wars.
8. Access. I personally have a pathway in, given my training, my health, and the shape of my career.

Multiply the eight and you have the headline number. The multiplication is the whole reason the number is small, and you can see why without doing any math: every one of those has to go right, and a chain with eight links breaks at any one of them. No single link looks hopeless, though. Cheap launch by 2071 is a coin flip or better, and large-scale power generation off Earth is likelier than not. It is all of them together that is small.

Under each link sits a tree of concrete events, seventy of them as I write, and each one has three parts. It has a plain-English name. It has a criterion, which says exactly what would count as the event having happened and where to look. And it has a list of the other events it cannot happen without. “A hundred tonnes of material dug or made on the Moon are delivered to orbit in one year” is a node. So is “a crew off Earth lives for a year with most of its food, water, and air recycled on site.” So is “I graduate from my current training.” I think the criteria matter more than the probabilities, because a criterion is what lets the forecast be wrong later, and a forecast that cannot be wrong is an opinion.

What Counts as Out There

“Live and work off Earth” needs a definition or the number means nothing, so the project uses four rungs for the person and four for the solar system.

For the person:

1. Contributing from Earth. Working in or for the off-world industry without leaving.
2. Having flown. At least one trip to space, by purchase or by the job.
3. Working off Earth on rotation. Months at a stretch at an off-world site, the way people work Antarctica or an oil platform today.
4. Living off Earth for good.

The headline is the third rung, rotation, because that is what living and working out there actually means, and because a single flight is a different thing with different odds. By 2071 the flight rung sits near 35 percent. The rotation rung is the 0.5.

For the solar system:

1. An outpost. Hundreds of people, fully supplied from Earth.
2. A settlement. Thousands, with some local self-sufficiency.
3. A slow Expanse. Tens of thousands, at least one site beyond the Earth-Moon system, something mined or made out there sold at a profit, and nuclear propulsion in routine use.
4. A full Expanse. Millions, a Belt population with politics of its own.

The bar for the headline is the third rung, the slow Expanse, since working out there on rotation needs an outer site with an economy and does not need millions of people or the fictional drives that let the show’s ships cross the solar system in weeks. Setting the bar at the full Expanse would put the headline at zero by definition and hide all the movement in the range that matters.

The bar cuts the other way too. A rotation at a station or a lunar base, in a world that has an outpost but no Belt, is what many people picture when they hear “work off Earth,” and it is a much nearer thing. The tree puts it at 8.9 percent by 2071, nearly twenty times the headline. I kept the headline where it was, because a solar system where industry reaches past Mars is the question I am most interested in, and I put the nearer number on the site beside it so the gap is visible instead of buried in a definition.

How a Tree Becomes a Number

Each node carries five probabilities, one per deadline, because the deadline is the thing that changes. The five deadlines are:

1. 2071. This is the baseline, my life expectancy on current trends, age 85.
2. 2080. A moderate extension, age 94, the kind a first generation of drugs that slow aging might buy.
3. 2095. A strong extension, age 109, which would need treatments that do not yet exist in any form.
4. 2136. A 150-year life, which nothing on Earth has ever come close to.
5. No deadline at all. The solar system arrives whenever it arrives and I am somehow still there, which is the version of the question with mortality taken out.

A node’s number under a deadline is the chance it happens before that year given that everything it depends on has already happened. That conditional form is the one a person can actually estimate. “How likely is orbital manufacturing at scale by 2071” is a guess about the whole world; “if launch is cheap and a hundred people already work up there, how likely is manufacturing then” is a question with a shape.

A script then plays the whole tree out twenty thousand times per deadline. In each play-through it visits the nodes in dependency order, rolls each one against its probability if its prerequisites came up yes, and records which rungs were reached. The headline number is the fraction of play-throughs in which I end up working off Earth on rotation. This is a Bayesian network evaluated by simulation, which is the standard way to get one probability out of a graph of conditional probabilities when the graph is too large to multiply by hand.

Done naively, it is wrong in a known way, and the first run showed it. Rolling every node as if it were independent of every other put the odds of a Belt existing by 2095 at a fifth of a percent, even though every step on the way is individually plausible. That is what happens when fifteen moderately likely things are all required and are multiplied as if unrelated. But they are related, and closely. Cheap launch, sustained money, and a working off-Earth economy are causes shared across most of the tree, and a world where one of them comes good is a world where the others tend to as well. So before each play-through the script now draws one number for how favorable the world turned out and shifts every node’s odds by it, up or down together. That single adjustment is the one free parameter in the method, and at the 2095 deadline it is worth the difference between about a tenth of a percent and 3.5 percent at the headline. The script prints both results on every run so a reader can see exactly what the parameter buys.

The probabilities themselves are the weakest part. They were proposed one at a time by Claude, each with a one-line reason, and accepted or moved by me. So before anything on the site counted as final, every factor’s nodes, criteria, and numbers went to two other frontier AI models, Google’s Gemini and OpenAI’s GPT-6, with a fixed brief: name a missing node, challenge a criterion, argue a number up or down with a reason and a confidence. Where the two pulled in opposite directions on a number, a third model broke the tie. Their answers are filed in the public repository.

The review cut the headline from 0.9 percent to 0.4 (later changes to the tree’s shape have nudged it to the 0.5 it sits at today), and most of that fall came from what the reviewers said was missing rather than from what they said was wrong. Nine events joined the tree, seven of them new requirements on the chain: a staple crop grown from seed to harvest off Earth, cryogenic propellant kept in orbit for six months and then burned, a tonne of propellant made off Earth and fired, a surgical operation performed off Earth, commercial insurance written on a lunar asset, the United States and China recognizing each other’s keep-out zones around installations, and a space traffic authority with real enforcement among the major powers. Each is something that has to happen before the thing above it can, and each can only lower the odds of the tiers that need it. Fifteen probabilities moved, in both directions, and forty-one criteria were tightened so that two readers would agree when an event has happened.

A forecast is only worth something if it gets checked against what actually happened, so the numbers are scored every January. Some of the seventy events will resolve every year, either happening or plainly failing to, and each one that does is a test of the probability that was on record for it. Every January the project computes a Brier score over the nodes that resolved during the year, the standard measure of how far a set of probabilities sat from what happened: zero is perfect, a quarter is what you get by saying fifty percent about everything, and worse than a quarter means the forecasts were worse than silence. About a third of the tree is near-term enough to resolve within five years, which is why the score arrives in years rather than decades. The scores go in a public changelog beside the year’s movement in the headline.

What Holds the Number Down

Four nodes dominate the result at the baseline deadline, and rockets are not among them. Each figure is the event’s chance by 2071 once everything it depends on is counted:

1. Something mined or made off Earth is sold at a profit. About 6 percent. This is the tightest link in the tree, and it carries the insurance and the keep-out zones the review put under it.
2. I hold a job whose holders go on off-Earth rotations. About 9 percent. This one is mine, and it depends on a job category that does not yet exist.
3. A site beyond the Earth-Moon system is crewed without a break for a year. About 10 percent.
4. A hundred tonnes of lunar material are delivered to orbit in a year. About 17 percent.

The launch and energy links that draw the most public attention are, by comparison, the healthy part of the chain. At this deadline the Belt is gated by whether anyone ever makes money out there more than by rockets.

The other thing the number is made of is how long I live. Read across the five deadlines, the headline goes:

1. By 2071: 0.5 percent.
2. By 2080: 1.2 percent.
3. By 2095: 3.5 percent.
4. By 2136: 11 percent.
5. No deadline: 15 percent.

The gap between the first figure and the last is the share of the question that is about medicine rather than spaceflight, and it ends up being most of the equation. The project reports the five columns side by side rather than blending them into one number, because the spread is the finding, and a single weighted figure would hide it.

Why the Long Shots Stay on the Board

A 150-year life is not a forecast. Nothing tested in humans has yet slowed the rate at which the very old die, and the best results in mice are gains of ten to thirty percent. The drives that would make the outer solar system a place people cross in weeks rather than years would need a fusion reactor a hundred to a thousand times lighter, for its power, than any design on the ground. A detected intelligence not descended from us has, so far, a perfect record of not showing up.

All of these are in the tree anyway, intentionally, and the reason is the first rule I set when the project began. Low-probability, high-consequence events belong in the tree even when they are 99.9 percent dreaming, because they are what make the dream vivid enough to act on. The far end of the horizon is there to change what you do now. A dream vivid enough to feel real makes the nearer steps toward it, the ones you can actually take this year, worth taking, and if the far end is trimmed off for respectability the near steps lose their pull. A node is excluded only for being unresolvable, meaning no criterion could ever settle it, or irrelevant, meaning nothing depends on it. It is never excluded for being unlikely.

The second rule is about how such nodes must be written, and it comes from the show. What makes The Expanse work as fiction is that every wild turn is plausible in sequence, so that even an alien technology acting outside known physics feels like something that could happen in the real solar system. A long-shot node has to be written the same way: each step from here to there believable, the mechanism named, and the point where current physics or engineering would have to give way stated plainly rather than waved past. A node without a stated breaking point fails review exactly as a node without a resolution criterion does.

I argued in Everything Is Amazing and Nobody’s Happy that keeping your sense of what is astonishing in working order is a discipline that keeps your models honest, and this project is that discipline with a spreadsheet attached. Holding a long-horizon hope as a mood is easy; holding it as a number you have committed to revising is harder, and it is the only version that can change what you decide to do today.

The Clause Beside the Equation

Underneath the whole project is a hope with no practical place in it. Drake’s equation was about contact with other minds, the whole reason for the meeting at Green Bank. The Belt Equation is about becoming the kind of people who could be out there to make contact, and I did not want to lose the thread between the two. So there is a ninth term, published beside the equation and never multiplied into it, because nothing about the Belt depends on it. I call it the Contact Clause.

It is a short list of the ways contact with a mind that is not our own could show up in the record, held to the same standard as everything else in the tree: each one is an event that either happens or does not, with a written test for what would count, and it gets scored at the beginning of each year with the rest of the project. I am not claiming any of it is likely, and the tree says as much. The clause is there because the possibility is the oldest reason anyone wanted to go out there in the first place. Writing the possibility down as a probability with a criterion attached is what keeps it a valid question.

It has five rungs, each with a resolution criterion like everything else:

1. A non-human mind produces knowledge beyond us. An artificial system originates the key idea of a result, a construction or a proof its operators did not specify, and the published record says so.
2. Humans learn from it. We come to understand something conceptual we could not have reached alone, well enough to teach it.
3. An intelligence not descended from us is detected.
4. A message from elsewhere is understood. A signal from a source placed beyond human reach is decoded into something researchers can use to produce a result of their own.
5. A real exchange with a machine mind. A machine we built turns out to have a point of view of its own, shown by a test the field agrees on rather than by anything the machine says about itself, and the two of us change each other: it gives us an idea we could not have had, and what we give back changes its later work.

The first two may resolve through machine intelligence within my lifetime. The tree gives the first of them roughly 90 percent by 2071, and machine-found mathematical constructions from the last three years may already meet it. The alien rungs are kept on the board by the founding rule, and the detection rung sits near three percent, which is consistent with the case I made in The Quiet Galaxy Hypothesis that civilizations which last long enough tend to go quiet, keeping to themselves and staying hard to detect on purpose, so that a galaxy full of old civilizations would look empty from here. The machine-exchange rung sits near four percent.

Whether a machine mind counts as a mind of another perspective at all, whether the first two rungs are contact in any sense that matters, is the question my book, The Calibration Problem, is about. That book argues for holding the verdict open and calibrating instead of deciding, and the Contact Clause is written to respect that: its criteria are about what enters human knowledge and how, and they say nothing about what it is like to be the thing that produced it. The Contact Clause is where the two projects meet.

What a Forecast Is For

A forecast you cannot act on is a fantasy. As my life goes on I will have chances to make choices that either bring me closer to this long-term vision or push me further from it, and most of them will not announce themselves as such. By following the state of the science, the technology, and the industry that would have to come together for any of this to happen, I can put myself in a better position to recognize those choices when they arrive and to make the ones that bring the dream closer.

The probability tree is built to help with exactly that. A handful of nodes in my own branch are choices rather than events. When evaluating certain life decisions, I can run the probability tree once per option, with that choice forced and everything else as usual, and see the headline for each. The difference between the rows is what the decision is worth, in probability, under the tree’s current beliefs about the world. The shape of the tool is already clear. It answers a question I could not otherwise ask with any rigor: which of the choices in front of me in the next few years put me on the most interesting path, given everything the world would also have to do.

That, more than the headline, is the reason to keep the project updated. A number under one percent on its own is a curiosity. One that moves when I change a decision, and again when the world changes, is a way of steering.

Add Your Perspective

Every event on the site has a page: its criterion, its reasoning, its number under each deadline, what it depends on, and what depends on it. You can shift the birth year and the route and see what the tree says about you. If you know something about one of these fields that the tree does not, if an event is missing, or if a number looks too high or too low to you, the site’s feedback page explains how to send it in. Every change that comes from a reader gets a dated entry in the public ledger, with their reasoning attached and the movement it caused computed beside it, and the tree and the scripts that produce its numbers are in a public repository for anyone who wants to look under the hood.

The most useful thing you can do is point at one specific event and tell me what I have missed. The first scored review is January 2027.