Life builds molecules far too intricate to happen by chance. Given enough time, so does plain chemistry. This programme is about what actually separates the two, and whether anything now flying could measure it.
The assembly index of an object is the smallest number of joins needed to build it from its parts, where anything already built may be reused for free.
Start with single characters. Each step joins two things you already have. A piece you made earlier costs nothing to use again, so a structure that repeats is cheap and a structure that never repeats is expensive. The index is the length of the shortest pathway. There is no shortcut to finding it: you search, and you prove that nothing shorter exists.
The three sequences above are the same length and use the same alphabet, and each is being built by its own shortest pathway. Nothing is illustrated. The solver worked each one out and proved it minimal, so each animation runs exactly as many joins as that proof allows — no more, and it could not be done in fewer.
The repetitive one finishes in four joins. The random one takes ten. They advance at the same rate, so you watch the random sequence still grinding away long after the tidy one has stopped. That is the first result, and it is the one most people guess backwards: a random object has a high assembly index, because nothing in it repeats and nothing can be reused.
Complexity is not the signature of life. It is the signature of noise. What distinguishes a living chemistry is complexity at abundance — a structure that is expensive to make, found in many identical copies. One improbable molecule is an accident. A million of the same improbable molecule is a mechanism.
Earth’s own biology begins below the point where lifeless chemistry already reaches.
If the index separated life from chemistry, there would be a value above which only biology sits. Measured against real inventories, there is not. On Titan — Saturn’s largest moon, where there is no life — chemistry reaches an assembly index of 8. One of the things it makes is guanine, which is one of the four letters of DNA. Earth’s own biology runs from 6, at glucose, the sugar in your blood, up to 19, at ATP, the molecule your cells use to move energy around. The two ranges overlap, and the guanine made on a dead moon is more complicated than the sugar keeping you alive.
Set the bar high enough to keep out everything Titan manages on its own, and it also throws out glucose, cholesterol, and every amino acid — the parts every protein in your body is built from. Set it low enough to keep those, and dead chemistry walks in alongside them. The bar is either too strict or too loose. There is no height at which it is neither.
None of which breaks the measure. It means complexity was never going to do this job by itself. The work is done by the copies.
Two soups, started from the same eight simple molecules, and grown by making chemical bonds that obey real chemistry.
The eight starting molecules are unremarkable ones — formaldehyde, hydrogen cyanide, formic acid and five others of that sort. All of them turn up in space, and in the classic origin-of-life experiments. Rather than argue about what lifeless chemistry can reach, the reactor builds molecules and measures what came out. On the left nothing is steering it: take two molecules and join them anywhere they will join. On the right a crude copier builds the same chain over and over. Both run until there are 250 molecules.
The undirected soup is the one that made the more complex molecules. Its wildest products reach assembly index 14, where the copier’s target only reaches 12. Judged on complexity alone, the soup with nothing steering it wins. Judged on complexity and copies together, it loses by a factor of about a million, because every one of those elaborate molecules was made exactly once and never again.
This is the same lesson as the three strings, now in covalent chemistry rather than in symbols. It is also a limit rather than a proof: the reactor is a rough model of how molecules combine, not a simulation of real reaction rates, and it is reported as one. What it establishes is the shape of what each process can reach, and the shape is that undirected chemistry explores structures while copying accumulates them.
The reactor above is the Python rule, ported. It was checked against the original before it went anywhere near this page: 486 runs driven through both on the same choices, agreeing on every atom count, every bond count, every bond order. The live species counter was checked the same way, against the chemistry toolkit’s own canonical form.
The measurement depends on how a molecule is put together. Every instrument we have sent looks at what it weighs.
Two molecules made of exactly the same atoms, arranged differently, weigh exactly the same. A mass spectrometer — the instrument that identifies molecules by weighing them — cannot tell those two apart at any precision, so it cannot recover the number we want. Breaking the molecule into pieces first does not rescue it: the pieces put neither an upper nor a lower limit on the whole, and once you account for size, counting the pieces carries no information at all.
Reach is the worse problem. Everything ever identified in the plume of Enceladus — one of Saturn’s icy moons, and one of the best places anyone can name — tops out at an assembly index of 4. The instrument that flew there could only weigh molecules far too small to carry the signal at all.
There is a way through, and it is almost annoying how simple it is: fly slower. Cassini passed Enceladus between 2.3 and 5.3 times faster than a molecule’s structure survives the impact, which is why its samples arrived as wreckage. An orbiter loitering in the plume would be moving comfortably slowly enough to bring one back intact. The window is open. Nothing has flown through it.
This programme recommended an instrument for ten experiments running before its own apparatus took the recommendation away — it had been contradicting an entry in the same database the entire time. The withdrawal is on the record and has not been quietly tidied up. What stands is that the most promising way to tell life from chemistry has no funded instrument anywhere, which is a better problem than another argument about where to put the bar.
“One improbable molecule is an accident. A million identical ones is a mechanism.”
