The value and the path
A thermostat has one job: keep a reading near a number. Body temperature near 37°C, blood pH near 7.4, a chamber's line voltage within a band — these are set points, and the systems that defend them are homeostatic. Walter Cannon named the pattern in 1932: sense the deviation, act to cancel it, repeat. The defended quantity is a level. Nothing about the calendar matters to it. A thermostat that has run for ten minutes and one that has run for ten years respond to the same reading in the same way.
Homeorhesis defends something else: not a level but a course. A growth curve, a developmental sequence, a lactation cycle — these are trajectories, and the values that make them up can swing far from any fixed band while the trajectory itself stays intact. A calf recovering from scours may run a haemoglobin count that would alarm a homeostatic reading, and be entirely on schedule. C. H. Waddington, working on Drosophila development, called the paths that developing systems return to after disturbance chreods — necessary paths, valleys in a landscape of possible development that the system is canalised to fall back into. Knock an embryo off course and, within limits, it does not seek a fixed value. It resumes the sequence, often at an altered rate, until it rejoins where it should be.
The distinction is not cosmetic. A homeostatic system asks: what is the reading now, and how far is that from the set point? A homeorhetic system asks a longer question: what is the reading now, what time is it in the sequence, what reading was expected at this time, and how large is the gap between the two? The second question cannot be answered by an instant. It needs a clock and a memory.
Where the term comes from
Waddington coined homeorhesis in 1957, in The Strategy of the Genes, extending ideas about canalisation he had been developing since the 1940s. The problem he was solving was specific: embryology kept observing that development is robust to perturbation in a way homeostasis could not explain. Cannon's framework accounted for a system returning to a value. It gave no account of a system returning to a schedule — recovering the correct stage of gastrulation after a temperature shock, arriving at the correct limb proportions after a nutritional insult partway through growth. Waddington's answer was that selection canalises development into channels, and that a chreod, once entered, exerts a restoring tendency along its whole length, not just at its endpoint.
The term migrated out of embryology. Bauman and Currie, in 1980, applied it to mammalian lactation physiology, where it remains standard usage: a cow beginning lactation mobilises body fat and diverts glucose to the udder, letting blood metabolites and body condition swing well outside their ordinary ranges in the service of a milk yield curve that is expected to peak around week six and decline thereafter on a known shape. The animal is not defending a metabolite level. It is defending a curve, at the expense of levels.
What holding a trajectory costs in observation
Here is where the concept starts to bear on machinery that has nothing to do with cows or embryos.
Defending a value is memoryless. The current reading and a threshold are sufficient; nothing else about the past is needed. Defending a trajectory is not memoryless. To know whether you are on course you need the current reading, an estimate of elapsed time, the value the course predicts for this point in time, and the residual between the two — the gap between where you are and where you ought to be by now. That residual cannot be computed from an instant. It requires observation that spans the interval being regulated, dated well enough to place the present measurement against an earlier baseline.
This is a genuine escalation in what intake must supply, and it maps cleanly onto a distinction worth drawing across three kinds of system, arranged by how much of the world they take in and for how long.
A system trained once on a fixed corpus — call it a Large Language Model — has absorbed an enormous number of trajectories described in text, and can recite the shape of a lactation curve or a growth chart in convincing detail. But it has no clock running against its own corpus and no position estimate on any trajectory in the world, because nothing in a frozen archive tells it what time it currently is. It knows shapes. It does not know where anything, including itself, currently sits on one.
A system that senses a bounded scene and holds a value within it — a Large World Model — can do real homeostasis. It can keep a reading steady against disturbance for the length of an episode. But an episode has a beginning and an end, and when it ends the clock resets. There is no elapsed time carried from one scene to the next against which a longer course could be judged. Homeorhesis needs the interval to persist across episodes, not restart with each one.
A system built to take in every relevant stream continuously, timestamp each observation, carry belief forward as something revised rather than replaced, and attach provenance and decay to what it knows — a Large Universe Model, in the sense the term is used on this axis — is the first arrangement where the residual computation is even well-posed. Not because it is cleverer, but because it is the first one with a clock that does not stop and a memory that does not reset. Position-on-trajectory becomes a computable quantity rather than an undefined one.
The misreading to disown
The weak version of this argument says continuous intake is needed because nothing is predictable and everything must be watched constantly to catch any change. That is false, and homeorhesis is direct evidence against it: canalised systems are highly predictable, which is exactly why a deviation from the expected curve is informative rather than noise. Waddington's chreods are valleys precisely because they constrain outcomes strongly. Strong priors reduce how much observation is needed. They do not eliminate the need to know where you currently are on the path the prior describes. Prediction and position estimation are different quantities, and a system can be excellent at one and blind on the other — which is exactly the Large Language Model's situation.
Three objections, taken seriously
A well-understood system with sparse measurement beats a poorly-controlled system with continuous measurement. Spacecraft cross millions of kilometres on ephemerides and a handful of ranging passes, not permanent telemetry.
Correct, and this is the strongest challenge to the whole argument. It holds wherever the underlying dynamics are known and stationary — where the disturbance spectrum has already been characterised. It fails wherever the process generating the trajectory can itself change: a herd's feed formulation shifts, a market's participants adapt, a chamber's wall deposits alter its drift. Dead-reckoning error compounds with the square of unmodelled disturbance and elapsed time since the last fix; sparse sampling is only optimal once that disturbance spectrum is already known, and that knowledge was purchased by earlier continuous watching.
Homeorhesis is really an argument for strong priors, not for sensing everything. The chreod is inherited, not discovered from data.
Substantially right, and underweighted in most accounts. The target trajectory can indeed be specified almost entirely in advance. But an inherited valley is not an inherited position within it. Nothing about the genome tells the organism where along the curve it currently sits after an insult — that is measured, not inherited — and Waddington's own recovery examples require exactly this sensing. The prior, the belief about current position, and the belief about whether the prior itself needs revision are three separate things, and only the first is fixed in advance.
High-bandwidth observation with a naive controller chases noise. Endocrine systems integrate over hours specifically to prevent this; unfiltered continuous intake produces overcorrection, not canalisation.
The physiology is right; the inference is not. Observation bandwidth and response bandwidth are separable choices. A system can take in a stream continuously and still act on a slow integrated summary of it — that is filtering, applied after intake, not a restriction on intake itself. What does survive from this objection is real: continuous streams make overreaction easy, and provenance-tagged data invite spurious attribution to whichever source is loudest. That is a case for discipline in the control law. It is not a case against watching.
What this establishes, and what it does not
Homeorhesis establishes that trajectory control is strictly more demanding of observation than value control, and that the extra demand is a difference in kind — a clock and a persisting record — not merely a difference in how much data is collected. On the intake axis running from a frozen corpus, through a bounded present scene, to continuous provenance-bearing streams, this gives a principled reason to expect the third position to be the first at which trajectory questions are even well-formed, and therefore a plausible top rung for that particular ladder.
What remains open after the residual is computable is everything downstream of the number: what decay rate to assign old evidence, how to weight conflicting streams, when a deviation is a transient dip and when it is a change of course. Homeorhesis answers what must be watched to know where you are. It says nothing about what to do once you know.