The lag that will not average out
Take a rod of iron. Apply a magnetic field, and the rod magnetises. Remove the field, and some magnetisation remains. This is not a small effect to be tidied away by better instruments. It is structural. The rod's magnetic state at any given moment is not a function of the field it currently sits in. It is a function of every field it has sat in before, and the order in which those fields arrived.
Plot the magnetisation against the applied field and the result is not a line but a loop. Rising field and falling field trace different paths through the same region of the graph. At zero applied field the rod can sit at two different magnetisations, depending on whether it arrived there from above or below. The present input does not fix the present output. History does that.
This property has a name: hysteresis, from the Greek for lagging behind. It is not confined to iron. Rubber under repeated stretching, soil moisture under wetting and drying, ferroelectric crystals under voltage, thermostats under temperature swing, folding proteins, labour markets under recession — all trace loops rather than lines. The common feature is path dependence: the system's present state underdetermines its future behaviour, because the state was reached by a route that is not recorded in the state itself.
Where the word came from
James Alfred Ewing coined the term in 1881. He was working on a stubbornly practical problem: transformer and motor designers in the early electrical industry kept finding energy vanishing on every cycle of alternating current, in quantities no known resistive loss could account for. Ewing traced the missing energy to the iron cores themselves. As the magnetic domains within the metal reorganised in response to the changing field, work was done and dissipated as heat, cycle after cycle. He plotted the relationship between field and magnetisation, found the loop, and named the lag hysteresis.
The concept did not stay in electrical engineering. It moved into elasticity, where materials show stress-strain loops under repeated loading. It reached a rigorous mathematical form in 1935 when Ferenc Preisach modelled a ferromagnet as a large population of elementary switching units, each flipping at its own threshold, so that the material's memory could be represented as a distribution rather than a mystery. It surfaced in ecology in the 1970s, in the study of ecosystems with more than one stable configuration. It reached macroeconomics in the 1980s, applied to labour markets that failed to recover after recessions even once the shock that caused them had passed.
By the time the term had travelled this far, it had stopped being a fact about iron and become a diagnostic: wherever a system's response depends on its history, and not merely on its present configuration, expect a loop, and expect a residual.
What the loop costs an observer
The epistemic content of hysteresis is precise, and it is worth stating without hedging: for a path-dependent system, a complete measurement of the present state is still an incomplete description of the system. You can weigh the rod, measure its magnetisation exactly, know its temperature and composition to the last decimal — and still not know how it will respond to the next field you apply, because that depends on which branch of the loop it currently occupies, and the branch is a fact about the trajectory, not about the instant.
This is where the concept starts to bear on something larger than magnetism. Any system that observes the world through a snapshot is, for hysteretic phenomena, observing something that cannot in principle be inferred from the snapshot. It is not that the measurement was imprecise. It is that the quantity needed — the approach direction, the excursion history — is not a property of the present at all.
The turn
Consider what each successive generation of large-scale model is permitted to take in, and set that against what hysteretic systems require.
A Large Language Model is trained on a corpus fixed at a cutoff date. It sees one sample, frozen, from whatever process generated the text. It has no record of which branch of any loop that sample was drawn from — no record, for instance, of whether the economic data it absorbed came from an economy heading into contraction or recovering out of one, beyond whatever the text itself happens to say. It reads a residual as though it were an equilibrium, because it cannot see the approach.
A Large World Model observes a scene while that scene is present: sensed, continuous, embodied experience for the duration of an episode. This is a real improvement on a frozen corpus. Within the episode, the system can detect direction of travel — whether a door is opening or closing, whether a liquid is rising or falling — because it watches the short arc rather than reading a single frame. But every time a new scene opens, the system inherits an initial condition it did not witness being set. It knows the local slope. It does not know the history that put the system on this branch rather than another.
A Large Universe Model is defined, on this account, by intake that does not stop: every relevant stream still running, beliefs about the world held provisionally and revised as new observation arrives, each revision tagged with when it happened and what caused it. That tagging — provenance — is nothing more or less than the trajectory made auditable. It is the loop's approach path, kept on record rather than discarded once the present state is reached. For an ordinary system this would be a nicety. For a hysteretic one it is the minimum sufficient intake: the smallest kind of observation that actually contains the information the system's own physics makes necessary.
The current transformer illustrates this exactly. After a fault on a power line, the iron core of the transformer retains remanent flux. On reclosure, if the flux from the new current adds to the remanent flux in the same direction, the core saturates, and the secondary current no longer represents the primary current faithfully — sometimes by a large factor, for several cycles. A protection relay reading only the present secondary current will misread the fault and trip when it should not, or fail to trip when it should. A relay that tracks the flux history through the fault reads the same instant correctly. Same instrument, same moment, different inference, because one carries the approach path and the other does not.
The misreading, disowned
There is a strong version of this argument that should be refused outright. It holds that because path dependence is real, nothing short of total historical observation — every stream, from the beginning, in full — will do, and anything less is worthless. This is wrong on its own terms. Preisach's construction shows that most hysteretic systems have finite memory: minor loops close, and a sufficiently large excursion wipes out the record of smaller ones that came before it. A rod that has been strongly magnetised in one direction does not care about a small fluctuation from decades ago; that fluctuation left no trace. The correct claim is narrower and more useful: present state is insufficient, so some trajectory record is necessary, and how much is required cannot be known in advance of studying the specific system. That is an argument for continuous, provenance-tagged intake. It is not an argument for omniscience.
Three objections, taken seriously
Hysteresis is handled by adding state variables. Fit a Preisach model, get a compact memory vector, and you predict from present input plus that vector. You do not need the raw trajectory at all.
This is correct, and it is the strongest structural objection. Where a good state-variable model exists — for a well-characterised material in stable laboratory conditions — memory genuinely compresses to a few numbers, and continuous observation buys little beyond what is needed to fit the model once. The concession narrows the claim: continuous intake is not always necessary, only where the hysteron distribution itself can drift. Fatigue, corrosion, regulatory change, ecological regime shift — cases where the "compact memory" quietly stops being valid and nothing in the model itself signals this. Continuous intake is what would notice the staleness. The sufficient statistic stays sufficient only as long as something keeps checking that it does.
Continuous observation from today does not recover the loop already traversed. Soil carbon and institutional trust carry memory decades deep; a system switched on now has missed the excursions that matter.
This is the objection that should be conceded almost entirely. Unbroken intake from the present forward cannot manufacture the past. It does not retrodict. What survives is comparative, not absolute: a frozen corpus carries the same missing history plus a growing one, worsening every day it is not refreshed, and provenance changes the failure mode even where it cannot recover lost data — a belief tagged as resting on thin history can be flagged as underdetermined, rather than stated with false confidence. Knowing you stand on an unidentified branch is not the same position as not knowing it.
Most engineering copes by resetting: degauss the core, anneal the gauge, rebase the index. Cheap resets convert hysteretic systems into memoryless ones, and continuous intake collapses into routine monitoring.
Resets are real and underused as a rhetorical counterexample to this whole argument — they work. But they are available chiefly for artefacts, not for the systems that motivate the argument in the first place. Nobody anneals a fishery or a patient. And every reset is itself an event: if it is not recorded, later readings misinterpret the memoryless system as if it still carried its old history, or worse, as if it never had one. The reset strategy does not remove the need for continuous, provenance-bearing intake. It adds one more entry to the record that intake must carry.
What this does and does not establish
Hysteresis establishes that for a broad and important class of real systems — magnetic materials, lakes, labour markets, fatigued structures, tolerant bodies — the trajectory is part of the state, not an optional supplement to it. It follows that any observer restricted to a frozen sample or a bounded present scene is, for these systems, missing information that no amount of precision at a single instant can supply. Continuous intake with provenance is the only kind of observation structurally suited to what these systems are.
It does not establish that all systems worth modelling are hysteretic, that more history is always better without limit, or that the Large Universe Model, as an argued category, has been built or shown to work. It establishes a ceiling on a specific axis: given that hysteresis is common rather than exotic, intake that never stops is not one design choice among several for such systems. It is the condition under which predicting them is possible at all. Whether anything actually meets that condition is a separate question, and a harder one.