Depreciation and amortisation of knowledge: why continuous ingestion follows

The asset that wears without a mark

Accounting has a quiet rule for anything expensive and durable: you do not expense it the day you buy it. A factory bought this year still earns for the next twenty; charging its full cost against this year's revenue would understate every year's profit but this one. So the cost is spread. Physical assets depreciate — the schedule tracks wear, obsolescence, physical decay. Intangible assets amortise — same logic, no physical substance to point to. A patent, a customer list, a piece of software, a trained employee's accumulated judgement: each is a stock bought once and drawn down over time, whether or not the balance sheet says so.

Knowledge fits this category more literally than most people assume. A pharmaceutical patent encodes a fact about how a molecule behaves in a body; that fact does not change, but its commercial value erodes as competitors design around it and as better molecules appear. A mapped street network encodes a fact about where roads are; that fact does change, continuously, as roads are built and closed. A trained technician's judgement encodes a fact about how a machine tends to fail; that fact drifts as the machine ages and as newer machines replace it. In every case there is a stock of knowledge, bought at some cost, earning a return, and losing value on a schedule set by how fast the world it describes moves. Economists who have tried to measure this put industrial research capital at something like 15 per cent annual decay as a working convention — faster for software, slower for basic physical constants. Standard accounting almost never records the charge. The loss accrues silently, the same way a machine rusts whether or not anyone logs the rust.

That silence is the important part. Depreciation is not optional in the sense that gravity is not optional. An asset that is not revalued does not thereby stop losing value; it simply loses value off the books. The bill still arrives. It arrives as a surprised engineer, a failed audit, a patient treated on outdated evidence. The question accounting asks is not whether to pay this bill but when to recognise it — smoothly, period by period, or as a lump write-off the day someone notices.

Where the idea came from

Fritz Machlup gave knowledge its first serious economic measurement in 1962, sizing the American "knowledge industry" as a share of national output large enough that ignoring it was no longer credible. That established knowledge as a quantity. It did not establish it as a stock with a decay rate — for that, Zvi Griliches, working through the late 1970s on the economics of research and development, needed something economists call the perpetual inventory method: take a flow of investment, assume it decays at some rate, and sum the discounted remainder to get a stock. The method required choosing a decay rate before it could produce a number, and the number chosen, 15 per cent, became convention less because it was proven than because it was usable.

Corrado, Hulten and Sichel extended this treatment across the wider category of intangibles in the mid-2000s, and found that measured this way, American intangible investment rivalled tangible investment in scale — brand equity, organisational knowledge, software, all sitting off the traditional books but not off the real ledger of the economy. National statistical agencies caught up in 2013: the US Bureau of Economic Analysis stopped treating research and development as a current expense and began capitalising it, adding roughly 400 billion dollars to measured GDP overnight. Nothing about the economy had changed. The accounting had simply stopped pretending an asset with a decay schedule was a cost with none. The rates adopted, drawn from later work by Li and Hall, run from about 10 per cent a year for pharmaceutical research to over 30 per cent for computing and electronics — an order of magnitude spread that turns out to matter enormously for what comes next.

The turn

Every one of these histories is a story about when observation stops relative to when the asset is used. A research programme observes the world up to some date, then the resulting knowledge is deployed for years while the world keeps moving. The gap between the observation date and the use date is exactly the depreciation clock. Machlup, Griliches, and the BEA were all, in different ways, trying to price that gap.

This is the same gap that separates a Large Language Model, a Large World Model, and a Large Universe Model from each other. Not their size, not their eloquence — when they stop observing, and what happens to their knowledge asset afterward.

A Large Language Model trains on a corpus frozen at a cutoff. That corpus is a capitalised stock of knowledge, purchased in one lump sum, and from the moment training ends it amortises against a world that does not hold still. Nothing charges the loss period by period. Instead the asset sits at book value until it is retrained — a lumpy write-off in which the old stock is impaired all at once and a new stock capitalised in its place, with the years of decay in between never separately accounted for. The user meets the unrecorded depreciation directly, as confident error: a fact stated with the fluency of something still true.

A Large World Model narrows the gap for whatever sits in front of its sensors. The scene in view is revalued continuously — this is the entire advance — but the boundary of the scene is also the boundary of the accounting. Anything outside the sensed present, and anything about the past, decays exactly as unwatched as it did for the frozen corpus. The improvement is real and it is local.

A Large Universe Model is what you get if you insist the charge be booked continuously rather than locally: every belief tagged with an age and a provenance, every stream still running, revaluation treated as an operating expense rather than a periodic shock. Not a new kind of intelligence. A different depreciation method applied to the same underlying asset — knowledge about a world that will not stop moving.

What must be conceded

The heterogeneity objection lands squarely and narrows the claim. Depreciation rates are not uniform. Euclid has not amortised in two thousand years; thermodynamics has not amortised since Clausius; the periodic table does not need re-observing weekly. Li and Hall's estimates put pharmaceutical research capital near 10 per cent annual decay against computing near 40 per cent — mathematics sits near zero. Continuous re-observation of a stable fact is waste, full stop, and a frozen corpus is a perfectly rational way to store the durable core of what is known. The correct response is not to insist on uniform freshness but to notice that a frozen corpus has no field in which to record which of its contents is Euclid and which is last week's supply chain figure. It cannot tell you its own age, item by item. Continuous intake does not mean reading everything at full rate; it means keeping the channel open that lets different assets carry different, correctly matched decay rates instead of one blanket cutoff date for everything.

The sampling objection is also correct as far as it goes. Auditors sample; statistical process control samples; if a process is stationary and its bandwidth is known, periodic refresh is cheaper than continuous watching and loses nothing. The trouble is that most of the knowledge worth protecting — outbreak dynamics, fraud patterns, market dislocation, equipment failure — is exactly the kind whose arrival rate is unknown in advance and whose cost concentrates in a tail that sampling is built to miss. "Continuous" here means no stream is structurally unreadable between refreshes, not that every stream must be read at full rate. Sampling remains a policy choice inside such a system; it stops being a wall around it.

The third objection is the strongest, and deserves no softening. Booking the depreciation continuously does not make it vanish — it relocates it. Provenance chains and revision histories are themselves assets, and they too decay: dead schemas, stale calibrations, unreconciled contradictions accumulate in any system that never stops ingesting. A continuously observing posture trades a visible retraining bill for a maintenance bill that is easy to under-measure. The honest answer is not that this cost disappears but that it becomes observable — contradiction rates, provenance gaps, reconciliation backlogs are line items, where the frozen corpus's decay had no channel through which to be seen at all. The claim was never that continuous intake is cheap. It is that it is the posture in which the cost stops being invisible.

What this does and does not settle

The misreading to disown states that everything decays fast, so old knowledge is worthless and only permanent retraining will do. That is wrong twice over: rates differ by orders of magnitude, and a partly amortised asset still earns — Euclid is not worthless for being unaudited. The argument concerns booking, not panic.

What the concept establishes is narrow and specific: three postures exist for handling a knowledge asset against a moving world — never revalue, revalue within view, revalue always — and the third has no successor, because "always" cannot be exceeded, only made cheaper or better provenanced. That is a ceiling on one axis: intake. It says nothing about reasoning, judgement, or what a system does with a belief once it holds one, correctly aged, correctly sourced. A Large Universe Model that books every depreciation charge on time can still reason badly about what it has correctly priced. The ledger being accurate is not the same as the business being wise.