Haute Lumière
Commerce · VII · MMXXVI · daylight
Volume VII — Planetary and Cosmic · Extension III of III · and the last of the twenty-one
Nine movements, two vocabularies, three permanent blanks.
There are two vocabularies in the room and by now everybody knows it.
One says boundary, sink, stock, resilience, regeneration. The other says covenant, liability, endowment, reserve, depreciation. The first group is told, politely, that it is describing values rather than facts. The second is told, less politely, that it is describing money rather than the world. Both then repeat themselves more loudly, and the meeting ends.
For most of what those two lists cover, the argument is unnecessary. This chapter is a term table in which each row is one object under two names, with the arithmetic that shows it is one object. A planetary boundary is a covenant with a step loss function; a sink is a liability once somebody writes a price against it; a stock is an endowment with a draw rate; resilience is a funded reserve. Thirteen rows, and in every one the two sides compute the same number or reconcile to the same published figure. Where they do, the argument was about words.
And then the part that is worth more than the table: the terms that do not cross at all. Six in one direction, seven in the other, seven false friends, and a joint vocabulary of 26 terms of which a translation table can carry exactly half. The remaining half is not a gap in anybody's dictionary. It is a bound, and it has a shape — every finance-only term is about time and the order of claims, and every planetary-only term is about a place, a grade or an owner.
Then the cut, which is a fact about this volume rather than an argument. Seven of Volume VII's eleven honest negatives turn on a missing word rather than on a missing measurement — 63.6 percent — and the four that do not are exactly the four whose negatives are measurements. The places where this volume had to admit failure are, mostly, translation failures.
And because this is the last of the twenty-one extensions, it does one thing the other six could not do alone: it looks across all seven volumes and asks what the seven translations reveal together. One row maps cleanly in every volume. Three terms have no counterpart in any of them. Two of those three run the same way, and both of them are about an owner or a grade.
— The Editors
Translation between these two vocabularies is not an aspiration. It has been built, at national scale, by statisticians and lawyers, and the builds are public.
Ecosystem accounting, which reconciles line by line. The System of Environmental-Economic Accounting was adopted as an international statistical standard — the same status as the national accounts themselves — with the ecosystem volume following in 2021. The feature that makes it a translation rather than a rival is that it does not replace a headline number with a better one. It builds physical and monetary accounts for water, energy, timber, fish, land and ecosystem services that reconcile against the national accounts, so a finance ministry reads both without converting.
Water accounting with an auditor's opinion. Australia's Water Accounting Standards Board did the thing this chapter argues for and did it in the language of finance: general-purpose water accounting reports, a statement of water assets and water liabilities, a statement of changes, and an assurance regime modelled on financial audit, with a National Water Account published against it. Chapter VII.06's claim that a basin is a set of books is not a metaphor somebody in this edition invented. It is a published standard with an opinion attached.
A catch certificate, which is a translation stapled to a box. Chapter VII.04's sharpest finding is that the only mechanism that has ever worked on the high seas is a testable property attached to a physical object passing through a named place. A catch documentation scheme translates legality, which is a fact about a history, into a document, which is a fact about an object. Illegal catch in the Convention Area fell by an order of magnitude on the strength of it. The translation was the instrument.
A river that was given legal personality because it could not be modelled. Te Awa Tupua made the Whanganui a legal person with two guardians, one appointed by the Crown and one by the iwi. Read it here as a translation event: a concept with no counterpart in commercial law was given one by legislation, because it could not be given one by arithmetic. That is the honest route for an untranslatable term, and it is the exception that shows why the list in the fourth movement matters.
And a dose ceiling where a price would not go. The Yucca Mountain standard runs to one million years, and Chapter VII.08 shows why it is a ceiling and not a rate: a pound arriving in year ten thousand, discounted at one percent — the lowest rate in the best-constructed public schedule in the world — is worth ten to the minus 43.2 pounds. When the translation breaks, the surviving institutions did not find a lower rate. They changed instrument.
Five builds, one pattern: in each, somebody wrote the dictionary down in a document with a signature on it, and the argument stopped being about words and started being about numbers.
Every figure below is computed in lib/verify/VII_E3.py, which prints each input with its unit and its source before it prints a result.
First, the table. Thirteen rows, each one object under two names.
| Planetary term | Finance term | The identification | Ch. |
|---|---|---|---|
| a planetary boundary | a covenant, level-tested with a step loss | headroom = (reading − boundary) / boundary; ozone 3.3 %, aragonite 1.8 %, aerosol 24.0 % | VII.01 |
| a sink | a liability, once a price is written against it | unpriced marginal damage = (190 − 5) × 52 Gt = 9.62 trillion dollars a year | VII.02 · VII.10 |
| a stock | an endowment with a draw rate | corpus × real draw ≥ operating cost; 2,850,000 / 0.040 = 71,250,000 | VII.07 · VII.11 |
| resilience | a funded reserve | reserve = board fraction × unpriced exposure; 0.10 × 36,940,000 = 3,694,000 | VII.02 |
| the residual | the suspense account | P = ET + Q + ΔS + ε; the books must close, so ε is the finding | VII.06 |
| the catchment | the reporting entity | the only boundary in environmental economics at which the accounts must close | VII.06 |
| carrying capacity | covenant headroom, as a bracket | n* runs 4,412 to 196,111, geometric mean 29,417, against a catalogue of 40,500 | VII.09 |
| overshoot | an impairment charge against named assets | forest cover 60 / 75 = 0.800, so 20.0 % below; intactness 79 / 90 = 0.878, 12.2 % below | VII.01 |
| a flow at the place of effect | a throughput covenant, by catchment | 190 Mt over 1,600 Mha is 118.75 kg N/ha; on a fifth of it 593.75 — the same total | VII.01 |
| position | freight | P* = 1.049 × C_LEO; at 3,059 dollars a kilogram to low Earth orbit that is 3,208 | VII.09 |
| co-management | a share plus a funded counting institution | 0.50 / 0.05 = 10.0×, and runs must fall to 0.10 of 1974 before the share is worth less | VII.07 |
| deep time | the rate's floor, where present value stops answering | one pound at year ten thousand at 1.0 percent is ten to the minus 43.2 pounds | VII.08 |
| substitutability | the parameter that sets the sign of the account | θ* = −ΔN / ΔM; 0.738 with land, 3.388 without it | VII.11 |
Four of those rows, recomputed, so the table can be checked rather than believed:
headroom, ozone column 3.3 %
headroom, aragonite saturation 1.8 %
headroom, interhemispheric aerosol 24.0 %
unpriced marginal damage 9.62 trillion $/yr
forest cover, share of the line 0.800 -> 20.0 % below
intactness, share of the line 0.878 -> 12.2 % below
corpus at a 4.0 % draw on a $2,850,000 duty $71,250,000
And the split that decides which rows can be relied on:
rows resting on an identity 9 69.2 %
rows resting on a chosen parameter 4 30.8 %
An identity round-trips. Translate overshoot into impairment and back and the number returns, because a ratio read in either direction is the same function. A chosen parameter does not, and the loss is silent. Four rows — the sink, resilience, carrying capacity and substitutability — carry a number somebody selected: a price, a board fraction, a collision cross-section, an ethical position. Translate one of those and the parameter travels invisibly inside the result, which is the fault the ninth movement's instrument exists to prevent.
Second, and this is the chapter: where the translation fails.
rows that translate 13
planetary terms with no finance counterpart 6
finance terms with no planetary counterpart 7
---------------------------------------------------------
the joint vocabulary 26 terms
share a translation table can carry 50.0 %
share it cannot 50.0 %
The six with no counterpart in finance. A sink with no owner — the sky's aperture exports six hundred and twelve trillion watts per kelvin, continuously, and appears on no balance sheet anywhere. The grade of energy — no accounting standard recognises work capacity, and a megawatt-hour is a megawatt-hour in every contract ever signed. A threshold with no cost function — Nordhaus's objection, which is correct: a limit with no damage function and no rate tells you a place not to go and nothing about which of the ten thousand paths short of it to take. A sum of local limits that never tips — Brook and colleagues found the terrestrial biosphere is a mosaic of local transitions, and no consolidation rule in any standard produces a threshold from a mosaic. An uncertainty band wider than its own boundary — a published band of 900.0 percent fails the measurement-reliability test by a distance, and the nearest accounting object, a contingent liability, is a different thing wearing the same coat. Title to a stock nobody owns — the high seas, the orbital shell and the aquifer are assets with no owner of record, and title is precisely what they lack.
The seven with no counterpart in the planetary vocabulary, and this is the list this tradition does not like to write down. The discount rate — nothing here converts a future flow into a present number. Seniority and the order of claims — nothing ranks claimants when a system fails; a boundary breach has no waterfall. Liquidity — an ecosystem cannot exit a position and a planet cannot be sold at short notice. Time consistency — a successor re-applying your own published table values your commitment at 64.5 percent and is not cheating, and there is no ecological operator that describes this. An arm's-length price where no market exists — five permitted methods and a range, because a number is required and there is nothing to read it off. Legal personality — which had to be legislated, because it could not be modelled. An equity cure — a covenant breach can be cured; a crossed threshold in a well-mixed system cannot.
Now look at what each list contains, because that is the finding. Every finance-only term is about time and the order of claims: when the money arrives, who is paid first, how fast you can leave, whether a breach can be cured. Every planetary-only term is about a place, a grade or an owner: where the flow lands, what temperature the joules are carried at, whose the stock is.
The two vocabularies are not rivals describing one world in different words. They are two projections of it, and what each is missing is orthogonal to what the other is missing. Neither contains the other, and 50.0 percent is not a measure of how hard anybody has tried. It is the bound.
Third, the false friends, which are worse than the blanks.
Seven words cross between these vocabularies without anybody stopping them, and change meaning on the way.
| Word | On one side | On the other |
|---|---|---|
| boundary | a threshold in a well-mixed system, past which behaviour changes | the perimeter of a reporting entity, elected by a consolidation test |
| sink | a place waste goes, with a finite capacity and a temperature | a use of funds |
| reserve | a stock deliberately not drawn | an appropriation of retained earnings — and, elsewhere, a proved quantity |
| stock | a standing quantity with a regeneration rate | an equity security |
| yield | tonnes per hectare, or streamflow per unit area | the return on a security |
| capacity | what a shell, a basin or an airshed can carry | installed plant, or the headroom to borrow |
| recovery | a stock rebuilding toward a reference condition | a creditor's share of a claim in insolvency |
A false friend is caught only when somebody who holds both vocabularies reads the operative clause. Put the share of such readers at 0.15 and the number who read a clause closely at four:
n = 2 P(caught) 0.2775 expected to pass 5.06
n = 4 P(caught) 0.4780 expected to pass 3.65
n = 8 P(caught) 0.7275 expected to pass 1.91
one named bilingual reviewer P(caught) 1.0000 expected to pass 0.00
Even eight careful readers leave nearly two of the seven standing. The countermeasure is not a longer glossary and not more reviewers; it is one named bilingual reader, and it takes the expected number of silent crossings to zero in a single step. A term with no counterpart announces itself at first reading, because somebody asks what it means. A word that translates silently reaches the term sheet, the covenant and the board minute, and is discovered in the quarter when the two parties turn out to have signed different agreements.
Fourth — and this is the cut — the volume's honest negatives are mostly translation failures, not measurement failures.
Every one of Volume VII's eleven chapters carries at least one honest negative. Classify each by what it actually turns on:
VII.01 translation a band wider than its boundary; a boundary is not a price
VII.02 measurement the damage function rests on a narrow empirical base
VII.03 translation substitutability is false for slow-forming systems
VII.04 translation a fine is a price, and normative compliance has no finance term
VII.05 measurement the premium is regressive, and load factor decides the carbon
VII.06 translation no scheme can attribute the service it buys to a parcel
VII.07 measurement a recognised right is unfunded by thirteen years
VII.08 translation a declining schedule is time-inconsistent; PV stops answering
VII.09 measurement no material clears the floor; the bracket is wide
VII.10 translation an entropy account ranks no two goods and prices nothing
VII.11 translation one unpublished parameter sets the sign of the account
---------------------------------------------------------------------------
turning on a missing WORD 7 of 11 63.6 %
turning on a missing MEASUREMENT 4 of 11 36.4 %
Seven of eleven. The intuition almost everyone brings to this volume is that its failures are empirical — that we do not yet know enough about extinction rates, or soil carbon, or the shape of a damage function. Four of them are exactly that. The other seven are places where the measurement exists and there is no word to receive it: a band that cannot be covenanted, a service that cannot be attributed to a parcel, a schedule that cannot bind a successor, an entropy budget that cannot rank two goods, a parameter with no published value. More funding fixes four of the eleven. A dictionary fixes seven.
And the honest negative of this chapter is about that classification. It is a judgement, not a measurement, and a different reader would move one or two. So move them:
reclassify 0 as measurement 7 of 11 63.6 % a majority
reclassify 1 as measurement 6 of 11 54.5 % a majority
reclassify 2 as measurement 5 of 11 45.5 % NOT a majority
reclassify 3 as measurement 4 of 11 36.4 % NOT a majority
The claim survives one reclassification and fails at two. That is the honest width of it, printed here rather than left for somebody to find, because a finding whose sensitivity is not stated is an assertion with a number attached.
Fifth: what the seven translations reveal together.
This is the last of the twenty-one extensions, and it is the only one in a position to ask the question across all seven volumes. The tally below is this chapter's own construction over those volumes, not a measurement of them, and it is labelled that way in the module.
One row maps cleanly in all seven. It is not a subtle one, and that is the point: a stock with a rate is an asset with a schedule. Volume I's regeneration facility, Volume II's circulation multiplier, Volume III's monetary stocks, Volume IV's regenerated life, Volume V's human capital, Volume VI's common-pool resource, Volume VII's standing timber and forest extent and biosphere intactness — in every volume, the object at the centre of the argument is a quantity that changes at a rate, and finance has had the machinery for booking exactly that object for a century. Chapter VII.11 says it in one line: this edition spent seventy-six chapters establishing that a stock with a regeneration rate behaves differently from a stock without one. The translation of that sentence is a depreciation schedule with the sign reversed, and it holds in 7 of the 7 volumes.
And three terms have no counterpart in any of them.
Two of the three run the same way — 66.7 percent — and both of them are about an owner or a grade. That is the same asymmetry the failure list produced inside one volume, arriving independently from seven. A single volume's blank list could be an accident of subject matter. The same shape in all seven is a property of the two vocabularies.
And there is one more thing worth saying about those three, because it is what the edition does with them. The last chapter of the edition turns one of them into an instrument. Chapter VII.11's θ sits exactly where the missing translation would be: it is not a belief about the world, it is the exchange rate between the two vocabularies, and publishing it is what makes the disagreement productive rather than total. The permanent gaps are not a residue. They are the places where a parameter has to be named, signed and shown.
In the practice that has absorbed this, every serious document carries a definitions schedule with two parts, and the second part is the one people read.
Part A is the translated terms, each with the arithmetic that identifies the two sides and a mark saying whether the row rests on an identity or on a chosen parameter. Nobody argues about whether overshoot and impairment mean the same thing. They check, and the check is a division, and it takes forty seconds.
Part B is the untranslatable list, and beside each entry is the name of the party who carries the risk of the gap. The discount rate is on the face of the paper with the answer rather than buried in a model. The grade of the energy is a column in the tariff. The absence of title over a shared stock is written down as an absence, with the party who bears it named, rather than papered over with a proxy. Often the answer is benign — the lender carries the rate risk because the facility is fixed-rate — and writing it down is what makes the benign cases visible as benign.
There is one named bilingual reader on every document that matters. Not a committee; one person, named in the process, whose job is to read the operative clauses for the seven words that do two jobs. Everybody knows who it is. It costs an afternoon and it is the highest-return afternoon in the whole apparatus.
The words themselves are still used, freely and warmly, in the letter and in the conversation, where ambiguity is a feature and precision would be cold. They are not used in a covenant.
And θ is published. Nobody is vaguely in favour of the next generation any more; a person who says the account is positive states the substitutability they are using, and a person who says it is negative does the same. The disagreement is still total and it is now productive, because both sides point at the same number and argue about one parameter rather than pointing at two numbers and arguing about everything.
One artifact, two parts, a fortnight — and the order is the reverse of the obvious one.
Part B first, always. The untranslatable list takes an afternoon, needs no arithmetic, and is the half that prevents disputes rather than settling them. A team that starts with Part A will spend three weeks perfecting identities and never reach the part where the money is.
Part B — the untranslatable schedule. Three columns: the term, the vocabulary it lives in, and the party who bears the risk of the gap. That third column will be resisted, because it names somebody. Name them anyway. In a document touching Volume VII's material, four entries appear almost every time: the discount rate, the grade specification, the title to a regenerating stock, and the ordering of claims when a physical threshold is crossed.
Part A — the translated terms. Four columns: the term in each vocabulary, the identification — an equation or a published reconciliation — and whether the row rests on an identity or on a chosen parameter. That last column is the one people leave out and the one that matters, because it tells a later reader which rows can be relied on to round-trip. The test for Part A is mechanical and it is the only test that works: can you write the identity? If two people cannot compute the same number from both sides, the row is not in Part A.
The false-friend clause. Seven words, listed, each defined once and used only in that sense throughout the document. One paragraph, and it is the highest-return paragraph in the schedule.
The named bilingual reader. One person, named in the process rather than in the document, who reads the operative clauses before execution. The arithmetic above is the whole argument for the appointment: four careful readers leave 3.65 of the seven standing and one bilingual reader leaves none.
Governance. The schedule is owned by whoever owns the document — counsel on a facility, the controller on a set of accounts, the programme director on a business case — and it is reviewed when the document is amended and at no other time. A schedule with its own review cycle becomes a separate artifact that drifts from the agreement it defines. A change to any Part A identity requires the previous identification to remain visible in the amended schedule, which removes almost all of the value of changing a definition quietly.
What to resist. This is not a campaign to translate everything. A term forced across when it does not go is worse than a term left in Part B, because it now carries a number somebody will rely on. The purpose is to make the translations checkable and the gaps visible — and some of the gaps should stay gaps.
Three things keep a dictionary alive, and they are all about attachment.
It is attached to a document that is signed. A glossary published on its own is read once. A numbered schedule to an agreement is read every time somebody argues about a clause, which is the only reliable form of readership.
It is used to settle something in its first year. An instrument that has never been used in an argument is quietly dropped at the next amendment. Use it the first time two parties disagree about capacity — and they will, because that word does three jobs.
Somebody who is not the drafter reads it. The drafter is the one person who cannot see the gap between what the word means to them and what it says on the page, because they read the page through the meaning.
Now the failure modes, named.
It fails when Part B is dropped at the second revision, because it has no numbers in it and it looks like commentary. The guard is the risk column: a term with a named party attached is harder to delete than a term with a definition attached.
It fails when a parameter row is quietly regraded — a row whose chosen parameter has been changed so that it no longer reconciles, and nobody versioned it. Four of the thirteen rows are exposed to this, and they are named on the face of the table so that a later reader knows which four to check.
It fails when the dictionary is used in one direction only. Translating a planetary claim into finance vocabulary makes it financeable, which makes it worth misstating — and a schedule that only ever converts stocks into cash flows has become a marketing instrument. The countermeasure is Part B: a schedule that names seven things finance can say and this vocabulary cannot is visibly not a piece of advocacy.
And it fails when somebody mistakes the dictionary for an agreement. Two parties who share definitions can disagree completely, and should be able to. The schedule buys a shorter argument, not a shared position, and a room that expects the second from it will abandon the first.
There is a specific pleasure in the moment a long argument dissolves because somebody wrote down what a word meant. Two teams discover they have been using capacity for different quantities, both correctly, and the disagreement was never about the plant at all. The hour they get back is not the good part. The good part is the quality of the argument that follows, which is about something real.
And there is the pleasure of the blank entry, which is rarer and better. Writing no counterpart in a column is a small act of honesty that costs nothing and changes the temperature of a room. The finance people relax, because somebody from the other side has just conceded that a discount rate does real work that nothing in their vocabulary does. The people who came in from the field relax, because somebody has written down that a megawatt-hour at sixty degrees and a megawatt-hour at three hundred are not the same object and no contract in the world currently knows it.
Best of all — and this is the right last pleasure for a last chapter — is the moment somebody from the other vocabulary uses one of your rows in their own argument, in their own words, without noticing that it came across. That is a translation having worked. Not when both sides agree, but when one side stops being able to tell which language the sentence started in.
The instrument: a published θ, and a standing register of the terms that have none.
One page, produced annually, attached to something with a signature. It is the only instrument in this edition's catalogue that raises, saves and allocates no money at all — and every other instrument in the catalogue turns on a word that means two things.
The structure.
θ. The substitutability at which the organisation's own position crosses zero — θ = −ΔN / ΔM — computed from its own accounts, with the natural position stated as a lower bound and everything unmeasured registered as UNMEASURED rather than as zero.θ = 1 and θ = 0, on both treatments of the largest contested asset. On the worked national account they are +22,052 and −62,228 with land, and −43,863 and −62,228 without it.The balance-sheet treatment. The register is a drafting cost and runs through the year it is made; it is not an asset and should not be capitalised. Its value is informational and it belongs in the notes. What it changes is elsewhere and is material: where Part A identifies a regeneration rate with a useful economic life, that identification is the evidence supporting a depreciation estimate, and your auditors will ask for it. Take it to them at the planning meeting, where it is a conversation about useful economic life that they have every year.
The number that decides it. One line, on the front page:
θ* = − ΔN / ΔM
with land 62,228 / 84,280 = 0.738
excluding land 62,228 / 18,365 = 3.388
Below your own working θ, the position is positive on your own stated beliefs and you should publish it. Above 1, no belief anybody holds clears it, and that is not a reason to withhold the account — it is the reason the account exists.
And here is why the parameter belongs on the face of the page rather than in a footnote. The four cells span 84,280 pounds a head, and ΔM — the entire transfer being argued about — is 84,280 pounds a head:
the spread across the four cells 84,280 GBP/head
against ΔM itself 84,280 GBP/head
the ratio 1.0000
The spread is exactly ΔM. One unpublished parameter is worth one hundred percent of the quantity under discussion. Against that, the register costs an analyst fortnight — 80 hours at 150.00 dollars, which is 12,000 dollars — and it pays wherever a single decision turning on θ is worth more than a fortnight, which is every decision this edition describes.
The first ninety days.
| Day | Action | Artifact |
|---|---|---|
| 1–10 | List every term in the live document that means something financial | The term list, taken from the document |
| 11–20 | Sort into Part A, Part B and false friend; write the false-friend clause | The false-friend clause |
| 21–35 | Fill the risk column in Part B; take it to the parties named in it | Part B, with risk allocated |
| 36–50 | Write the identity for every Part A row; mark identity or parameter | Part A, with its arithmetic |
| 51–65 | Compute ΔM, ΔN as a lower bound, and θ*; register the UNMEASURED | The four cells |
| 66–75 | Name the bilingual reader; put the name in the process | The appointment |
| 76–90 | Attach the page to a signature — covenant, rule, duty or coupon | The signed document |
And the one thing to do before any of it. Take the live agreement and mark every occurrence of the seven false friends. It costs an hour, it requires no arithmetic, and it is the only step in this chapter that has never once been done without finding something.
Discovery — what is already working
Dream — what becomes possible
θ published beside our cost of capital. What would we want it to be, and what would we want people to conclude from it?Design — what we build
Destiny — how it holds
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Note on figures. Every figure in this chapter is computed in lib/verify/VII_E3.py and printed there with its inputs, its units and its source by python3 lib/verify.py VII.E3. Figures carried from VII.01 to VII.11 are recomputed or reprinted here with their chapter named. Three of this chapter's objects are constructions rather than measurements and are labelled as such in the module: the term table itself, the classification of the eleven honest negatives into translation and measurement failures — whose sensitivity is printed, and which survives one reclassification and fails at two — and the cross-volume tally over the seven volumes. The share of readers holding both vocabularies and the number who read an operative clause closely are stated assumptions; the false friends' expected passes move with them and the module prints the sweep.