Sixteen parallaxes

After the earthquake of 1 November 1755, the Portuguese Secretary of State, Sebastião José de Carvalho e Melo, later Marquis of Pombal, sent the bishops a questionnaire to be copied to every parish priest; the letter to the Cardinal-Patriarch of Lisbon reproduced by the Lisbon Quake Museum is dated 20 January 1756 (the museum's running text gives 26 January), the priests were given a month to answer, and the Bishop of Coimbra had the questions printed D [Lisbon Quake Museum n.d., the museum's transcription]. There were thirteen questions: the hour and duration of the shock, its direction, the houses ruined and the people killed, changes in the sea, springs and rivers, the behaviour of the tide, fissures in the ground, the measures taken by clergy, soldiers and ministers, aftershocks, earlier earthquakes remembered, the parish's population, shortages, and fire D [Lisbon Quake Museum n.d., the questionnaire as transcribed there]. The returns went to the Secretariat of State and are kept at the Torre do Tombo; a study of the Aveiro lagoon that uses them records that, within its study area, some parishes of the diocese of Coimbra and all of those of the diocese of Porto are missing from the collection, and fills the gaps from the distinct general inquiry of 1758, whose question 20 asked whether the parish had suffered ruin in 1755 and whether it had been repaired D [Sarmento and Cardoso 2006, pp. 94–95].

The inquiry is the data stage of Figure 11.1 (p. 434) in an early form: a fixed schema (the thirteen questions), a transmission chain (ministry, bishop, priest, parishioner), a provenance record (which parish answered and which did not), and a second instrument to repair coverage. Model C1 takes its feature space as given; the inquiry shows the feature space being chosen, and the missing cells travelling with the data R.

What the ministry could know in 1756 was bounded by the chain: a question had to be copied, carried, answered by someone who had been there and returned, at the pace of the post and of the Church's administration, and a parish that did not answer was a blank that no analysis could fill. Satellite imagery, multilingual transcription and automated extraction have changed the scale and the latency of that chain beyond recognition (the two situations at the end of Section 11.7 (p. 447)); they have not changed the two things the inquiry got right — that testimony is comparable only when the witnesses were asked the same question, and that the omissions must be recorded next to the answers. A common questionnaire was an information technology; faster processing does not repair an unobserved location.

The account rests on one published study and a museum's reproductions of the documents. The box claims nothing about what the inquiry achieved for the science of earthquakes.

John Snow's On the Mode of Communication of Cholera appeared in its second edition in London in 1855, with a preface dated 11 December 1854 D [Snow 1855]. Its account of the outbreak around Broad Street records that Snow put his case to the Board of Guardians on Thursday 7 September 1854 and that the pump handle was removed the following day; it also records that “the attacks had so far diminished before the use of the water was stopped, that it is impossible to decide whether the well still contained the cholera poison in an active state” D [Snow 1855, pp. 40, 51–52]. The book's second argument rests on south London's water. The Lambeth Company had moved its works in 1852 from opposite Hungerford Market to Thames Ditton, above the city's sewage, while the Southwark and Vauxhall Company had not; the two companies' pipes passed together down all the streets of several south districts, so that the effect of the change was not evident from district totals; Snow took lists of cholera deaths at the General Register Office and traced the supply of the houses concerned D [Snow 1855, the water supply of the south districts].

The two arguments are the two halves of Model L5. The decline after the handle was removed is one regime observed before and after an intervention, and Snow wrote that it could not decide between the structures: an exhausted outbreak and a poisoned well predict the same curve. The intermixed supply is the separating observation: houses in the same streets, supplied by different companies, on which two structures that agree on district totals predict different rates — provided the houses of the two companies are comparable in the other determinants of cholera, an assumption that the intermingling of the pipes makes plausible but does not establish. Field 3 is what changed: the analyst observed a variable the structures disagree about R.

Snow's discriminating variable was expensive: a registry list, then a visit to each house to learn its supplier. Digital records make that linkage cheap, and a large table of before-and-after counts can be assembled in a day. Model L5's arithmetic is indifferent to the size of the table: a million further observations of the baseline regime do not choose between structures that agree on it, while observations of a variable on which the structures imply different distributions can, subject to comparability and sampling uncertainty; Snow went looking for such a variable. Better access helps locate discriminating evidence; it does not turn an association into the effect of an intervention.

A public-health analogy for an identification problem, not an interstate game: no one here optimises against Snow. A comparison of intermixed households is not randomised assignment.

The Met Office was founded in 1854 under Robert FitzRoy D [Met Office 2026]. Observations from stations around the British and Irish coasts were sent to London by telegraph and collated into Daily Weather Reports; after the Royal Charter gale of 1859 FitzRoy developed a national storm-warning service, which began in February 1861; and on 1 August 1861 he published the first public weather forecast in The Times, written in his own hand on the Daily Weather Report for 31 July D [Met Office 2026].

Model O1's experiment is a kernel from the state to a signal, and its decision rule acts on the signal. The telegraph changed no barometer's kernel. It changed field 3 by making distant observations available before the decision (a ship sailing, a harbour closing) rather than after it, and field 6 by giving a warning somewhere to go while the action was still feasible. In the language of Exercise 1.1 (p. 52), it raised the receipt probability of an observation from near zero to something, for a decision whose window was hours R.

A warning chain has three clocks: observation, interpretation (collation into a report, a warning), and action (the warning reaching a port while a protective action is still possible). Telegraphy shortened the first two. A storm warning that is right but late is worth exactly nothing for the decision it was meant to inform: the receipt factor of Exercise 1.1 (p. 52) is zero. The same three clocks run in the two situations above, with different sensors and a different hazard.

No probability from the episode enters any model. The archive records dates and documents, not the hit rate of the warnings or the decisions they changed, and the box makes no claim about lives saved; a modern warning service differs in hazards, coverage and protective capacity.

In the first decades of electric telegraphy, where lines crossed national borders, messages had to be stopped and translated into the system of the next jurisdiction D [International Telecommunication Union 2026]. Representatives of twenty states gathered in Paris at an International Telegraph Conference; on 17 May 1865 they signed the first International Telegraph Convention, a framework to standardise telegraph equipment, set uniform operating instructions and lay down common international tariff and accounting rules, and they established the International Telegraph Union to supervise later amendments to the agreement D [International Telecommunication Union 2026].

The wire was field 6 of each administration's card: the action “send a message across the border” was feasible. The re-encoding at the border was field 3 and field 5 at once: the receiving office could not read the record as sent, and the cost of making it readable was paid in time by a clerk. In the coordination game of Exercise 0.9 (p. 25), the convention raises the return to joint adoption of one process (a change in payoffs, field 5), and the Union is a standing device for the public recommendation of Definition 0.12 (p. 13), whose only power is that obeying it is a best response when the other side obeys too R.

Before the convention the speed of electricity was available and the message crossed the border at the speed of a clerk. What changed in 1865 was not the channel but the rule for what crosses it: the convention fixed the interface between organisations, so that a record readable on one side was readable on the other. Information can cross a physical border without crossing a semantic or legal one; the electronic-records situation at the end of Section 0.8 (p. 20) is the same sentence a century and a half later, with the legal standing of a record in place of its encoding.

The convention is not a realisation of the numerical game: twenty administrations, tariffs and a standing union are not two players and a coin, and nineteenth-century institutions and market power differed. The box takes one mechanism from the episode, not a calibration; no number of 1865 enters any model.

On 13 July 1870 Heinrich Abeken telegraphed from Ems to Bismarck in Berlin an account, on King Wilhelm's behalf, of the King's exchange that day with the French ambassador, Count Benedetti; the telegram and the shortened text Bismarck released to the newspapers survive side by side D [German Historical Institute Washington 1870: both texts, in Snyder's translation]. The telegram gives a sequence: the ambassador stopped the King on the promenade and asked him to undertake never again to approve the Hohenzollern candidacy for the Spanish throne; the King declined to bind himself for all time; he later received a message from the prince confirming the renunciation the ambassador already knew of from Paris; he then decided not to receive the ambassador again and had an adjutant tell him so; and he left it to Bismarck whether to communicate the demand and its rejection to the embassies and the press. The released text kept the demand, the refusal to receive the ambassador again and the adjutant's message, and dropped the promenade, the King's reasons, the message from the prince and the discretion left to the recipient D [German Historical Institute Washington 1870, the two texts compared].

Field 3, on the receiver's side R. The released text's provenance was authentic; what the two texts show side by side is selection and compression — the release passes from the demand directly to the refusal to receive the ambassador again, without the prince's message that came between them — not the truth of every statement in it, which the pair alone cannot establish. What the reader did not have was the channel's kernel: that the text was a selection, and that selecting was the sender's move. A reader who took a communiqué for a report of the exchange updated correctly inside the wrong model of the channel, as in Exercise 5.1 (p. 208); in Model M4's terms the claim was authored by a party with a stake in the reader's inference.

The channel of 1870 was fast for its day (a telegram the same day, a release to the newspapers), and the omitted context was unavailable to the readers of the release at any speed: what the press carried was the shorter text. The impersonation campaign above inverts the parameters, forged provenance behind an authentic-sounding voice, but the remedy its advisory names is the operation the reader of 1870 could not perform: check the message against a source the sender does not control. More bandwidth would not have restored the context; it would have carried the shorter text further, faster.

The box is about two texts and a receiver's model of a channel. The diplomatic crisis of July 1870 and what followed it are not analysed here; nothing is claimed about what the release caused, and nothing about any party's intentions is inferred from the texts.

The treaty forming a General Postal Union was signed at Berne on 9 October 1874 by twenty-one states, among them Germany, Austria-Hungary, France, Great Britain, Russia, Turkey and the United States; ratifications were exchanged on 3 May 1875, and it came into force on 1 July 1875 (Art. 19). Article 1 made the contracting countries, “under the title of General Postal Union, a single postal territory for the reciprocal exchange of correspondence between their post-offices”. Article 14 provided that the treaty's stipulations “do not involve any alteration in the interior postal legislation of any country”. Article 15 organised an International Office, “a central office, which shall be conducted under the surveillance of a Postal Administration to be chosen by the Congress”, its expenses borne by all the contracting administrations, charged with collecting and distributing information on the international service, giving opinions on disputes when asked, and facilitating the international accounts D [General Postal Union 1874, Arts. 1, 14, 15, 19, the treaty text].

Fields 1, 4 and 5 of Models A1 and A2, as the worked case reads them. The administrations remain the decision-makers (Article 14 keeps each one's row of the matrix its own); the Union is the protocol agreed in advance, field 4; and the International Office is a mechanism, not a player (the price board of Model A1, the ring of Model A2), which collects and circulates but does not decide. The treaty fixes an interface and a tariff. It defines no common objective, and the auction's certificate proves optimality only for an objective that has been agreed (Exercise 8.1 (p. 328)) R.

In 1875 the Office's information travelled by the mails it served, disputes were settled by opinions given on request, and accounts were reconciled after the fact. A data-sharing network of the kind in the WIS2 situation above makes an observation available to every subscribed node through a common protocol as soon as it is published, and an assignment of units to requests can be recomputed as the requests change. What the faster interface changes is the resolution at which distributed action can be coordinated. What it leaves unchanged is that a common protocol is not a common preference, and that an agreement reached by averaging across the interface is a weighted value whose weights someone set (Exercise 8.3 (p. 329)) R.

Postal interoperability is not consensus and not an optimal allocation; the treaty of 1874 was replaced by a convention of 1 June 1878; and the models' four or five agents are not twenty-one administrations.

On 20 May 1875 seventeen states signed at Paris the Metre Convention D [Bureau International des Poids et Mesures 1875; the count of signatories from BIPM's page on the Convention]. Article 1 created a permanent scientific body, the International Bureau of Weights and Measures, at Paris, at the common expense of the parties; Article 3 placed it under the exclusive direction and supervision of an International Committee, itself answerable to a General Conference of delegates of all the contracting governments. Article 6 fixed the Bureau's work: comparisons and verifications of the new prototypes of the metre and the kilogram; custody of the international prototypes; periodic comparisons of national standards with them; comparisons of geodetic, precision and non-metric standards. Article 9 financed it by contributions on a scale based on population. The edition dates each article: Articles 7 and 8 carry the date of the amending convention of 1921, the rest 1875 D [Bureau International des Poids et Mesures 1875, Articles 1, 3, 6, 9].

Field 3 R. In Model S1 and in the worked case below the experiment is a kernel — the probability of a pass in each state — that the receiver knows. The treaty is the institution that makes a kernel common knowledge for physical quantities: a measurement made in one country means the same as one made in another because both are tied, by published comparisons, to one prototype. The two situations above have the same structure: a field called “emissions” is a signal whose kernel is set by a boundary, a method and a verifier, not by the database that stores it.

In 1875 a national standard was compared by bringing it to the prototype: comparability moved at the speed of a physical object and was renewed at the intervals Article 6 calls periodic. A product passport moves a figure in a fraction of a second to anyone with the right to read it. What transmission does not do is what Article 6 did: establish, by procedure, that two figures measure the same thing. The remedy of 1875 was institutional (a bureau, a committee, a conference, a budget rule), not a faster channel, and the accreditation framework and registry above are institutions of the same kind. Computation widens what can be combined and checked; it also lengthens the chain between the reader of a dashboard and the measurement, and the signal is specified only as well as that chain.

A metrology convention is not a strategic-disclosure problem: no party in 1875 chose which measurements to reveal, and the Bureau's duties were comparison, not persuasion. Nor should the present definitions of units be projected back: the convention governs prototypes and their comparison, nothing more.

On 29 October 1888 nine powers — Great Britain, Germany, Austria-Hungary, Spain, France, Italy, the Netherlands, Russia and Turkey — signed at Constantinople a convention on the Suez Canal D [Suez Canal Authority 1888; “The World and Japan” Database 1888, the treaty text]. Article I declares the Maritime Canal free and open, in time of war as in time of peace, to every vessel of commerce or of war without distinction of flag, and never subject to blockade. Article II records that the Fresh-Water Canal is indispensable to the Maritime Canal, takes note of the Khedive's engagements to the canal company concerning it in a convention of 18 March 1863, and binds the parties not to interfere with its security; Article III extends the undertaking to the plant, establishments, buildings and works of both canals. Article VIII charges the signatories' agents in Egypt with watching over the treaty's execution, and Article XIV provides that the engagements are not limited by the duration of the company's concession D [the treaty text, Articles I–III, VIII and XIV].

The treaty draws the two graphs the worked case needs (Section 9.7 (p. 353), field 3 of the card): the passage itself, and the dependencies that keep it usable — the water supply, the works, and the right to pass. In Model K4 capacity belongs to routes, and a route is available only while every chokepoint it crosses is open: a chokepoint is a failure condition shared by the routes through it, not a capacity of its own. The convention's drafters, nearly seventy years before the max-flow min-cut theorem (Theorem 9.2 (p. 373)), listed the chokepoints that were not on the chart R.

Whether the canal was open was, by 1888, something a telegram or a company notice could say; whether the promise of passage would hold was a matter of nine governments' conduct, observable only after the fact. A modern operator sees manifests, vessel positions and queue lengths within minutes and estimates from them usable capacity, delay and arrival. That information improves the use of capacity. It cannot create a right of passage, and it cannot make two routes independent when they share a water supply, a port process or an authority. The second drawing, of the dependencies, is made from documents, not from tracking data, and it is the one that decides what the first is worth.

The treaty's text is not evidence that passage was continuously respected afterwards, and the box makes no claim about any later closure of the canal.

On 28 March 1895, in a debate in the House of Commons on England and France in Africa, raised on the vote for the Foreign Office, the Under-Secretary for Foreign Affairs, Sir Edward Grey, said that “the advance of a French Expedition under secret instructions right from the other side of Africa, into a territory over which our claims have been known for so long, would be not merely an inconsistent and unexpected act, but it must be perfectly well known to the French Government that it would be an unfriendly act, and would be so viewed by England” D [House of Commons 1895, cols. 405–406]. Three and a half years later a second Blue Book on Fashoda, reported by The Spectator of 29 October 1898 as published that week, included a despatch covering a letter from Major Marchand, who wrote of Fashoda, “which I entered on July 10th last”. On 9 February 1899 Mr Brodrick, answering a question put to the Under-Secretary for Foreign Affairs, told the Commons that discussions were taking place with a view to settling a line of delimitation between the French and Anglo-Egyptian spheres; on 24 March he said that the accounts which had appeared of the agreement between Great Britain and France as to the delimitation of territory in Africa were in the main correct, that he hoped to lay it on the Table in a few days, and that it stipulated for equal treatment of British and French trade between the Nile and Lake Chad D [House of Commons 1899, col. 331; House of Commons 1899, col. 345].

Fields 3 and 4 of Model S6 R. A statement in the Commons is public and recorded, and the same audience can later compare it with what is done; a Blue Book published while a dispute is open puts correspondence on the same footing. In the model these are the moves to which a cost of backing down can attach; a message to which no cost attaches is free talk. The model needs more than the channel: a cost $c$ large enough, and a sender uncertain whether it will be resisted.

The documents of 1895–99 record the channel and the dates, and nothing about $c$: whether any audience would have penalised a retreat, and by how much. A statement made today is recorded and searchable at once and for good, which makes a retreat cheaper to observe. In the model, observation is a precondition of the cost, not the cost: the cost is what an audience does with what it observes, the quantity that survey experiments measure (Tomz 2007).

The box reads documents for their channel. It does not analyse the crisis of 1898, say why any statement was made or published, or claim that the statement of 1895 shaped what followed; no number of the model comes from the record. A historical study that counts the Fashoda crisis among a dozen great-power crises argues that audience costs were not a major factor in any of them (Trachtenberg 2012, pp. 3, 13–17, 32).

The India Meteorological Department's history of its science records that seasonal forecasting of the monsoon began after the famines of the 1860s and 1870s, with a first operational forecast in 1886 by Blanford from the inverse relation between Himalayan snow and the following monsoon; that Gilbert Walker became Director General in 1904 and began a systematic search for objective predictors, from a paper of 1908, issuing the first regression-based forecast in 1909; that his regression models were used for north-west and peninsular India from 1924 to 1987; and that in the course of that search he identified three large-scale seesaws in pressure — the Southern Oscillation, between the sea-level pressures of Tahiti and Darwin, the North Atlantic Oscillation and the North Pacific Oscillation. The same history records that the Southern Oscillation was linked to the warming of the eastern tropical Pacific by Bjerknes in the 1960s, and that the coupled phenomenon was then named ENSO D [India Meteorological Department n.d.]. Walker's memoir of 1923 speaks of “a swaying of pressure on a big scale backwards and forwards between the Pacific Ocean and the Indian Ocean”; the three names follow in 1924 D [Katz 2002, pp. 99–101, quoting the memoirs].

Walker's predictors fill field 3 of Model F3's card — what each forecaster observes — with a fact the model takes as given: the information relevant to a local decision may lie thousands of kilometres away, and whether two observations are two pieces of evidence or one depends on a dependence structure that must be known before they are combined R.

In Walker's time the information set was bounded by the stations that existed and by what could be brought to one desk; a predictor was a correlation found by hand in a few decades of tables. Today the information set is far broader: station and satellite observations can be combined with outputs from model ensembles within hours. What has not changed is the arithmetic of Proposition 10.7 (p. 416) and Exercise 10.1 (p. 411): two outputs trained on the same record are closer to two summaries of one witness than to two witnesses, and a long list of agreeing forecasts hides shared ancestry more easily than a short one. Broader access expands the information set; dependence determines how much information it contains, and the dependence assumption belongs on the model card.

The account rests on the Department's history and a study quoting Walker's memoirs; nothing here claims that his forecasts used a model like F3 or that present ensembles share his limitations.

On 7 July 1911 the United States, Great Britain, Japan and Russia signed at Washington a convention for the protection of the fur seals of the North Pacific, in force from 15 December 1911 D [United States Department of State 1911]. Article I prohibited their nationals and vessels from pelagic sealing (taking seals at sea) north of the thirtieth parallel, and allowed an offending vessel to be seized. Article III barred the import of skins taken in that area unless taken under the authority of the government owning the breeding grounds and officially marked and certified; Article VII had the United States, Japan and Russia each keep a patrol. Article X had the United States deliver each season, at the Pribilof Islands, fifteen per cent “gross in number and value” of the skins taken under its authority to an agent of the Canadian government and fifteen per cent to an agent of the Japanese government; Article XII made the same provision for Russia's take on the Commander Islands. Article IV exempted aborigines sealing from canoes, without firearms and not employed by others D [United States Department of State 1911, Articles I, III, IV, VII, X, XII, XVI].

The worked case keeps apart two tasks that this treaty joined R. Field 5: the parties that gave up sealing at sea were paid in kind, every season, from the land harvest they had agreed to leave alone, in shares fixed in the text rather than left to goodwill; whether that made staying in better than each party's outside option the text cannot show, since it states no payoffs. Fields 3 and 6: the mark, the certificate, the import ban and the patrol made lawful activity recognisable, so that an unmarked skin was evidence in itself. In Model B4's terms the first task sets $R-P$ against $T-R$, the second $p$ and $q$.

In 1911 the signal of compliance was slow and expensive (a patrol on the grounds, an inspection at the port, one season at a time) but nearly binary where it existed: a skin carried the mark or it did not. The coalition of this section observes compliance through documents and voyage data: continuous, fast, cheap to produce and for that reason cheap to produce falsely, which in Model B4 moves $q$ towards $p$. Faster observation shortened the delay; it did not restore the discreteness of the evidence. And the compensation of 1911 was specified in the text, as skins delivered at a named place each season, which made the payment side an auditable obligation but not one free of monitoring: the skins still had to be counted and valued, and Article XI provided advances, minimum deliveries and an umpire for disputes over their market value D [United States Department of State 1911, Article XI].

Four parties, one species and a colonial legal order with a restricted exemption for aboriginal sealing; the shares of skins transfer to no other agreement, and nothing in the treaty is a parameter of Model B4.

The Colorado River Compact was signed at Santa Fe on 24 November 1922. It apportions to the Upper Basin and to the Lower Basin, in perpetuity, the exclusive beneficial consumptive use of $7,500,000$ acre-feet of water a year each (Art. III(a)); and it fixes the dividing point, Lee Ferry, one mile below the mouth of the Paria River (Art. II). Article V directs the chief water-rights official of each signatory state, together with the Directors of the Reclamation Service and of the Geological Survey, to cooperate ex officio “to promote the systematic determination and co-ordination of the facts as to flow, appropriation, consumption and use of water” and “the interchange of available information in such matters”, and “to secure the ascertainment and publication of the annual flow of the Colorado River at Lee Ferry” D [Colorado River Compact 1922, Arts. II, III(a), V, the compact text as ratified in Arizona].

Field 3 of Model D5's card (“both capacities are observed before every move”) and the worked case's lesson that the gap is not the state. An apportionment is a number on an annual total; whether a path of releases that honours it is feasible is a condition on the stock at every date (Exercise 7.1 (p. 290)); and neither can be checked without the measured flow. Article V is the compact's provision for observing the state. What it requires to be published is the annual flow at Lee Ferry; it does not fix how often the river is gauged or how quickly a decision can respond to what is measured R.

In 1922 the figure the compact required to be published was a yearly total, and the apportionment itself is stated in annual totals; how often anyone could observe the river and act on it is not settled by the text. The operating guidelines of August 2026 (the situation above) fix an elevation to be held, adjust releases through the spring to hold it and set the year's volume in April from the winter's observations: a rule contingent on information arriving inside the year. What the guidelines add is a rule written to be contingent on observations within the year; the resource has not grown, and the water-balance equation does not say whose claim yields when the measured flow falls short of the apportioned totals. That was an institutional decision in 1922 and is one in 2026 R.

The compact is one instrument among the many that govern the river; deliveries to Mexico under the treaty of 1944 and obligations to the tribes are separate; the parties are several states, not a leader and a follower; and no number of the compact enters Model D5 or the exercise.

The International Load Line Convention was signed at London on 5 July 1930. A certificate in the form of its Annex III attests the load line mark (Art. 13); it runs for at most five years, is renewed only after a survey, and must be cancelled if the hull or superstructures are materially altered, if the fittings protecting openings are not kept as certified, or if the ship is not periodically inspected (Art. 14). Each Contracting Government accepts the others' certificates “as having the same force as the certificates issued by them” (Art. 15). In a foreign port, when a valid certificate is on board, control is limited to three checks: that the ship is not loaded beyond the certificate's limits, that “the position of the load line on the ship corresponds with the certificate”, and that it has not been altered so as to be manifestly unfit for sea; where proceedings or detention are likely, the ship's Consul is to be informed (Art. 16) D [International Load Line Convention 1930, Arts. 13–16, pp. 267–268, the treaty text].

Fields 3 and 4 of Model N's card. The certificate is a signal issued by another inspector — the flag Administration's survey — and Article 15 is a commitment not to repeat that survey; Article 16 is a published response rule: given a clear signal, the port may check only the correspondence between document, mark and loading. Its three checks are exactly the ways in which the signal can have gone stale, and Article 14's cancellation cases name them in advance R.

In 1930 a port officer could verify a certificate against the Administration that issued it only by correspondence; what could be checked on the spot was the paper against the hull and the hull against the water, and the control was written for that. A register of certificates and inspection histories can now be consulted before a ship berths, and selection targeted on it (the port state control situation above). What has become fast and cheap is the check of the credential, not the check of the object: a certificate speaks of the ship at its last survey, and Model N's signal is about the current action. A database shortens the first check and leaves the second where Article 16 put it, at the hull R.

The provisions are those of 1930, not of the later Convention of 1966; the parties inspect one another's ships reciprocally rather than in Model N's fixed roles; and no number of the model is read from the treaty.

On 19 July 1956 the Secretary of State told the Egyptian ambassador that it was not feasible at present for the United States to go forward with the High Aswan Dam undertaking; the memorandum records financial reasons (the burden the project would place on the Egyptian economy) and political ones, including doubt that funds could be obtained from Congress and the opposition of cotton interests, and the ambassador's statement that the Soviet Union was making a very generous offer for the dam D [U.S. Department of State 1956, pp. 868–872]. A State Department circular telegram of 25 October 1958, sent about a 400,000,000-rouble Soviet loan to the United Arab Republic, recalled that in July 1956 the Soviet ambassador had announced the Soviet Union's readiness to help finance the project on Egyptian request, and that this offer had remained open; it did not give the 1956 offer an amount. It also recorded Egyptian planning for a two-phase, ten-year construction with its own resources, and the possibility of outside credits from the uncommitted Soviet line or the IBRD D [U.S. Department of State 1958]. These are one government's records; they give no access to every participant's preferences.

The project looks like a field in a two-sponsor allocation contest: one prize, two offers, the larger offer wins. Field 1 of the card is where the mapping fails. The recipient was a decision-maker: it could seek another offer, change the financing arrangement, bargain over conditions, and build in phases with its own resources. The field was a third player with a card of its own, and the contest-success rule of Definition 2.1 (p. 74), by which more wins, is not what the record shows R.

What each sponsor knew of the other's offer, and when, shaped what the recipient could do: the July 1956 memorandum already records the American side weighing the Soviet offer as the ambassador reported it, and the 1958 telegram tracks the offer's standing two years on. Information about outside offers changed the recipient's bargaining opportunities, not only the sponsors' allocations. A project pipeline of the kind in the Global Gateway situation above makes alternatives easier to compare and cheaper to document; it does not remove the recipient's agency.

The analogy is imperfect by design: it is placed here to mark what Model E1 leaves out (a recipient that chooses, and domestic approval constraints on each sponsor) and to say that the next model needs a third player (Chapter 3 is the place). Nothing that followed the conversation is analysed, and no number from the records enters any model.

The Limits to Growth, a report for the Club of Rome by Donella and Dennis Meadows, Jørgen Randers and William Behrens, was published by Universe Books in New York in 1972. Its authors wrote that determining a system's behaviour modes is “prediction” only in the most limited sense, and that the printed graphs “are not exact predictions of the values of the variables at any particular year in the future” but “indications of the system's behavioral tendencies only” D [Meadows et al. 1972, pp. 92–93]. The model treated one general population; “National boundaries are not recognized”; and “World trade balances, migration patterns, climatic determinants, and political processes are not specifically treated” D [Meadows et al. 1972, pp. 93–94]. Numerical changes, the book said, “may well affect the period of an oscillation or the rate of growth or the time of a collapse, but they will not affect the fact that the basic mode is oscillation or growth or collapse”; the feedback-loop structure was the primary concern; and the vertical scales of the graphs were deliberately omitted D [Meadows et al. 1972, pp. 121–124].

The declaration fills the fields a simulation's card must state before a run is read: field 1, whose decisions are in the model (no political decision-maker); field 3, what is observed (aggregates, not the process that produced them); and item (i) of the analysis contract, what kind of statement the output is — a behaviour mode under a stated structure, not a value at a date. Model W3 is the same declaration read from the other side: a reproduced aggregate is evidence about the structure declared, and an omitted mechanism is not identified by a striking trajectory R.

In 1972 a world-model run was scarce — one team, a handful of curves printed without scales — and what a reader could know about the simulated world was what the text declared. A digital twin or an agent-based exercise now runs thousands of scenarios cheaply, which buys this chapter's second layer honestly: replications, dispersion, paired designs. It does not buy the third. The evidential reach of a run is still conditional on the structure declared, and a mechanism the model omits stays omitted at any resolution. The price of a run has changed, not the logic of the conditional, which the 1972 authors stated themselves.

A system-dynamics world model is not an agent simulation or a language-model wargame; the parallel concerns how a simulated trajectory is read, not a shared method or an equal standing. Nothing here evaluates the 1972 projections against later data.

On 1 June 1984 the Security Council condemned recent attacks on commercial ships en route to and from the ports of Kuwait and Saudi Arabia and asked the Secretary-General to report; his report of 31 December summarised replies from governments and communications from the International Maritime Organization about incidents D [United Nations Security Council 1984, paras. 4, 7; United Nations Secretary-General 1984]. Counts depended on the counter: for 1984–87 a tabulation from Lloyd's Shipping Intelligence Unit and the Center for Defense Information gives $71$, $47$, $111$ and $179$ ships attacked, $408$ in all; one compiled from the Secretary-General's reports gives $37$, $50$, $84$ and $169$, $340$ in all D [O'Rourke 1988, Tables 1–2]. On 7 March 1987 the United States offered to reflag eleven Kuwaiti tankers and to provide US Navy protection; escort began in July, and on 24 July, on the first convoy, the reflagged tanker Bridgeton struck a mine. Three tankers struck mines that month D [Department of the Navy, Office of the Chief of Naval Operations 1991, p. 4; Mobley 2016, pp. 3–4]. The Bridgeton reached Kuwait with its escorts following in its wake, and further convoys were postponed while mine-warfare helicopters were deployed D [Cox 2018]. Resolution 598 of 20 July 1987 deplored attacks on neutral shipping and demanded a ceasefire between Iran and Iraq, which came into effect on 20 August 1988 D [United Nations Security Council 1987; United Nations Peacekeeping n.d.].

Fields 3 and 4 of Model K5's card R. Escort was attached to a declared set of ships, recognisable by their flag: visibility of that kind bears on field 3. If the whole realised allocation were observed before an attack could be chosen, Proposition 9.15 (p. 380)(b) would hold it to the guarantee of the best fixed one, whatever plan lay behind it; the cited record establishes recognisable convoys, not the observation of a full draw. Gathering ships into convoys is a choice of fewer windows, worth more or less according to the escorts available against the threat (Proposition 9.16 (p. 381)(b)). A mine does not choose its ship: it is a hazard of the lane, outside the allocation game and closer to the shared interruption of Exercise 9.10 (p. 371); the order in which the first convoy finished its voyage, the tanker ahead of its escorts, fits that reading R.

The record of attacks consisted of compilations made after the fact, whose totals for 1984 differed by nearly a factor of two. Since the end of 2004 ships of $300$ gross tonnage and upwards on international voyages have been required to carry an automatic identification system, which broadcasts the ship's identity, type, position, course and speed D [International Maritime Organization n.d.]; in 2026 transits through the strait are counted daily from these broadcasts, with a warning about jamming, spoofing and ships going dark (Section 9.8 (p. 360)). Tracking shortens the delay to the record. It does not settle what counts as an attack or who counts, the choices on which two counts of one war can differ, and it shows where ships are, not where mines are.

The box takes no position on who attacked which ship, on who laid the mines, on any party's aims, or on whether escort changed the number of attacks; no count enters the model.