Conjecture

Conjecture (pronounced kuhn-jek-cher)

(1) The formation or expression of an opinion or theory without sufficient evidence for proof; an opinion or theory so formed or expressed; guess; speculation; to conclude or suppose from grounds or evidence insufficient to ensure reliability.

(2) The interpretation of signs or omens (obsolete though still used in some superstitious circles and a common phrase among occultists).

(3) In mathematics and philology, a technical term for a statement which, based on available evidence, is likely to be true but for which there’s no formal proof.

1350–1400: From the Middle English conjecturen (infer, predict, form (an opinion or notion) upon probabilities or slight evidence), from the Old and Middle French from the Latin conjectūra (a guess; inferring, an assembling of facts; reasoning), the construct being conject(us), past participle of conjicere (to throw together; to form a conclusion).  The late Middle English verb conjecturen was a direct borrowing from the Middle French, from the Late Latin conjecturāre, derivative of the noun.  The Latin conjicere is a combining form jacere (to throw) + -ūra –ure (the Latin suffix used to form nouns of quality from adjectives).  The Latin coniectūra is derived from coniectus, perfect passive participle of cōniciō (throw or cast together; guess), the construct being con- (together) + iaciō (throw, hurl).  In Middle English, there were also peacefully co-existing forms, the noun conjecte & the verb conjecten.

Derived forms include the adjective conjecturable, the adverb conjecturably, the noun conjecturer and the verbs (used with our without the object) conjectured and conjecturing.  The verbs misconjecture & misconjectured and the noun misconjecturing are valid words but so rare that some dictionaries list them as obscure.  Indeed, given the meaning of the root, it can be argued there’s little difference between conjecture and misconjecture although it could be useful in describing things in retrospect.  For those times when conjecture seems not quite right, there’s surmise, inference, supposition, theory, hypothesis, suppose, presume, guesswork, hunch, presumption, guess, fancy, opinion, conclusion, notion, guesstimate, gather, figure, conclude, feel, deem & expect.

The Oesterlé–Masser Conjecture

The Oesterlé–Masser conjecture, a problem in number theory, is named after the mathematicians Joseph Oesterlé (b 1954) and David Masser (b 1948) who first published their speculation in the 1980s and popularly known as the abc conjecture, based on the equation which underlies it all.  The conjecture postulates that if a lot of small prime numbers divide two numbers (a) and (b), then only a few large ones divide their sum (c); basically, if you add lots of primes together the result is divisible only by a few large numbers.  Mathematicians concur that intuitively this seems likely because of the nature of prime numbers but a proof has proved elusive.  It’s of interest to the profession because it might resolve some of the fundamental problems in Diophantine geometry, a typically arcane fork of number theory but beyond the implications for mathematics, given the importance of prime numbers in commerce, ICT and diplomacy (primes underpin encryption), other fields may be significantly affected. 

Japanese mathematician Shinichi Mochizuki san (b 1969) has been working on the problem for some thirty years and, over the decades has circulated within the community many un-published papers, none of which garnered much support.  Not discouraged, Mochizuki San persisted and in 2012 posted on his website, four papers 500 pages in length, claiming they contained the definitive proof (including a new theory called inter-universal Teichmüller theory (IUTT)).  While some of his peers actively disagreed with his methods or conclusions, most either ignored his work or said it couldn’t be understood, one recently commenting his experience was something like “reading a paper from the future, or from outer space”.

Several years later, despite conferences staged to explain Mochizuki san’s work to other mathematicians, there is no consensus and he has been accused of not doing enough to communicate (in the sense of explaining) his ideas.  While there are some who claim to have both read his work (that alone an achievement) and understood it (more admirable still given how much that depends on knowledge of other work he has developed over decades), they're a small sub-set of number theorists, most of whom remain sceptical or dismissive .  Interest was stirred in 2018 when two noted German mathematicians, Peter Scholze (b 1987) and Jakob Stix (b 1974), published a paper in which they asserted a critical part of Mochizuki san’s work (said to be central to the proof), was wrong.  Unusually in this matter, their work was based not only on analysis but a face-to-face meeting with Mochizuki san.  The discussion however concluded with neither sided able to persuade the other, something like three pocket calculators sitting on a table, unable to agree on the best method of determining a number without knowing that number.

In April 2020, it was announced the claimed proof would be published in the Japanese journal Publications of the Research Institute for Mathematical Sciences (RIMS).  Although Mochizuki san was RIMS's chief editor, the institution noted he was “…not involved in the review” or the decision to publish.  There was scepticism but in 2021, the material appeared in RIMS and the number theory community awaits with interest to see if there are defections from the tiny “proven” faction or the more populated “unproven”.

It's not just number theorists who have engaged with Mochizuki san.  Ted Nelson (b 1937), a US sociologist who as long ago as 1963 invented the term hypertext, thinks the controversial Japanese professor may be the inventor of Bitcoin.  Dr Nelson noted that that Bitcoin creator "Satoshi Nakamoto san" appears to have existed long enough only to (1) introduce Bitcoin, (2) stimulate excitement and (3) disappear and thought this similar behavior to that of Mochizuki san who has some history of making mathematical discoveries and posting them to the internet to be found, rather than publishing.  Not many share the suspicion, noting that while a grasp of high-level mathematics would have been essential to build the Blockchain, Mochizuki san is not known to have any background in software development although, given Bitcoin may have been developed by a team, that may not be significant.  Dr Nelson remained convinced and in 2013 offered to donate one Bitcoin (then trading at $US123) to charity were Mochizuki san to deny being the inventor.  It's not known if Dr Nelson revised the terms of his offer as the Bitcoin price moved.

Limbo

Limbo (pronounced lim-boh)

(1) In (informal) Roman Catholic theology, a region on the border of hell or heaven, serving as the abode after death of unbaptized infants (limbo of infants) and of the righteous who died before the coming of Christ (limbo of the fathers, or limbo of the patriarchs); often with initial capital letter.

(2) A place or state of oblivion to which persons or things are regarded as being relegated when cast aside, forgotten, past, or out of date.

(3) An intermediate, transitional, or midway state or place.

(4) A place or state of imprisonment or confinement.

(5) A dance from the West Indies (originally restricted to men), in which the dancer bends backward from the knees and moves with a shuffling step under a horizontal bar that is lowered after each successive pass.  Among university under-graduates (and other disreputable types), the activity is now often combined with drinking contests where the bar's height is inversely proportional to the contestant’s consumption of alcohol.

(6) Used loosely, a synonym for oblivion, nothingness or nowhere.

(7) In the slang of the military slang, a demilitarized zone (DMZ).

(8) A colloquial form used to refer to a Limburger, a person from Limburg (the southernmost of the twelve provinces of the Netherlands; the French form being Limbourgeois).

1300–1350: From the Middle English, from the Medieval Latin phrase in limbō (“on hell's border” literally “on the edge”), the being construct in + limbō, ablative of limbus (edge, border) the term in Medieval Latin best translated as a “place bordering on hell”.  The West Indian English limba (to bend, easily bending) is relatively recent, emerging 1955-1960 and is of uncertain origin but most etymologists suggest it likely came from Jamaica, probably an alteration of limber as it is a test of physical agility.  Limbo is a noun & verb, limbo-like is an adjective (limbolike is a registered trademark and thus a noun), limboed & limboing are verbs; the noun plural is limbos or limboes.

Medieval conjecture which became informal theology

Surprisingly, despite the place it has in language and popular imagination, limbo has never formerly been part of Roman Catholic doctrine and was a bit of a medieval fudge.  It was championed by Italian Dominican friar, philosopher & theologian Saint Thomas Aquinas (1225–1274), taking hold in the western Church and perhaps most influential in the popularity was the Italian Dante (Dante Alighieri (circa 1265–1321) who, in his Divina Commedia (Divine Comedy (circa 1310-1321)) used limbo as the resting place for virtuous pagans.  Dante sticks in the mind.

In April 2007, early in his papacy, Pope Benedict XVI (1927–2022; pope 2005-2013, pope emeritus 2013-2022) authorized the publication of “The Hope of Salvation for Infants Who Die without Being Baptised” which some suggested appeared to render defunct limbo, the place centuries of tradition and much teaching held was the place the souls of babies who die without baptism were sent.  An explanatory memorandum from the Church’s International Theological Commission accompanied the document, suggesting it was issued to correct what was “…an unduly restrictive view of salvation”.

The commission however stressed there was no change to Church doctrine.  It remains Church teaching that baptism removes original sin which stains all souls since the fall from grace in the Garden of Eden and that its conclusions should not be interpreted as questioning original sin or “…used to negate the necessity of baptism or delay the conferral of the sacrament”.  Instead, the document merely notes “… God is just and merciful and would not …exclude infants, who have no personal sins, from eternal happiness… from the kingdom of heaven”.  It added the need for publication was not without urgency because the number of “…non-baptised infants has grown considerably, and therefore the reflection on the possibility of salvation for these infants has become urgent”.

Christ in Limbo (1510), one of a series of twelve woodcuts (eleven scenes and a title page) from The Large Passion by Albrecht Dürer (1471-1528).

In theology, limbo had long been understood in two senses:  Firstly (denoted as limbus partum) as the temporary place of rest for the souls of the just awaiting the salvation of the Messiah and secondly (limbus infantium or limbus puerorum), as the final state of the souls of those who died without baptism yet without mortal sin.  Because the Church never officially defined this as doctrine, it’s regarded as theological supposition or, as Benedict put it “medieval conjecture”, constructed probably to avoid the creation of a loophole which unworthy sinners and lawyers might exploit to get into heaven.  All the same, scripture does seem explicit, Jesus teaching that no one “can enter into God’s kingdom without being begotten of water and Spirit” (John 3:5), thus the old assertion in the old Catechism that God Himself “…affirms that Baptism is necessary for salvation.” 

In Constantinople, because the Byzantines were never as in thrall of Augustine as they were in Rome, Limbo never really bothered the many but over the centuries, the issue attracted the attention of notables.  Saint Gregory Nazianzen (circa 329–390) implied somewhere like limbo might exist, believing the unfortunate infants would neither “…be admitted by the just judge to the glory of Heaven nor condemned to suffer punishment” and Tertullian (155–circa 220) before and Saint Ambrose (circa 340–397) after, concurred.  Saint Augustine of Hippo (354–430) was more stern and said there was no limbo, there was just Heaven and Hell and that of course unbaptized souls are sent to Hell because they were born in original sin and nor could they go to Purgatory since that is a pathway to Heaven.  All he would concede was of those in Hell, the torment of infants would be the mildest although he didn't go into detail.  Eight-hundred odd years later, Aquinas was more generous, noting the original sin was committed by the parents and not by the child and since (1) Hell was the place where unrepentant mortal sinners are sent for eternal punishment (2) only the baptized could enter Heaven, then (3) the souls of unbaptized children must go somewhere else and here was the (admittedly shaky) foundation of limbo.  In a quite modern flourish, Aquinas helpfully added that because they’d never been born, the infants would never have learned of the glories of Heaven so, not knowing what they’d missed, they’d probably find limbo rather nice.  It was a fudge worthy of any Lambeth conference.

Luca Signorelli (circa 1444-1523), The Resurrection of the Flesh (1499-1502) Fresco Chapel of San Brizio, Duomo, Orvieto.

The issue didn’t go away and in the eighteenth century, a radical group of neo-Augustinites, a kind of Romish version of the Republican Party's Freedom Caucus and known as the Jansenists, rejected limbo, the idea of which had for hundreds of years provided comfort to grieving parents, forcing Pope Pius VI (1717–1799; pope 1775-1799) in 1794 to issue the Papal Bull Auctorem Fidei (Of our Faith), condemning, inter alia, the denial that there is a place “which the faithful generally designate by the name of limbo for children”.  It was a rare official mention of limbo but well short of a definitive statement.  Interest was renewed in the twentieth century but Pope Pius XII (1876-1958; pope 1939-1958), hardly one fond of radical change, in 1943 issued a statement in the Holy See’s periodic gazette again neither defining nor rejecting limbo.  

So, press releases aside, the commission’s document suggests in the eight centuries between Aquinas and Benedict XVI, in limbo, not much has changed; the Catechism still asserts only that children who die before baptism are entrusted into the mercy of God.  Benedict XVI, no stranger to dancing on the head of a pin, seemed both to clarify and cloud the waters by saying limbo was only ever “medieval conjecture” and given there is no explicit answer from Scripture, people seem still free to make of it what they will.

Purgatory

Purgatory (pronounced pur-guh-tree (U), pur-guh-tawr-ee (non-U) or pur-guh-tohr-ee (non-U)

(1) In the orthodox theology of the Roman Catholic Church (and in some other Christian denominations), a condition or place in which the souls of those dying penitent (in a state of grace) are purified from venial sins, or undergo the temporal punishment that, after the guilt of mortal sin has been remitted, still remains to be endured by the sinner.

(2) In the Italian Purgatorio (pronounced poor-gah-taw-ryaw), the second part of Dante's (Dante Alighieri (circa 1265–1321)) Divine Comedy (1320), in which repentant sinners are depicted.

(3) Any condition or place of temporary punishment, suffering, expiation, or the like; any place of suffering, usually for past misdeeds.

(4) Serving to cleanse, purify, or expiate.

1160-1180: From the Middle English purgatorie (place or condition of temporal punishment for spiritual cleansing after death of souls dying penitent and destined ultimately for Heaven), from the Old French purgatore & purgatorie, from the Medieval Latin pūrgātōrium (means of cleaning), noun use of neuter of the Late Latin pūrgātōrius (purging, literally “place of clensing”), the construct being pūrgā(re) (to purge) + -tōrius (-tory), the adjectival suffix, from purgat-, past-participle stem of pūrgāre (to purge, cleanse, purify).  The adjectival form developed in the late thirteenth century, independent of the evolution in Church Latin.  The figurative use (state of mental or emotional suffering, expiation etc) dates from the late fourteenth century, originally used poetically especially despairingly when speaking of unrequited love, or (and this may seem a paradox to same and merely descriptive to others), of marriage.   In old New England it was used of narrow gorges and steep-sided ravines, a reference to the difficulties to be dad when negotiating such terrain.  Purgatory, purgatorium & purgatorian are nouns and purgatorial is an adjective; the noun plural is purgatories.

Mankind's Eternal Dilemma: The Choice Between Virtue and Vice (1633) by Frans Francken the Younger (1581–1642), Museum of Fine Arts (MFA), Boston.

In the teachings of the Roman Catholic Church, the purgatory is the condition of souls of the dead who die with punishment but not damnation due them for their sins committed on Earth.  Purgatory is conceived as a condition of suffering and purification that leads to union with God in heaven and is something thus inherently temporary and has always been a bit of a theological problem because it’s not mentioned (or even alluded to) in the Bible.  The usual rationalization of this scriptural lacuna is the argument that prayer for the dead is an ancient practice of Christianity and one which has always assumed the dead can be in a state of suffering, something which the living can improve by their prayers.  Theological positions have hung on thinner strands than that and within Roman Catholicism, purgatory has never attracted the controversy which so excited critics of limbo, a rather more obviously unjust medieval conjecture, but many branches of Western Christianity, notably the Protestant tradition, deny its existence although among the more ritualistic, there are those who conceive purgatory as a place and one often depicted as filled with fire.  The transitory nature of the condition has often encouraged misunderstanding for it is not a place of probation; the ultimate salvation of those in purgatory assured, the impenitent not received into purgatory.  Instead, the souls in purgatory receive relief through the prayers of the faithful and through the sacrifice of the mass, the confusion perhaps arising from the imagining the destructive nature of fire on Earth whereas upon the soul with no earthly attachment, it can be only cleansing.

So purgatory is the state of those who die in God's grace but are not yet perfectly purified; they are guaranteed eternal salvation but must undergo purification after death to gain the holiness needed to enter heaven.  The purgatory, the framework of which was fully developed at the Councils of Florence (1431-1449) and Trent (1545 and 1563), is totally different from the punishment of the damned who are subject to a cleansing fire, the scriptural explanation being "The person will be saved, but only through fire" (1 Corinthians 3:15) but even then the Church recognized degrees of sin as Pope Gregory I (Saint Gregory the Great, circa 540–604; pope 590-604) helpfully clarified: "As for certain lesser faults, there is a purifying fire."  The possibilities were made explicit during the Council of Trent in the statement “God predestines no one to hell” which made clear that damnation is visited upon sinners only by a persistence in mortal sin until death and God would much prefer "all to come to repentance" (2 Peter 3:9).   In the Roman ritual, the relevant line is "save us from final damnation and count us among those you have chosen" and through purgatory, souls "achieve the holiness necessary to enter the joy of heaven".  Mortal sin incurs both temporal punishment and eternal punishment, venial sin ("forgivable sin” in this context) incurs only temporal punishment. The Catholic Church makes a distinction between the two.

Dante and Virgil Entering Purgatory (1499-1502) by Luca Signorelli (circa 1444-1523), Chapel of San Brizio, Duomo, Orvieto, Italy.  The pair are shown in the first terrace watching souls of the prideful being made to cat stones on their backs.

The noun purgatory appeared perhaps between 1160 and 1180, giving rise to the idea of purgatory as a place but the Roman Catholic tradition of purgatory as a transitional condition has a history that pre-dates even the birth of Christ.  There was, around the world, a widespread practice of both caring for and praying for the dead, the idea that prayer contributed to their purification in the afterlife.  Anthropologists note the ritual practices in other traditions, such as the way medieval Chinese Buddhists would make offerings on behalf of the dead, said to suffer numerous trials so there is nothing novel in the practice which is mentioned in what the Roman Catholic Church has declared to be part of Sacred Scripture, and which was adopted by Christians from the beginning, a practice that pre-supposes that the dead are thereby assisted between death and their entry into their final and eternal abode.

Whether purgatory is actually a place has in Roman circles been discussed for centuries.  In 2011 Pope Benedict XVI (b 1927; pope 2005-2013, pope emeritus since), speaking of Saint Catherine of Genoa (1447–1510), said that in her time the purgatory was pictured as a location in space, but that she saw it as a purifying inner fire, such as she experienced in her profound sorrow for sins committed, such a contrast with God's infinite love.  The failing of man she said was being bound to the desires and suffering that derive from sin and that makes it impossible for the soul to enjoy the beatific vision of God.  Noting that little appeared to have changed, Benedict noted "We too feel how distant we are, how full we are of so many things that we cannot see God. The soul is aware of the immense love and perfect justice of God and consequently suffers for having failed to respond in a correct and perfect way to this love; and love for God itself becomes a flame, love itself cleanses it from the residue of sin."

The Eastern Catholic Churches are Catholic churches sui iuris of Eastern tradition, (in full communion with the Pope) but there are some differences with Rome on aspects of purgatory, mostly relating to terminology and speculation.  The Eastern Catholic Churches of Greek tradition do not generally use the word "purgatory", but agree that there is a "final purification" for souls destined for heaven and that prayers can help the dead who are in that state of "final purification".  In neither east nor west are these matters thought substantive and are regarded as nuances and differences of tradition.  The Eastern Catholic Churches belonging to the Syriac Tradition (Chaldean, Maronite and Syriac Catholic), generally believe in the concept of Purgatory but use a different name (usually Sheol) and claim there is contradiction with the Latin-Catholic doctrine.  Rome appears never to have pursued the matter.

La Divina Commedia di Dante (Dante and His Poem), oil on canvas by Domenico di Michelino  (1417–1491) after Alesso Baldovinetti  (1425–1499), collection of Florence Cathedral, Italy.  This work, in depicting the seven terraces in the form of the mountain were one approach to Dante's Purgatory, the other a focus on one level. 

The Eastern Orthodox Church rejects the term "purgatory" but does admit an intermediate state after death, the determination of Heaven and Hell being stated in the Bible and it notes prayer for the dead is necessary.  The position of Constantinople and environs is that the moral progress of the soul, for better or worse, ends at the very moment of the separation of body and soul; it is in that instant the definite destiny of the soul in the everlasting life is decided.  There is no way of repentance, no way of escape, no reincarnation and no help from the outside world, the eternal place of the soul decided forever by its Creator and judge.  Thus the Orthodox position is that while all undergo judgment upon death, neither the just nor the wicked attain the final state of bliss or punishment before the last day, the obvious exception being the righteous soul of the Theotokos (the Blessed Virgin Mary), "who was borne by the angels directly to heaven".

Generally, Protestant churches reject the doctrine of purgatory although more than one Archbishop of Canterbury may have come to regard Lambeth Palace as Purgatory on Earth.  One of Protestantism's most cited tenets is sola scriptura (scripture alone) and because the Bible (from which Protestants exclude deuterocanonical books such as 2 Maccabees) contains no obvious mention of purgatory, it’s therefore rejected as an unbiblical and thus un-Christian.  There are however variations such as the doctrine of sola fide (by faith alone) which hold that pure faith, apart from any action, is what achieves salvation, and that good deeds are but mere manifestations of that faith so salvation is a discrete event that takes place once for all during one's lifetime, not the result of a transformation of character.  What does seem to complicate that is that most Protestant teaching is that a transformation of character naturally follows the salvation experience; instead of distinguishing between mortal and venial sins, Protestants believe that one's faith dictates one's state of salvation and one's place in the afterlife, those saved by God destined for heaven, those not excluded.  Purgatory is thus impossible.

Divina Commedia, Purgatorio (circa 1478), illuminated manuscript commissioned by Federico da Montefeltro (1422–1482), Vatican Library collection, Rome.  Again, the carring of stones on the first terrace, the style is recognizable in the later schools of mannerism and surrealism.  

Wishing to excise any hint of popery from religion, purgatory was addressed in two of the foundation documents of Anglicanism in the sixteenth century.  Prayers for the departed were deleted in the 1552 revision to the 1549 Book of Common Prayer because they implied a doctrine of purgatory (it was the nineteenth century Anglo-Catholic that saw them restored to some editions) and Article XXII of the the Thirty-Nine Articles of Religion (1571) was most explicit: "The Romish Doctrine concerning Purgatory . . . is a fond thing, vainly invented, and grounded upon no warranty of Scripture, but rather repugnant to the Word of God."  In the twenty-first century, the Anglicans, finding it hard to sit anywhere but on the fence, now say “Purgatory is seldom mentioned in Anglican descriptions or speculations concerning life after death, although many Anglicans believe in a continuing process of growth and development after death.”  The post-modern church writ small; one wonders if the PowerPoint slides of Anglican accountants and Anglican theologians greatly differ.

In Judaism, Gehenna is a place of purification where, according to some traditions, sinners spend up to a year before release.  For some, there are three classes of souls: (1) the righteous who shall at once be written down for the life everlasting, (2) the wicked who shall be damned and (3), those whose virtues and sins counterbalance one another shall go down to Gehenna and float up and down until they rise purified.  Other sects speak only of the good and the bad yet, confusingly, most also mention an intermediate state.  There’s also variance between the traditions regarding the time which purgatory in Gehenna lasts, some saying twelve months and others forty-nine days, both opinions based upon Isaiah 66:23–24: "From one new moon to another and from one Sabbath to another shall all flesh come to worship before Me, and they shall go forth and look upon the carcasses of the men that have transgressed against Me; for their worm shall not die, neither shall their fire be quenched"; the former interpreting the words "from one new moon to another" to signify all the months of a year; the latter interpreting the words "from one Sabbath to another", in accordance with Leviticus 23:15-16, to signify seven weeks.  Whatever the specified duration, there are exceptions made for the souls of the impure which prove resistant to the persuasions of the Gehenna.  According to the Baraita (a Jewish oral law tradition), the souls of the wicked are judged, and after these twelve months are are consumed and transformed into ashes under the feet of the righteous whereas the "great seducers and blasphemers" are to undergo eternal tortures in Gehenna without cessation.  The righteous however and, according to some, also the sinners among the people of Israel for whom Abraham intercedes because they bear the Abrahamic sign of the covenant, are not harmed by the fire of Gehenna even when they are required to pass through the intermediate state of purgatory.

Relief sculpture on a side wall at the Chapel of Souls, (Capilla de Animas) in Compostela, Spain.  These are the souls of the lustful on the seventh terrace, praying for release, which they have been promised will (eventually) be granted by the cleansing flames, something dependent on true repentance.

It was the Florentine poet Dante (Dante Alighieri, circa 1265–1321) who, in the second cantica of the epic poem Divine Comedy (1320) gave the world a vivid depiction of the place he called Purgatorio.  Dante described Purgatory as a mountain which rose on the far side of the world, opposite Jerusalem, with seven terraces, each corresponding to the one of the seven deadly sins, each terrace a place of purification for souls who are penitent and seeking to cleanse themselves of their sins, so to be judged worthy of entering Paradise.  In the valley at the base of the mountain is Ante-Purgatory and here sit the souls of the excommunicated and those who delayed repentance (the so called the “late repentant”) as they await their turn to begin their ascent of the terraces.  Throughout Purgatory, angels and guides assist the souls and Dante's guide is the Roman poet Virgil (symbolizing human reason).  Virgil leads Dante until they reach Earthly Paradise where Beatrice (representing divine wisdom) takes over as the guide to Heaven.

The seven terraces

First Terrace (Pride): Here the souls are humbled by being made to carry heavy stones on their backs, forcing them to bend and contemplate humility.

Second Terrace (Envy): Envious souls are punished by having their eyes sewn shut with twists of iron wire so they may learn to appreciate the beauty of charity and generosity.

Third Terrace (Wrath): Souls of the wrathful Souls enveloped in a thick smoke that blinds them, teaching them to cultivate patience and peace.

Fourth Terrace (Sloth): The slothful are punished by being forced incessantly to run, encouraging diligence and zeal.

Fifth Terrace (Avarice and Prodigality): These souls have to lie face down in the dirt and weep, teaching them to balance their desire for material wealth with the virtues of generosity and moderation.

Sixth Terrace (Gluttony): The gluttonous are starved so extreme hunger and thirst constantly will remind them of the importance of temperance.

Seventh Terrace (Lust): Souls here walk through walls of flames, purging the sin of lust, teaching chastity and love for God.

Lindsay Lohan and her lawyer in court, Los Angeles, December 2011.

That all sound rather grim but at the mountain’s summit sits the reward: Earthly Paradise (the Garden of Eden).  Here, in this place of peace and beauty, symbolizing the restored innocence and grace, souls are purified completely and ready to ascend to Heaven.  So, the purpose of Dante's Purgatory is less the punishments which must be endured than the possibility of redemption from sin through repentance to purification, leading ultimately to the soul's readiness for Paradise. In this it contrasts with the eternal sufferings which are the fate of those souls condemned to the circles of Hell.

Conjunction

Conjunction (pronounced kuhn-juhngk-shuhn)

(1) In grammar, any member of a small class of words distinguished in many languages by their function as connectors between words, phrases, clauses, or sentences, as and, because, but, however.

(2) Any other word or expression of similar function, as in any case.

(3) The act of conjoining; combination.

(4) The state of being conjoined; union; association.

(5) A combination of events or circumstances.

(6) In formal logic, a compound proposition that is true if and only if all of its component propositions are true.

(7) In formal logic, the relation among the components of such a proposition, usually expressed by the ∧ (∧) operator.

(8) Sexual intercourse (obsolete except for historic or poetic use).

(8) In astronomy, the coincidence of two or more heavenly bodies at the same celestial longitude; also called solar conjunction (the position of a planet or the moon when it is in line with the sun as seen from the earth. The inner planets are in inferior conjunction when the planet is between the earth and the sun and in superior conjunction when the sun lies between the earth and the planet).

(9) The state of two or more such coinciding heavenly bodies.

(10) In astrology, the coincidence of two or more heavenly bodies at the same celestial longitude, characterized by a unification of the planetary energies; an astrological aspect (an exact aspect of 0° between two planets, etc, an orb of 8° being allowed).

1350–1400: From the Middle English conjunccio(u)n, a borrowing from the Anglo-French and Old French conjonction, from the Latin conjunctiōn- (stem of conjunctiō (joining) from coniungere (to join), the second-person singular future passive indicative of coniungō.  Conjunction is a noun, conjunctive is a noun & adjective and conjugate is a noun, verb & adjective; the noun plural is conjunctions.

Beginning a sentence with a conjunction

Unlike French, which has the Académie Française, English has no central authority; assessments of correctness can be made by anyone, judgments of whom others can make of what they will; it's something like the concept of the fatwa in Islam and from this linguistic free-for-all emerged the “rule” a sentence shouldn’t begin with a conjunction.  In English, there’s actually no rule against a sentence beginning with a coordinating conjunction like and, but or yet but the mistaken belief in some sort of prohibition is widespread.  In the literature, thoughts on the origin of this are all conjecture but the theme of most suggestions is the practice is somehow inelegant (although harsher critics describe it as lazy and sloppy) and with a little effort, a more complex and pleasing construction might emerge.  That said, the prohibition has no historical or grammatical foundation and examples exist in the Magna Carta (1215), the United States Constitution (1787), judgments from the US Supreme Court (since at least 1803) and Abraham Lincoln's (1809–1865; US president 1861-1865) Gettysburg Address (1863) and Merriam-Webster’s Dictionary of English Usage traced instances of use even in Old English.  That one is allowed to do something doesn’t mean one should do something and even then, it can be done too often.  A work like however doesn’t have the same feel as but; it’s in a higher register so the choice of which to use to start a sentence may be dictated by style as much as meaning.  So while beginning a sentence with and is permissible English, if overused it makes for dull and repetitive text.

The Great Conjunction of Jupiter and Saturn, 21 December 2021.

In an alignment dubbed the “Christmas Star”, Jupiter and Saturn, the solar system’s two largest planets, appeared on 21 December 2021 to be closer together than they have in nearly 400 years.  From the earth, the giant planets appeared a tenth of a degree apart although they are hundreds of millions of miles apart.  Also, as NASA confirmed, it’s been some 800 years since the planets aligned at night, timing that gave almost everyone on planet Earth the chance to observe the astronomical event known as a “Great Conjunction”, a similar alignment not due until 2080, with the next close conjunction following 337 years later, in 2417.  The event was unusual also because it fell on the winter solstice, the longest night of the year, a “rare coincidence,” NASA advised because “the date of the conjunction is determined by the positions of Jupiter, Saturn, and the Earth in their paths around the Sun, while the date of the solstice is determined by the tilt of Earth’s axis.”

Lindsay Lohan (2011).

Screened in conjunction with the 54^th international exhibition of the Venice Biennale (June 2011), Lindsay Lohan was a short film the director said represented a “new kind of portraiture.”  Filmed in Malibu, California, the piece was included in the Commercial Break series, presented by Venice’s Garage Center for Contemporary Culture and although the promotional notes indicated it would include footage of the ankle monitor she helped make famous, the device doesn't appear in the final cut.

Directed by: Richard Phillips & Taylor Steele
Director of Photography: Todd Heater
Costume Designer: Ellen Mirojnick
Creative Director: Dominic Sidhu
Art Director: Kyra Griffin
Editor: Haines Hall
Color mastering: Pascal Dangin for Boxmotion
Music: Tamaryn & Rex John Shelverton

Doppelganger

Doppelganger (pronounced dop-uhl-gang-er or daw-puhl-geng-er (German))

(1) In legend, a ghostly apparition of a living person, especially one that haunts such a person.

(2) A counterpart of a living person, identical in appearance; a person remarkably similar in appearance to another.

(3) In the pop-culture fantasy genre, a monster that takes the forms of people, usually after killing them.

(4) An evil twin (often as alter ego)

1826 (1824 as a German word in English): From the German Doppelgänger, literally "double-goer" or “double walker” originally with a ghostly sense.  Although now less common, it was once sometimes the practice to use the half-English spelling doubleganger.  Doppel was from doppelt (double), from doppeln (double (made up of two matching or complementary elements)), from the Old French doble (to double), from the Latin dūplus, from the Proto-Italic dwiplos, the construct being duo (two) +‎ plus, from the Old Latin plous, from the Proto-Italic plous, from the primitive Indo-European pleh- & pelhu- (many) and cognate with the Ancient Greek πολύς (polús) (many) and the Old English feolo (much, many).  It was influenced by the Ancient Greek διπλόος (diplóos) (double), the construct being δι- (di-), from δύο (dúo) (two), + -πλόος (-plóos) (-fold) and the Proto-Germanic twīflaz (doubt). A doublet of Zweifel.  Gänger was from Middle High German genger (to go, to walk), the construct being Gang +‎ -er.  Gang was from the Middle High German ganc, from the Old High German gang, from the Proto-Germanic gangaz (pace, step, gait, walk) and cognate with the English gang.  The synonyms in the various senses include double, lookalike, dead-ringer & alter ego.

Kim Jong-un, 2019-2020.

Rumors that Kim Jong-un (b circa 1994, Supreme Leader of the Democratic People’s Republic of Korea (North Korea, the DPRK) since 2011) was incapacitated with (unspecified) health problems spiked in late 2021 when he appeared looking notably thinner than in his appearances only months earlier, the conspiracy theory hinging on the idea the part of the Supreme Leader was being played by a doppelganger.  Most speculation centered on Mr Kim’s apparently chronic obesity, chain smoking and legendarily enthusiastic intake of his favorite Swiss cheese, some suggesting the doppelganger would fulfill the role until a team of foreign doctors working in secret restored the Supreme Leader to good working order while others opined he may actually be dead and the elite of the ruling Workers' Party of Korea (the WPA, a kind of cross between the a communist party and the Kim family’s holding company) was just buying time while they worked out what to do next.

Noted DPRK watchers, the National Intelligence Service (NIS), the Republic of Korea's (South Korea, the ROK) spy agency, dismissed the idea and said the new, sexy, slimmed-down Supreme Leader was real, their findings based on a comparison using facial recognition software, weight-tracking models and analysis of high-resolution video.  According to the NIS, Mr Kim’s weight which by 2019 had reached 142 kg (313 lb), less than a year later had further ballooned to around 146 kg (322 lb) while his appearances in late 2021 indicated a loss of between 20-25 kg (44-55 lb).  They added he appeared to be in rude good health.

Kim Jong-un, 2021.

If that’s true, the weight-loss could be accounted for either by Mr Kim’s desire to slim down for reasons of health or may be political, the DPRK facing one of its worst food shortages in many years and he may wish to convey the impression he’s sharing in the deprivations being suffered by his people.  Various seasonal factors would anyway have squeezed the food supply but the COVID-19 measures taken certainly exacerbated the problem, the closure of the borders inducing the sharpest economic contraction since the loss in the early 1990s of economic assistance from the Soviet Union.  The DPRK’s trade with its main trading partner, the People’s Republic of China (PRC), dropped by between 80-90% from pre-pandemic levels and the NIS noted it was the “mismanagement” of the economy which had caused inflation rates to surge beyond that afflicting all but a few other countries but, with a chronic shortage of ink and paper, the DPRK was unable to resort to the short-term expedient of printing money.  Still, things appear not actually on the point of collapse, ballistic missile tests continuing and the COVID-19 policy has, as stated by official DPRK propaganda, proved an outstanding success, Pyongyang confirming the country has suffered zero cases since the pandemic began.  It does seem to prove a “shoot to kill” border policy works, something a few Western politicians have long suspected and probably longed for.

Kim Jong-un looking at morning tea.

Targeted sanctions imposed in response to the regime’s nuclear weapons recalcitrance had already resulted in some humanitarian suffering but the closure of the PRC-DPRK border and has increased this by blocking shipments of grain, fertilizer and farming equipment.  Severe flooding caused by powerful typhoons in 2020 which so lowered that year’s harvest also had effects which lingered, crop yields again very low in 2021.  It had become so bad that in a rare public admission, Mr Kim in 2021 told a Worker’s Party meeting that the “people’s food situation is now getting tense” and his immediate policy switch was to order all citizens to devote all their effort to farming, making sure to secure “every grain” of rice.  With apparently all NGO and UN staff having left the country, most sources of foreign aid have evaporated and the DPRK is more dependent on its own resources than at any time since the end of the Korean War (1950-1953).  All this might explain Mr Kim’s weight-loss, although not yet obviously malnourished, he’s at least setting an example.

Manchu Tuan, Shenyang, PRC (left) and the Supreme Leader (right).

In general circulation, Kim Jong-un doppelgangers are not actually rare, at least two known to be available for hire from talent agencies.  Regardless of what happens in the DPRK, it may be a good gig because in 2012, satirical site The Onion named Kim Jong-un the world’s sexiest man, either because he was, in their words, “devastatingly handsome” or a nod to Henry Kissinger’s (b 1923; US secretary of state 1973-1977) claim (actually probably a boast) that “power is the ultimate aphrodisiac”.  The Onion’s winner in 2011 had been Syrian dictator Bashar al-Assad (b 1965; president of Syria 2000-) so the editors may have found Dr Kissinger persuasive.  Manchu Tuan sells kebabs in the north-eastern Chinese city of Shenyang and says business has boomed since this resemblance to Mr Kim appeared on social media and he has hired another cook to prepare the kebabs, much of his time now absorbed with customers taking selfies with him.

Donald Trump doppelganger: Dolores Leis Antelo, a farmer from Nanton, La Coruna, Spain.  The two are reportedly not related and have never met.

Shao Jianhua Changsha, Hunan, PRC and his queue of selfie-requesting customers.

Shao Jianhua, who five years ago moved from his native Zhejiang to Changsha, makes and sells meat pies with dried and pickled vegetables, a dish associated with costal Zhejiang.  His shop operates from a cluster near the university halls of residence and the students, although very fond of his highly-regarded pies, also request selfies, business having expanded since word spread of his resemblance to PRC president Xi Jinping (b 1953; PRC president 2013-).  Mr Shao, whose pies sell for 3.5 yuan (US$0.55) has increased production to 1,600 a day during peak season and the queues are frequently long.

The conspiracy theorists do apply some science to their subjects.  Of particular interest are ears, cosmetic surgeons noting that ears are so difficult to modify to match those of another person and that latex versions attached with surgical glue are the best solution for these purposes although even with these there are limitations.  It’s not the first time a head of government’s ears have attracted interest.  In 1939, Adolf Hitler (1889–1945; Führer of Germany 1933-1945) sent his court photographer Heinrich Hoffmann (1885–1957) with the party which in 1939 went to Moscow to execute the Nazi-Soviet Pact, his task, inter alia, to get a good shot of Comrade Stalin’s (1878-1953; Soviet leader 1924-1953) ear-lobes, the Führer wishing to be reassured his new (and temporary) ally’s lobes were “separate and Ayran” and not “attached and Jewish”.  He was satisfied with Hoffman’s evidence but that didn’t stop him later double-crossing Stalin.

Front and back of blood sample of prisoner #7 (Hess), “Spandau #7 Pathology SVC Heidelberg MEDDAC 1139.

The flight to England by Rudolf Hess (1894–1987; Deputy Führer 1933-1941) in 1941, an attempt to persuade the British to conclude the war on the eve of the invasion of Russia, was one of the strangest episodes of the war and whether or not his flight was approved by Hitler remained a matter of conjecture for decades although the available evidence does suggest the Führer was as shocked as everyone else.  Another conspiracy theory ran for years, that of whether the Hess the British produced for trial in Nuremberg (1945-1946) and who was subsequently imprisoned in Spandau until his suicide (other conspiracy theories explore this) in 1987 was actually a doppelganger.  Books with various explanations about why the British might have done this were written, including one by a doctor who examined Hess while a prisoner and couldn’t reconcile his physiology with the injuries he’s suffered while serving in the Imperial Army in the First World War.  Eventually even the suspicious authors conceded the incarcerated Hess was the real one and in 2019, after one of Hess’s hermetically sealed blood samples was discovered and subjected to a DNA analysis which found a 99.99% likelihood of a match with one of Hess’s living relatives.

Lindsay Lohan and body double Aoife Bailey during filming of Irish Wish (Netflix, 2024).

The most obvious doppelgangers are "body doubles", actors used when filming scenes when, for whatever reason, the lead actor can't be used.  Such are the tricks and techniques of film production, the body doubles don't have to be even close to exact doppelgangers, they need only be vaguely similar though they often share some distinctive characteristic (such a long red hair).  Generally, body doubles are used for three reasons:

(1) Dangerous stunts: Body doubles with specific expertise are often hired to perform dangerous scenes, such as car chases, fight scenes, or jumps from great heights.

(2) Time constraints: In some cases, the lead actor or actress may not be available to film certain scenes due to scheduling conflicts.  In these situations, a body double can be used to film the scene in their place, allowing production to continue without delay.

(3) Privacy: In some instances, actors may not wish to appear in certain scenes, typically those involving nudity.  Sometimes contractual clauses include these stipulations.

What stunt doubles do, Lindsay Lohan and body double Aoife Bailey during filming of Irish Wish (Netflix, 2024).  The car is a 1965 Triumph TR4A.