Algorithm

Algorithm (pronounced al-guh-rith-um)

(1) A set of rules for solving a problem in a finite number of steps.

(2) In computing, a finite set of unambiguous instructions performed in a prescribed sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result.

(3) In mathematics and formal logic, a recursive procedure whereby an infinite sequence of terms can be generated.

1690s: From the Middle English algorisme & augrym, from the Anglo-Norman algorisme & augrimfrom, from the French algorithme, re-fashioned (under mistaken connection with Greek αριθμός (arithmos) (number)) from the Old French algorisme (the Arabic numeral system) from the Medieval Latin algorismus, a (not untypical) mangled transliteration of the Arabic ⁧الخَوَارِزْمِيّ⁩ (al-ḵawārizmiyy), the nisba (the part of an Arabic name consisting a derivational adjective) of the ninth century Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī and a toponymic name meaning “person from Chorasmia” (native of Khwarazm (modern Khiva in Uzbekistan)).  It was Muḥammad ibn Mūsā al-Khwārizmī works which introduced to the West some sophisticated mathematics (including algebra). The earlier form in Middle English was the thirteenth century algorism from the Old French and in English, it was first used in about 1230 and then by the English poet Geoffrey Chaucer (circa 1344-1400) in 1391.  English adopted the French term, but it wasn't until the late nineteenth century that algorithm began to assume its modern sense.  Before that, by 1799, the adjective algorithmic (the construct being algorithm + -ic) was in use and the first use in reference to symbolic rules or language dates from 1881.  The suffix -ic was from the Middle English -ik, from the Old French -ique, from the Latin -icus, from the primitive Indo-European -kos & -ḱos, formed with the i-stem suffix -i- and the adjectival suffix -kos & -ḱos.  The form existed also in the Ancient Greek as -ικός (-ikós), in Sanskrit as -इक (-ika) and the Old Church Slavonic as -ъкъ (-ŭkŭ); A doublet of -y.  In European languages, adding -kos to noun stems carried the meaning "characteristic of, like, typical, pertaining to" while on adjectival stems it acted emphatically; in English it's always been used to form adjectives from nouns with the meaning “of or pertaining to”.  A precise technical use exists in physical chemistry where it's used to denote certain chemical compounds in which a specified chemical element has a higher oxidation number than in the equivalent compound whose name ends in the suffix -ous; (eg sulphuric acid (H₂SO₄) has more oxygen atoms per molecule than sulphurous acid (H₂SO₃).  The noun algorism, from the Old French algorisme was an early alternative form of algorithm; algorismic was a related form.  The meaning broadened to any method of computation and from the mid twentieth century became especially associated with computer programming to the point where, in general use, this link is often thought exclusive.  The spelling algorism has been obsolete since the 1920s.  Algorithm, algorithmist, algorithmizability, algorithmocracy, algorithmization & algorithmics are nouns, algorithmize is a verb, algorithmic & algorithmizable are adjectives and algorithmically is an adverb; the noun plural is algorithms.

Babylonian and later algorithms

An early Babylonian algorithm in clay.

Although there is evidence multiplication algorithms existed in Egypt (circa 1700-2000 BC), a handful of Babylonian clay tablets dating from circa 1800-1600 BC are the oldest yet found and thus the world's first known algorithm.  The calculations described on the tablets are not solutions to specific individual problems but a collection of general procedures for solving whole classes of problems.  Translators consider them best understood as an early form of instruction manual.  When translated, one tablet was found to include the still familiar “This is the procedure”, a phrase the essence of every algorithm.  There must have been many such tablets but there's a low survival rate of stuff from 40 centuries ago not regarded as valuable.

So associated with computer code has the word "algorithm" become that it's likely a goodly number of those hearing it assume this was its origin and any instance of use happens in software.  The use in this context, while frequent, is not exclusive but the general perception might be it's just that.  It remains technically correct that almost any set of procedural instructions can be dubbed an algorithm but given the pattern of use from the mid-twentieth century, to do so would likely mislead or confuse confuse many who might assume they were being asked to write the source code for software.  Of course, the sudden arrival of mass-market generative AI (artificial intelligence) has meant anyone can, in conversational (though hopefully unambiguous) text, ask their tame AI bot to produce an algorithm in the syntax of the desired coding language.  That is passing an algorithm (using the structures of one language) to a machine which interprets the text and converts it to language in another structure, something programmers have for decades been doing for their clients.

A much-distributed general purpose algorithm (really more of a flow-chart) which seems so universal it can be used by mechanics, programmers, lawyers, physicians, plumbers, carpet layers, concreting contractors and just about anyone whose profession is object or task-oriented.   

The AI bots have proved especially adept at such tasks.  While a question such as: "What were the immediate implications for Spain of the formation of the Holy Alliance?" produces varied results from generative AI which seem to range from the workmanlike to the inventive, when asked to produce computer code the results seem usually to be in accord with a literal interpretation of the request.  That shouldn't be unexpected; a discussion of early nineteenth century politics in the Iberian Peninsular is by its nature going to to be discursive while the response to a request for code to locate instances of split infinitives in a text file is likely to vary little between AI models.  Computer languages of course impose a structure where syntax needs exactly to conform to defined parameters (even the most basic of the breed such as that PC/MS-DOS used for batch files was intolerant of a single missing or mis-placed character) whereas something like the instructions to make a cup of tea (which is an algorithm even if not commonly thought of as one) greatly can vary in form even though the steps and end results can be the same.

An example of a "how to make a cup of tea" algorithm.  This is written for a human and thus contains many assumptions of knowledge; one written for a humanoid robot would be much longer and include steps such as "turn cold tap clockwise" and "open refrigerator door".

The so-called “rise of the algorithm” is something that has attracted much comment since social media gained critical mass; prior to that algorithms had been used increasingly in all sorts of places but it was the particular intimacy social media engenders which meant awareness increased and perceptions changed.  The new popularity of the word encouraged the coining of derived forms, some of which were originally (at least to some degree) humorous but beneath the jocularity, many discovered the odd truth.  An algorithmocracy describes a “rule by algorithms”, a critique in political science which discusses the implications of political decisions are being made by algorithms, something which in theory would make representative and responsible government not so much obsolete as unnecessary.  Elements of this have been identified in the machinery of government such as the “Robodebt” scandal in Australia in which one or more algorithms were used to raise and pursue what were alleged to be debts incurred by recipients of government transfer payments.  Despite those in charge of the scheme and relevant cabinet ministers being informed the algorithm was flawed and there had been suicides among those wrongly accused, the politicians did nothing to intervene until forced by various legal actions.  While defending Robodebt, the politicians found it very handy essentially to disavow connection with the processes which were attributed to the algorithm.

The feeds generated by Instagram, Facebook, X (formerly known as Twitter) and such are also sometimes described as algorithmocracies in that it’s the algorithm which determines what content is directed to which user.  Activists have raised concerns about the way the social media algorithms operate, creating “feedback loops” whereby feeds become increasingly narrow and one-sided in focus, acting only to reinforce opinions rather than inform.  In fairness, that wasn’t the purpose of the design which was simply to keep the user engaged, thereby allowing the platform to harvest more the product (the user’s attention) they sell to consumers (the advertisers).  Everything else is an unintended consequence and an industry joke was the word “algorithm” was used by tech company CEOs when they didn’t wish to admit the truth.  A general awareness of that now exists but filter bubbles won’t be going away but what it did produce were the words algorithmophobe (someone unhappy or resentful about the impact of algorithms in their life) and algorithmophile (which technically should mean “a devotee or admirer of algorithms” but is usually applied in the sense of “someone indifferent to or uninterested in the operations of algorithms”, the latter represented by the great mass of consumers digitally bludgeoned into a state of acquiescent insensibility.

Some of the products are fighting back: The Algorithm: How AI Decides Who Gets Hired, Monitored, Promoted, and Fired and Why We Need to Fight Back Now (2024) by  by Hilke Schellmann, pp 336, Hachette Books (ISBN-13: 978-1805260981).

Among nerds, there are also fine distinctions.  There are subalgorithms (sub-algorithm seems not a thing) which is a (potentially stand-alone) algorithm within a larger one, a concept familiar in many programming languages as a “sub-routine” although distinct from a remote procedure call (RPC) which is a subroutine being executed in a different address space.  The polyalgorithm (again hyphens just not cool) is a set of two or more algorithms (or subalgorithms) with instructions for choosing which in some way integrated.  A very nerdy dispute does exist within mathematics and computer science around whether an algorithm, at the definitional level, really does need to be restricted to a finite number of steps.  The argument can eventually extend to the very possibility of infinity (or types of infinity according to some) so it really is the preserve of nerds.  In real-world application, a program is an algorithm only if (even eventually), it stops; it need not have a middle but must have a beginning and an end.

There is also the mysterious pseudoalgorithm, something les suspicious than it may first appear.  Pseudoalgorithms exist usually for didactic purposes and will usually interpolate (sometime large) fragments of a real algorithm bit it may be in a syntax which is not specific to a particular (or any) programming language, the purpose being illustrative and explanatory.  Intended to be read by humans rather than a machine, all a pseudoalgorithm has to achieve is clarity in imparting information, the algorithmic component there only to illustrate something conceptual rather than be literally executable.  The pseudoalgorithm model is common in universities and textbooks and can be simplified because millions of years of evolution mean humans can do their own error correction on the fly.

Of the algorithmic

The Netflix algorithm in action: Lindsay Lohan (with body-double) during filming of Irish Wish (2024).  The car is a Triumph TR4 (1961-1967), one of the early versions with a live rear axle, a detail probably of no significance in the plot-line.

The adjective algorithmic has also emerged as an encapsulated criticism, applied to everything from restaurant menus, coffee shop décor, choices of typefaces and background music.  An entire ecosystem (Instagram et al) has been suggested as the reason for this multi-culture standardization in which a certain “look, sound or feel” becomes “commoditised by acclamation” as the “standard model” of whatever is being discussed.  That critique has by some been dismissed as something reflective of the exclusivity of the pattern of consumption by those who form theories about what seem not very important matters; it’s just they only go to the best coffee shops in the nicest parts of town.  In popular culture though the effect of the algorithmic is widespread, entrenched and well-understood and already the AI bots are using algorithms to write music will be popular, needing (for now) only human performers.  Some algorithms have become well-known such as the “Netflix algorithm” which presumably doesn’t exist as a conventional algorithm might but is understood as the sets of conventions, plotlines, casts and themes which producers know will have the greatest appeal to the platform.  The idea is nothing new; for decades hopeful authors who sent manuscripts to Mills & Boon would receive one of the more gentle rejection slips, telling them their work was very good but “not a Mills & Boon book”.  To help, the letter would include a brochure which was essentially a “how to write a Mills & Boon book” guide and it included a summary of the acceptable plot lines of which there were at one point reputedly some two dozen.  The “Netflix algorithm” was referenced when Falling for Christmas, the first fruits of Lindsay Lohan’s three film deal with the platform was released in 2022.  It was an example of followed a blending of several genres (redemption, Christmas movie, happy ending etc) and the upcoming second film (Irish Wish)  is of the “…always a bridesmaid, never a bride — unless, of course, your best friend gets engaged to the love of your life, you make a spontaneous wish for true love, and then magically wake up as the bride-to-be.” school; plenty of familiar elements there so it’ll be interesting to see if the algorithm was well-tuned.

Math of the elliptic curve: the Cox–Zucker machine can help.

Some algorithms have become famous and others can be said even to have attained a degree of infamy, notably those used by the search engines, social media platforms and such, the Google and TikTok algorithms much debated by those concerned by their consequences.  There is though an algorithm remembered as a footnote in the history of linguistic oddities and that is the Cox–Zucker machine, published in 1979 by Dr David Cox (b 1948) and Dr Steven Zucker (1949–2019).  The Cox–Zucker machine (which may be called the CZM in polite company) is used in arithmetic geometry and provides a solution to one of the many arcane questions which only those in the field understand but the title of the paper in which it first appeared (Intersection numbers of sections of elliptic surfaces) gives something of a hint.  Apparently it wasn’t formerly dubbed the Cox–Zucker machine until 1984 but, impressed by the phonetic possibilities, the pair had been planning joint publication of something as long ago as 1970 and undergraduate humor can’t be blamed because they met as graduate students at Princeton University.  The convention in academic publishing is for authors’ surnames to appear in alphabetical order and the temptation proved irresistible.

Random

Random (pronounced ran-duhm)

(1) Proceeding, made, or occurring without definite aim, reason, or pattern; lacking any definite plan or prearranged order; haphazard.

(2) In statistics, of or characterizing a process of selection in which each item of a set has an equal probability of being chosen (the random sample); having a value which cannot be determined but only described probabilistically.

(3) Of materials used in building and related constructions, lacking uniformity in size or shape.

(4) Of ashlar (stonework), laid without continuous courses and applied without regularity:

(5) In slang (also clipped to “rando” and some on-line sources insist “randy” is also used), something or someone unknown, unidentified, unexpected or out of place; anything odd or unpredictable (not necessarily a pejorative term and used as both noun & adjective).

(6) In slang, someone unimportant; a person of no consequence (always a pejorative).

(7) In printing, the sloping work surface at the top of a compositor's workbench on which type is composed (also called a bank and use now almost exclusive to the UK).

(8) In mining, the direction of a rake-vein.

(9) Speed, full speed; impetuosity, force (obsolete).

(10) In ballistics, the full range of a bullet or other projectile and thus the angle at which a weapon is tilted to gain maximum range (obsolete).

(11) In computing (as pseudorandom), mimicking the result of random selection.

1650s: From the earlier randon, from the Middle English randoun & raundon, from the Old French randon, a derivative of randir (to run; to gallop) of Germanic origin (related to the Old High German rinnan (to run) (from which Modern French gained randonnée (long walk, hike), from either the Frankish rant (a running) & randiju (a run, race) or the Old Norse rend (a run, race), both from the Proto-Germanic randijō, from rinnaną (run), from the primitive Indo-European r̥-nw- (to flow, move, run).  It was cognate with the Middle Low German uprinden (to jump up) and the Danish rende (to run).  The development of the adjective to mean “having no definite aim or purpose, haphazard, not sent in a special direction” evolved in the 1650s from the mid-sixteenth century phrase “at random” (at great speed) which picked up the fourteenth century sense from the Middle English noun randon & randoun (impetuosity; speed).  In English, the meaning closely mirrored that in the Old French randon (rush, disorder, force, impetuosity), gained from Frankish or other Germanic sources.  The spelling shift in Modern English from -n to –m was not unusual (seldom, ransom et al).  Random is a noun & adjective, randomness & randomosity are nouns, randomize is a verb and randomly is an adverb; the noun plural is randoms.

A “random person” is one variously unknown, unidentified, unexpected or out of place.

In general use, the meanings related to speed (full speed; force, trajectory of delivery etc) faded from use between the fourteenth & seventeenth centuries but persisted in the field of ballistics where “random” described the limit of the range of a bullet or other projectile (thus the angle at which a weapon was tilted to gain the maximum range.  Even that was largely obsolete by the early twentieth century but the idea of the angle being “a random” persists still in pockets in the UK to describe a sloping work surface on which printers compose pages (although few now use physical metal type).  The now familiar twenty-first century slang use can be either pejorative (someone unimportant; a person of no consequence) or neutral tending to the amused (something or someone unknown, unidentified, unexpected or out of place; anything odd or unpredictable).  The modern adoption appears to have its origin in 1980s US college student slang when “a person who does not belong on our dormitory floor” was so described; from this the hint of “inferior, undesirable” was perhaps inevitable.  “Rando” seems to be the standard abbreviation but some on-line sources also list “randy” which would seem to risk confusion or worse.

School lunch social engineering: Some sources recommend parents cut their children’s sandwiches in random ways.  The theory is it helps train their minds to accept change and helps them learn to adapt.

In computing, random access memory (RAM) had since the 1980s become familiar as one of a handful of the critical specifications of a computer (CPU, RAM, drive space) and the origin of the terms dates from IBM’s labs in the early 1950s when it was used to describe a new form of memory which could be read non-sequentially.  The modern RAM used by personal computers, servers, smart phones etc is an evolution from the original memory model; in the world of the early mainframes there was simply storage which could fulfil the functions now performed by both RAM and media like hard disks & solid state drives.  RAM is now a well-known commodity but the companion ROM (Read-Only Memory) is understood only by nerds and only an obsessional few of them give it much thought.  RAM volatile in that the contents are inherently temporary lost when the device is powered-down or re-started; it can thus be thought of as using static electricity for data storage.  That characteristic means it’s fast, affording the most rapid access by the CPU (Central Processing Unit) so is used to hold whatever data is at the time most in demand and that can be parts of the operating system, applications or documents.  ROM is non-volatile and whatever is written to ROM remains even if a device is switched-off; it’s thus used for essential, information like firmware and hardware information.

In mathematics and statistics, random does have precise definitions but in general use it’s used also as a vague synonym for “typical or average”.  To a statistician, the word implies “having unpredictable outcomes to the extent all outcomes are equally probable and if any statistical correlation is found to exist it will be wholly coincidental.  Thus, although all dictionaries list the comparative as more random and the superlative as most random, a statistician will insist these are as absurd as “very unique” although even among mathematicians phrases like “increasingly random” or “tending to randomness” are probably not unknown.  For others, the forms are useful and the colloquial use to mean “apropos of nothing; lacking context; unexpected; having apparent lack of plan, cause or reason” is widely applied to events, even those which to a specialist may not be at all random and may even be predictable.  For most of us, any sub-set of numbers which appears to have no pattern will appear random but mathematicians need to be more precise.  In the strict, technical sense, a true random number set exists only when two conditions are satisfied: (1) the values are uniformly distributed over a defined interval or set and (2) it is impossible to predict future values based on past or present ones.  In the pre-computer age, creating random number lists was challenging and subsequent analysis has found some of the sets created by manual or mechanical means were not truly random although those which were sufficiently large probably were functional for the purposes to which they were put.

“Random news” is something strange, unexpected and often amusing.    

Now, random number generators (RNG) are used and they can exist either in hardware or software and there are two types (1) pseudorandom number generators (PRNG) and true random number generators (TRNG).  A software algorithm, a PRNG emulates a TRNG by mimicking the selection of a value to approximate true randomness, the limitation being the algorithm being based on a distribution (the origin of the term pseudorandom) which can only produce something ultimately deterministic and predictable (although to determine the pattern can demand much computational power).  Relying on a seed number, if that can be isolated, other numbers can be predicted although, if the subset is large, for many purposes, what PRNGs generate is functional.  TRNGs don’t use an algorithm (although their processes can be represented by one) but are instead based on an unpredictable physical variable such as radioactive decay of isotopes, airwave static, or the behaviour of subatomic particles, the latter now favoured for their utterly unpredictable movements, now called “pure randomness”.  So random is the behaviour of subatomic particles that their observation appears to be immune to measurement biases which can (at least in theory) afflict other methods.

Random numbers are important in a number of fields including (1) statistical sampling and experimentation where it’s essential to select a random sample to ensure that the results are representative of the entire population, (2) cryptography where random numbers are used to generate the encryption keys which ensure the security of data and communications, (3) simulation and modelling where there’s a need to replicate real-world scenarios, (4) gaming & gambling where the need exists to create unpredictable outcomes and (5) randomized controlled trials (RCT), notably in medical and scientific research where true randomness is needed to assist in the assessment of the effectiveness of treatments, interventions, or policies.

Ziggurat

Ziggurat (pronounced zik-kur-at, zik-u-rat or zig-oo-rat)

(1) In the architecture of the ancient Babylonians and Assyrians, a temple of Sumerian origin in the form of a pyramidal tower, consisting of a number of stories and having about the outside a broad ascent winding round the structure, presenting the appearance of a series of terraces.

(2) In architecture, any structure similar in appearance.

(3) In statistics and mathematical modeling, as ziggurat algorithm, an algorithm for pseudorandom number sampling, relying on an underlying source of uniformly-distributed random numbers as well as computed tables.

1875–1880: Various cited as from the Akkadian word ziqquratu; from the Assyrian ziqqurati (summit, height) or from an extinct Semitic language, derived from a verb meaning "to build on a flat space." The various spellings were zikkurrat, ziqqurrat, ziqqurat (rare) and ziggurat.  Ziggurat is a noun and zigguratic & zigguratical are adjectives; the noun plural is ziggurate or ziggurats.

The Chogha Zanbil ziggurat was built circa 1250 BC by Untash-Napirisha, King of Elam, probably to honour the Elamite god Inshushinak.  Destroyed in 640 BC by Ashurbanipal, King of Assyria, part of it was excavated between 1951-1961 by Roman Ghirshman (1895-1979), a Ukrainian-born French archeologist who specialized in ancient Persia.  It was the first Iranian site to be added to UNESCO’s World Heritage List.

Ziggurats were massive structures with particular architectural characteristics.  They served as part of a temple complex in the various local religions of Mesopotamia and the flat highlands of what is now western Iran.  Sumer, Babylonia, and Assyria were home to about twenty-five ziggurats.  The shape of a ziggurat makes it clearly identifiable.  It has a platform base which is close to square with sides that recede inward as the structure rises and a flat top presumed to have supported some form of a shrine.  Sun-baked bricks form the core of a ziggurat, with fire-baked bricks used for the outer faces and unlike the Egyptian pyramids, a ziggurat was a solid structure with no internal chambers, an external staircase or spiral ramp provided access to the top platform.  The handful of ziggurats still visible are ruins, but, based on the dimensions of their bases, it’s estimated they may have been as much as 150 feet (46m) high.  It’s possible the terraced sides were planted with shrubs and flowering plants, and some scholars have suggested the legendary Hanging Gardens of Babylon (one of the Seven Wonders of the Ancient World), was a ziggurat.  Ziggurats were some of the oldest structures of ancient religions, the first examples dating from circa 2200 BC and the last circa 500 BC; only a few of the Egyptian pyramids predate the oldest ziggurats.  The Tower of Babel is thought to have been a ziggurat.

Depiction of Lindsay Lohan in ziggurat dress, part of the Autumn-Winter 1994-1995 "Staircase Pleats" collection by Japanese designer Issey Miyake (1938-2022).  Miyake San was noted for his technology-focused clothing designs.

Granular

Granular (pronounced gran-yuh-ler)

(1) Of the nature of granules; grainy.

(2) Composed of or bearing granules or grains.

(3) Showing a granulated structure.

(4) In computing, an object existing as a singular form at the level of the file system but which exists at the application level in multiple parts.

(5) Relating to or containing particles having a strong affinity for nuclear stains, as in certain bacteria.

1762 (although use not widespread until 1794): From the Late Latin granulum (granule, a little grain), diminutive of the Latin granum (grain, seed) from the primitive Indo-European gre-no- (grain) + -ar (from the From Latin -āris (of, near, pertaining to), the suffix appended to various words, often nouns, to make the adjectival form; added most often, but not exclusively, to words of Latin origin).  The word seems rather suddenly to have replaced the late fourteenth century granulous.  Granular, granularity, granule & granulation are nouns, granulate is a verb & adjective and granulatory is an adjective.

Terminology describing degrees of granularity

As granular has become a more widely used word, fastidious types have noted the increasing frequency of things being described as "more granular" or "less granular" and this elicits disapproval because it’s imprecise.  Something granular is composed of (usually small), discrete entities as opposed to being continuous and that’s a binary distinction, not a matter of degree so it’s inherently unclear if "more granular" and "less granular" indicate finer or coarser granularity.  For clarity, one should speak only of finer or coarser granularity.

Lindsay Lohan represented in granular art, an artificial intelligence (AI) generated artwork created by Wout from AI Fountain as part of the Curated Community Art initiative (CCAI) and finished in Adobe Photoshop.  Each digital artwork created by this algorithm is unique and made from a set of parameters; process and output are thus both inherently granular.

In computing, the concept of granularity exists in many forks and layers.  Users deal frequently with granular data, most typically when handling what appears to exist in many parts but which is, to the system, at least one layer, a single object.  For system administrators, it’s an especially handy attribute when it’s necessary to recover one small piece of data which has been copied or backed-up as something really huge and there are big machine operators which now routinely handle data sets of a size which only a few years ago were unimaginably large.  For them, the ability to look at the whole and be able to extract pieces, drilling down if need be to individual bytes, makes easily possible what would otherwise require much time and hardware; hence the metaphor of granularity, a mechanism to find a particular grain in a silo of many trillions.

That’s useful but really is just brute-force, the massive up-scaling up of something which has existed since the earliest forms of digital storage.  More intriguing is the recent emergence of Granular computing (GrC), a fork in information processing, the focus of which is information granules, entities created from the processes of data abstraction and derivations from data.  The source and structure of this data is not the imperative; what matters are the relationships (of which there may be many) which can, for example, simultaneously be both the extent of difference and a dependence on indistinguishability.  GrC, as it now exists, is more of a conceptual direction than a coherent process or even a theoretical perspective.  Its most promising implication is perhaps the granules which might form as relationships between previously disparate data sets are explored.  This may allow previously unrealized correlates to be identified, perhaps enabling humanity to mine the accumulate data sets for what Donald Rumsfeld (1932–2021: US Secretary of Defense 1975-1977 & 2001-2006) called the unknown knowns.  Rumsfeld may have been evil but his mind could sparkle and many unknown knowns may await.  

Pardon

Pardon (pronounced pahr-dn)

(1) A kind indulgence, as in forgiveness of an offense or discourtesy or in tolerance of a distraction or inconvenience.

(2) In law, release from the penalty of an offense; a remission of penalty, as by a governor, monarch or viceroy.

(3) Forgiveness of a serious offense or offender.

(4) In Roman Catholic canon law, a technical term for a papal indulgence (obsolete).

(5) To make a courteous allowance for or to excuse.

(6) When used with rising inflection, as an elliptical form, as when asking a speaker to repeat something not clearly heard or understood (non-U).

1250-1300: From the Middle English pardonen or pardoun (papal indulgence, forgiveness of sins or wrongdoing), from Old French pardon from pardoner (to grant; to forgive; remission, indulgence (which entered Modern French in the eleventh century as pardonner), from the Medieval Latin perdonum, from the Vulgar Latin perdōnāre (to remit, overlook (literally “to forgive”)), the construct being per- (for; through, thoroughly) + dōnāre (to give, donate) which emerged in Medieval Latin, though a translation from a Germanic source possibly a calque (if not vice-versa) of a Germanic word represented by the Frankish firgeban (to forgive, give up completely) which was akin to the Old High German fargeban & firgeban (to forgive) and the Old English forġiefan (to forgive).  The Latin per was from the primitive Indo-European root per- (forward (hence “through”)) and donare was from donum (gift), from the primitive Indo-European root donum (gift), from the root do- (to give).  The verb pardon was from pardounen, (to forgive for offense or sin).  The noun pardoner (a man licensed to sell papal pardons or indulgences) was a late fourteenth century form (it was noted earlier in the 1300s as a surname), the agent noun from the verb.  The adjective pardonable (forgivable, capable of being pardoned) was a mid-fifteenth century form from the twelfth century Old French pardonable, from pardoner.  Some sources insist pardonable was a back-formation from pardonable which is interesting.  The meaning “a passing over of an offense without punishment” was first noted around the turn of the fourteenth century (also in the strictly ecclesiastical sense) while as a “pardon for a civil or criminal offense; release from penalty or obligation”, use emerged in the late 1300s (mirroring the earlier Anglo-French).  The use in polite society to “request one be excused for some minor fault” was in use by at least the 1540s.

Pardon is one of those “cross-over words”, migrating from the technical use (an act by an official or a superior, remitting all or the remainder of the punishment that belongs to an offense (eg a sovereign or governor pardoning a convict before expiration of the sentence)) to become a synonym for “forgive” in the sense of feelings or social mores.  By convention, asking for another’s pardon re-establishes amicable relations between transgressor and the offended.  In idiomatic use, dating from the mid seventeenth century, the phrase “I beg your pardon” (the variations including “beg pardon”, “begging your pardon”, “pardon me” etc) is used (1) to apologise for something (typically a social faux pas), (2) to request clarification of something said if it is unexpected, odd or seen as rude without context and (3) to request something be repeated.  In the last case, Nancy Mitford (1904–1973) in Noblesse Oblige: An Enquiry Into the Identifiable Characteristics of the English Aristocracy (1956) insisted “pardon” was a non-U (lower & middle class) word and the “U” (upper class) form was “what?”.  The phrase “pardon my French” was an exclamation of apology for obscene language, noted since the late nineteenth century.  Pardon is a noun, verb & interjection, pardoning is a verb & noun, pardoned is a verb & adjective, pardonableness & pardoner are nouns, pardonable & pardonless are adjectives and pardonably is an adverb; the noun plural is pardons.

Pardons from the president: Without check or balance

Article Two of the United States Constitution describes the office of the President.  One of the powers granted is that he or she may grant reprieves and pardons except regarding congressional impeachment of himself or other federal officers.  A president cannot issue a pardon for future actions; he can't pardon someone in advance for something someone does next week.  The pardon power is reserved for past actions and the president can pardon an individual even if he or she has not yet been convicted or even charged.

An executive pardon can be invoked to help victims of injustice.

It's an interesting power and the only one in the US constitution not subject to "checks and balances", an inheritance of one of the entitlements enjoyed by absolute and later monarchs.  The power, in the form exercised by a US president, doesn't exist in the UK or elsewhere in the Commonwealth where, when a pardon is granted, it’s a decision of the executive (the prime-minister (or premier) & cabinet) which is done in the name of the sovereign or their representative; in other words, by the state.  It’s different from vesting the power as a personal prerogative of an individual; US presidents have granted pardons which would have no chance of success were they subject to confirmation by the Senate.

The most interesting recent speculation about the presidential pardon is whether as president can pardon themselves.  This was something Donald Trump (b 1946; US president 2017-2021) probably pondered with especial interest during the diggings of special counsel Robert Mueller's (b 1944; Director of the Federal Bureau of Investigation (FBI) 2001-2013) into certain matters relating to the 2016 presidential election.  Mr Trump did tweet suggesting he could pardon himself even though there's no precedent, no president has ever done so (though at least one was surely tempted) and all that is certain is that the chief magistrate has the power to grant pardons "for offenses against the United States, except in cases of impeachment."  That means he couldn't have pardoned himself from impeachment, nor anyone facing charges under state laws, and when asked, most constitutional law experts suggested he couldn't have pardoned himself for anything else either.  However, even if a presidential self-pardon were to be held to be constitutional, politically, it would be a challenge to manage so an extra-constitutional check on the power is political; the court of public opinion as it were.

When there was mush speculation about a possible prosecution of Richard Nixon (1913-1994; US president 1969-1974) for matters associated with the Watergate scandal, the Justice Department did issue an opinion saying a president could not pardon himself because, under long-established legal principle, no person can be the judge in their own case.  So, the legal status of a self-pardon has never been tested because, at the federal level, it’s never been done and nothing is definitive until ruled upon by the US Supreme Court.  There are records of state governors self-pardoning but one instance appears to have been technical, one a clerical error and one so murky it not clear what happened.  The state of US politics is now both so poisonous and so fluid that a second term for Mr Trump is no longer unthinkable if the Democrat Party insists on nominating Joe Biden (b 1942; US president since 2021) it become more likely still.  Mr Biden may or may not be senile but he certainly seems senile.  In his first term, Mr Trump proved remarkably uninterested in pursuing any of the vendettas he'd mentioned during the 2016 campaign; when asked if he would be pursuing the threatened legal action against the Clintons, he brushed off the question with a quick "...they're good people" and moved on.  In a second term, given the events of the last few years, he may not be so indulgent towards those who have slighted or pursued him so there's the intriguing prospect of an elected president attempting to pardon himself so he can move into the Oval Office and begin his revenge.  Interestingly, constitutional experts have all said that even if a self-pardon is declared unconstitutional, there is nothing to prevent a convicted felon being elected president from his jail cell, a place which would certainly focus one's mind on revenge.           

Pardons from God (via the pope)

In late medieval Christianity, the noun pardonmonger was a derogatory term directed at those who sold papal indulgences; the noun plural pardonmongers should also be noted because there were a lot of them about.  The indulgences had become big business in the medieval church and their abuse was one of the emblematic issues which triggered the Protestant Reformation.  The system worked by permitting a (sinful) individual to purchase from the church an indulgence which would reduce the length and severity of punishment that heaven would require as payment for their transgressions.  Indulgences were in a sense transferable because one could buy one for another and according to legend, those on their death bed would implore relations to buy them one so they would avoid an eternal damnation in Hell.

Historically, the indulgence system was able to evolve because the doctrine of the medieval western Christian church (the Eastern Orthodox would follow a different path) was: (1) Folk knew that after they died they were going to be punished for the sins they accumulated in life, something ameliorated only partially by good works (pilgrimage, prayers, charitable work etc) and earthly absolution; the more sin, the greater the punishment and (2) There was the concept of purgatory, a product of the theological imagination which meant that rather than being damned to hell, the sinful soul would be sent to purgatory where they would endure whatever punishment deemed appropriate, the suffering continuing until the stain was washed from them and they could be set free.  This was obviously not an attractive prospect and seeing a way to cement in society the world-view that church, God & sin were central, popes granted bishops the authority to reduce punishments while they were still alive.  It proved a highly useful tool in making unshakable the worldview in which the church, God and sin were central.

Quite when papal indulgences were first introduced isn’t known but the system was formalized by Pope Urban II (circa 1035–1099; pope 1088-1099) during the Council of Clermont in 1095.  The protocols reflected the diligent order which characterized church bureaucracy: Were one to perform sufficient good deeds to earn a full (Plenary) indulgence from the pope or a bishop, all sins would be expunged (and thus no punishment).  Partial indulgences would erase fewer evil deeds and an intricate system of layers came to be used; essentially an algorithm with which a cleric could calculate (to the day!) how much sin a person had wiped from their record.  Indulgences rapidly developed into a significant structural aspect of church administration and during the Crusades (Urban II’s other great contribution to history), many participated on the basis that in exchange for fighting to regain the Holy Land, they would be granted an indulgence, cancelling all sin.

This system of reducing sin and punishment worked well and having people perform good deeds (whatever the motivation) presumably made for a more harmonious society.  However, in something with a modern echo, rich people began to wonder why, instead of the time consuming, boring or sometimes distasteful business of actually doing good deeds, might it not be easier just to purchase an indulgence, the church thereby able to use the funds for good deeds.  The early example of outsourcing began in the thirteenth century and proved so popular (and profitable) for both governments and the church that it became an important revenue source, the catchment soon extended to allow the rich to buy indulgences for their ancestors, relatives, and friends already dead. 

The nature of this business soon became scandalous, notably during the reign of the Medici Pope Leo X (1475–1521; pope 1513-1521) and indulgences were among the issues the monk Martin Luther (1483–1546) listed in his 95 Theses (1517), a j’accuse directed at what he believed to be an institutionalized corruption and in saying that, Luther had a point, the pope having commissioned a Dominican friar to sell indulgences for the sole purpose of the construction of St. Peter's Basilica in Rome.  Luther’s attack led to fragmentation within the church, many new sects abandoning the idea of indulgences and while the papacy banned the sale of indulgences in 1567, they didn’t entirely vanish and this wasn’t enough to prevent the subsequent schism within Western Christianity.  So, in the modern Roman Catholic Church, indulgences still exist but they no longer work in the medieval way when they could be something like a presidential pardon.  According to the Vatican: “An indulgence is a remission before God of the temporal punishment due to sins whose guilt has already been forgiven, which the faithful Christian who is duly disposed gains under certain defined conditions through the Church’s help when, as a minister of redemption, she dispenses and applies with authority the treasury of the satisfactions won by Christ and the saints”.  The salient points of the system are:

(1) A person cannot buy their way out of hell with indulgences.  Because indulgences remit only temporal penalties, they cannot remit the eternal penalty of hell. Once a person is in hell, no amount of indulgences will ever change that and the only way to avoid hell is by appealing to God’s eternal mercy while still alive; after death, one’s eternal fate is set.

(2) One cannot buy indulgences for sins not yet committed.  Historically, the church has always taught that indulgences do not apply to sins not yet committed although it’s clear some were sold on that basis prior to the Protestant Reformation.  The position now is that: “An indulgence is not a permission to commit sin, nor a pardon of future sin; neither could be granted by any power.”  Theologically that may sound dubious because presumably God could grant exactly that but, as any pope will tell you, God never would.

(3) An indulgence does not “buy forgiveness” because, by definition, the issue of an indulgence presupposes forgiveness has already taken place: “An indulgence is a remission before God of the temporal punishment due to sins whose guilt has already been forgiven.”  Indulgences therefore do not forgive sins and deal only with the punishments left after sins have been forgiven.

(4) It is not true an indulgence will shorten one’s time in purgatory by a fixed number of days.  While it’s true that prior to the Reformation such calculations did appear in documents, the church maintains these were references to the period of penance one might undergo during life on earth and the Catholic Church does not claim to know anything about how long or short purgatory is in general, much less any specific.

(5) Indulgences may not be purchased.  The Council of Trent (1545-1563) instituted many reforms in the practice of granting indulgences and, because of prior abuses, “...in 1567 Pope Pius V (1504–1572; pope 1566-1572) cancelled all grants of indulgences involving any fees or other financial transactions.”  To this day the Roman Catholic Church maintains indulgences were “never sold”, an interpretation of history still used by politicians and political parties when explain why donations (sometimes in the millions) are really “not buying anything”.

Heaven & Hell

Heaven (pronounced hev-uhn)

(1) In theology, the abode of God, the angels, and the spirits of the righteous after death; the place or state of existence of the blessed after the mortal life.

(2) The celestial powers; God (initial capital letter and often in the plural).

(3) A metonym for God.

(4) In architecture, as heavens (used with a singular verb), a wooden roof or canopy over the outer stage of Elizabethan theatres.

(5) In poetic and (mostly historic) scientific & legal use, often in the plural, the sky, firmament, or expanse of space surrounding the earth, including the moon, Sun, planets & stars.

(6) A place or state of supreme happiness, often expressed as “heaven on earth”.

(7) A component of expression (variously singular & plural), used in exclamatory phrases of surprise, exasperation, emphasis etc.

(8) In mythology, a place, such as Elysium or Valhalla, to which those who have died in the gods' favour are brought, there eternally to dwell in happiness.

Pre 900: From the Middle English heven, hevin, heuen & hewin (heaven, sky), from the Old English heofon (home of God (and earlier) the visible sky, firmament), probably from the Proto-Germanic hibin (heaven, sky), a dissimilation of himin and source also of the Middle Low German heven, the Old Saxon heban, the Old Swedish himin, the Low German heben, the Old Norse himinn, the Old Danish himæn, the Gothic himins, the Old Frisian himul, the Scots heaven & hewin, the Dutch hemel and the German Himmel (heaven, sky).  The mysterious Proto-Germanic hibin (which existed also as hebn) is of uncertain and disputed origin.  It was cognate with and possibly the rare Icelandic and Old Norse hifinn (heaven, sky), which may be dissimilated forms of the Germanic root was more familiar in the Old Norse himinn (heaven, sky).  Among etymologists, the most popular alternative root is the Proto-Germanic himinaz (cover, cloud cover, firmament, sky).  A now archaic alternative spelling (in both sacred and secular writing) which persisted in poetry into the twentieth century because of the rhythmic advantages was heav'n.

Stairway to Heaven, sculpture by David McCracken, Bondi, Sydney, Australia.

From the late fourteenth century, the word in English assumed the meaning "a heavenly place; a state of bliss”.  The plural use in sense of "sky" may have emerged from a simple habit of use influenced by other words although a link has been suggested with the Ptolemaic theory of space as composed of many spheres.  It had also been used in the same sense in the singular in Biblical language, as a translation of Hebrew plural shamayim.  The earliest adjectival sense “heaven-sent” is attested from the 1640s.

Hell (pronounced hel)

(1) In theology, the place or state of eternal punishment of the wicked after death; the abode of evil and condemned spirits; Gehenna or Tartarus.  The ruler of hell is said often to be Satan; the Devil.

(2) Any place or state of torment or misery; something that causes torment or misery.

(3) The powers of evil.

(4) The abode of the dead; Sheol or Hades.

(5) Extreme disorder or confusion; chaos.

(6) In informal use, something remarkable of its kind (as in “one hell of a…”).

(7) A receptacle into which a tailor throws scraps and off-cuts (a practice in many industries).  In commercial printing, as the hellbox, a box into which a printer throws discarded type.

(8) A general purpose utterance of in swearing or for emphasis, now generally regarded as not actually obscene; used as an intensifier to express surprise, anger, impatience etc; an general intensifier in many phrases.

(9) A gambling house or booth in which bets are placed (archaic).

(10) In metal-working, to add luster to, burnish silver or gold (now rare).

Pre 900: From the Middle English, from the Old English hel & hell (nether world, abode of the dead, infernal regions, place of torment for the wicked after death), it was cognate with the Old High German hella & hellia (source of the Modern German Hölle), the Icelandic hella (to pour), the Norwegian helle (to pour), the Swedish hälla (to pour), the Old Norse hel & hella and the Gothic halja.  It was related to the Old English helan (to cover, hide) and to hull.  The Old English gained hel & hell from the Proto-Germanic haljō (the underworld) & halija (one who covers up or hides something), the source also of the Old Frisian helle, the Old Saxon hellia, the Dutch hel, the Old Norse hel, the German Hölle & the Gothic halja (hell).  The meaning in the early Germanic languages was derived from the sense of a "concealed place", hence the Old Norse hellir meaning "cave or cavern", from the primitive Indo-European root kel (to cover, conceal, save).  In sacred art, hell, whether frozen or afire, is almost always depicted as a cavernous place.

The English traditions of use may have been influenced by Norse mythology and the Proto-Germanic forms.  In the Norse myths, Halija (one who covers up or hides something) was the name of the daughter of Loki who rules over the evil dead in Niflheim, the lowest of all worlds (nifl "mist") and it was not uncommon for pagan concepts and traditions to be grafted onto Christian rituals and idiom.  Hell was used figuratively to describe a state of misery or bad experience (of which there must have been many in the Middle Ages) since the late fourteenth century and as an expression of disgust by the 1670s.  In eighteenth century England, there were a number of Hellfire Clubs, places where members of the elite could indulge their immoral proclivities.  They were said to attract many politicians.

Lindsay Lohan at a promotion for John John "Made in Heaven" jeans, Rua Oscar Freire, Sao Paulo, Brazil, March 2013.

It proved adaptable in the English vernacular.  To have all hell break loose is from circa 1600; to hell in a handbasket is attested by 1867 (an in a context implying earlier use) although it may simply have been derivative of to heaven in a handbasket from 1853 which was a happy phrase implying an easy passage to a nice place.  Hell or high water from 1874 seems to have been a variation of the earlier between the devil and the deep blue sea and the first recorded instance of wishing someone would go to hell seems to have been in Shakespeare’s Merchant of Venice although it’s hard to believe it hadn’t before then been a familiar oral form and one with which the bard may well have been acquainted.  The snowflake’s (later snowball's) chance in hell meaning "no chance" is from 1931 and till hell freezes over meaning "never" is documented from 1832.  To do something just for the hell of it is from 1921, to ride (a horse) hell for leather is from 1889 and hell on wheels was noted (in the US) first in 1843, a reference to the river steamboats which, for propulsion, used large wheels rather than propellers and gained a general popularity after 1869 after it was used in reference to the temporary vice-ridden towns established along the path of the US transcontinental railroad.  Unrelated to this was the earlier (1580s) Scottish hell-wain (a phantom wagon seen in the sky at night).

What happens to snowflakes and snowballs in hell is interesting.  In the writings drawn from the Abrahamic traditions of Judaism, Christianity and Islam, hell is certainly a hot place, the “fire and brimstone” of the New Testament used in the US as a description of a certain type of preacher.  However, in the Divine Comedy (1320), Dante Alighieri (circa 1265–1321) located hell in Earth’s innermost core and he wrote of its characteristics in ways consistent with Aristotelian dynamics; it was mostly hot and fiery but in some places frozen and immobile:

When we were down in that ditch’s darkness, well below the giant’s feet, my gaze still drawn by the wall above us, I heard a voice say: ‘Watch where you walk. Step so as not to tread upon our heads, the heads of wretched, weary brothers.’ At that I turned to look about. Under my feet I saw a lake so frozen that it seemed more glass than water. Never in winter did the Austrian Danube nor the far-off Don, under its frigid sky, cover their currents with so thick a veil as I saw there.

This prison of ice is reserved for a variety of different species of traitors. Depending on the severity of their offense, they may only be frozen from the waist down; or, they may be completely immersed.

A vision of Hell: Pandæmonium (1841) by John Martin (1789–1854).

Dante lists the intricate layers of location for the punishment of sinners and evildoers and while some are hot, the ninth and innermost circle, reserved for the worst of the worst, is icy cold.  Dante goes further, noting that even within the ninth circle, there are gradations, the worst and coldest spot kept for Judas Iscariot.  A colder conception of hell than that familiar from scripture but the idea of a cold hell exists also in Buddhism and some Christian texts of the first millennium.  Dante’s marvelous work was however for centuries neglected and others took the chance to make sure the Biblical stories held sway, John Milton (1608-1674) in Paradise Lost (1667-1674) having the last word, convincing all that Hell was no place for snowflakes.  So today it remains.

“At once, as far as Angel’s ken, he views

The dismal situation waste and wild.

A dungeon horrible, on all sides round,

As one great furnace flamed; yet from those flames

No light; but rather darkness visible

Served only to discover sights of woe,

Regions of sorrow, doleful shades, where peace

And rest can never dwell, hope never comes

That comes to all, but torture without end

Still urges, and a fiery deluge, fed

With ever-burning sulphur unconsumed.”

For those wondering about the fate of certain friends and family members or contemplating their own eternal fate, Dante’s Lonely Planet Guide to Hell summarizes the nine circles thus:

(1) Limbo: The first circle of Hell is Limbo, where the souls of the unbaptized and virtuous pagans reside; while there are no actual punishments, those in Limbo are forever denied the joy of God's presence.  Limbo, frankly, was a bit of a fudge, concocted by medieval theologians as a work-around to avoid the worst injustices of strict Christian rules (notably the souls of the stillborn being sent to Hell on the basis of being unbaptized).  Still it was orthodox Christian thought in Dante’s time and although in subsequent centuries there was much debate, it never went away.  Benedict XVI (1927–2022; pope 2005-2013, pope emeritus 2013-2022), 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.

(2) Lust: The second circle is for the lustful.  They are punished by being blown around in a violent storm, symbolizing their lack of self-control.  Perhaps surprisingly, given the fixation many modern denominations seem to have upon anything to do with sex, historically the Christian churches regarded lust usually as the “least to be condemned” of the seven deadly sins, the basis of that, as Saint Thomas Aquinas (1225–1274) pointed out: it was a sin “of the flesh and not the soul” and thus both understandable and forgivable as would one forgive one’s pet cat for eating the meat; it’s just what cats do.  Lust (sometimes expressed as “lechery) included not only fornication but also rape, adultery and “unnatural acts upon beasts of the field” so it was an uncharacteristically generous view from the pulpit.  Of course, given the well-documented predilection of priests, bishops and the odd pope to lustful ways, the relaxed view may have been corporate self-interest.

(3) Gluttony: The third circle is for the gluttonous. They are forced to lie in a vile slush of filth, symbolizing the garbage of their excessive consumption.  Theologians had a broader view of gluttony than is now current in that they were thinking also in terms of social justice; one person’s excessive consumption meant there were others who went hungry.  Some also explored aspects of gluttony as an example of “the idolatry of food” and thus a violation of one of the Ten Commandments.  One improbable supporter of this was Benito Mussolini (1883-1945; Duce (leader) & prime-minister of Italy 1922-1943) who re-purposed the notion in his forlorn attempt to convince Italians it was time to re-create the Roman Empire, lambasting his countrymen for “…following the French into the decadence of elevating cooking to high art while letting the blade of the sword fall to rust.”

(4) Greed: The fourth circle is for the greedy. They are divided into two groups and forced to push heavy weights, symbolizing their excessive desire for material wealth.  Again it’s linked to worship of a “false idol”, the “worship of money” being the “root of all evil” long accepted as orthodox Christian theology (often acknowledged rather than practiced) although the distinction seems lost in many of the modern evangelical congregations (notably those which sing, clap and strum guitars) where it’s made clear McMansions, surf-skis and a big TV in as many rooms as possible is most Godly.

(5) Wrath: The fifth circle is for the wrathful. They are submerged in the river Styx and must fight each other on the surface.  Wrath does seem a curious basis on which to be condemned to Hell, if only because if too rigorously enforced there would be few not damned.  The point seemed to be that the Christian message was not that one should never feel anger (indeed the Church would clarify this by saying mere anger was “neutral”) but that one should “practice Christian charity” and never allow wrathful thoughts to lead to the harming of one’s neighbour. 

(6) Heresy: The sixth circle is for the heretics. They are trapped in flaming tombs, symbolizing their rejection of God's love.  Heresy really is about as bad as it gets because it means one has disagreed with what the priest says and that means defying the pope who, as the “Vicar of Christ on Earth” is uniquely able to express the thoughts of God.  So, what the pope says goes which is why he is “infallible” in such matters; the internal logic is perfect.  While wrathful souls may end up in the fifth circle, a wrathful God is going to punish heretics by sending them for eternity to the sixth: “Vengeance is Mine” said the Lord.

(7) Violence: The seventh circle is divided into three rings, each for a different type of violence: against others, against oneself, and against God. The punishments include being boiled in blood, being transformed into trees and bushes, and being chased and mauled by dogs with sharp teeth.  It’s been hard for critics to resist the feeling Dante enjoyed writing of the sufferings in the seventh circle more than any other, possibly because of the exalted positions many of the victims enjoyed during however many of their four score & ten they managed.  The sanction of violence against self (suicide & attempted suicide) entered the criminal law systems in many jurisdictions and it’s only in recent decades that in some places it has been reclassified from crime to health condition of some type.

(8) Fraud: The eighth circle is for the fraudulent. It is divided into ten bolgias (from the Italian bolgia used here in the sense of “ditch”), each for a different type of fraud. The punishments include being whipped by demons, being immersed in excrement, and being transformed into reptiles.  In the matter of fraud, Dante casts a wider net than the offence captures in the modern imagination where it ranges from shop-lifting to Bernie Madoff’s (1938–2021) Ponzi scheme.  Instead of involving just financial matters, Dante encompasses fraud in a kind of omnibus bill which captures sins as diverse as those who corrupt others with flattery, those who seduce the innocent with lies and deception, those who practice magic & sorcery, those who corrupt the truth by the pedalling of fake news as well as, most obviously, thieves.

(9) Treachery: The ninth circle is for the treacherous. It is divided into four rounds, each for a different type of treachery. The punishments include being frozen in ice, being gnawed on by a three-headed demon, and being devoured by Lucifer himself.  Dante makes clear the sin of treachery is the worst of all and because there’s obviously some overlap with the offences which justify being sent to the other eight, the ninth is reserved for the worst of the worst.  Interestingly, the ninth circle is the part of Hell Dante describes as an icy, frozen place, something usually ignored in pop-culture, film-makers and Satanists staging their video clips almost always preferring fire, molten lava and red-hot pokers.  It could though be worse still because in the centre of Hell sits miserably the Devil, cast there for committing the ultimate sin: his personal treachery against God which saw him forever banished from Heaven.

Benedict XVI looking for Cardinal George Pell (1941-2023).  Canto XVIII, part of the eighth circle of Hell, in Divine Comedy (circa 1494), illustrated by Sandro Botticelli (Alessandro di Mariano di Vanni Filipepi; circa 1445–1510).

Cuius est solum, eius est usque ad coelum et ad inferos

The legal doctrine cuius est solum, eius est usque ad coelum et ad inferos (whoever's is the soil, it is theirs all the way to Heaven and all the way to Hell) is a historic principle of property law which holds the owner of a piece of land enjoys rights not just to the defined soil but to the air above (stretching to Heavens, ie to infinity) and what lay below (as far as Hell, ie all the way down); the legal shorthand is ad coelum.  Developments in technology, such as radio waves and flight, have much modified the doctrine but it continues, with limitations, to operate.  Some of the airspace above a piece of land can be recognized as a property right and as something therefore transferable but the right does not extend far, a position modified also in international law as long ago as the 1950s to accommodate the implication of satellites and, later, space flight, realizing the implications of discussions which had been going on since the advent of flight.  The rights to ownership of what lies below the soil and even the right to deny access to others now varies between jurisdictions but has long since ceased to be absolute.

Although there are no specific references in the record, it may be the origin of the maxim lies in in Roman or Jewish law, or at least customary practice.  The earliest surviving mention in English law is recorded in Bury v Pope (1587) Cro Eliz 118, [1653] EngR 382, (1653) Cro Eliz 118, (1653) 78 ER 375 (B), the Chief Justice, Sir Edward Coke (1552–1634), holding “the earth hath in law a great extent upwards, not only of water as hath been said, but of aire, and all other things even up to heaven, for cujus est solum ejus est usque ad coelum, as it is holden.”, finding for a plaintiff seeking to erect a structure which would block to his neighbor’s window the light which had fallen there for thirty years.  Even then however, limits were noted, Sir Edward saying ad coelum might be defeated if a claim for a right in conflict could be found to have existed prior to 1189, the significance of the date being the beginning of the reign of King Richard I (1157–1199; King of England 1189-1199) and, mentioned here as a legal fiction, the end point of time immemorial.

English law seems to have picked it up from the writings of thirteenth century Italian jurist Accursius (circa 1182–1263), and is said to have been used in common law during the reign of Edward I (1239–1307; King of England 1272- 1307) and the legal framework (air above and ground below) was defined by William Blackstone in his treatise Commentaries on the Laws of England (1766).

Land hath also, in its legal signification, an indefinite extent, upwards as well as downwards. Cujus est solum, ejus est usque ad coelum, is the maxim of the law, upwards; therefore no man may erect any building, or the like, to overhang another's land: and, downwards, whatever is in a direct line between the surface of any land, and the center of the earth, belongs to the owner of the surface; as is every day's experience in the mining countries. So that the word "land" includes not only the face of the earth, but every thing under it, or over it. And therefore if a man grants all his lands, he grants thereby all his mines of metal and other fossils, his woods, his waters, and his houses, as well as his fields and meadows.

Heaven and Hell: Google and Bing

In a study hardly scientific but with a consistent methodology, a Google search for Heaven yielded 1.1 billion results and one for Hell, 784 million.  The same search using Microsoft’s Bing engine delivered 51.4 million hits for Heaven and 48.9 million for Hell.  Noting the method in the search engines' algorithm which underpins how results are delivered, this suggests 58.82% of Google’s users favor God and 41.18% prefer the Devil while Microsoft’s users are more evenly divided, 51.25% being godly and 48.75% Satanists.  Given the state of the world, both God and Satan might have hoped for better numbers but the results are unlikely greatly to have surprised either and it seems to confirm what Google have long said: Use Bing and burn in Hell.