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, TikTok etc) 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 etc).  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.  

Epoch

Epoch (pronounced ep-uhk or ee-pok)

(1) A particular period of time marked by distinctive features, events etc.

(2) The beginning of a distinctive period in the history of anything.

(3) A point in time distinguished by a particular event or state of affairs; a memorable date.

(4) In geology, any of several divisions of a geologic period during which a geologic series is formed (much associated with rock formation).  An epoch (the shortest division of geologic time) is a sub-division of a period.  As a geochronologic unit, an epoch can range between hundreds of thousands to millions of years.

(5) In astronomy, an arbitrarily fixed instant of time or date, usually the beginning of a century or half century, used as a reference in giving the elements (such as coordinates of a planetary orbit) relating to a celestial body.

(6) In astronomy, the mean longitude of a planet as seen from the sun at such an instant or date.

(7) In chronology, astronomy & computing, a specific instant in time, chosen as the point of reference or zero value of a system that involves identifying instants of time.

(8) In physics, the displacement from zero at zero time of a body undergoing simple harmonic motion (the displacement of an oscillating or vibrating body at zero time).

(9) In AI (artificial intelligence), one complete presentation of the training data set to an iterative machine learning algorithm.

1605-1615: From the Medieval Latin epocha, from the Ancient Greek ἐποχή (epokhḗ) (epochē) (a check, cessation, stop, pause, fixed time, epoch of a star (ie the point at which it seems to halt after reaching the highest, and more generally the place of a star (thus the extension of use to “a historical epoch”))), from ἐπέχω (epékhō, (to hold in, check), the construct being ἐπι- (epi-) (upon) + ἔχω (ékhō) (to have, hold), from the primitive Indo-European root segh- (to hold).  The early seventeenth century adoption in English of epocha was in the sense of “point marking the start of a new period in time” and it was used by scholars and theologians of momentous events in history (the crucifixion of Christ; the Visigoths gathering at the gates of Rome etc).  Less than a decade after epocha had entered the language, the transferred meaning “a period of time” was in use and it entered the jargon of geology in 1802 although the technology then did not permit precise measurements and exploration was then embryonic (what are now understood as dinosaur fossils not so classified until 1824) so most of the early estimates of geological epochs were inaccurate.

Confusingly, “epoch” can be used either to refer to a distinct and defined historic period (ie with an agreed beginning & end) or the event associated with the beginning of that period.  The latter concept is best understood in the adjectival forms “epoch-making” and “epochful”.  Subepoch is a technical term from geology, used as a geochronologic unit comprising one or more ages, being a period of generally agreed significance within an epoch.  The companion superepoch (two or more sequential epochs references as one for illustrative or didactic purposes is non-standard.  In statistical analysis, sub_epoch, base-epoch, super_epoch & primary_epoch exist as commands in aspects of database handling and manipulation, the link being the use of “datum” as epoch’s coordinate term in cartography and engineering.  The alternative form epocha was in use between the seventeenth & nineteenth centuries.  Epoch is a noun & verb, epochful, epocjless & epochal are adjectives and epochally is an adverb; the noun plural is epochs.

Bal du moulin de la Galette (Dance at Le Moulin de la Galette, 1876), oil on canvas by Pierre-Auguste Renoir (1841–1919), Musée d'Orsay, Paris

The Belle Époque (appearing in texts often as La Belle Époque with capitalization not always used) was a period in European history characterized by peace, progress, cultural refinement and artistic innovation; the term was an adoption of the French La Belle Époque (literally “the beautiful era” and best understood as “the golden age”).  Historians date the start of the Belle Époque from the end of the Franco-Prussian War (1970-1871) although, “on the ground” it likely wasn’t so clear-cut because the impositions of war reparations made the first few post-war years “difficult” in France so “mid-1870s” may be a better point of origin.  The Belle Époque lasted until the blast of World War I (1914-1918) destroyed the continent’s sense of optimism and ended an era characterized by what might now be call an “end of history” feeling that held things like wars, famines and plagues were in the past and the future would be one of progress and improvement.

Art Nouveau.

An advertisement (1899) for Moët & Chandon's champagnes, designed by Czech painter & graphic artist Alphonse Mucha (1860–1939):  “White Star” champagne (left) & “Grand Crémant Imperial” (right).  The product is very much a period piece, Art Nouveau characterized by swirling shapes, stylized representations of women and intricate floral motifs.  For those with enough disposable income, La Belle Époque must have been an amusing time to live.  The “modern industrial” sense later summoned by the straight, sharp and geometric lines of Art Deco was a deliberate rejection of Art Nouveau's intricate, hand-crafted aesthetic yet in Art Deco the influence of the earlier style often is apparent.  Although by the 1920s unfashionable and in the inter-war years casually dismissed by many critics and historians, Art Nouveau's popular appeal never went away.  While there was never really a “revival”, the style's motifs remained a staple of commercial graphic art and the various “nostalgia movements” before being “cherry picked” by pop art, psychedelia and postmodernists.   

Those 40-odd years of what came to be called La Belle Époque were not without conflict or economic disruptions and it must be remembered Europe’s “golden age” was one of untroubled pleasure only for a select few, most of the population living lives of hard labor and drudgery, many on a variation of the Hobbesian (the very clever and deliciously wicked English philosopher Thomas Hobbes (1588-1679)) path: “nasty, crowded, brutish and short”.  La Belle Époque is a selective construct of the era’s intellectual and aesthetic landmarks in art, literature and architecture, characterized by opulence, eclecticism and an undeniable dynamism from which emerged movements such as Futurism, Cubism and Art Nouveau.  Viewed from our troubled times, the Belle Époque exists in a warm nostalgic glow and it’s telling the term first gained popularity in France during the 1930s, the decade of the Great Depression.  Even then, La Belle Époque was still in living memory but because it became mythologised as a “golden age”, it was as myth it passed into history.

Lindsay Lohan entering her fifth decade.  Her five eras thus far may loosely be labelled: (1) child star, (2) troubled Hollywood starlet, (3) nemesis, (4) reinvention and (5) redemption.

Signed to the Ford agency, Lindsay Lohan secured her first modelling gig aged three but what’s understood as the “Lindsay Lohan era” ran for the decade after the release of Mean Girls (2004).  It was characterized by her low-speed car crashes, court appearances and becoming a staple of the tabloid press and lower reaches of the glossy magazine industry, a reasonable contribution to GDP (gross domestic product), providing predictable cash flow for paparazzi on both sides of the Atlantic.  Improbable as it once seemed, she proved a survivor in the churn of the industry's destructive “child star” machine and on 2 July, 2026 celebrated her 40^th birthday.  That happened during the 23^rd FIFA (Fédération Internationale de Football Association (the International Federation of Association Football which, for historic reasons, recognizes more countries than the UN (United Nations)) World Cup and, on the day, playing at the Bay Area Stadium in Santa Clara, San Francisco, USA beat Bosnia-Herzegovina 2-0 so that was a good birthday present.  

Geologyin's illustration of the concept of geological epochs.

In scientific usage there is precision, the ICS (International Commission on Stratigraphy) codifying a strict hierarchy on the discipline of geology, the structure being Eon → Era → Period → Epoch → Age.  However, in ordinary English discourse (and even in the work of professional scholars and historians) there is no fixed hierarchy in that an age may be longer than an era and an era may be longer than an epoch; unless following established conventions, writers can opt for whichever word best conveys the intended nuance, a choice that can be influenced by the search for rhetorical effect or the rhythm of the narrative.  So, in the way of English, there are no “rules” but, as a general principle, (1) Age = “known for...”, (2) Era = “lasting period of...” and (3) Epoch = “a period with a turning point that defined its nature.”  The overlaps in use don’t usually cause confusion but among the fastidious there are acknowledged nuances and accepted conventions of use:

(1) An epoch is a distinct period marked by particular characteristics or events, thus the use in geology where defining changes or sets of conditions can be established by scientific techniques such as chemical analysis or radiocarbon dating.  In non-scientific use, because of the etymological lineage, an epoch typically begins with some sort of event thought a turning point or watershed and this can be an organic development with no exact fixed date (the Industrial Revolution) or something decidedly exact (the epoch of the computer operating system Unix is defined as 00:00:00 UTC, 1 January 1970 although this was not first set precisely then).

(2) An age is a period with a specific, dominant association.  That might be a technology (bronze age; oil age; jet age etc), a characteristic (age of empires; age of European colonialism etc) or an individual (Napoleonic age; Elizabethan Age etc).  Unlike the epochs of geologists and astronomers, “ages” can run in parallel or overlap.  While some are sequential such as the “Three Age System” (Stone Age; Bronze Age; Iron Age) tracking the evolution of humanity's tools and metalworking capabilities between prehistory and Antiquity, others can co-exist such as the Age of Sail & Age of Enlightenment.  Because of the nature of the word and historic pattern of use, of the three, “age” is the most flexible and adaptable because it’s merely associative, not exclusive and often with no precise chronology.

(3) An era is a period (by human standards usually but not necessarily long) with origins at a certain point (usually an event) and characterized by an enduring pattern; eras tend to be major historical phases or systems (the Nazi era; the analogue era etc).  Generally “era” is used to denote something coherent (though it need not be long); a stretch of history with a recognizable character, a beginning and an end.  That can reference the life of an individual (Queen Victoria lent her name to the “Victorian era” 1837-1901), several individuals (there were four Kings of England named George whose collective reign defined the “Georgian era” 1714-1830) or a specific closed-time set (the “inter war era”: 1918-1939).

Eras tour merchandise.  Canvas tapestry featuring photographs from Taylor Swift’s The Eras Tour, cotton canvas, 800 mm (31½ inches) x 1220 mm (48 inches).

Taylor Swift’s “Eras” project tends to be thought of as a concert tour but it’s better imagined as pop culture’s greatest ever exercise in vertical integration, a merging of music (audio streaming, packaged (in multiples in the case of the vinyl releases) & live performance), video content, merchandise ranging from framed posters, a “limited edition” book, a film with concert footage, outfits emulating those worn on stage, jewellery, hoodies, pillows, stainless steel tumblers and more.  Although there has in recent years been a bit of mission creep, the idea of a canvas tapestry as a piece of tour merchandise in the pop music business would, until recently, likely have occurred to few.  Commerce has moved on from a half-century earlier when, at a Led Zeppelin concert, one might be able to buy a Tee-shirt (in S, M, L & XL), maybe with a choice of black or white (black quickly selling out).

Ms Swift is good with words and for the “Eras” project may have pondered using “Ages” or “Epochs”.  Given the accepted conventions (Age = “known for...”, Era = “lasting period of...” and Epoch = “a period with a turning point that defined its nature.”) and the concept of the “Eras” project, a convincing case could have been made for “Ages” because each subset was thematically distinct while the use of “Epochs” would have worked because the word is understood as a “period of time with a beginning and end” but linking each with a single “triggering event” might have descended to abstractions so “Eras” seems the best choice.  Certainly it’s unlikely she long considered using “Periods”; although etymologically defensible, it would have been decarded on much the same basis as that of the publishers of the magazine Australian Women’s Weekly who, upon in 1983 switching to issuing monthly editions, opted not to change the title to “Women’s Monthly”.

There is of course a vagueness associated with the definitions because not all “eras” and “ages” have as convenient bookends the end of one war and the start of another; that’s why context can matter.  In speaking of the time after World War II (1939-1945), “post-war era” is a common term but the meaning can vary depending on what’s being discussed.  It’d be absurd to speak of 2026 as being in the “post-war” era (although in a sense that’s true) so meaning must be gleaned from context.  The two decade period 1918-1939 came to be called both the “inter-war” and “pre-war” era (although many tend to restrict the latter to a start-point in the mid-1930s) and in much historiography there's sometimes the suggestion the “post-war” era can usefully be said to have ended some 20 years hence; that’s about 1965 so conveniently (1) in the new era of the High Cold War, (2) about the length of a then typical “generation” and (3) in the 1960s, a very different era.  So it can be inexact and some with a focus on political economy fix the end date on exactly 17 October 1973, the day OAPEC (Organization of Arab Petroleum Exporting Countries) proclaimed an oil embargo targeting the US and other states providing military aid to Israel during the 1973 Yom Kippur War.  At that point, the West’s long post-war boom, although already stuttering, ended.  In a similar vein, although also very much a Western-centric view, some historians have argued the nineteenth century is best imagined as a construct running from the close of the Congress of Vienna (1814-1815) to the outbreak of World War I (1914-1918).  There’s much support for that although there are different views about the conceptual view of the twentieth century. While 1914 seems a logical starting-point, candidates for the end date include 1989 (fall of the Berlin Wall (1961-1989)), 1991 (dissolution of the Soviet Union (1922-1911)) and the 9/11 terrorist strikes in 2001.

Taylor Swift Style: Fashion through the eras.

Between March 2023 and December 2024, Taylor Swift’s “Eras” tour took in 149 shows in 51 cities over five continents; each performance ran for a remarkable 3½ hours and there was a mid-tour revision of the song set to interpolate material The Tortured Poets Department (2024), her eleventh studio album.  The “Eras” title was an allusion to the show’s format, a retrospective in which each of her albums was designated as a “musical era”, the many outfits worn tied to those themes and just as each song and each performance was a product, so could be each outfit, some available on-line for purchase by devoted Swifties.  So, as set piece events go, Ms Swift set a high bar and, on revenues in excess of US$2 billion, profits were high and continue to grow.

Even when there are precise start and end dates, things can at the margin become blurred.  Pedants enjoy pointing out the 1960s began on 1 January 1961 so an expression like “the 1960s” ends on 31 December 1969 but the decade in which most of those years existed actually includes 1970, a quirk which extends also to centuries and millennia, something ultimately a product of there being no year zero in the calendar now defining BCE (before Common Era) and CE (Common Era) (the pair the secular version of BC (Before Christ) and AD (from the Latin Anno Domini (in the year of the Lord)), all based on the (nominal) birth date of Jesus Christ.  “Ages” and “eras” can at once be “exact” and “indicative”.  Many of the civilizations of antiquity all had their so-called “golden ages” and these tended to be associated with particular dynasties or reigns.  The examples are many and are cross-cultural, including the Gupta Empire in India (mid-third to mid-sixth century AD) founded by Mahārāja Śrī-Gupta, the Tang dynasty (626-684) & the reign of Tae-tsong (618-626) in China and, in Egypt, the reigns of Sethos I and Ram'eses II (1336-1224 BC).  In the West, the use of “golden ages” is legion including in Russia during the rule of Czar Peter the Great (1672-1725) (memorable because the Russian people have not enjoyed many “golden ages”) and, of course, in England, the “Elizabethan age”, referencing the reign of Elizabeth I (1533–1603; Queen of England & Ireland 1558-1603).  However, at the granular level, the idea of the term “Elizabethan age” denoting a “golden age” in literature was contested by the English writer, literary scholar and Anglican lay theologian C. S. Lewis (1898–1963) who, in his Introduction to English Literature in the Sixteenth Century (1654), distinguished the “estimable” literature of the later Elizabethan period from what he called that of the earlier “drab age”.  Lewis found drabness in the poetry and prose of the later medieval period up to the early Renaissance, distinguishing it from the “golden era style” between circa 1580-1603.  Lewis was an uncompromising critic but while most in the profession may well agree much that was written in the fifteenth century and early Tudor period was “drab”, among those published in the period were Sir Thomas Wyatt (1503-1542) and John Skelton (circa 1460-1529); their writing was not beyond criticism but the works were hardly drab.

Sarah Chapelle's (b 1992) Swiftie site documenting looks from The Eras tour: Fearless v6 (worn 18 October, 2024, far left), Midnights v5 (worn 16 August, 2024, centre left), 1989 v2 (worn 19 March, 2023, centre right) and Reputation v1 (worn 18 March, 2023, far right).  Some outfits can be purchased on-line but buyers should note they should not expect their appearance exactly to emulate what's “on the tin”.  

Simulacrum describes an image that while not purely realistic, maintains enough of a likeness for the subject to be recognizable.  In some jurisdictions it can be deemed “deceptive and misleading” if a product is represented in manner judged to be a “deliberate misrepresentation” intended to induce a purchase.  Legal recourse is available but is practical only if enough money is involved (such as real estate); although in theory someone purchasing a McDonalds Big Mac after being tempted by the image in the advertising might have grounds for an action, a claim of under $US10 would not impress a judge and even a class action would, on several grounds, be thrown out.  Presumably a disgruntled consumer could lodge a claim for the “pain & suffering” caused by one's Big Mac not looking as attractive as the one in the advertising but that'd likely anger the judge still more.  The classic simulacrums were the stylish images rendered in the 1960s by Art Fitzpatrick (1919–2015) & Van Kaufman (1918-1995) for GM’s (General Motors) PMD (Pontiac Motor Division) and those of Ms Swift in the Eras Tour outfits are in the same “mannerist but not quite surrealist” tradition.  Although obviously “unrealistic”, these depictions are not “deceptive and misleading” because they’re so obviously simulacral and exist only as devices, the extent of the licence taken illustrated by them appearing next to a flesh & blood Ms Swift in the same outfit.  They are “impossible” rather than “idealized”.

Super simulacrum: The Colossus of Rhodes (circa 1560), hand-colored by Dutch portrait and religious painter Maarten van Heemskerck (1498–1574) on an engraving by Dutch publisher & designer Philip Galle (1537–1612).

The Colossus of Rhodes was one of the Seven Wonders of the Ancient World and although it stood for barely half a century before being felled by an earthquake, it's ruins lying for almost a millennium as a kind of tourist attraction before the metal was carted of as scrap to be melted-down an re-cycled.  The notion the statue's legs straddled the entrance to Rhodes Harbor with tall-masted ships passing between them was wholly fanciful; even with modern materials and techniques, such a construction would be impossible.  The engineers and architects of the sixteenth century would of course have known it couldn't be done but such was the allure of the era of Classical Antiquity that brilliant myths seduced the public imagination better than tiresome facts.

Other “era-related” terminology also often used interchangeably relates to that long span of history between the fall of the Western Roman Empire (476 AD) and the dawn of the Renaissance in the late fourteenth century: (1) Middle Ages, (2) Dark Ages and (3) Medieval.  “Middle Ages” is the most obviously descriptive because it refers to the period between the dying gasps of Classical Antiquity and the cultural & artistic revival of the Renaissance while Medieval simply means “relating to the Middle Ages” (although by virtue of association and use, it came to be used also as a slur).  As general principle, historians tend to divide the Middle Ages into (1) Early (476-circa 1000), (2) High (circa 1000-circa 1300) and (3) Late (circa 1300-circa 1500).  “Dark Ages” reflected the prejudices of fifteenth century writers who regarded the earlier Middle Ages (476-circa 1000) as a period of stagnation, lack of progress and “intellectual darkness”, a stark contrast to the idealized vision of Classical Antiquity they constructed from what evidence there was, “filling in the gaps” with imaginations as famously vivid as any of the Medieval scribes and artists responsible for some fabulous beasts.  The Seven Wonders of of the Ancient World” they found especially compelling, some of their speculative depictions of the Colossus of Rhodes and the Walls and Hanging Gardens of Babylon such examples of architectural gigantism even Albert Speer (1905–1981; Nazi court architect 1934-1942; Nazi minister of armaments and war production 1942-1945) might have been embarrassed.  Maybe they looked in awe at the scale of Great Pyramid of Giza and assumed all the ancients operated in “think big” mode.

Tony Abbott (b 1957; Prime Minister of Australia 2013-2015) agitprop.

Mr Abbott's combination of relentless negativity and repetition of 3WSs (three word slogans) contributed to his resounding victory in the 2013 general election although, in office, the results were mixed and it ended badly.  Recently revived as the Liberal Party's federal president (the institution's third “Lazerus with a triple bypass” after Sir Robert Menzies (1894–1978; Prime Minister of Australia 1939-1941 & 1949-1966) and John Howard (b 1939; Prime Minister of Australia 1996-2007)), Mr Abbott unquestionably was one of history's most effective leaders of the opposition but as Roy Jenkins (1920–2003) remarked of Lord Randolph Churchill (1849–1895):  “He was essentially a opposition politician and behaved as such even when in government”.  Of such matters, Jenkins was a fair judge.  Although medieval may literally mean “relating to the Middle Ages” and can be used as a neutral adjective (medieval architecture, medieval manuscripts etc), it is also used as a term of derision: “Mr Abbott’s views on certain topics seem distinctly medieval although, to be fair, the thirteenth century probably never produced a finer mind”.  Used in that way, it implies “outdated, harsh or unenlightened”, a throwback to the stereotypes of the Dark Ages but more recent scholarship has cast doubt on whether the “Dark Ages” was a time as culturally sterile and technologically stagnant and was for centuries an orthodoxy among historians.  A view now more popular is the earlier conceptions of the period were formed because of the relative scarcity of written records and although it’s now clear there was progress in agriculture, law, architecture, theology, literature, engineering and state formation, it is true that compared with what came before and what followed, progress often was fitful.  Of note also is there were in the Renaissance and beyond not a few who didn’t count “advances in theology” as progress worth mentioning.