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.
