Mental Calculator
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Mental calculation (also known as mental
computation A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, hist ...
) consists of
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
al
calculation A calculation is a deliberate mathematical process that transforms a plurality of inputs into a singular or plurality of outputs, known also as a result or results. The term is used in a variety of senses, from the very definite arithmetical ...
s made by the
mind The mind is that which thinks, feels, perceives, imagines, remembers, and wills. It covers the totality of mental phenomena, including both conscious processes, through which an individual is aware of external and internal circumstances ...
, within the
brain The brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for ...
, with no help from any supplies (such as pencil and paper) or devices such as a
calculator An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. The first solid-state electronic calculator was created in the early 1960s. Pocket-si ...
. People may use mental calculation when computing tools are not available, when it is faster than other means of calculation (such as conventional educational institution methods), or even in a competitive context. Mental calculation often involves the use of specific techniques devised for specific types of problems. Many of these techniques take advantage of or rely on the
decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...
numeral system. Capacity of
short-term memory Short-term memory (or "primary" or "active memory") is the capacity for holding a small amount of information in an active, readily available state for a short interval. For example, short-term memory holds a phone number that has just been recit ...
is a necessary factor for the successful acquisition of a calculation, specifically perhaps, the
phonological loop Alan Baddeley, Baddeley's model of working memory is a model of human memory proposed by Alan Baddeley and Graham Hitch in 1974, in an attempt to present a more accurate model of primary memory (often referred to as short-term memory). Working memo ...
, in the context of addition calculations (only). Mental flexibleness contributes to the probability of successful completion of mental effort - which is a concept representing adaptive use of knowledge of rules or ways any number associates with any other and how multitudes of numbers are meaningfully associative, and certain (any) number
pattern A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated l ...
s, combined with
algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
s process. It was found during the eighteenth century that children with powerful mental capacities for calculations developed either into very capable and successful scientists and or mathematicians or instead became a counter example having experienced personal retardation. People with an unusual fastness with reliably correct performance of mental calculations of sufficient relevant complexity are prodigies or
savants Savant syndrome ( , ) is a phenomenon where someone demonstrates exceptional aptitude in one domain, such as art or mathematics, despite significant social or intellectual impairment. Those with the condition generally have a neurodeve ...
. By the same token, in some contexts and at some time, such an exceptional individual would be known as a:
lightning Lightning is a natural phenomenon consisting of electrostatic discharges occurring through the atmosphere between two electrically charged regions. One or both regions are within the atmosphere, with the second region sometimes occurring on ...
calculator, or a
genius Genius is a characteristic of original and exceptional insight in the performance of some art or endeavor that surpasses expectations, sets new standards for the future, establishes better methods of operation, or remains outside the capabiliti ...
. In a survey of children in England it was found that mental imagery was used for mental calculation. By neuro-imaging, brain activity in the parietal lobes of the right hemisphere was found to be associated with mental imaging. The teaching of mental calculation as an element of schooling, with a focus in some teaching contexts on mental strategies


Exceptional calculational ability

An exceptional ability is mental calculation such as adding, subtracting,
multiplying Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a '' product''. Multiplication is often de ...
or dividing large numbers. Skilled calculators were necessary in research centers such as
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
before the advent of modern electronic calculators and computers. See, for instance, Steven B. Smith's 1983 book ''The Great Mental Calculators'', or the 2016 book ''
Hidden Figures ''Hidden Figures'' is a 2016 American Biographical film, biographical Drama (film and television), drama film directed by Theodore Melfi and written by Melfi and Allison Schroeder. It is loosely based on the 2016 non-fiction Hidden Figures (boo ...
'' and the film adapted from it.


Competitions


World Cup

The Mental Calculation World Cup is an international competition that attempts to find the world's best mental calculator, and also the best at specific types of mental calculation, such as addition, multiplication, square root or calendar reckoning. The first Mental Calculation World Cup took place in 2004. It is an in-person competition that occurs every other year in Germany. It consists of four different standard tasks --- addition of ten ten-digit numbers, multiplication of two eight-digit numbers, calculation of square roots, and calculation of weekdays for given dates --- in addition to a variety of "surprise" tasks. The last edition was organized in September 2024 and won by Aaryan Nitin Shukla, who successfully defended his title to become two time World Champion.


Mental Calculation & Speed Reading Olympiad

The
Mind Sports Olympiad The Mind Sports Olympiad (MSO) is an annual international multi-sport event, multi-disciplined competition and festival for game of skill, games of mental skill and mind sports by Mind Sports Organisation. The inaugural event was held in 1997 i ...
has staged annual world championships since 1998.


Memoriad – World Memory

The first international Memoriad was held in
Istanbul Istanbul is the List of largest cities and towns in Turkey, largest city in Turkey, constituting the country's economic, cultural, and historical heart. With Demographics of Istanbul, a population over , it is home to 18% of the Demographics ...
, Turkey, in 2008. The second Memoriad took place in
Antalya Antalya is the fifth-most populous city in Turkey and the capital of Antalya Province. Recognized as the "capital of tourism" in Turkey and a pivotal part of the Turkish Riviera, Antalya sits on Anatolia's southwest coast, flanked by the Tau ...
, Turkey, on 24–25 November 2012. 89 competitors from 20 countries participated. Awards and money prizes were given for 10 categories in total; of which 5 categories had to do about ''Mental Calculation'' (Mental addition, Mental Multiplication, Mental Square Roots (non-integer), Mental Calendar Dates calculation and Flash Anzan). The third Memoriad was held in Las Vegas, USA, from November 8, 2016 through November 10, 2016.


Mind Sports Organisation

The Mind Sports Organisation recognizes six grandmasters of mental calculation: Robert Fountain (1999), George Lane (2001), Gert Mittring (2005), Chris Bryant (2017), Wenzel Grüß (2019), and Kaloyan Geshev (2022), and one international master, Andy Robertshaw (2008). In 2021, Aaryan Nitin Shukla became the youngest champion ever at an age of just 11 years.


World records

Shakuntala Devi from
India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...
has been often mentioned on the
Guinness World Records ''Guinness World Records'', known from its inception in 1955 until 1999 as ''The Guinness Book of Records'' and in previous United States editions as ''The Guinness Book of World Records'', is a British reference book published annually, list ...
. Neelakantha Bhanu Prakash from
India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...
has been often mentioned on the Limca Book of Records for racing past the speed of a calculator in addition. Sri Lankan- Malaysian performer Yaashwin Sarawanan was the runner-up in 2019 '' Asia's Got Talent''.


Media


Literary

*
Frank Herbert Franklin Patrick Herbert Jr. (October 8, 1920February 11, 1986) was an American science-fiction author, best known for his 1965 novel Dune (novel), ''Dune'' and its five sequels. He also wrote short stories and worked as a newspaper journalist, ...
's novel ''
Dune A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, flat ...
'', specially trained mental calculators known as Mentats have replaced mechanical computers completely. Several important supporting characters in the novel, namely
Piter De Vries ''Dune'' is a science fiction media franchise that originated with the 1965 novel of the same name by American author Frank Herbert. ''Dune'' is frequently cited as the best-selling science fiction novel in history, and won the 1966 Hugo Award ...
and Thufir Hawat, are Mentats.
Paul Atreides Paul Atreides (; later known as Paul Muad'Dib, and later still as The Preacher) is a fictional character in the Dune (franchise), ''Dune'' universe created by Frank Herbert. He is a main character in the first two novels in the series, ''Dune ( ...
was originally trained as one without his knowledge. However, these Mentats do not specialize in mathematical calculations, but in total recall of many different kinds of data. For example, Thufir Hawat is able to recite various details of a mining operation, including the number of various pieces of equipment, the people to work them, the profits and costs involved, etc. In the novel he is never depicted as doing actual academic mathematical calculations. Mentats were valued for their capacity as humans to store data, because "thinking machines" are outlawed. *
Roald Dahl Roald Dahl (13 September 1916 – 23 November 1990) was a British author of popular children's literature and short stories, a poet, screenwriter and a wartime Flying ace, fighter ace. His books have sold more than 300 million copies ...
's novel '' Matilda'', the lead character is portrayed having exceptional computational skills as she computes her father's profit without the need for paper computations. During class (she is a first-year elementary school student), she does large-number multiplication problems in her head almost instantly. *Andrew Jackson "Slipstick" Libby is a calculating prodigy in Robert A. Heinlein's
Sci-Fi Science fiction (often shortened to sci-fi or abbreviated SF) is a genre of speculative fiction that deals with imaginative and futuristic concepts. These concepts may include information technology and robotics, biological manipulations, space ...
story '' Methuselah's Children''. *
Haruki Murakami is a Japanese writer. His novels, essays, and short stories have been best-sellers in Japan and internationally, with his work translated into 50 languages and having sold millions of copies outside Japan. He has received numerous awards for hi ...
's novel ''
Hard-Boiled Wonderland and the End of the World is a 1985 novel by Japanese author Haruki Murakami. It was awarded the Tanizaki Prize in 1985. The English translation by Alfred Birnbaum was released in 1991. A new translation by Jay Rubin was released December 2024. A strange and dreamlike ...
'', a class of mental calculators known as ''Calcutecs'' perform
cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...
in a sealed-off portion of their brains, the results of which they are unable to access from their normal waking consciousness.


Film


Fiction


=Twentieth century

=


1980s

*In the 1988 movie '' Rain Man'', Raymond Babbitt, who has
savant syndrome Savant syndrome ( , ) is a phenomenon where someone demonstrates exceptional aptitude in one domain, such as art or mathematics, despite significant social or intellectual impairment. Those with the condition generally have a neurodevel ...
, can mentally calculate large numbers, amongst other abilities.


1990s

*In the 1991 movie '' Little Man Tate'', Fred Tate in the audience blurts out the answer during a mental calculation contest. *In the 1997 Sci-Fi thriller ''
Cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...
'', one of the prisoners, Kazan, appears to be mentally disabled, but is revealed later in the film to be an autistic savant who is able to calculate prime factors in his head. *In 1998
Darren Aronofsky Darren Aronofsky (born February 12, 1969) is an American Filmmaking, filmmaker. His films are noted for their surreal, dramatic, and often disturbing elements, frequently in the form of psychological realism. His accolades include a Golden Lion ...
's film '' Pi'', Maximillian Cohen is asked a few times by a young child with a calculator to do large multiplications and divisions in his head, which he promptly does, correctly. *In 1998 film '' Mercury Rising'', a 9-year-old autistic savant with prodigious math abilities cracks a top secret government code.


=Twenty-first century

=


2000s

*In the 2006 film '' Stranger than Fiction'', the main character, Harold Crick, is able to perform rapid arithmetic at the request of his co-workers.


2010s

*In the 2012 film ''
Safe A safe (also called a strongbox or coffer) is a secure lockable enclosure used for securing valuable objects against theft or fire. A safe is usually a hollow cuboid or cylinder, with one face being removable or hinged to form a door. The body ...
'', a female child math genius is kidnapped to be used by the Chinese Triad. *In the 2016 film '' The Accountant'', Christian Wolff is a high-functioning autistic man who tracks insider financial deceptions for numerous criminal organizations. *In the 2017 film '' Gifted'', an intellectually gifted seven-year-old, Mary Adler, becomes the subject of a custody battle between her uncle and grandmother.


Bio

*In 2020, an eponymous film ''Shakuntala Devi'' on the life of Indian mathematician, writer, astrologer and mental calculator Shakuntala Devi.


Television

*In the
USA Network USA Network (or simply USA) is an American basic cable television channel owned by the NBCUniversal Media Group division of Comcast's NBCUniversal. It was launched in 1977 as Madison Square Garden Sports Network, one of the first national sports ...
legal drama '' Suits'', the main character, Mike Ross, is asked to multiply considerably large numbers in his head to impress two girls, and subsequently does so. *In the Fox television show ''
Malcolm in the Middle ''Malcolm in the Middle'' is an American television sitcom created by Linwood Boomer for the Fox Broadcasting Company. The series premiered on January 9, 2000, and ended on May 14, 2006, after seven seasons consisting of 151 episodes. The ...
'', Malcolm Wilkerson displays astounding feats of automatic mental calculation, which causes him to fear his family will see him as a "freak", and causes his brother to ask, "Is Malcolm a robot?". *In the 1990s NBC TV sitcom ''
NewsRadio ''NewsRadio'' is an American television sitcom that aired on NBC from March 21, 1995, to May 4, 1999, focusing on the work lives of the staff of a New York City AM news radio station. It had an ensemble cast featuring Dave Foley, Stephen R ...
'', reporter/producer Lisa Miller can mentally calculate products, quotients, and square roots effortlessly and almost instantly, on demand. *In the 2007 sitcom ''
The Big Bang Theory ''The Big Bang Theory'' is an American television sitcom created by Chuck Lorre and Bill Prady for CBS. It aired from September 24, 2007, to May 16, 2019, running for 12 seasons and 279 episodes. The show originally centered on five charact ...
'', the main character,
Sheldon Cooper Sheldon Lee Cooper, B.S., M.S., M.A., Ph.D., Sc.D., is a fictional character and one of the protagonists in the 2007–2019 CBS television series ''The Big Bang Theory'' and its 2017–2024 spinoff series ''Young Sheldon'', portrayed by act ...
, calculates numbers and solutions in his head for his theoretical physics research. *In the 2008 show ''
Breaking Bad ''Breaking Bad'' is an American crime drama television series created and produced by Vince Gilligan for AMC (TV channel), AMC. Set and filmed in Albuquerque, New Mexico, the series follows Walter White (Breaking Bad), Walter White (Bryan Cran ...
'', the main character, Walter White, is shown to calculate most of the numbers to his deals, such as profit and production costs, purely within his head. *In another Fox television show, ''
Fringe Fringe may refer to: Arts and music * "The Fringe", or Edinburgh Festival Fringe, the world's largest arts festival * Adelaide Fringe, the world's second-largest annual arts festival * Fringe theatre, a name for alternative theatre * Purple fri ...
'', in the third episode of the third season, Olivia and her fellow Fringe Division members encounter an individual with severe cognitive impairment who has been given experimental nootropics and as a result has become a mathematical genius. The individual is able to calculate hundreds of equations simultaneously, which he leverages to avoid being returned to his original state of cognitive impairment. *In the 2014 TV series ''
Scorpion Scorpions are predatory arachnids of the Order (biology), order Scorpiones. They have eight legs and are easily recognized by a pair of Chela (organ), grasping pincers and a narrow, segmented tail, often carried in a characteristic forward cur ...
'', Sylvester Dodd, a gifted mathematician and statistician with an IQ of 175; he is described as a "human calculator".


Animation

In the 2009 Japanese animated film '' Summer Wars'', the main character, mathematical genius Kenji Koiso, is able to mentally break purely mathematical encryption codes generated by the OZ virtual world's security system. He can also mentally calculate the day of the week a person was born, based on their birthday.


See also

*
Child prodigy A child prodigy is, technically, a child under the age of 10 who produces meaningful work in some domain at the level of an adult expert. The term is also applied more broadly to describe young people who are extraordinarily talented in some f ...
* Doomsday rule for calculating the day of the week *
Hypercalculia Hypercalculia is "a specific Developmental psychology, developmental condition in which the ability to perform mathematics, mathematical calculations is significantly superior to general learning ability and to school attainment in maths." A 20 ...
* Mental abacus * Mnemonist *
Soroban The is an abacus developed in Japan. It is derived from the History of Science and Technology in China, ancient Chinese suanpan, imported to Japan in the 14th century. Like the suanpan, the soroban is still used today, despite the proliferation ...
* Subitizing


Notes


References


Further reading

*Frank D. Mitchell, "Mathematical Prodigies", The American Journal of Psychology, Vol. 18, No. 1 (Jan., 1907), pp. 61–143 (free access)


External links

* *
Mental Calculation World Cup siteMemoriad siteMethods and Relevance to Brain efficiency of Neelakantha BhanuMSO ResultsLightning Calculators
is a three-part essay that discusses these individuals, their methods, and the media coverage of them. {{Authority control Games of mental skill