Mental calculation

Mental calculation (also known as mental computation ^[1]) consists of arithmetical calculations made by the mind, within the brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator. 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 numeral system.

Capacity of short-term memory is a necessary factor for the successful acquisition of a calculation, ^[2] specifically perhaps, the phonological loop, in the context of addition calculations (only). ^[3] 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 patterns, combined with algorithms process. ^[4]

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. ^[5] People with an unusual fastness with reliably correct performance of mental calculations of sufficient relevant complexity are prodigies or savants. ^[6] By the same token, in some contexts and at some time, such an exceptional individual would be known as a: lightening calculator, or a genius. ^[7]

In a survey of children in England it was found that mental imagery was used for mental calculation. ^[8] By neuro-imaging, brain activity in the parietal lobes of the right hemisphere was found to be associated with mental imaging. ^[9]

The teaching of mental calculation as an element of schooling, with a focus in some teaching contexts on mental strategies ^[10]

Exceptional calculational ability

An exceptional ability is mental calculation such as adding, subtracting, multiplying or dividing large numbers.

Skilled calculators were necessary in research centers such as CERN 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^[11] 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 ^[12] 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.^[12] 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 has staged annual world championships since 1998.

Memoriad – World Memory

The first international Memoriad ^[13] was held in Istanbul, Turkey, in 2008. The second Memoriad took place in Antalya, 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 has been often mentioned on the Guinness World Records. Neelakantha Bhanu Prakash from India has been often mentioned on the Limca Book of Records for racing past the speed of a calculator in addition.^[14] Sri Lankan-Malaysian performer Yaashwin Sarawanan was the runner-up in 2019 Asia's Got Talent.

Media

Literary

Frank Herbert's novel Dune, specially trained mental calculators known as Mentats have replaced mechanical computers completely. Several important supporting characters in the novel, namely Piter De Vries and Thufir Hawat, are Mentats. Paul Atreides 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'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 story Methuselah's Children.
Haruki Murakami's novel Hard-Boiled Wonderland and the End of the World, a class of mental calculators known as Calcutecs perform 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, 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, 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'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 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 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 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, 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 main character, Sheldon Cooper, calculates numbers and solutions in his head for his theoretical physics research.
In the 2008 show Breaking Bad, 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, 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, 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.

Notes

References

^ Alistair McIntosh (2004). "Mental Computation: A strategies approach" (PDF). amsi.org.au. University of Tasmania: Department of Education. ISBN 1920865209.
^ Hope, John Alfred (1984). Characteristics of unskilled, skilled and highly skilled mental calculators (Thesis). University of British Columbia. doi:10.14288/1.0096641.
^ Noël, Marie-Pascale; Désert, Michel; Aubrun, Anne; Seron, Xavier (January 2001). "Involvement of short-term memory in complex mental calculation". Memory & Cognition. 29 (1): 34–42. doi:10.3758/BF03195738. PMID 11277462.
^ Timo Flückiger; Elisabeth Rathgeb-Schnierer (February 2022). "Capturing flexibility in mental calculation". hal.science. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12): HAL – via John Threlfall Flexible Mental Calculation doi:10.1023/A:1020572803437.
^ Clawson, C.C. (1994). "The Genius Calculators". The Mathematical Traveler. Springer. doi:10.1007/978-1-4899-6014-6_14. ISBN 978-0-306-44645-0.
^ Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred (April 2010). "Neural correlates in exceptional mental arithmetic—About the neural architecture of prodigious skills". Neuropsychologia. 48 (5): Abstract. doi:10.1016/j.neuropsychologia.2010.01.007.
^ Bousfield, W. A.; Barry, Jr., H. (April 1933). "The Visual Imagery of a Lightning Calculator". The American Journal of Psychology. 45 (2). University of Illinois Press: JSTOR: 233. doi:10.2307/1414296.
^ Chris Bills; Eddie Gray. "THE USE OF MENTAL IMAGERY IN MENTAL CALCULATION" (PDF). Education Resources Information Center. University of Warwick: Institute of Education Sciences. p. 97. What is apparent is that these children have shown a preference for concrete or abstract visual images in both calculation and non calculation contexts.
^ O'Boyle, Michael W.; et al. (October 2005). "Mathematically gifted male adolescents activate a unique brain network during mental rotation". Cognitive Brain Research. 25 (2): 583–587. doi:10.1016/j.cogbrainres.2005.08.004. PMID 16150579.
^ Thompson, Ian (November 1999). "Mental Calculation Strategies for Addition and Subtraction. Part 1". Mathematics in School. 28 (5): 2–4. JSTOR 30215422.
^ Shetterly, Margot Lee (2016). Hidden Figures: The American Dream and the Untold Story of the Black Women Who Helped Win the Space Race. William Morrow and Company. pp. 115. ISBN 978-0062363596. Some of the women were capable of lightning-fast mental math, rivaling their mechanical calculating machines for speed and accuracy. Others, like Dorothy Hoover and Doris Cohen, had highly refined understandings of theoretical math, differentiating their way through nested equations ten pages deep with nary an error in sign. The best of the women made names for themselves for accuracy, speed, and insight.
^ ^a ^b "Mental Calculation World Cup - the World Championship for Mental Calculators". www.recordholders.org.
^ Memoriad - World Mental Olympics
^ Adke, Arti (6 May 2019). "I love to be quicker than anyone else, Hans India, May 2019". Archived from the original on 2020-12-09. Retrieved 2020-08-17.

External links

Tzourio-Mazoyer, Nathalie; Pesenti, Mauro; Zago, Laure; Crivello, Fabrice; Mellet, Emmanuel; Samson, Dana; Duroux, Bruno; Seron, Xavier; Mazoyer, Bernard (2001). "Mental calculation in a prodigy is sustained by right prefrontal and medial temporal areas". Nature Neuroscience. 4 (1): 103–7. doi:10.1038/82831. PMID 11135652. S2CID 23829063.
Rivera, S.M.; Reiss, AL; Eckert, MA; Menon, V (2005). "Developmental Changes in Mental Arithmetic: Evidence for Increased Functional Specialization in the Left Inferior Parietal Cortex". Cerebral Cortex. 15 (11): 1779–90. doi:10.1093/cercor/bhi055. PMID 15716474.
Mental Calculation World Cup site
Memoriad site
Prodigy Calculators by Viktor Pekelis
Willem Klein
Thought and machine processes
Methods and Relevance to Brain efficiency of Neelakantha Bhanu
Tricks and techniques
MSO Results
Lightning Calculators is a three-part essay that discusses these individuals, their methods, and the media coverage of them.

[1] Alistair McIntosh (2004). "Mental Computation: A strategies approach" (PDF). amsi.org.au. University of Tasmania: Department of Education. ISBN 1920865209.

[2] Hope, John Alfred (1984). Characteristics of unskilled, skilled and highly skilled mental calculators (Thesis). University of British Columbia. doi:10.14288/1.0096641.

[3] Noël, Marie-Pascale; Désert, Michel; Aubrun, Anne; Seron, Xavier (January 2001). "Involvement of short-term memory in complex mental calculation". Memory & Cognition. 29 (1): 34–42. doi:10.3758/BF03195738. PMID 11277462.

[4] Timo Flückiger; Elisabeth Rathgeb-Schnierer (February 2022). "Capturing flexibility in mental calculation". hal.science. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12): HAL – via John Threlfall Flexible Mental Calculation doi:10.1023/A:1020572803437.

[5] Clawson, C.C. (1994). "The Genius Calculators". The Mathematical Traveler. Springer. doi:10.1007/978-1-4899-6014-6_14. ISBN 978-0-306-44645-0.

[6] Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred (April 2010). "Neural correlates in exceptional mental arithmetic—About the neural architecture of prodigious skills". Neuropsychologia. 48 (5): Abstract. doi:10.1016/j.neuropsychologia.2010.01.007.

[7] Bousfield, W. A.; Barry, Jr., H. (April 1933). "The Visual Imagery of a Lightning Calculator". The American Journal of Psychology. 45 (2). University of Illinois Press: JSTOR: 233. doi:10.2307/1414296.

[8] Chris Bills; Eddie Gray. "THE USE OF MENTAL IMAGERY IN MENTAL CALCULATION" (PDF). Education Resources Information Center. University of Warwick: Institute of Education Sciences. p. 97. What is apparent is that these children have shown a preference for concrete or abstract visual images in both calculation and non calculation contexts.

[9] O'Boyle, Michael W.; et al. (October 2005). "Mathematically gifted male adolescents activate a unique brain network during mental rotation". Cognitive Brain Research. 25 (2): 583–587. doi:10.1016/j.cogbrainres.2005.08.004. PMID 16150579.

[10] Thompson, Ian (November 1999). "Mental Calculation Strategies for Addition and Subtraction. Part 1". Mathematics in School. 28 (5): 2–4. JSTOR 30215422.

[11] Shetterly, Margot Lee (2016). Hidden Figures: The American Dream and the Untold Story of the Black Women Who Helped Win the Space Race. William Morrow and Company. pp. 115. ISBN 978-0062363596. Some of the women were capable of lightning-fast mental math, rivaling their mechanical calculating machines for speed and accuracy. Others, like Dorothy Hoover and Doris Cohen, had highly refined understandings of theoretical math, differentiating their way through nested equations ten pages deep with nary an error in sign. The best of the women made names for themselves for accuracy, speed, and insight.

[MCWC-12] "Mental Calculation World Cup - the World Championship for Mental Calculators". www.recordholders.org.

[13] Memoriad - World Mental Olympics

[14] Adke, Arti (6 May 2019). "I love to be quicker than anyone else, Hans India, May 2019". Archived from the original on 2020-12-09. Retrieved 2020-08-17.

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