John Edmund Kerrich (1903–1985) was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

noted for a series of experiments in

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

which he conducted while interned in

Nazi Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in ...

-occupied Denmark in the 1940s.

Biography

John Kerrich was born in

Norfolk Norfolk () is a ceremonial and non-metropolitan county in East Anglia in England. It borders Lincolnshire to the north-west, Cambridgeshire to the west and south-west, and Suffolk to the south. Its northern and eastern boundaries are the No ...

, England and grew up in

South Africa South Africa, officially the Republic of South Africa (RSA), is the southernmost country in Africa. It is bounded to the south by of coastline that stretch along the South Atlantic and Indian Oceans; to the north by the neighbouring countri ...

. He was educated there and in the UK (First class Honours in Mathematics & MSc Astronomy,

University of the Witwatersrand The University of the Witwatersrand, Johannesburg (), is a multi-campus South African Public university, public research university situated in the northern areas of central Johannesburg. It is more commonly known as Wits University or Wits ( o ...

; Diploma in Actuarial Mathematics,

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

). He was appointed lecturer in mathematics in 1929, and senior lecturer six years later. In April 1940, while visiting in-laws in Copenhagen, Kerrich was caught up in the Nazi invasion and interned in Hald Ege, Viborg,

Midtjylland The Central Denmark Region ( da, Region Midtjylland), or more directly translated as the Central Jutland Region and sometimes simply Mid Jutland, is an administrative region of Denmark established on 1 January 2007 as part of the 2007 Danish muni ...

. While there he conducted simple experiments using coins and

ping-pong Table tennis, also known as ping-pong and whiff-whaff, is a sport in which two or four players hit a lightweight ball, also known as the ping-pong ball, back and forth across a table using small solid rackets. It takes place on a hard table div ...

balls to demonstrate the empirical validity of a number of fundamental laws of probability. On his release after the end of the

Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

, Kerrich published an account of his experiments in a short book entitled ''An Experimental Introduction to the Theory of Probability''.A Brief History
, The Department of Statistics at the University of the Witwatersrand, Johannesburg. Originally published in Denmark, the book was later reprinted by the

University of Witwatersrand The University of the Witwatersrand, Johannesburg (), is a multi-campus South African public research university situated in the northern areas of central Johannesburg. It is more commonly known as Wits University or Wits ( or ). The university ...

Press. In 1957, Kerrich was appointed Foundation Professor of Statistics at the University of Witwatersrand and retired in 1971. He was married with two sons.

Experiments in empirical probability

During his

internment Internment is the imprisonment of people, commonly in large groups, without charges or intent to file charges. The term is especially used for the confinement "of enemy citizens in wartime or of terrorism suspects". Thus, while it can simpl ...

, Kerrich worked with fellow internee Eric Christensen. The most famous was a demonstration of

Jacob Bernoulli Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Le ...

's famous

Law of Large Numbers In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials shou ...

using a coin which they tossed 10,000 times. By recording the number of heads obtained as the trials continued, Kerrich was able to demonstrate that the proportion of heads obtained asymptotically approached the theoretical value of 50 percent (the precise number obtained was 5,067, which is 1.34

standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...

s above the mean for a "fair" coin thrown that many times). Kerrich and Christensen also performed experiments using a "biased coin", made from a wooden disk partly coated in lead, to show that it too tended towards a stable asymptotic state with probability of approximately 70 percent. In addition, the pair used ping-pong balls to demonstrate

Bayes's theorem In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For exampl ...

. Until the advent of computer simulations, Kerrich's study, published in 1946, was widely cited as evidence of the asymptotic nature of probability. It is still regarded as a classic study in empirical mathematics. 2,000 of their fair coin flip results are given by the following table, with 1 representing heads and 0 representing tails.

References

External links

Newsletter
of the South African Statistical Association that describes Kerrich biography, as the second president of the association.

of The Department of Statistics at the University of the Witwatersrand, that was founded with Kerrich as its head
Stack Exchange Thread
about Kerrich's coin flip data, 2015. {{DEFAULTSORT:Kerrich, John Edmund 1903 births 1985 deaths 20th-century British mathematicians Alumni of St John's College (Johannesburg) University of the Witwatersrand academics University of the Witwatersrand alumni English statisticians