W. T. Williams
Encyclopedia
William Thomas Williams FAA
OBE
(18 April 1913 – 15 October 1995) was an English and Australian botanist and plant taxonomist
, known for his work on algorithm
s for numerical taxonomy
.
, London, England, the only child of a Welsh coal miner.
He went to the Stationers' Company's School in London and then to the Imperial College of Science and Technology, also in London, from which he earned a
Bachelor's degree 1933, a Ph.D. and diploma in 1940, and a D.Sc. in 1956. While studying for his Ph.D.,
Williams taught at Imperial College from 1933 to 1936, and at Sir John Cass Technical College
from 1936 to 1940.
During World War II
, he served in the Royal Artillery
, Royal Army Ordnance Corps
, and Royal Electrical and Mechanical Engineers
. He enlisted as a private (neglecting to inform the military about his degrees) but eventually reached the rank of major.
After the war, he became
a lecturer at Bedford College for Women, where he stayed from 1946 to 1951. He then moved to the University of Southampton
, where he was professor of botany and head of the department of botany from 1951 to 1965.
In 1965, Williams' former Southampton colleague Godfrey Lance invited him to visit the Commonwealth Scientific and Industrial Research Organisation
(CSIRO) in Canberra, Australia. A year later, Williams moved to CSIRO himself, at the same time becoming an Australian citizen. He worked in CSIRO's Division of Computing Research in Canberra from 1966 to 1968, and then transferred to the Division of Tropical Pastures in Brisbane
, where he worked from 1968 to 1973.
Williams retired from CSIRO in 1973, at which point he moved from Brisbane to Townsville. During his retirement he continued to work as a consultant for several institutions.
, and more specifically on leaf expansion and the function of the stomata
. However, while at Southampton he became interested in more mathematical and statistical research topics such as the spatial distribution of plants. At the same time, he began writing software for his statistical analysis, using the Ferranti Pegasus computer then available at Southampton's computer centre. The centre's director, Godfrey Lance, was later to become a regular research collaborator of Williams.
Williams' most heavily cited research work, with Lance, makes the observation that five different hierarchical clustering
strategies then in use could all be related to each other: all five use formulas for the distance between clusters that vary only in the weights of certain numerical coefficients. This unification allowed the coefficients to be chosen based on their effect on the overall clustering rather than, as had been done before, selecting the clustering strategy on an ad hoc basis.
Williams and Lance also introduced the Canberra distance
, a form of Manhattan distance between pairs of points normalized by dividing by the total Manhattan distance of the points from the origin. The normalization makes this distance measure particularly suited for data sets in which some data values may significantly differ from the rest.
Recognizing the general applicability of these methods, Williams went on at CSIRO to apply them to problems other than plant taxonomy, as well as to the classification of angiosperms and grass
es. In this work, he viewed numerical taxonomy as a form of exploratory data analysis
, intended more to generate new hypotheses than to confirm them.
puzzle "The Little Pigley Farm" (also known as Dog’s Mead, Little Pigley, Little Piggly Farm, Little Pigsby, Pilgrims’ Plot, or Dog Days) which he first published in 1935 in The Strand Magazine.
Long a self-taught piano
player, Williams took lessons after moving to Australia, earned a credential, and taught piano himself. He also organized the first North Queensland Piano Competition.
awarded Williams an honorary doctorate. He was elected as a fellow
of the Australian Academy of Science
in 1978, and in 1980 he became an officer of the Order of the British Empire
.
Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The Academy is modelled after the Royal Society and operates under a Royal Charter; as such it is...
OBE
Order of the British Empire
The Most Excellent Order of the British Empire is an order of chivalry established on 4 June 1917 by George V of the United Kingdom. The Order comprises five classes in civil and military divisions...
(18 April 1913 – 15 October 1995) was an English and Australian botanist and plant taxonomist
Plant taxonomy
Plant taxonomy is the science that finds, describes, classifies, identifies, and names plants. It thus is one of the main branches of taxonomy.Plant taxonomy is closely allied to plant systematics, and there is no sharp boundary between the two...
, known for his work on algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s for numerical taxonomy
Numerical taxonomy
Numerical taxonomy is a classification system in biological systematics which deals with the grouping by numerical methods of taxonomic units based on their character states.. It aims to create a taxonomy using numeric algorithms like cluster analysis rather than using subjective evaluation of...
.
Biography
Williams was 18 April 1913 in FulhamFulham
Fulham is an area of southwest London in the London Borough of Hammersmith and Fulham, SW6 located south west of Charing Cross. It lies on the left bank of the Thames, between Putney and Chelsea. The area is identified in the London Plan as one of 35 major centres in Greater London...
, London, England, the only child of a Welsh coal miner.
He went to the Stationers' Company's School in London and then to the Imperial College of Science and Technology, also in London, from which he earned a
Bachelor's degree 1933, a Ph.D. and diploma in 1940, and a D.Sc. in 1956. While studying for his Ph.D.,
Williams taught at Imperial College from 1933 to 1936, and at Sir John Cass Technical College
London Metropolitan University
London Metropolitan University , located in London, England, was formed on 1 August 2002 by the amalgamation of the University of North London and the London Guildhall University . The University has campuses in the City of London and in the London Borough of Islington.The University operates its...
from 1936 to 1940.
During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, he served in the Royal Artillery
Royal Artillery
The Royal Regiment of Artillery, commonly referred to as the Royal Artillery , is the artillery arm of the British Army. Despite its name, it comprises a number of regiments.-History:...
, Royal Army Ordnance Corps
Royal Army Ordnance Corps
The Royal Army Ordnance Corps was a corps of the British Army. It dealt only with the supply and maintenance of weaponry, munitions and other military equipment until 1965, when it took over most other supply functions, as well as the provision of staff clerks, from the Royal Army Service...
, and Royal Electrical and Mechanical Engineers
Royal Electrical and Mechanical Engineers
The Corps of Royal Electrical and Mechanical Engineers is a corps of the British Army that has responsibility for the maintenance, servicing and inspection of almost every electrical and mechanical piece of equipment within the British Army from Challenger II main battle tanks and WAH64 Apache...
. He enlisted as a private (neglecting to inform the military about his degrees) but eventually reached the rank of major.
After the war, he became
a lecturer at Bedford College for Women, where he stayed from 1946 to 1951. He then moved to the University of Southampton
University of Southampton
The University of Southampton is a British public university located in the city of Southampton, England, a member of the Russell Group. The origins of the university can be dated back to the founding of the Hartley Institution in 1862 by Henry Robertson Hartley. In 1902, the Institution developed...
, where he was professor of botany and head of the department of botany from 1951 to 1965.
In 1965, Williams' former Southampton colleague Godfrey Lance invited him to visit the Commonwealth Scientific and Industrial Research Organisation
Commonwealth Scientific and Industrial Research Organisation
The Commonwealth Scientific and Industrial Research Organisation is the national government body for scientific research in Australia...
(CSIRO) in Canberra, Australia. A year later, Williams moved to CSIRO himself, at the same time becoming an Australian citizen. He worked in CSIRO's Division of Computing Research in Canberra from 1966 to 1968, and then transferred to the Division of Tropical Pastures in Brisbane
Brisbane
Brisbane is the capital and most populous city in the Australian state of Queensland and the third most populous city in Australia. Brisbane's metropolitan area has a population of over 2 million, and the South East Queensland urban conurbation, centred around Brisbane, encompasses a population of...
, where he worked from 1968 to 1973.
Williams retired from CSIRO in 1973, at which point he moved from Brisbane to Townsville. During his retirement he continued to work as a consultant for several institutions.
Research
Williams' early work was on plant physiologyPlant physiology
Plant physiology is a subdiscipline of botany concerned with the functioning, or physiology, of plants. Closely related fields include plant morphology , plant ecology , phytochemistry , cell biology, and molecular biology.Fundamental processes such as photosynthesis, respiration, plant nutrition,...
, and more specifically on leaf expansion and the function of the stomata
Stoma
In botany, a stoma is a pore, found in the leaf and stem epidermis that is used forgas exchange. The pore is bordered by a pair of specialized parenchyma cells known as guard cells that are responsible for regulating the size of the opening...
. However, while at Southampton he became interested in more mathematical and statistical research topics such as the spatial distribution of plants. At the same time, he began writing software for his statistical analysis, using the Ferranti Pegasus computer then available at Southampton's computer centre. The centre's director, Godfrey Lance, was later to become a regular research collaborator of Williams.
Williams' most heavily cited research work, with Lance, makes the observation that five different hierarchical clustering
Hierarchical clustering
In statistics, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:...
strategies then in use could all be related to each other: all five use formulas for the distance between clusters that vary only in the weights of certain numerical coefficients. This unification allowed the coefficients to be chosen based on their effect on the overall clustering rather than, as had been done before, selecting the clustering strategy on an ad hoc basis.
Williams and Lance also introduced the Canberra distance
Canberra distance
The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966and refined in 1967 by G. N. Lance and W. T. Williams. It is similar to the Manhattan distance...
, a form of Manhattan distance between pairs of points normalized by dividing by the total Manhattan distance of the points from the origin. The normalization makes this distance measure particularly suited for data sets in which some data values may significantly differ from the rest.
Recognizing the general applicability of these methods, Williams went on at CSIRO to apply them to problems other than plant taxonomy, as well as to the classification of angiosperms and grass
Grass
Grasses, or more technically graminoids, are monocotyledonous, usually herbaceous plants with narrow leaves growing from the base. They include the "true grasses", of the Poaceae family, as well as the sedges and the rushes . The true grasses include cereals, bamboo and the grasses of lawns ...
es. In this work, he viewed numerical taxonomy as a form of exploratory data analysis
Exploratory data analysis
In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...
, intended more to generate new hypotheses than to confirm them.
Other activities
Williams was an avid composer of mathematical puzzles; for instance, he wrote the cross-figureCross-figure
A cross-figure is a puzzle similar to a crossword in structure, but with entries which consist of numbers rather than words, with individual digits being entered in the blank cells...
puzzle "The Little Pigley Farm" (also known as Dog’s Mead, Little Pigley, Little Piggly Farm, Little Pigsby, Pilgrims’ Plot, or Dog Days) which he first published in 1935 in The Strand Magazine.
Long a self-taught piano
Piano
The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...
player, Williams took lessons after moving to Australia, earned a credential, and taught piano himself. He also organized the first North Queensland Piano Competition.
Awards and honours
In 1973, the University of QueenslandUniversity of Queensland
The University of Queensland, also known as UQ, is a public university located in state of Queensland, Australia. Founded in 1909, it is the oldest and largest university in Queensland and the fifth oldest in the nation...
awarded Williams an honorary doctorate. He was elected as a fellow
Fellow
A fellow in the broadest sense is someone who is an equal or a comrade. The term fellow is also used to describe a person, particularly by those in the upper social classes. It is most often used in an academic context: a fellow is often part of an elite group of learned people who are awarded...
of the Australian Academy of Science
Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The Academy is modelled after the Royal Society and operates under a Royal Charter; as such it is...
in 1978, and in 1980 he became an officer of the Order of the British Empire
Order of the British Empire
The Most Excellent Order of the British Empire is an order of chivalry established on 4 June 1917 by George V of the United Kingdom. The Order comprises five classes in civil and military divisions...
.