Gabriel Kron (1901 – 1968) was a
Hungarian American
Hungarian Americans ( Hungarian: ''amerikai magyarok'') are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people wit ...
electrical engineer who promoted the use of methods of
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrices ...
,
multilinear algebra
Multilinear algebra is a subfield of mathematics that extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of ''p' ...
, and
differential geometry in the field. His method of system decomposition and solution called
Diakoptics is still influential today. Though he published widely, his methods were slow to be assimilated. At
Union College
Union College is a private liberal arts college in Schenectady, New York. Founded in 1795, it was the first institution of higher learning chartered by the New York State Board of Regents, and second in the state of New York, after Columbia Co ...
a symposium was organized by Schaffer Library on "Gabriel Kron, the Man and His Work", held October 14, 1969. H.H. Happ edited the contributed papers, which were published by Union College Press as ''Gabriel Kron and Systems Theory''.
Early life
Gabriel Kron was born in 1901 in Baia Mare in Transylvania, Hungary.
[Alger, P. L. (1969) ''The Life and Times of Gabriel Kron'', Mohawk Publishing] In 1919 he graduated from the
gymnasium. By that time Transylvania had been ceded to
Romania
Romania ( ; ro, România ) is a country located at the crossroads of Central, Eastern, and Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, Serbia to the southwest, Moldova to the east, and ...
. Kron's older brother Joseph returned home, which he had left when he was ten years old. Joseph wished for a professional degree, but had no schooling after grade five. Gabriel
tutor
TUTOR, also known as PLATO Author Language, is a programming language developed for use on the PLATO system at the University of Illinois at Urbana-Champaign beginning in roughly 1965. TUTOR was initially designed by Paul Tenczar for use in ...
ed Joseph, who passed various exams, culminating in the high-school exam in 1920. In December of that year the two left home for the United States. The brothers earned their living in
New York City
New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...
with odd jobs such as dish washer, bus boy, or working machines in garment factories.
In the fall of 1922 the brothers had saved enough money to enter engineering school at
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
. They continued supporting themselves with casual employment. Gabriel found digging ditches more congenial than dishwashing. He coined the motto: "There are only two occupations compatible with human dignity. One is the study of atomic structure. The other is digging ditches."
In 1925 Gabriel graduated and started on a trip around the world. He planned to walk and hitch hike as much as possible. He ran out of money when he reached Los Angeles, where he worked for the United States Electrical Manufacturing Company. He then transferred to the Robbins and Myers Company in Springfield, Ohio. In 1926 he set out again. From
California
California is a state in the Western United States, located along the Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the most populous U.S. state and the 3rd largest by area. It is also the m ...
he took passage on an oil tanker bound for
Tahiti
Tahiti (; Tahitian ; ; previously also known as Otaheite) is the largest island of the Windward group of the Society Islands in French Polynesia. It is located in the central part of the Pacific Ocean and the nearest major landmass is Austra ...
. In
Sydney, Australia he ran out of money.
After saving 35 pounds from work at the Electricity Metering Manufacturing Company he set out for
Northern Australia
The unofficial geographic term Northern Australia includes those parts of Queensland and Western Australia north of latitude 26° and all of the Northern Territory. Those local government areas of Western Australia and Queensland that lie p ...
.
In
Fiji he had finished, and buried, ''Treatise on Differential Equations'' by
Forsyth. In Sydney he searched for a worthy successor, settling on ''Advanced Vector Analysis with Application to Mathematical Physics'' by the Australian
C.E. Weatherburn. During long hikes in Queensland, Kron saw that vector analysis would be a powerful tool in engineering.
Sea voyages took him to Saigon via Borneo, Manila, and Hong Kong. Hence overland to Cairo and Alexandria by rail, supplemented by many hours of walking. In the spring of 1928 Kron arrived in Romania and stayed with his family till the fall.
After his return Kron was employed as electrical engineer for brief periods with several companies the last of which was
Warner Brothers
Warner Bros. Entertainment Inc. (commonly known as Warner Bros. or abbreviated as WB) is an American film and entertainment studio headquartered at the Warner Bros. Studios complex in Burbank, California, and a subsidiary of Warner Bros. D ...
in New York. They closed his department while he was on a continuing highly paid contract.
He economized by living with his family in Romania. There he studied the mathematical tools of the
general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
and conceived his method for applying
tensor analysis
In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis ...
to electrical power engineering. This was described in a paper entitled "Non-Riemannian Dynamics of Rotating Electrical Machinery" printed in Romania and distributed to friends. In 1933 Kron returned to the US where his paper had been well received. He worked at
General Electric
General Electric Company (GE) is an American multinational conglomerate founded in 1892, and incorporated in New York state and headquartered in Boston. The company operated in sectors including healthcare, aviation, power, renewable en ...
from 1934 until he retired in 1966.
Kron was awarded the Montefiore Prize of the
University of Liège
The University of Liège (french: Université de Liège), or ULiège, is a major public university of the French Community of Belgium based in Liège, Wallonia, Belgium. Its official language is French. As of 2020, ULiège is ranked in the 301 ...
, Belgium, for the paper written in Romania.
["Gabriel Kron, IEEE Transactions on Circuit Theory 15(3):174, September 1968, see IEEE Xplore external link]
Career
Kron's career developed within the
General Electric
General Electric Company (GE) is an American multinational conglomerate founded in 1892, and incorporated in New York state and headquartered in Boston. The company operated in sectors including healthcare, aviation, power, renewable en ...
corporation and has been described by P.L. Alger Alger explains that Kron made a positive impression at an
AIEE
The American Institute of Electrical Engineers (AIEE) was a United States-based organization of electrical engineers that existed from 1884 through 1962. On January 1, 1963, it merged with the Institute of Radio Engineers (IRE) to form the Institu ...
conference held in New York in January 1934. The behavior of an electrical network was described as a
dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...
confined to a
Non-Riemannian space. General Electric vice president Roy C. Muir "invited Gabe to join the staff of the Advanced Engineering Program under A.R. Stevenson." Furthermore,
Philip Franklin of
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
approved Kron's paper for publication in
MIT Journal of Mathematics and Physics
The journal ''Studies in Applied Mathematics'' is published by Wiley–Blackwell on behalf of the Massachusetts Institute of Technology.
It features scholarly articles on mathematical applications in allied fields, notably computer science, ...
, May 1934. "The paper instantly provoked widespread discussion and controversy. Many mathematicians derided his work: it was just for show, it was needlessly complex, or it was of no practical use."
According to Alger, Kron "worked with fifteen different managers while with General Electric." Alger explained, "Kron’s value was largely in the inspiration he gave to others and in distant objectives that seemed to business managers to be merely dreams." From 1936 to 1942 Kron published primarily in the ''General Electric Review''. In 1942
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, ...
published his ''A Short Course in Tensor Analysis for Electrical Engineers''. As recalled by Keith Bowden, "In the fifties, when Kron’s ideas were first introduced, controversy raged over their validity."
Banesh Hoffmann
Banesh Hoffmann (6 September 1906 – 5 August 1986) was a British mathematician and physicist known for his association with Albert Einstein.
Life
Banesh Hoffmann was born in Richmond, Surrey, on 6 September 1906. He studied mathematics and ...
was one academic that supported Kron's initiative. Hoffman wrote the Introduction to the second edition of Kron's book, now titled ''Tensors for Circuits'' (1959), distributed by
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, book ...
.
In 1945 Kron suggested an approach to
Schrödinger's equation with networks. The same year he used
equivalent circuit In electrical engineering and science, an equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly ...
s to solve
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s.
Kron proved to be a versatile employee: He worked in the Large Steam Turbine Engineering Department (1942), contributed to the control of atomic reactor piles (1945), and collaborated with
Simon Ramo
Simon "Si" Ramo (May 7, 1913 – June 27, 2016) was an American engineer, businessman, and author. He led development of microwave and missile technology and is sometimes known as the father of the intercontinental ballistic missile (ICBM). He ...
, Selden Crary, and Leon K. Kirchmayer on
power systems. Alger notes that Kron "was a pioneer, not an educator. He used to imply that hard work is necessary for the mastery of any subject, and it does no good to make the way to understanding too easy." In 1951 Kron published ''Equivalent Circuits of Electrical Machinery''. While continuing with laboratory and turbine assignments on weekdays, Kron began to prepare
Diakoptics on his own. His vision realized with publication, in 1963 Kron was assigned to Analytical Engineering Division with H.H. Happ. Together they reviewed Kron's theory, and after Kron's death Happ published ''Diakoptics and Networks'' (1971).
A
bibliography of Kron's writings is given as an appendix to ''Gabriel Kron and Systems Theory'', pages 165 to 172. An earlier bibliography was compiled in 1959 and appeared in pages xiii to xviii of his book ''Tensors for Circuits''.
Awards and honors
Kron received the following awards and honors:
[
*Doctor of Science ''honoris causa'', University of Nottingham, 1961
*Montefiore Prize, University of the Liège, Belgium, 1935
*Coffin Award, General Electric Company, 1942
*Master of Science in Electrical Engineering, Honorary, University of Michigan, 1936
*Patron and Honorary Member of the Tensor Club of Great Britain
*Honorary Member, Research Association of Applied Geometry, Tokyo
]
Books by Kron
*
* 2nd edn. 1965.
*
*
* Dover reprint 1967.
* (Dover 2nd edition of the book formerly entitled ''A short course in tensor analysis for electrical engineers'')
*
Notes
Further reading
* Alger, P., (ed), 1969, ''The Life and Times of Gabriel Kron''. Mohawk Development Publ., Schenectady, NY. LCCN 70-99590.
* Bowden, K., 1998, ''Huygens Principle, Physics and Computers''. Int. J. General Systems, Vol 27(1-3), pp 9–32.
* Duffy, M.C., 1994, §9.12 "Electrical machines: Tensors and topology", pp 1228 to 1234 in ''Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences'', volume 2, edited by Ivor Grattan-Guinness, Routledge
Routledge () is a British multinational publisher. It was founded in 1836 by George Routledge, and specialises in providing academic books, journals and online resources in the fields of the humanities, behavioural science, education, law ...
.
* Happ, H.H. editor, 1973, ''Gabriel Kron and Systems Theory'', Union College Press .
External links
Early Ideas in the History of Quantum Chemistry - Gabriel Kron 1901-1968
contains excerpts from Alger, P., (ed), 1969, ''The Life and Times of Gabriel Kron''. Mohawk Development Publ., Schenectady, NY. LCCN 70-99590, and other sources.
from Quantum-chemistry-history.com by Udo Anders.
Gabriel Kron 1901 — 1968
from IEEE Xplore
IEEE Xplore digital library is a research database for discovery and access to journal articles, conference proceedings, technical standards, and related materials on computer science, electrical engineering and electronics, and allied fields. It ...
.
{{DEFAULTSORT:Kron, Gabriel
1901 births
1968 deaths
Baia Mare
Romanian emigrants to the United States
American electrical engineers
American systems scientists
University of Michigan College of Engineering alumni
General Electric people
University of Michigan alumni
20th-century American engineers