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Murray Gell-Mann

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Murray Gell-Mann
Gell-Mann in 2007
Born(1929-09-15)September 15, 1929
Manhattan, New York City, U.S.
DiedMay 24, 2019(2019-05-24) (aged 89)
Santa Fe, New Mexico, U.S.
Alma mater
Known for
Spouses
J. Margaret Dow
​
​
(m. 1955; died 1981)​
Marcia Southwick
​
(m. 1992)​
Children2
Awards
Scientific career
FieldsPhysics
Institutions
ThesisCoupling strength and nuclear reactions (1951)
Doctoral advisorVictor Weisskopf[2]
Doctoral students
Websitesantafe.edu/~mgm

Murray Gell-Mann (/ˈmʌri ˈɡɛl ˈmæn/; September 15, 1929 – May 24, 2019)[4][5] was an American physicist who received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles. He was the Robert Andrews Millikan Professor of Theoretical Physics Emeritus at the California Institute of Technology, a distinguished fellow and one of the co-founders of the Santa Fe Institute, a professor of physics at the University of New Mexico, and the Presidential Professor of Physics and Medicine at the University of Southern California.[6]

Gell-Mann spent several periods at CERN, a nuclear research facility in Switzerland, among others as a John Simon Guggenheim Memorial Foundation fellow in 1972.[7][8]

Early life and education

Gell-Mann was born in lower Manhattan into a family of Jewish immigrants from the Austro-Hungarian Empire, specifically from Chernivtsi (historical name: Czernowitz) in present-day Ukraine.[9][10] His parents were Pauline (née Reichstein) and Arthur Isidore Gell-Mann, who taught English as a second language (ESL).[11]

Propelled by an intense boyhood curiosity and love for nature and mathematics, he graduated valedictorian from the Columbia Grammar & Preparatory School aged 14 and subsequently entered Yale College as a member of Jonathan Edwards College.[4][12] At Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University (along with Murray Gerstenhaber and Henry O. Pollak) that won the second prize in 1947.[13]

Gell-Mann graduated from Yale with a bachelor's degree in physics in 1948 and intended to pursue graduate studies in physics. He sought to remain in the Ivy League for his graduate education and applied to Princeton University as well as Harvard University. He was rejected by Princeton and accepted by Harvard, but the latter institution was unable to offer him any of the financial assistance that he needed. He was accepted by the Massachusetts Institute of Technology (MIT) and received a letter from Victor Weisskopf urging him to attend MIT and become Weisskopf's research assistant, which would provide Gell-Mann with the financial assistance he needed. Unaware of MIT's eminent status in physics research, Gell-Mann was "miserable" with the fact that he would not be able to attend Princeton or Harvard and considered suicide. He stated that he realized he could try to first enter MIT and commit suicide afterwards if he found it to be truly terrible. However, he couldn't first choose suicide and then attend MIT; the two were not "commutable", as Gell-Mann said.[14][15]

Gell-Mann received his Ph.D. in physics from MIT in 1951 after completing a doctoral dissertation, titled "Coupling strength and nuclear reactions", under the supervision of Victor Weisskopf.[16][17][2]

Career

Gell-Mann was a postdoctoral fellow at the Institute for Advanced Study in 1951,[4] and a visiting research professor at the University of Illinois at Urbana–Champaign from 1952 to 1953.[18] He was a visiting associate professor at Columbia University and an associate professor at the University of Chicago in 1954–1955 before moving to the California Institute of Technology, where he taught from 1955 until he retired in 1993.[19]

Nuclear physics

In 1958, Gell-Mann in collaboration with Richard Feynman, in parallel with the independent team of E. C. George Sudarshan and Robert Marshak, discovered the chiral structures of the weak interaction of physics and developed the V-A theory (vector minus axial vector theory).[20] This work followed the experimental discovery of the violation of parity by Chien-Shiung Wu, as suggested by Chen-Ning Yang and Tsung-Dao Lee, theoretically.[21]

Gell-Mann's work in the 1950s involved recently discovered cosmic ray particles that came to be called kaons and hyperons. Classifying these particles led him to propose that a quantum number called strangeness would be conserved by the strong and the electromagnetic interactions, but not by the weak interactions.[22] (Kazuhiko Nishijima arrived at this idea independently, calling the quantity -charge after the eta meson.[23][24]) Another of Gell-Mann's ideas is the Gell-Mann–Okubo formula, which was, initially, a formula based on empirical results, but was later explained by his quark model.[25] Gell-Mann and Abraham Pais were involved in explaining the puzzling aspect of the neutral kaon mixing.[26]

Murray Gell-Mann's fortunate encounter with mathematician Richard Earl Block at Caltech, in the fall of 1960, "enlightened" him to introduce a novel classification scheme, in 1961, for hadrons, elementary particles that participate in the strong interaction.[27][28] A similar scheme had been independently proposed by Yuval Ne'eman, and is now explained by the quark model.[29] Gell-Mann referred to the scheme as the eightfold way, because of the octets of particles in the classification (the term is a reference to the Eightfold Path of Buddhism).[4][17]

Gell-Mann, along with Maurice Lévy, developed the sigma model of pions, which describes low-energy pion interactions.[30]

In 1964, Gell-Mann and, independently, George Zweig went on to postulate the existence of quarks, particles of which the hadrons of this scheme are composed. The name was coined by Gell-Mann and is a reference to the novel Finnegans Wake, by James Joyce ("Three quarks for Muster Mark!" book 2, episode 4). Zweig had referred to the particles as "aces",[31] but Gell-Mann's name caught on. Quarks, antiquarks, and gluons were soon established as the underlying elementary objects in the study of the structure of hadrons. He was awarded a Nobel Prize in Physics in 1969 for his contributions and discoveries concerning the classification of elementary particles and their interactions.[32]

In the 1960s, he introduced current algebra as a method of systematically exploiting symmetries to extract predictions from quark models, in the absence of reliable dynamical theory. This method led to model-independent sum rules confirmed by experiment and provided starting points underpinning the development of the Standard Model (SM), the widely accepted theory of elementary particles.[33][34]

In 1972 he and Harald Fritzsch introduced the conserved quantum number "color charge", and later, together with Heinrich Leutwyler, they coined the term quantum chromodynamics (QCD) as the gauge theory of the strong interaction.[35] The quark model is a part of QCD, and it has been robust enough to accommodate in a natural fashion the discovery of new "flavors" of quarks, which superseded the eightfold way scheme.[36]

Gell-Mann was responsible, together with Pierre Ramond and Richard Slansky,[37] and independently of Peter Minkowski, Rabindra Mohapatra, Goran Senjanović, Sheldon Lee Glashow, and Tsutomu Yanagida, for the seesaw theory of neutrino masses, that produces masses at the large scale in any theory with a right-handed neutrino. He is also known to have played a role in keeping string theory alive through the 1970s and early 1980s, supporting that line of research at a time when it was a topic of niche interest.[38][39]

At the time of his death, Gell-Mann was the Robert Andrews Millikan Professor of Theoretical Physics Emeritus at California Institute of Technology as well as a University Professor in the Physics and Astronomy Department of the University of New Mexico in Albuquerque, New Mexico, and the Presidential Professor of Physics and Medicine at the University of Southern California.[40] He was a member of the editorial board of the Encyclopædia Britannica. In 1984 Gell-Mann was one of several co-founders of the Santa Fe Institute—a non-profit theoretical research institute in Santa Fe, New Mexico intended to study complex systems and disseminate the notion of a separate interdisciplinary study of complexity theory.[41][42]

Murray Gell-Mann in Nice, 2012

He wrote a popular science book about physics and complexity science, The Quark and the Jaguar: Adventures in the Simple and the Complex (1994).[43] The title of the book is taken from a line of a poem by Arthur Sze: "The world of the quark has everything to do with a jaguar circling in the night".[44][45]

The author George Johnson has written a biography of Gell-Mann, Strange Beauty: Murray Gell-Mann, and the Revolution in 20th-Century Physics (1999),[46] which was shortlisted for the Royal Society Book Prize.[47] Gell-Mann himself criticized Strange Beauty for some inaccuracies, with one interviewer reporting him wincing at the mention of it.[48] In a review in the Caltech magazine Engineering & Science, Gell-Mann's colleague, the physicist David Goodstein, wrote: "I don't envy Murray the weird experience of reading so penetrating and perceptive a biography of himself. . . . George Johnson has written a fine biography of this important and complex man."[49] Physicist and Nobel laureate Philip Anderson, called the book "a masterpiece of scientific explication for the layman" and a "must read" in a review for the Times Higher Education Supplement and in his chapter on Gell-Mann from a 2011 book.[50] Sheldon Lee Glashow, another Nobel laureate, gave Strange Beauty a generally positive review while noting some inaccuracies,[51] and physicist and science historian Silvan S. Schweber called the book "an elegant biography of one of the outstanding theorists of the twentieth century" though he noted that Johnson did not go into depth about Gell-Mann's work with military-industrial organizations like the Institute for Defense Analyses.[52] Johnson has written that Gell-Mann was a perfectionist and that The Quark and the Jaguar was consequently submitted late and incomplete.[50][53] In an item on Edge.org, Johnson described the back story of his relationship with Gell-Mann[54] and noted that an errata sheet appears on the biography's webpage.[55] Gell-Mann's one-time Caltech associate Stephen Wolfram called Johnson's book "a very good biography of Murray, which Murray hated".[56] Wolfram also wrote that Gell-Mann thought the writing of The Quark and the Jaguar to be responsible for a heart attack he (Gell-Mann) had had.

In 2012 Gell-Mann and his companion Mary McFadden published the book Mary McFadden: A Lifetime of Design, Collecting, and Adventure.[57]

Quantum foundations

Gell-Mann was a proponent of the consistent histories approach to understanding quantum mechanics, which he advocated in papers with James Hartle.[39][58]

Personal life

Gell-Mann married J. Margaret Dow (d. 1981) in 1955; they had a daughter and a son. Margaret died in 1981, and in 1992 he married Marcia Southwick, with whom he had a stepson.[4]

Gell-Mann's interests outside of physics included archaeology, birdwatching and linguistics.[59][60] Along with S. A. Starostin, he established the Evolution of Human Languages project[61] at the Santa Fe Institute. As a humanist and an agnostic, Gell-Mann was a Humanist Laureate in the International Academy of Humanism.[62][63]

Gell-Mann died on May 24, 2019, at his home in Santa Fe, New Mexico.[4][60][64] He was remembered by, among others, novelist Cormac McCarthy, who saw Murray as a polymath who "knew more things about more things than anyone I've ever met." "Losing Murray is like losing the Encyclopædia Britannica."[65]

Awards and honors

Gell-Mann won numerous awards and honours including the following:

Universities that gave Gell-Mann honorary doctorates include Cambridge, Columbia, the University of Chicago, Oxford and Yale.[59]

See also

References

  1. ^ a b "Professor Murray Gell-Mann ForMemRS". London: Royal Society. Archived from the original on November 17, 2015.
  2. ^ a b c d e f g Murray Gell-Mann at the Mathematics Genealogy Project
  3. ^ "Higgs Scalars and the Nonleptonic Weak Interactions" (1977)
  4. ^ a b c d e f Johnson, George (May 24, 2019). "Murray Gell-Mann, Who Peered at Particles and Saw the Universe, Dies at 89". Obituaries. The New York Times. ISSN 0362-4331. Retrieved May 24, 2019.
  5. ^ Carroll, Sean (May 28, 2019). "The Physicist Who Made Sense of the Universe - Murray Gell-Mann's discoveries illuminated the most puzzling aspects of nature, and changed science forever". The New York Times. Retrieved May 28, 2019.
  6. ^ "Nobel Prize Winner Appointed Presidential Professor at USC". Archived from the original on September 19, 2010.
  7. ^ Gell-Mann, M. (1972). "Quarks". CERN-affiliated article by Gell-Mann. Springer. pp. 733–761. doi:10.1007/978-3-7091-4034-5_20. ISBN 978-3-7091-4036-9.
  8. ^ Scientific publications of M. Gell-Mann on INSPIRE-HEP
  9. ^ M. Gell-Mann (October 1997). "My Father". Web of Stories. Retrieved October 1, 2010.
  10. ^ J. Brockman (2003). "The Making of a Physicist: A talk with Murray Gell-Mann". Edge Foundation, Inc. Retrieved October 1, 2010.
  11. ^ Profile, NNDB; accessed April 26, 2015.
  12. ^ "Notable Alumni". Jonathan Edwards College. Retrieved May 27, 2019.
  13. ^ G. W. Mackey (1947). "The William Lowell Putnam Mathematical Competition". The American Mathematical Monthly. 54 (7): 400–3. doi:10.1080/00029890.1947.11990193. JSTOR 2304390.
  14. ^ Murray Gell-Mann - MIT or suicide (17/200), retrieved June 6, 2020
  15. ^ Strogatz, Steven (2013). The Joy of x: A Guided Tour of Math, from One to Infinity. Mariner Books. p. 27. ISBN 978-0544105850.
  16. ^ Gell-Mann, Murray (1951). Coupling strength and nuclear reactions (Thesis thesis). Massachusetts Institute of Technology.
  17. ^ a b "Murray Gell-Mann, Nobel Prize-winning physicist who named quarks, dies at 89". The Guardian. May 26, 2019. Retrieved May 27, 2019.
  18. ^ in 1954, there, with Francis E. Low, he discovered the renormalization group equation of QED.
  19. ^ "Interview with Murray Gell-Mann [Oral History]". Caltech Institute Archives. Retrieved May 25, 2019.
  20. ^ Sudarshan, E. C. G.; Marshak, R. E. (June 1, 2016). "Origin of the Universal V‐A theory". AIP Conference Proceedings. 300 (1): 110–124. doi:10.1063/1.45454. hdl:2152/29431. ISSN 0094-243X.
  21. ^ Gleick, James (1992). Genius: The Life and Science of Richard Feynman. Pantheon Books. ISBN 0-679-40836-3. OCLC 243743850. {{cite book}}: Invalid |ref=harv (help)
  22. ^ Gell-Mann, M. (1956). "The Interpretation of the New Particles as Displaced Charge Multiplets". Il Nuovo Cimento. 4 (supplement 2): 848–866. Bibcode:1956NCim....4S.848G. doi:10.1007/BF02748000.
  23. ^ Nishijima, K (1955). "Charge Independence Theory of V Particles". Progress of Theoretical Physics. 13 (3): 285–304. Bibcode:1955PThPh..13..285N. doi:10.1143/PTP.13.285.
  24. ^ Nambu, Y. (2009). "Kazuhiko Nishijima". Physics Today. 62 (8): 58. Bibcode:2009PhT....62h..58N. doi:10.1063/1.3206100.
  25. ^ Georgi, Howard (1999). Lie Algebras in Particle Physics: from Isospin to Unified Theories (2nd ed.). Perseus Books. ISBN 9780738202334. OCLC 479362196.
  26. ^ Squires, Gordon Leslie (July 26, 1999). "Quantum mechanics – Applications of quantum mechanics – Decay of the Kaon". Encyclopedia Britannica. Retrieved May 27, 2019.
  27. ^ Gell-Mann, M. (March 15, 1961). "The Eightfold Way: A Theory of Strong Interaction Symmetry" (TID-12608). Pasadena, CA: California Inst. of Tech., Synchrotron Laboratory. doi:10.2172/4008239. {{cite journal}}: Cite journal requires |journal= (help)
  28. ^ Murray Gell-Mann - Sheldon Glashow. The SU(2) times U1 theory: Part 2 (91/200). Web of Stories. May 19, 2016. Retrieved June 3, 2019 – via YouTube.
  29. ^ Ne'eman, Y. (August 1961). "Derivation of Strong Interactions from a Gauge Invariance". Nuclear Physics. 26 (2). Amsterdam: North-Holland Publishing Co.: 222–229. Bibcode:1961NucPh..26..222N. doi:10.1016/0029-5582(61)90134-1.
  30. ^ Gell-Mann, M.; Lévy, M. (1960). "The axial vector current in beta decay". Il Nuovo Cimento. 16 (4): 705–726. Bibcode:1960NCim...16..705G. doi:10.1007/BF02859738.
  31. ^ G. Zweig (1980) [1964]. "An SU(3) model for strong interaction symmetry and its breaking II". In D. Lichtenberg; S. Rosen (eds.). Developments in the Quark Theory of Hadrons. Vol. 1. Hadronic Press. pp. 22–101.
  32. ^ Simple listing of Nobel Prize in Physics, 1969 Retrieved February 15, 2017
  33. ^ Ellis, John (2011). "Prospects for New Physics at the LHC". In Fritzsch, Harald; Phua, K. K.; Baaquie, B. E. (eds.). Proceedings of the Conference in Honour of Murray Gell-Mann's 80th Birthday: Quantum Mechanics, Elementary Particles, Quantum Cosmology and Complexity : Nanyang Technological University, Singapore, February 24–26, 2010. World Scientific. ISBN 9789814335607.
  34. ^ Cao, Tian Yu (2010). From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism. Cambridge University Press. ISBN 9781139491600.
  35. ^ Fritzsch, H.; Gell-Mann, M.; Leutwyler, H. (1973). "Advantages of the color octet gluon picture". Physics Letters. 47B (4): 365–368. Bibcode:1973PhLB...47..365F. CiteSeerX 10.1.1.453.4712. doi:10.1016/0370-2693(73)90625-4.
  36. ^ Baez, John C. (2003). "The Eightfold Way". Quantum Gravity Seminar — Spring 2003. University of California, Riverside. Retrieved May 28, 2019.
  37. ^ M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, ed. by D. Freedman and P. Van Nieuwenhuizen, North Holland, Amsterdam (1979), pp. 315–321. ISBN 044485438X
  38. ^ Rickles, Dean (2014). A Brief History of String Theory: From Dual Models to M-Theory. Springer Science & Business Media. ISBN 9783642451287. OCLC 968779591.
  39. ^ a b Siegfried, Tom (May 24, 2019). "Murray Gell-Mann gave structure to the subatomic world". Science News. Retrieved May 26, 2019.
  40. ^ "Caltech Mourns the Passing of Murray Gell-Mann (1929–2019)". California Institute of Technology. May 24, 2019. Retrieved May 25, 2019.
  41. ^ Mitchell M. Waldrop (1993). Complexity: The Emerging Science at the Edge of Order and Chaos. Simon & Schuster. ISBN 9780671872342.
  42. ^ George A. Cowan (2010). Manhattan Project to the Santa Fe Institute: The Memoirs of George A. Cowan. University of New Mexico Press.
  43. ^ Reviews of The Quark and the Jaguar:
  44. ^ "Murray Gell-Mann – Physicist – The decision to write "The Quark and the Jaguar" – Web of Stories". Retrieved July 17, 2020.
  45. ^ "Murray Gell-Mann - The decision to write "The Quark and the Jaguar" (190/200)". Retrieved July 17, 2020.
  46. ^ Johnson, George. "Strange Beauty". Talaya.net. Retrieved June 3, 2019.
  47. ^ Royal Society Insight Investment Science Book Prize winners list at docs.google.com/spreadsheets Retrieved February 15, 2017
  48. ^ Rodgers, Peter (June 1, 2003). "The many worlds of Murray Gell-Mann". Physics World. Retrieved May 26, 2019.
  49. ^ Goodstein, David L. (1999). "Strange Beauty: Murray Gell-Mann and the Revolution in Twentieth-Century Physics". Engineering and Science. 62 (4). CalTech. ISSN 0013-7812. Retrieved June 3, 2019.
  50. ^ a b Anderson, Philip W. (2011). "Ch. V Genius. Search for Polymath's Elementary Particles". More and Different: Notes from a Thoughtful Curmudgeon. World Scientific. pp. 241–2. ISBN 978-981-4350-14-3. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)Philip Anderson, More and Different, Chapter V, World Scientific, 2011.
  51. ^ Glashow, Sheldon Lee (2000). "Strange Beauty: Murray Gell-Mann and the Revolution in Twentieth-Century Physics". American Journal of Physics. 68 (6): 582. Bibcode:2000AmJPh..68..582J. doi:10.1119/1.19489.
  52. ^ Schweber, Silvan S. (2000). "Strange Beauty: Murray Gell‐Mann and the Revolution in Twentieth‐Century Physics". Physics Today. 53 (8): 43–44. Bibcode:2000PhT....53h..43J. doi:10.1063/1.1310122.
  53. ^ Johnson, George (July 1, 2000). "The Jaguar and the Fox". The Atlantic. Retrieved May 27, 2019.
  54. ^ West, Geoffrey (May 28, 2019). "Remembering Murray". Edge Foundation, Inc. Retrieved June 3, 2019.
  55. ^ Johnson, George. "Errata". Talaya.net. Retrieved June 3, 2019.
  56. ^ Stephen Wolfram, Remembering Murray Gell-Mann (1929-2019), Inventor of Quarks
  57. ^ Mary McFadden; Murray Gell-Mann (2012). Mary McFadden: A Lifetime of Design, Collecting, and Adventure. Random House Incorporated. ISBN 978-0-8478-3656-7.
  58. ^ Kent, Adrian (April 14, 1997). "Consistent Sets Yield Contrary Inferences in Quantum Theory". Physical Review Letters. 78 (15): 2874–2877. arXiv:gr-qc/9604012. Bibcode:1997PhRvL..78.2874K. doi:10.1103/PhysRevLett.78.2874.
  59. ^ a b c d "Murray Gell-Mann – Biographical". The Nobel Prize. Retrieved May 25, 2019.
  60. ^ a b Marshall, Jenna (May 24, 2019). "Murray Gell-Mann passes away at 89". Santa Fe Institute (Press release). Retrieved May 24, 2019.
  61. ^ Peregrine, Peter Neal (2009). Ancient Human Migrations: A Multidisciplinary Approach. The University of Utah Press. p. ix. ISBN 978-0-87480-942-8. Sergei Starostin and I established the Evolution of Human Languages project
  62. ^ The International Academy of Humanism at the website of the Council for Secular Humanism. Retrieved October 18, 2007. Some of this information is also at the International Humanist and Ethical Union Archived April 18, 2012, at the Wayback Machine website
  63. ^ Herman Wouk (2010). The Language God Talks: On Science and Religion. Hachette Digital, Inc. ISBN 9780316096751. Feynman, Gell-Mann, Weinberg, and their peers accept Newton's incomparable stature and shrug off his piety, on the kindly thought that the old man got into the game too early. ... As for Gell-Mann, he seems to see nothing to discuss in this entire God business, and in the index to The Quark and the Jaguar God goes unmentioned. Life he called a "complex adaptive system", which produces interesting phenomena such as the jaguar and Murray Gell-Mann, who discovered the quark. Gell-Mann is a Nobel-class tackler of problems, but for him the existence of God is not one of them.
  64. ^ Dombey, Norman (June 2, 2019). "Murray Gell-Mann obituary". The Guardian. ISSN 0261-3077. Retrieved June 6, 2019.
  65. ^ Frazier, Kendrick (2019). "In Memory of Murray Gell-Mann, Who Gave Us Quarks and Ordered the Subatomic World". Skeptical Inquirer. 43 (5): 10.
  66. ^ "1959 Dannie Heineman Prize for Mathematical Physics Recipient". American Physical Society. Retrieved May 25, 2019. For his contributions to field theory and to the theory of elementary particles.
  67. ^ Gell-Mann listing at member-directory of nasonline.org Retrieved February 15, 2017
  68. ^ "Murray Gell-Mann, Ph.D. Biography and Interview". www.achievement.org. American Academy of Achievement.
  69. ^ "Murray Gell-Mann". amacad.org.
  70. ^ "Murray Gell-Mann 1966". US Department of Energy, Ernest Orlando Lawrence Award. May 3, 2016. Archived from the original on May 22, 2017. Retrieved May 25, 2019. For his contributions of the highest significance to the theory of elementary and theoretical work in the field of physics.
  71. ^ "Murray Gell-Mann, Physics (1967)". The Franklin Institute. January 15, 2014. Retrieved May 25, 2019.
  72. ^ "John J. Carty Award for the Advancement of Science". National Academy of Sciences. Archived from the original on December 29, 2010. Retrieved March 7, 2011.
  73. ^ "Murray Gell-Mann". Global 500 Environmental Forum. Retrieved May 25, 2019.
  74. ^ "Albert Einstein Medal". Einstein Society | Einsteinhaus Bern. Retrieved May 25, 2019.
  75. ^ "The Humanist of the Year". American Humanist Association. Retrieved May 25, 2019.
  76. ^ Press Release, 10–2014, from Berlin-Brandenburgische Akademie der Wissenschaften Archived May 25, 2019, at the Wayback Machine Retrieved February 15, 2017

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