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My name is Erwin and I am studying Japanese Studies and Education Science at Preggraben / Austria.<br><br>my web-site ... [http://minimalexperimental.com Oltramare]
{{BLP primary sources|date=April 2012}}
{{Infobox scientist
|name             = David Orlin Hestenes
|image            =
|image_size        = 200px
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|birth_date        = 1933
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|ethnicity        =
|fields            = [[Physics]]
|workplaces        = [[Arizona State University]]
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|doctoral_advisor  =
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|doctoral_students =
|notable_students  =
|known_for        = '''[[Geometric Algebra]]'''
|author_abbrev_bot =
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|influences        =
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|awards            = '''[[Oersted Medal]]''' (2002)
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'''David Orlin Hestenes''', Ph.D. (born May 21, 1933) is a [[theoretical physicist]] and science educator. He is best known as chief architect of [[geometric algebra]] as a unified language for mathematics and physics,<ref>D. Hestenes: ''A Unified Language for Mathematics and Physics''. In:  J.S.R. Chisholm/A.K. Common (eds.): ''Clifford Algebras and their Applications in Mathematical Physics'' (Reidel: Dordrecht/Boston, 1986), p. 1–23.</ref> and as founder of Modelling Instruction, a research-based program to reform [[K–12 (education)|K–12]] Science, Technology, Engineering, and Mathematics (STEM) education.<ref>Home page on Modeling Instruction http://modeling.asu.edu/</ref>
 
For more than 30 years, he was employed in the Department of Physics and Astronomy of [[Arizona State University]] (ASU), where he retired with the rank of Research Professor and is now emeritus.
 
==Life and career==
===Education and doctorate degree===
David Orlin Hestenes (eldest son of mathematician [[Magnus Hestenes]]) was born 1933 in Chicago Illinois. Beginning college as a pre-medical major at [[UCLA]] from 1950 to 1952, he graduated from [[Pacific Lutheran University]] in 1954 with degrees in philosophy and speech. After serving in the U.S. Army from 1954 to 1956, he entered UCLA as an unclassified graduate student, completed a physics M.A. in 1958 and won a University Fellowship. His mentor at UCLA was the physicist Robert Finkelstein,<ref>[http://personnel.physics.ucla.edu/directory/faculty/finkelstein Robert Finkelstein]</ref> who was working on unified field theories at that time.<ref name="hestenes-1986-Clifford-algebra">D. Hestenes:[http://www.montgomerycollege.edu/Departments/planet/planet/Numerical_Relativity/Geometric_Algebra/caiqm.pdf ''Clifford algebra and the interpretation of quantum mechanics'']. In: J.S.R. Chisholm, A.K. Commons (eds.): ''Clifford Algebras and their Interpretations in Mathematical Physics'', Reidel, 1986, pp.&nbsp;321–346</ref> A serendipitous encounter with lecture notes by mathematician [[Marcel Riesz]] inspired Hestenes to study a geometric interpretation of [[Dirac matrices]]. He obtained his Ph.D. from [[UCLA]] with a thesis entitled ''Geometric Calculus and Elementary Particles''.<ref name="hestenes-1986-Clifford-algebra"/><ref>D. Hestenes: [http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4090305 ''Geometric Calculus and Elementary Particles''],--~~~~ University of California, Los Angeles</ref> Shortly thereafter he recognized that the [[Dirac algebra]]s and [[Pauli matrices]] could be unified in matrix-free form by a device later called a [[spacetime split]].<ref>D. Hestenes, Spacetime Physics with Geometric Algebra, American Journal of Physics 71: 691–714 (2003).</ref> Then he revised his thesis and published it in 1966 as a book, ''Space Time Algebra'',<ref>D. Hestenes, Space-Time Algebra (Gordon & Breach: New York, 1966).<br /></ref> now referred to as [[spacetime algebra]] (STA). This was the first major step in developing a unified, coordinate-free [[geometric algebra]] and [[calculus]] for all of physics.
 
===Postdoctorate research and career===
From 1964 to 1966, Hestenes was an [[National Science Foundation|NSF]] Postdoctoral Fellow at Princeton with [[John Archibald Wheeler]]. In 1966 he joined the physics department at [[Arizona State University]], rising to full professor in 1976 and retiring in 2000 to ''[[Emeritus Professor]] of Physics''.
 
In 1980 and 1981 as a ''[[NASA]] Faculty Fellow'' and in 1983 as a ''NASA Consultant'' he worked at [[Jet Propulsion Laboratory]] on [[orbital mechanics]] and [[attitude control]], where he applied geometric algebra in development of new mathematical techniques published in a textbook/monograph ''New Foundations for Classical Mechanics''.<ref>D. Hestenes, New Foundations for Classical Mechanics (Kluwer: Dordrecht/Boston, 1986), Second Edition (1999).<br /></ref>
 
In 1983 he joined with entrepreneur [[Robert Hecht-Nielsen]] and psychologist [[Peter Richard Killeen]] in conducting the first ever conference devoted exclusively to [[neural network]] modeling of the [[brain]]. Hestenes followed this in 1987 with appointment as the first Visiting Scholar in the Department of Cognitive and Neural Systems ([[Boston University]]) and a period of neuroscience research.<ref>D. Hestenes, How the Brain Works: the next great scientific revolution. In  C.R. Smith and G.J. Erickson (eds.), Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems (Reidel: Dordrecht/Boston, 1987). p. 173–205.</ref><ref>D. Hestenes, [http://geocalc.clas.asu.edu/pdf/InvarBK1.pdf Invariant Body Kinematics: I. Saccadic and compensatory eye movements.] Neural Networks 7: 65–77 (1994).</ref><ref>D. Hestenes, [http://geocalc.clas.asu.edu/pdf/InvarBK2.pdf Invariant Body Kinematics: II. Reaching and neurogeometry.] Neural Networks  7: 79–88 (1994).</ref><ref>D. Hestenes, Modulatory Mechanisms in Mental Disorders. In Neural Networks in  Psychopathology, ed. D.J. Stein & J. Ludik (Cambridge University Press: Cambridge, 1998). pp. 132–164.</ref>
 
Hestenes has been a [[principal investigator]] for [[US National Science Foundation|NSF]] grants seeking to teach physics through modeling and to measure student understanding of physics models at both the high school and university levels.
 
==Work==
Hestenes has worked in mathematical and [[theoretical physics]], [[geometric algebra]], [[neural networks]], and [[cognitive science|cognitive research]] in [[science education]]. He is the prime mover behind the contemporary resurgence of interest in geometric algebras and in other offshoots of [[Clifford algebra]]s as ways of formalizing theoretical physics,<ref>Abel Diek, R. Kantowski: ''Some Clifford algebra history'', in: Rafal Ablamowicz, P. Lounesto (eds.): ''Clifford Algebras and Spinor Structures: A Special Volume Dedicated to the Memory of Albert Crumeyrolle (1919–1992)'', Mathematics and Its Applications, Kluwer Academic, 1995, ISBN 978-07923-3366-7, pp.&nbp;3–12, [http://books.google.com/books?id=DnyUDg483kEC&pg=PA9 p. 9]</ref><ref>[[Chris J. L. Doran]], Anthony Lasenby: ''Geometric Algebra for Physicists'', Cambridge University Press, 2003, ISBN 978-0521480222, [http://books.google.de/books?id=VW4yt0WHdjoC&pg=PA123 p. 123]</ref>
 
===Geometric algebra and calculus===
Spacetime algebra provided the starting point for two main lines of research: on its implications for quantum mechanics specifically and for mathematical physics generally.
 
The first line began with the fact that reformulation of the [[Dirac equation]] in terms of spacetime algebra reveals hidden geometric structure<ref>D. Hestenes, Real Spinor Fields, Journal of Mathematical Physics 8: 798–808 (1967).</ref> Among other things, it reveals that the complex factor <math>i \hbar </math> in the equation is a geometric quantity (a [[bivector]]) identified with [[Spin (physics)|electron spin]], where <math>i</math> specifies the spin direction and <math>\hbar /2</math> is the spin magnitude. The implications of this insight have been studied in a long series of papers <ref>D. Hestenes and R. Gurtler, Local Observables in Quantum Theory, American Journal of Physics 39: 1028 (1971).</ref><ref>D. Hestenes, Local Observables in the Dirac Theory, Journal of Mathematical Physics 14: 893–905 (1973).</ref><ref>D. Hestenes, Observables, Operators and Complex Numbers in the Dirac Theory, Journal of Mathematical Physics. 16 556–572 (1975).</ref><ref>D. Hestenes (with R. Gurtler), Consistency in the Formulation of the Dirac, Pauli and  Schroedinger Theories, Journal of Mathematical Physics 16: 573–583 (1975).</ref><ref>D. Hestenes, Spin and Uncertainty in the Interpretation of Quantum Mechanics, American Journal of Physics 47: 399–415 (1979).</ref><ref>D. Hestenes, Geometry of the Dirac Theory. Originally published in A Symposium on the Mathematics of Physical Space-Time, Facultad de Quimica, Universidad Nacional Autonoma  de Mexico, Mexico City, Mexico (1981), p. 67–96.</ref> with the most significant conclusion linking it to [[Erwin Schrödinger|Schrödinger’s]] [[zitterbewegung]] and proposing a zitterbewegung interpretation of [[quantum mechanics]].<ref>D. Hestenes, The Zitterbewegung Interpretation of Quantum Mechanics, Foundations of Physics 20: 1213–1232 (1990).</ref> Research in this direction is still active.
 
The second line of research was dedicated to extending geometric algebra to a self-contained [[geometric calculus]] for use in theoretical physics. Its culmination is the book ''Clifford Algebra to Geometric Calculus''<ref name="hestenes-sobczyk-1984">D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, a unified language for mathematics and physics (Kluwer: Dordrecht/Boston, 1984).</ref> which follows an approach to differential geometry that uses the shape tensor ([[second fundamental form]]). Innovations in the book include the concepts of vector manifold, differential outermorphism, vector derivative that enables [[coordinate-free]] calculus on [[manifold]]s, and an extension of the [[Cauchy integral theorem]] to higher dimensions.<ref name="hestenes-sobczyk-1984"/><ref>D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313–325 (1968)</ref>
 
Hestenes emphasizes the important role of the mathematician [[Hermann Grassmann]]<ref>D. Hestenes, Grassmann's Vision. In G. Schubring (Ed.), Hermann Günther Grassmann (1809-1877) — Visionary Scientist and Neohumanist Scholar (Kluwer: Dordrecht/Boston, 1996), p. 191-201</ref><ref>D. Hestenes, Grassmann’s Legacy. In H-J. Petsche, A. Lewis, J. Liesen, S. Russ (eds.) From Past to Future: Grassmann’s Work in Context (Birkhäuser: Berlin, 2011)</ref> for the development of geometric algebra, with [[William Kingdon Clifford]] building on Grassmann's work. Hestenes is adamant about calling this mathematical approach “geometric algebra” and its extension “geometric calculus,” rather than referring to it as “Clifford algebra”. He emphasizes the universality of this approach, the foundations of which were laid by both Grassmann and Clifford. He points out that contributions were made by many individuals, and Clifford himself used the term “geometric algebra” which reflects the fact that this approach can be understood as a mathematical formulation of geometry, whereas, so Hestenes asserts, the term “Clifford algebra” is often regarded as simply “just one more algebra among many other algebras”,<ref>D. Hestenes: ''Differential forms in geometric calculus''. In: F. Brackx, R. Delanghe, H. Serras (eds.): ''Clifford Algebras and their Applications in Mathematical Physics: Proceedings of the Third Conference Held at Deinze, Belgium, 1993'', Fundamental Theories of Physics, 1993, ISBN 978-0792323471, pp.&nbsp;269–286, [http://books.google.com/books?hl=de&lr=&id=0-0hS8iWRmMC&oi=fnd&pg=PA270 p. 270]</ref> which withdraws attention from its role as a unified [[language]] for mathematics and physics.
 
Hestenes' work has been applied to Lagrangian field theory,<ref>A. Lasenby, C. Doran and S. Gull, A Multivector Derivative Approach to Lagrangian Field Theory, Foundations of Physics 23: 1295–12327 (1993)</ref> formulation of a [[gauge theory]] of [[gravity]] alternative to [[general relativity]] by Lasenby, Doran and Gull, which they call [[gauge theory gravity]] (GTG),<ref>A. Lasenby, C. Doran, & S. Gull, Gravity, gauge theories and geometric algebra, Philosophical Transactions of the Royal Society (London) A 356: 487–582 (1998)</ref><ref>C. Doran & A. Lasenby, Geometric Algebra for Physicists (Cambridge U Press: Cambridge, 2003)</ref> and it has been applied to spin representations of [[Lie group]]s.<ref>C. Doran, D. Hestenes, F. Sommen & N. Van Acker, Lie Groups as Spin Groups, Journal of Mathematical Physics 34: 3642–3669 (1993)</ref> Most recently, it led Hestenes to formulate [[conformal geometric algebra]], a new approach to [[computational geometry]].<ref>D. Hestenes, [http://geocalc.clas.asu.edu/pdf/OldWine.pdf Old Wine in New Bottles: A new algebraic framework for computational geometry.] In E. Bayro-Corrochano and G. Sobczyk (eds), Advances in Geometric Algebra with Applications in Science and Engineering (Birkhauser: Boston, 2001). pp. 1–14</ref> This has found a rapidly increasing number of applications in engineering and computer science.<ref>L. Dorst, C. Doran and J. Lasenby (Eds.), Applications of Geometric Algebra in Compute Science and Engineering, Birkhauser, Boston (2002)</ref><ref>L. Dorst, D. Fontjne and S. Mann, Geometric Algebra for Computer Science (Elsevier: Amsterdam, 2007)</ref><ref>D. Hestenes & J. Holt, The Crystallographic Space Groups in Geometric Algebra, Journal of Mathematical Physics 48: 023514 (2007)</ref><ref>H. Li, Invariant Algebras and Geometric Reasoning. (Beijing: World Scientific, 2008)</ref><ref>E. Bayro-Corrochano and G. Scheuermann (eds.), Geometric Algebra Computing for Engineering and Computer Science. (London: Springer Verlag, 2009)</ref><ref>L. Dorst and J. Lasenby, Guide to Geometric Algebra in Practice (Springer: London, 2011)</ref>
 
===Modeling theory and instruction===
Since 1980, Hestenes has been developing a ''Modeling Theory'' of science and cognition, especially to guide the design of science instruction.<ref>D. Hestenes, Wherefore a Science of Teaching? The Physics Teacher 17: 235–242 (1979)</ref><ref>D. Hestenes, Toward a Modeling Theory of Physics Instruction, American Journal of Physics 55: 440–454 (1987)</ref><ref>D. Hestenes, Modeling Games in the Newtonian World, American Journal of Physics 60: 732–748 (1992)</ref><ref>D. Hestenes, Modeling Software for learning and doing physics. In C. Bernardini, C. Tarsitani and M. Vincentini (Eds.), Thinking Physics for Teaching, Plenum, New York, pp. 25–66 (1996)</ref><ref>D. Hestenes (1997), Modeling Methodology for Physics Teachers. In E. Redish and J. Rigden (Eds.) The changing role of the physics department in modern universities, American Institute of Physics Part II. pp. 935–957</ref><ref>D. Hestenes, Notes for a Modeling Theory of Science, Cognition and Physics Education, In E. van den Berg, A. Ellermeijer and O. Slooten (Eds.) Modelling in Physics and Physics Education, (U. Amsterdam 2008)</ref><ref>D. Hestenes, Modeling Theory for Math and Science Education. In R. Lesh, P. Galbraith, Hines, A. Hurford (Eds.) Modeling Students’ Mathematical Competencies (New York: Springer, 2010)</ref>  The theory distinguishes sharply between conceptual models that constitute the content core of science and the mental models that are essential to understand them. ''Modeling Instruction'' is designed to engage students in all aspects of modeling, broadly conceived as constructing, testing, analyzing and applying scientific models.<ref>M. Wells, D. Hestenes, and G. Swackhamer, A Modeling Method for High School Physics Instruction, American Journal of Physics 63: 606–619 (1995)</ref> To assess the effectiveness of ''Modeling Instruction'', Hestenes and his students developed the ''Force Concept Inventory'',<ref>I. Halloun and D. Hestenes, The Initial Knowledge State of College Physics Students, American Journal of Physics 53: 1043–1055 (1985)</ref><ref>D. Hestenes, M. Wells, and G. Swackhamer, Force Concept Inventory, The Physics Teacher  30: 141–158 (1992)</ref> a [[concept inventory]] tool for evaluating student understanding of introductory physics.<ref>R.R. Hake, "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," American Journal of Physics 66: 64– 74 (1998)</ref>
 
After a decade of education research to develop and validate the approach, Hestenes was awarded grants from the National Science Foundation for another decade to spread the ''Modeling Instruction Program'' nationwide. As of 2011, more than 4000 teachers had participated in summer workshops on modeling, including nearly 10% of the United States' high school physics teachers. It is estimated that ''Modeling'' teachers reach more than 100,000 students each year.
 
One outcome of the program is that the teachers created their own non-profit organization, the ''American Modeling Teachers Association'' (AMTA),<ref>AMTA home page: http://modelinginstruction.org/</ref> to continue and expand the mission after government funding terminated. The AMTA has expanded to a nationwide community of teachers dedicated to addressing the nation's Science, Technology, Engineering, and Mathematics (STEM) education crisis. Another outcome of the Modeling Program was creation of a graduate program at Arizona State University for sustained professional development of STEM teachers.<ref>D. Hestenes, C. Megowan-Romanowicz, S.Osborn Popp, J. Jackson,and R. Culbertson, A graduate program for high school physics and physical science teachers, American Journal of Physics 79: 971–979 (2011)</ref> This provides a validated model for similar programs at universities across the country.<ref>D. Hestenes and J. Jackson (1997), Partnerships for Physics Teaching Reform ––a crucial role for universities and colleges. In E. Redish & J. Rigden (Eds.) The changing role of the physics department in modern universities, American Institute of Physics. Part I p. 449–459</ref>
 
==Awards and fellowships==
*2003 Award for excellence in [[educational research]] by the Council of Scientific Society Presidents
*2002 [[Oersted Medal]], awarded by the [[American Association of Physics Teachers]] for notable contributions to the teaching of physics
*Fellow of the [[American Physical Society]]
*Overseas Fellow of [[Churchill College, Cambridge]]
*[[Foundations of Physics]] Honoree (Sept.–Nov. issues, 1993)
*[[Fulbright Program|Fulbright]] Research Scholar (England) 1987–1988
*NASA Faculty Fellow ([[Jet Propulsion Laboratory]]) 1980, 1981
*NSF Postdoctoral Fellow (Princeton) 1964–1966
*University Fellow (UCLA) 1958–1959
 
==Publications==
;Books:
* D. Hestenes: ''New Foundations for Classical Mechanics'', Foundamental Theories of Physics, 2nd ed., Springer Verlag, 1999, ISBN 978-0792355144
* D. Hestenes, A. Weingartshofer (eds.): ''The Electron: New Theory and Experiment'', Fundamental Theories of Physics, Springer, 1991, ISBN 978-0792313564
* D. Hestenes, Garret Sobczyk: ''Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics'', Fundamental Theories of Physics, Springer, 1987, ISBN 978-9027725615
* D. Hestenes: ''Space-Time Algebra'', Routledge, 1966, ISBN 978-0677013909
 
==References==
{{Reflist|2}}
 
==External links==
* [http://www.ejmste.com/v8n2/EURASIA_v8n2_Tasar.pdf An interview with David Hestens: His life and achievements], M.F. Tasar et al., Eurasia Journal of Mathematics, Science and Technology Education, 2012, vol.&nbsp;8, no.&nbsp;2, pp.&nbsp;139–153
* Papers introducing geometric algebra: Research on [http://geocalc.clas.asu.edu/html/GeoCalc.html Geometric Calculus]
* [http://geocalc.clas.asu.edu/html/Oersted-ReformingTheLanguage.html Oersted Medal Lecture “Reforming the Mathematical Language of Physics” on Geometric Algebra in Physics.]
* Writings on pedagogy: [http://modeling.la.asu.edu/R&E/Research.html Papers on Modeling Instruction.]
* [http://www.mrao.cam.ac.uk/~clifford/publications/abstracts/imag_numbs.html Imaginary numbers are not real – the geometric algebra of spacetime], a tutorial introduction to the ideas of geometric algebra, by S. Gull, A. Lasenby, C. Doran
* [http://www.mrao.cam.ac.uk/~clifford/ptIIIcourse/ Physical Applications of Geometric Algebra] course-notes, see especially part 2.
* [http://www.mrao.cam.ac.uk/~clifford/ Cambridge University Geometric Algebra group]
* [http://physics.asu.edu/home/people/emeritus-faculty/david-hestenes Emeritus page at ASU], [http://physics.asu.edu/home/users/hestenes user page at ASU], [http://mathed.asu.edu/about/hestenes.shtml ASU Modeling Instruction Program page]
* [http://geocalc.clas.asu.edu/ Hestenes' homepage on geometric calculus at ASU]
* [http://modeling.asu.edu/PhysicsDepts-Role_K12Reform.pdf A Critical Role for Physicists in K–12 Science Education Reform] by David Hestenes and Jane Jackson
*[http://genealogy.math.ndsu.nodak.edu/id.php?id=17288 David Hestenes] at the [[Mathematics Genealogy Project]]
 
{{Authority control|VIAF=61611632}}
 
{{Persondata
| NAME              = Hestenes, David Orlin
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American physicist
| DATE OF BIRTH    = May 21, 1933
| PLACE OF BIRTH    =
| DATE OF DEATH    =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Hestenes, David Orlin}}
[[Category:American physicists]]
[[Category:1933 births]]
[[Category:Living people]]
[[Category:Arizona State University faculty]]

Revision as of 19:26, 5 June 2013

Template:BLP primary sources Template:Infobox scientist

David Orlin Hestenes, Ph.D. (born May 21, 1933) is a theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics,[1] and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education.[2]

For more than 30 years, he was employed in the Department of Physics and Astronomy of Arizona State University (ASU), where he retired with the rank of Research Professor and is now emeritus.

Life and career

Education and doctorate degree

David Orlin Hestenes (eldest son of mathematician Magnus Hestenes) was born 1933 in Chicago Illinois. Beginning college as a pre-medical major at UCLA from 1950 to 1952, he graduated from Pacific Lutheran University in 1954 with degrees in philosophy and speech. After serving in the U.S. Army from 1954 to 1956, he entered UCLA as an unclassified graduate student, completed a physics M.A. in 1958 and won a University Fellowship. His mentor at UCLA was the physicist Robert Finkelstein,[3] who was working on unified field theories at that time.[4] A serendipitous encounter with lecture notes by mathematician Marcel Riesz inspired Hestenes to study a geometric interpretation of Dirac matrices. He obtained his Ph.D. from UCLA with a thesis entitled Geometric Calculus and Elementary Particles.[4][5] Shortly thereafter he recognized that the Dirac algebras and Pauli matrices could be unified in matrix-free form by a device later called a spacetime split.[6] Then he revised his thesis and published it in 1966 as a book, Space Time Algebra,[7] now referred to as spacetime algebra (STA). This was the first major step in developing a unified, coordinate-free geometric algebra and calculus for all of physics.

Postdoctorate research and career

From 1964 to 1966, Hestenes was an NSF Postdoctoral Fellow at Princeton with John Archibald Wheeler. In 1966 he joined the physics department at Arizona State University, rising to full professor in 1976 and retiring in 2000 to Emeritus Professor of Physics.

In 1980 and 1981 as a NASA Faculty Fellow and in 1983 as a NASA Consultant he worked at Jet Propulsion Laboratory on orbital mechanics and attitude control, where he applied geometric algebra in development of new mathematical techniques published in a textbook/monograph New Foundations for Classical Mechanics.[8]

In 1983 he joined with entrepreneur Robert Hecht-Nielsen and psychologist Peter Richard Killeen in conducting the first ever conference devoted exclusively to neural network modeling of the brain. Hestenes followed this in 1987 with appointment as the first Visiting Scholar in the Department of Cognitive and Neural Systems (Boston University) and a period of neuroscience research.[9][10][11][12]

Hestenes has been a principal investigator for NSF grants seeking to teach physics through modeling and to measure student understanding of physics models at both the high school and university levels.

Work

Hestenes has worked in mathematical and theoretical physics, geometric algebra, neural networks, and cognitive research in science education. He is the prime mover behind the contemporary resurgence of interest in geometric algebras and in other offshoots of Clifford algebras as ways of formalizing theoretical physics,[13][14]

Geometric algebra and calculus

Spacetime algebra provided the starting point for two main lines of research: on its implications for quantum mechanics specifically and for mathematical physics generally.

The first line began with the fact that reformulation of the Dirac equation in terms of spacetime algebra reveals hidden geometric structure[15] Among other things, it reveals that the complex factor iℏ in the equation is a geometric quantity (a bivector) identified with electron spin, where i specifies the spin direction and ℏ/2 is the spin magnitude. The implications of this insight have been studied in a long series of papers [16][17][18][19][20][21] with the most significant conclusion linking it to Schrödinger’s zitterbewegung and proposing a zitterbewegung interpretation of quantum mechanics.[22] Research in this direction is still active.

The second line of research was dedicated to extending geometric algebra to a self-contained geometric calculus for use in theoretical physics. Its culmination is the book Clifford Algebra to Geometric Calculus[23] which follows an approach to differential geometry that uses the shape tensor (second fundamental form). Innovations in the book include the concepts of vector manifold, differential outermorphism, vector derivative that enables coordinate-free calculus on manifolds, and an extension of the Cauchy integral theorem to higher dimensions.[23][24]

Hestenes emphasizes the important role of the mathematician Hermann Grassmann[25][26] for the development of geometric algebra, with William Kingdon Clifford building on Grassmann's work. Hestenes is adamant about calling this mathematical approach “geometric algebra” and its extension “geometric calculus,” rather than referring to it as “Clifford algebra”. He emphasizes the universality of this approach, the foundations of which were laid by both Grassmann and Clifford. He points out that contributions were made by many individuals, and Clifford himself used the term “geometric algebra” which reflects the fact that this approach can be understood as a mathematical formulation of geometry, whereas, so Hestenes asserts, the term “Clifford algebra” is often regarded as simply “just one more algebra among many other algebras”,[27] which withdraws attention from its role as a unified language for mathematics and physics.

Hestenes' work has been applied to Lagrangian field theory,[28] formulation of a gauge theory of gravity alternative to general relativity by Lasenby, Doran and Gull, which they call gauge theory gravity (GTG),[29][30] and it has been applied to spin representations of Lie groups.[31] Most recently, it led Hestenes to formulate conformal geometric algebra, a new approach to computational geometry.[32] This has found a rapidly increasing number of applications in engineering and computer science.[33][34][35][36][37][38]

Modeling theory and instruction

Since 1980, Hestenes has been developing a Modeling Theory of science and cognition, especially to guide the design of science instruction.[39][40][41][42][43][44][45] The theory distinguishes sharply between conceptual models that constitute the content core of science and the mental models that are essential to understand them. Modeling Instruction is designed to engage students in all aspects of modeling, broadly conceived as constructing, testing, analyzing and applying scientific models.[46] To assess the effectiveness of Modeling Instruction, Hestenes and his students developed the Force Concept Inventory,[47][48] a concept inventory tool for evaluating student understanding of introductory physics.[49]

After a decade of education research to develop and validate the approach, Hestenes was awarded grants from the National Science Foundation for another decade to spread the Modeling Instruction Program nationwide. As of 2011, more than 4000 teachers had participated in summer workshops on modeling, including nearly 10% of the United States' high school physics teachers. It is estimated that Modeling teachers reach more than 100,000 students each year.

One outcome of the program is that the teachers created their own non-profit organization, the American Modeling Teachers Association (AMTA),[50] to continue and expand the mission after government funding terminated. The AMTA has expanded to a nationwide community of teachers dedicated to addressing the nation's Science, Technology, Engineering, and Mathematics (STEM) education crisis. Another outcome of the Modeling Program was creation of a graduate program at Arizona State University for sustained professional development of STEM teachers.[51] This provides a validated model for similar programs at universities across the country.[52]

Awards and fellowships

Publications

Books
  • D. Hestenes: New Foundations for Classical Mechanics, Foundamental Theories of Physics, 2nd ed., Springer Verlag, 1999, ISBN 978-0792355144
  • D. Hestenes, A. Weingartshofer (eds.): The Electron: New Theory and Experiment, Fundamental Theories of Physics, Springer, 1991, ISBN 978-0792313564
  • D. Hestenes, Garret Sobczyk: Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics, Fundamental Theories of Physics, Springer, 1987, ISBN 978-9027725615
  • D. Hestenes: Space-Time Algebra, Routledge, 1966, ISBN 978-0677013909

References

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External links

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He is a rip-off!! Severely trust me he's on of the scammer agent. He made me believe that I've a spot to remain then when I was about to move the place isn't out there. Then he just took my deposit and agent's charge. By the best way he's also the landlord of the place i am presupposed to lease. He took my money and ran away. However I went to the HDB and complain him, additionally I complain straight to the police. Then the police called him and he got scared. Finally each penny that I gave him, he give it again since HDB and police office is supporting me. Don't be lazy to complain. Go straight to the police and complain these individuals.

i imagine there are good ethical brokers in Singapore. But i have encounter unhealthy experiencing the Christina Fong from realty master. She is admittedly an unprofessional and never moral one. Only considering of undercutiing and squeezing money from ptther people without defending interest of her personal shopper. Proceed to the section Training and look at a map of all worldwide colleges in Singapore or visit the section residential areas for detailed data on the place to stay and why. Information District and Location Have completed no less than 30 property transactions up to now three years. At least 10 of these transactions will have to be for private properties, and at the very least one other 10 needs to be for HDB flats (also known as public housing); Singapore-Indonesia Commercial Affiliation

Agents need to be very resourceful and so they have to work doubly onerous to succeed in out to extra consumers as a result of when the market swings, it turns into very aggressive," said PropNex Chief Executive Mohamed Ismail. "Beforehand, an agent might focus on one space, comparable to HDB, however at this time you may't." An motion for misrepresentation arises beneath the law of tort. A Misrepresentation happens when the Representor (Property Agent) makes a false assertion of existing truth with data of its falsity and with the intention that the Representee (Buyer or Seller) ought to act on it with the consequence that the Representee does act on it to his detriment. Metropolis & South West (D01-08) Tiong Bahru MRT Quiet C/Room F/Furnished w AC No Agent Price

On February 19 we had an appointment with the proprietor and his agent (A and H!) at the condominium to hand over the keys. They went by means of all the things with a wonderful tooth comb. An important lesson we learned over all this is that you simply MUST ENGAGE YOUR PERSONAL AGENT and never rely on the homeowners agent as his priority is to the proprietor not you. Nevertheless, last night time my own agent called me and informed me suddenly that ECG instructed them a buyer goes handy them a check within the morning, so we higher act fast or we may lose the property. Stamp responsibility is to be paid inside 14 days from the date of acceptance of the OTP or Sale and buy a house in singapore (click hyperlink) (S&P) Settlement. For more information, please go to www.iras.gov.sg - Gown Up Your House Woodlands East Industrial & Industrial Affiliation

There may also be a Code of Ethics and a Skilled Conduct Commonplace, as well as the introduction of disciplinary motion in opposition to errant brokers/businesses and dispute decision mechanisms. Preparations shall be made to manage the transition of existing agencies and agents to these new standards, which have but to be finalized. The Proposed Enchancment in High quality for Actual Property Businesses Wheelock Properties put up 95 items of The Panorama in Ang Mo Kio for balloting. With a reduction of 12 p.c, they claimed to promote 80 to eighty five units. Whereas developers are clearing their existing stock, every month there are new projects acquiring their HIGH and new sites released by the government to construct more private housing. The due date of each rental payment; or

To know who pays actual property commissions - whether or not it's sellers or buyers or both or if it is Landlord's or Tenant's or both Divisions vary. All Brokers work on a commission scheme that is determined by the experience, efficiency and various other elements equivalent to recruitment and many others. New brokers can receive from a range of 60%-70% of the full fee received by them from the closure of a deal. High producing brokers would possibly obtain 100% and pay the company (broker) a desk fee. Everybody else falls somewhere in between. Kindly discuss with the FAQ part of the CEA web site-www.cea.gov.sg Co-Broking / sharing of fee There isn't a set formulation. This is based on the demand and supply circumstances in the market. present agents have tertiary education.

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  1. ↑ D. Hestenes: A Unified Language for Mathematics and Physics. In: J.S.R. Chisholm/A.K. Common (eds.): Clifford Algebras and their Applications in Mathematical Physics (Reidel: Dordrecht/Boston, 1986), p. 1–23.
  2. ↑ Home page on Modeling Instruction http://modeling.asu.edu/
  3. ↑ Robert Finkelstein
  4. ↑ 4.0 4.1 D. Hestenes:Clifford algebra and the interpretation of quantum mechanics. In: J.S.R. Chisholm, A.K. Commons (eds.): Clifford Algebras and their Interpretations in Mathematical Physics, Reidel, 1986, pp. 321–346
  5. ↑ D. Hestenes: Geometric Calculus and Elementary Particles,--~~~~ University of California, Los Angeles
  6. ↑ D. Hestenes, Spacetime Physics with Geometric Algebra, American Journal of Physics 71: 691–714 (2003).
  7. ↑ D. Hestenes, Space-Time Algebra (Gordon & Breach: New York, 1966).
  8. ↑ D. Hestenes, New Foundations for Classical Mechanics (Kluwer: Dordrecht/Boston, 1986), Second Edition (1999).
  9. ↑ D. Hestenes, How the Brain Works: the next great scientific revolution. In C.R. Smith and G.J. Erickson (eds.), Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems (Reidel: Dordrecht/Boston, 1987). p. 173–205.
  10. ↑ D. Hestenes, Invariant Body Kinematics: I. Saccadic and compensatory eye movements. Neural Networks 7: 65–77 (1994).
  11. ↑ D. Hestenes, Invariant Body Kinematics: II. Reaching and neurogeometry. Neural Networks 7: 79–88 (1994).
  12. ↑ D. Hestenes, Modulatory Mechanisms in Mental Disorders. In Neural Networks in Psychopathology, ed. D.J. Stein & J. Ludik (Cambridge University Press: Cambridge, 1998). pp. 132–164.
  13. ↑ Abel Diek, R. Kantowski: Some Clifford algebra history, in: Rafal Ablamowicz, P. Lounesto (eds.): Clifford Algebras and Spinor Structures: A Special Volume Dedicated to the Memory of Albert Crumeyrolle (1919–1992), Mathematics and Its Applications, Kluwer Academic, 1995, ISBN 978-07923-3366-7, pp.&nbp;3–12, p. 9
  14. ↑ Chris J. L. Doran, Anthony Lasenby: Geometric Algebra for Physicists, Cambridge University Press, 2003, ISBN 978-0521480222, p. 123
  15. ↑ D. Hestenes, Real Spinor Fields, Journal of Mathematical Physics 8: 798–808 (1967).
  16. ↑ D. Hestenes and R. Gurtler, Local Observables in Quantum Theory, American Journal of Physics 39: 1028 (1971).
  17. ↑ D. Hestenes, Local Observables in the Dirac Theory, Journal of Mathematical Physics 14: 893–905 (1973).
  18. ↑ D. Hestenes, Observables, Operators and Complex Numbers in the Dirac Theory, Journal of Mathematical Physics. 16 556–572 (1975).
  19. ↑ D. Hestenes (with R. Gurtler), Consistency in the Formulation of the Dirac, Pauli and Schroedinger Theories, Journal of Mathematical Physics 16: 573–583 (1975).
  20. ↑ D. Hestenes, Spin and Uncertainty in the Interpretation of Quantum Mechanics, American Journal of Physics 47: 399–415 (1979).
  21. ↑ D. Hestenes, Geometry of the Dirac Theory. Originally published in A Symposium on the Mathematics of Physical Space-Time, Facultad de Quimica, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico (1981), p. 67–96.
  22. ↑ D. Hestenes, The Zitterbewegung Interpretation of Quantum Mechanics, Foundations of Physics 20: 1213–1232 (1990).
  23. ↑ 23.0 23.1 D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, a unified language for mathematics and physics (Kluwer: Dordrecht/Boston, 1984).
  24. ↑ D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313–325 (1968)
  25. ↑ D. Hestenes, Grassmann's Vision. In G. Schubring (Ed.), Hermann Günther Grassmann (1809-1877) — Visionary Scientist and Neohumanist Scholar (Kluwer: Dordrecht/Boston, 1996), p. 191-201
  26. ↑ D. Hestenes, Grassmann’s Legacy. In H-J. Petsche, A. Lewis, J. Liesen, S. Russ (eds.) From Past to Future: Grassmann’s Work in Context (Birkhäuser: Berlin, 2011)
  27. ↑ D. Hestenes: Differential forms in geometric calculus. In: F. Brackx, R. Delanghe, H. Serras (eds.): Clifford Algebras and their Applications in Mathematical Physics: Proceedings of the Third Conference Held at Deinze, Belgium, 1993, Fundamental Theories of Physics, 1993, ISBN 978-0792323471, pp. 269–286, p. 270
  28. ↑ A. Lasenby, C. Doran and S. Gull, A Multivector Derivative Approach to Lagrangian Field Theory, Foundations of Physics 23: 1295–12327 (1993)
  29. ↑ A. Lasenby, C. Doran, & S. Gull, Gravity, gauge theories and geometric algebra, Philosophical Transactions of the Royal Society (London) A 356: 487–582 (1998)
  30. ↑ C. Doran & A. Lasenby, Geometric Algebra for Physicists (Cambridge U Press: Cambridge, 2003)
  31. ↑ C. Doran, D. Hestenes, F. Sommen & N. Van Acker, Lie Groups as Spin Groups, Journal of Mathematical Physics 34: 3642–3669 (1993)
  32. ↑ D. Hestenes, Old Wine in New Bottles: A new algebraic framework for computational geometry. In E. Bayro-Corrochano and G. Sobczyk (eds), Advances in Geometric Algebra with Applications in Science and Engineering (Birkhauser: Boston, 2001). pp. 1–14
  33. ↑ L. Dorst, C. Doran and J. Lasenby (Eds.), Applications of Geometric Algebra in Compute Science and Engineering, Birkhauser, Boston (2002)
  34. ↑ L. Dorst, D. Fontjne and S. Mann, Geometric Algebra for Computer Science (Elsevier: Amsterdam, 2007)
  35. ↑ D. Hestenes & J. Holt, The Crystallographic Space Groups in Geometric Algebra, Journal of Mathematical Physics 48: 023514 (2007)
  36. ↑ H. Li, Invariant Algebras and Geometric Reasoning. (Beijing: World Scientific, 2008)
  37. ↑ E. Bayro-Corrochano and G. Scheuermann (eds.), Geometric Algebra Computing for Engineering and Computer Science. (London: Springer Verlag, 2009)
  38. ↑ L. Dorst and J. Lasenby, Guide to Geometric Algebra in Practice (Springer: London, 2011)
  39. ↑ D. Hestenes, Wherefore a Science of Teaching? The Physics Teacher 17: 235–242 (1979)
  40. ↑ D. Hestenes, Toward a Modeling Theory of Physics Instruction, American Journal of Physics 55: 440–454 (1987)
  41. ↑ D. Hestenes, Modeling Games in the Newtonian World, American Journal of Physics 60: 732–748 (1992)
  42. ↑ D. Hestenes, Modeling Software for learning and doing physics. In C. Bernardini, C. Tarsitani and M. Vincentini (Eds.), Thinking Physics for Teaching, Plenum, New York, pp. 25–66 (1996)
  43. ↑ D. Hestenes (1997), Modeling Methodology for Physics Teachers. In E. Redish and J. Rigden (Eds.) The changing role of the physics department in modern universities, American Institute of Physics Part II. pp. 935–957
  44. ↑ D. Hestenes, Notes for a Modeling Theory of Science, Cognition and Physics Education, In E. van den Berg, A. Ellermeijer and O. Slooten (Eds.) Modelling in Physics and Physics Education, (U. Amsterdam 2008)
  45. ↑ D. Hestenes, Modeling Theory for Math and Science Education. In R. Lesh, P. Galbraith, Hines, A. Hurford (Eds.) Modeling Students’ Mathematical Competencies (New York: Springer, 2010)
  46. ↑ M. Wells, D. Hestenes, and G. Swackhamer, A Modeling Method for High School Physics Instruction, American Journal of Physics 63: 606–619 (1995)
  47. ↑ I. Halloun and D. Hestenes, The Initial Knowledge State of College Physics Students, American Journal of Physics 53: 1043–1055 (1985)
  48. ↑ D. Hestenes, M. Wells, and G. Swackhamer, Force Concept Inventory, The Physics Teacher 30: 141–158 (1992)
  49. ↑ R.R. Hake, "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," American Journal of Physics 66: 64– 74 (1998)
  50. ↑ AMTA home page: http://modelinginstruction.org/
  51. ↑ D. Hestenes, C. Megowan-Romanowicz, S.Osborn Popp, J. Jackson,and R. Culbertson, A graduate program for high school physics and physical science teachers, American Journal of Physics 79: 971–979 (2011)
  52. ↑ D. Hestenes and J. Jackson (1997), Partnerships for Physics Teaching Reform ––a crucial role for universities and colleges. In E. Redish & J. Rigden (Eds.) The changing role of the physics department in modern universities, American Institute of Physics. Part I p. 449–459
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