David Hestenes

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,[http://personnel.physics.ucla.edu/directory/faculty/finkelstein Robert Finkelstein] {{webarchive|url=https://web.archive.org/web/20120204091919/http://personnel.physics.ucla.edu/directory/faculty/finkelstein |date=2012-02-04 }} who was working on unified field theories at that time.D. Hestenes:[https://davidhestenes.net/geocalc/pdf/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. 321–346 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.D. Hestenes: [http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4090305 Geometric Calculus and Elementary Particles], –~~~~ University of California, Los Angeles 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.D. Hestenes, [https://davidhestenes.net/geocalc/pdf/SpacetimePhysics.pdf Spacetime Physics with Geometric Algebra], American Journal of Physics 71: 691–714 (2003). Then he revised his thesis and published it in 1966 as a book, Space–Time Algebra,D. Hestenes, Space-Time Algebra (Gordon & Breach: New York, 1966).
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.

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.D. Hestenes, New Foundations for Classical Mechanics (Kluwer: Dordrecht/Boston, 1986), Second Edition (1999).

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. In 1987, he became the first visiting scholar in the Department of Cognitive and Neural Systems (Boston University) and worked on neuroscience research for a period.D. Hestenes, [https://davidhestenes.net/misc/Hestenes_1987_-_How_the_brain_works.pdf 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). pp. 173–205.D. Hestenes, [https://davidhestenes.net/geocalc/pdf/InvarBK1.pdf Invariant Body Kinematics: I. Saccadic and compensatory eye movements.] Neural Networks 7: 65–77 (1994).D. Hestenes, [https://davidhestenes.net/geocalc/pdf/InvarBK2.pdf Invariant Body Kinematics: II. Reaching and neurogeometry.] Neural Networks 7: 79–88 (1994).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.

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.

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.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|978-9048145256}}, pp. 3–12, [https://books.google.com/books?id=DnyUDg483kEC&pg=PA9 p. 9]Chris J. L. Doran, Anthony Lasenby: Geometric Algebra for Physicists, Cambridge University Press, 2003, {{ISBN|978-0521480222}}, [https://books.google.com/books?id=VW4yt0WHdjoC&pg=PA123 p. 123]

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.D. Hestenes, [https://davidhestenes.net/geocalc/pdf/RealSpinorFields.pdf Real Spinor Fields], Journal of Mathematical Physics 8: 798–808 (1967). Among other things, it reveals that the complex factor $i\; \backslash hbar$ in the equation is a geometric quantity (a bivector) identified with electron spin, where $i$ specifies the spin direction and $\backslash hbar\; /2$ is the spin magnitude. The implications of this insight have been studied in a long series of papersD. Hestenes and R. Gurtler, [https://davidhestenes.net/geocalc/pdf/LocObsinQT.pdf Local Observables in Quantum Theory], American Journal of Physics 39: 1028 (1971).D. Hestenes, [https://davidhestenes.net/geocalc/pdf/LocalObserDirac.pdf Local Observables in the Dirac Theory], Journal of Mathematical Physics 14: 893–905 (1973).D. Hestenes, [https://davidhestenes.net/geocalc/pdf/Observ-opers.pdf Observables, Operators and Complex Numbers in the Dirac Theory], Journal of Mathematical Physics. 16 556–572 (1975).D. Hestenes (with R. Gurtler), [https://davidhestenes.net/geocalc/pdf/Consistency.pdf Consistency in the Formulation of the Dirac, Pauli and Schroedinger Theories], Journal of Mathematical Physics 16: 573–583 (1975).D. Hestenes, [https://davidhestenes.net/geocalc/pdf/Spin&uncert.pdf Spin and Uncertainty in the Interpretation of Quantum Mechanics], American Journal of Physics 47: 399–415 (1979).D. Hestenes, [https://davidhestenes.net/geocalc/pdf/Geom_Dirac.pdf 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), pp. 67–96. with the most significant conclusion linking it to Schrödinger's zitterbewegung and proposing a zitterbewegung interpretation of quantum mechanics.D. Hestenes, [https://davidhestenes.net/geocalc/pdf/ZBW_I_QM.pdf The Zitterbewegung Interpretation of Quantum Mechanics], Foundations of Physics 20: 1213–1232 (1990). 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 CalculusD. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, a unified language for mathematics and physics (Kluwer: Dordrecht/Boston, 1984). 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.D. Hestenes, [https://davidhestenes.net/geocalc/pdf/MultCalc.pdf Multivector Calculus], Journal of Mathematical Analysis and Applications 24: 313–325 (1968)

Hestenes emphasizes the important role of the mathematician Hermann GrassmannD. Hestenes, [https://davidhestenes.net/geocalc/pdf/GrassmannsVision.pdf Grassmann's Vision]. In G. Schubring (Ed.), Hermann Günther Grassmann (1809–1877) — Visionary Scientist and Neohumanist Scholar (Kluwer: Dordrecht/Boston, 1996), pp. 191–201D. 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) 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”,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, [https://books.google.com/books?hl=de&lr=&id=0-0hS8iWRmMC&oi=fnd&pg=PA270 p. 270] which withdraws attention from its role as a unified language for mathematics and physics.

Hestenes' work has been applied to Lagrangian field theory,A. Lasenby, C. Doran and S. Gull, A Multivector Derivative Approach to Lagrangian Field Theory, Foundations of Physics 23: 1295–12327 (1993) formulation of a gauge theory of gravity alternative to general relativity by Lasenby, Doran and Gull, which they call gauge theory gravity (GTG),A. Lasenby, C. Doran, & S. Gull, Gravity, gauge theories and geometric algebra, Philosophical Transactions of the Royal Society (London) A 356: 487–582 (1998)C. Doran & A. Lasenby, Geometric Algebra for Physicists (Cambridge U Press: Cambridge, 2003) and it has been applied to spin representations of Lie groups.C. Doran, D. Hestenes, F. Sommen & N. Van Acker, [https://davidhestenes.net/geocalc/pdf/LGasSG.pdf Lie Groups as Spin Groups], Journal of Mathematical Physics 34: 3642–3669 (1993) Most recently, it led Hestenes to formulate conformal geometric algebra, a new approach to computational geometry.D. Hestenes, [https://davidhestenes.net/geocalc/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 This has found a rapidly increasing number of applications in engineering and computer science.L. Dorst, C. Doran and J. Lasenby (Eds.), Applications of Geometric Algebra in Computer Science and Engineering, Birkhauser, Boston (2002)L. Dorst, D. Fontjne and S. Mann, Geometric Algebra for Computer Science (Elsevier: Amsterdam, 2007)D. Hestenes & J. Holt, [https://davidhestenes.net/geocalc/pdf/CrystalGA.pdf The Crystallographic Space Groups in Geometric Algebra], Journal of Mathematical Physics 48: 023514 (2007)H. Li, Invariant Algebras and Geometric Reasoning. (Beijing: World Scientific, 2008)E. Bayro-Corrochano and G. Scheuermann (eds.), Geometric Algebra Computing for Engineering and Computer Science. (London: Springer Verlag, 2009)L. Dorst and J. Lasenby, Guide to Geometric Algebra in Practice (Springer: London, 2011)

He has contributed to the main conferences in this field, the International Conference on Clifford Algebras (ICCA) and the Applications of Geometric Algebra in Computer Science and Engineering (AGACSE) series.{{Citation needed|date=June 2023}}

Since 1980, Hestenes has been developing a Modeling Theory of science and cognition, especially to guide the design of science instruction.D. Hestenes, [https://davidhestenes.net/modeling/R&E/Wherefore_SciOfTeaching.PDF Wherefore a Science of Teaching?] The Physics Teacher 17: 235–242 (1979)D. Hestenes, [https://davidhestenes.net/modeling/R&E/ModelingThryPhysics.pdf Toward a Modeling Theory of Physics Instruction], American Journal of Physics 55: 440–454 (1987)D. Hestenes, [https://davidhestenes.net/geocalc/pdf/ModelingGameswFig2.pdf Modeling Games in the Newtonian World], American Journal of Physics 60: 732–748 (1992)D. Hestenes, [https://davidhestenes.net/geocalc/pdf/ModelingSoftware.pdf 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)D. Hestenes (1997), [https://davidhestenes.net/modeling/R&E/ModelingMeth-jul98.pdf 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. 935–957D. Hestenes, [https://davidhestenes.net/geocalc/pdf/NotesforModelingTheory.pdf 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)D. Hestenes, [https://davidhestenes.net/geocalc/pdf/ModelingTheoryforMathandScience.pdf Modeling Theory for Math and Science Education]. In R. Lesh, P. Galbraith, Hines, A. Hurford (Eds.) Modeling Students’ Mathematical Competencies (New York: Springer, 2010) 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.M. Wells, D. Hestenes, and G. Swackhamer, [https://davidhestenes.net/modeling/R&E/ModelingMethod-Physics_1995.pdf A Modeling Method for High School Physics Instruction], American Journal of Physics 63: 606–619 (1995) To assess the effectiveness of Modeling Instruction, Hestenes and his students developed the Force Concept Inventory,I. Halloun and D. Hestenes, [https://davidhestenes.net/modeling/R&E/InitialKnowledge.pdf The Initial Knowledge State of College Physics Students], American Journal of Physics 53: 1043–1055 (1985)D. Hestenes, M. Wells, and G. Swackhamer, [https://davidhestenes.net/modeling/R&E/FCI.PDF Force Concept Inventory], The Physics Teacher 30: 141–158 (1992) a concept inventory tool for evaluating student understanding of introductory physics.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)

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),AMTA home page: http://modelinginstruction.org/ 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.D. Hestenes, C. Megowan-Romanowicz, S. Osborn Popp, J. Jackson, and R. Culbertson, [https://davidhestenes.net/modeling/R&E/Hestenes%20ASUgrad%20AJP11.pdf A graduate program for high school physics and physical science teachers], American Journal of Physics 79: 971–979 (2011) This provides a validated model for similar programs at universities across the country.D. Hestenes and J. Jackson (1997), [https://davidhestenes.net/modeling/STEPS/PARTNERS.PDF 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 pp. 449–459

On August 30, 2023, Hestenes was named in a United States District Court case in Utah filed by several venture capitalists claiming he endorsed and participated in a Ponzi scheme related to a discredited anti-gravity propulsion technology that was being marketed by Science Invents, LLC in Salt Lake City, Utah, a company owned by Joe Firmage, the former founder of USWeb. He was alleged to have taken over $100,000 in kickbacks from Firmage and other principals involved in the scheme and for recruiting investors into this scheme. The suit alleges Firmage and others falsely claimed the propulsion technology had been endorsed by the Department of Defense and was funded by them, and also claimed Hestenes had endorsed the validity of the science underlying the technology, a claim which Hestenes has adamantly denied. In total, the Ponzi scheme allegedly defrauded investors of $25,000,000 over a 10 year period. A default judgment was entered by the court on December 26, 2023 against the defendants.{{cite web | last=Miller | first=Ben | title=Tech Entrepreneur Sued Over $25 Million Lab Project Ponzi Scheme | website=The Brief – Top News of the Day From Bloomberg Law | date=2023-08-31 | url=https://news.bloomberglaw.com/litigation/tech-entrepreneur-sued-over-25-million-lab-project-ponzi-scheme | access-date=2023-10-07}}{{cite web | title=United States District Court Initial Complaint | url=https://storage.courtlistener.com/recap/gov.uscourts.utd.142025/gov.uscourts.utd.142025.1.0.pdf | access-date=2023-10-07}}{{cite web | title=Marmer et al v. Firmage et al (2:23-cv-00580), Utah District Court | website=PacerMonitor Federal Court Case Tools | date=2023-08-30 | url=https://www.pacermonitor.com/public/case/50233546/Marmer_et_al_v_Firmage_et_al | access-date=2023-10-07}}

• 2014 [http://www.aps.org/units/fed/awards/recipient.cfm?first_nm=High%20School&last_nm=Modeling%20Instruction&year=2014 Excellence in Physics Education Award] from the American Physical Society
• 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 Research Scholar (England) 1987–1988
• NASA Faculty Fellow (Jet Propulsion Laboratory) 1980, 1981
• NSF Postdoctoral Fellow (Princeton) 1964–1966
• University Fellow (UCLA) 1958–1959

;Books:

• D. Hestenes: Space-Time Algebra, 2nd ed., Birkhäuser, 2015, {{ISBN|978-3319184128}}
• D. Hestenes: New Foundations for Classical Mechanics, Fundamental 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}}

{{Reflist|2}}

• [https://davidhestenes.net/ Archive of Hestenes's papers]
• [https://davidhestenes.net/geocalc/ Archive of Hestenes's homepage on geometric calculus at ASU]
• [https://davidhestenes.net/misc/Hestenes_2012_-_Interview_(Tasar).pdf An interview with David Hestenes: His life and achievements], M.F. Tasar et al., Eurasia Journal of Mathematics, Science and Technology Education, 2012, vol. 8, no. 2, pp. 139–153
• [https://link.springer.com/article/10.1007/s00006-016-0664-z The Genesis of Geometric Algebra: A Personal Retrospective], Adv. Appl. Clifford Algebras 27, 351–379 (2017)
• [https://davidhestenes.net/geocalc/pdf/OerstedMedalLecture.pdf Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]
• [http://genealogy.math.ndsu.nodak.edu/id.php?id=17288 David Hestenes] at the Mathematics Genealogy Project
• [http://geometry.mrao.cam.ac.uk/ Cambridge University Geometric Algebra group]
• [http://geometry.mrao.cam.ac.uk/1993/01/imaginary-numbers-are-not-real-the-geometric-algebra-of-spacetime/ 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://geometry.mrao.cam.ac.uk/home/teaching-resources/ Physical Applications of Geometric Algebra] course-notes, see especially part 2.

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Category:21st-century American physicists

Category:1933 births

Category:Living people

Category:Arizona State University faculty

Category:Fellows of the American Physical Society

Category:Scientists from Chicago

Category:University of California, Los Angeles alumni

Category:Pacific Lutheran University alumni