skip to main content
10.1145/3545945.3569742acmconferencesArticle/Chapter ViewAbstractPublication PagessigcseConference Proceedingsconference-collections
research-article

Theoretical Computer Science Education from Impossibility and Undecidability Problems in Physics

Published: 03 March 2023 Publication History

Abstract

Classroom examples of non-computable problems most often involve sets of Turing machines, which makes these problems too abstract and far divorced from real-world practice, so some students are turned off by the abstract nature of theoretical CS. In this paper, we explore the pedagogical connection of undecidability results in theoretical computing with similar (un)computability results in physics that have recently appeared. We argue that incorporating these new impossibility and undecidability results can increase students' interest in theoretical computing topics, as well as improve their understanding of the underlying science and mathematics.

References

[1]
Daniel S. Abrams and Seth Lloyd. 1998. Computational Complexity and Physical Law. In QCQC.
[2]
A. Aguirre, Z. Merali, and D. Sloan. 2021. Undecidability, Uncomputability, and Unpredictability. Springer International Publishing. https://books.google.es/ books?id=p00uzgEACAAJ
[3]
Dorit Aharonov and Sandy Irani. 2022. Hamiltonian Complexity in the Thermo- dynamic Limit. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (STOC 2022). Association for Computing Machinery, New York, NY, USA, 750--763. https://doi.org/10.1145/3519935.3520067
[4]
Manuel Ansede. 2021. Four mathematicians demonstrate it is impossible to predict where 29,000 rubber ducks in the sea will wash up. (may 2021). https://english.elpais.com/usa/2021-05--12/four-mathematicians-demonstrate-it-is-impossible-to-predict-where-rubber-ducks-in-the-sea-will-wash-up.html#?prm=copy_link
[5]
John D. Barrow. 1999. Impossibility: The Limits of Science and the Science of Limits. Oxford University Press.
[6]
Lenore Blum, Felipe Cucker, Michael Shub, and Steve Smale. 1998. Complexity and Real Computation. Springer-Verlag, Berlin, Heidelberg.
[7]
Robert Cardona, Eva Miranda, and Daniel Peralta-Salas. 2021. Looking at Euler flows through a contact mirror: Universality and undecidability. https://doi.org/ 10.48550/ARXIV.2107.09471
[8]
Brian Conrad. 2005. Impossibility theorems for elementary integration. (2005). http://www2.maths.ox.ac.uk/cmi/library/academy/LectureNotes05/Conrad.pdf
[9]
Toby S. Cubitt, David Pérez-García, and Michael Wolf. 2018. The Unsolvable Problem. Scientific American (2018).
[10]
Toby S. Cubitt, David Perez-Garcia, and Michael M. Wolf. 2015. Undecidability of the spectral gap. Nature 528, 7581 (dec 2015), 207--211. https://doi.org/10.1038/ nature16059
[11]
Newton da Costa Jr and Francisco Doria. 1991. Undecidability and incompleteness in classical mechanics. International Journal of Theoretical Physics 30 (08 1991), 1041--1073. https://doi.org/10.1007/BF00671484
[12]
Martin Davis. 2013. Computability and Unsolvability. Dover Publications.
[13]
Rafael del Vado Vírseda. 2019. Computability and Algorithmic Complexity Questions in Secondary Education. In Proceedings of the ACM Conference on Global Computing Education, CompEd 2019, Chengdu, Sichuan, China, May 17-19, 2019. 51--57. https://doi.org/10.1145/3300115.3309507
[14]
Rafael del Vado Vírseda. 2019. Introducing Theoretical Computer Concepts in Secondary Education. In Proceedings of the 50th ACM Technical Symposium on Computer Science Education, SIGCSE 2019, Minneapolis, MN, USA, February 27 - March 02, 2019. 1272. https://doi.org/10.1145/3287324.3293784
[15]
Rafael del Vado Vírseda. 2019. Introducing Theoretical Computer Concepts in Secondary Education (Poster Session). In Proceedings of the 2019 ACM SIGCSE Technical Symposium on Computer Science Education, Minneapolis, Minnesota, USA, February 27th - March 2nd, 2019. https://doi.org/10.1145/3287324.3293784
[16]
Rafael del Vado Vírseda. 2020. From the Mathematical Impossibility Results of the High School Curriculum to Theoretical Computer Science. In Koli Calling '20: Proceedings of the 20th Koli Calling International Conference on Computing Education Research (Koli Calling '20). Association for Computing Machinery, New York, NY, USA, 5. https://doi.org/10.1145/3428029.3428038
[17]
Rafael del Vado Vírseda. 2020. Learning Theoretical Computing from the Mathematical Impossibility Results of the CS Curriculum. In Proceedings of the 2020 ACM Conference on Innovation and Technology in Computer Science Education, ITiCSE 2020, Trondheim, Norway, June 15-19, 2020. ACM, 521--522. https://doi.org/10.1145/3341525.3393986
[18]
Rafael del Vado Vírseda. 2021. Learning from the Impossible: Introducing Theo- retical Computer Science in CS Mathematics Courses. In SIGCSE '21: The 52nd ACM Technical Symposium on Computer Science Education, Virtual Event, USA, March 13-20, 2021. ACM, 952--958. https://doi.org/10.1145/3408877.3432475
[19]
Jedson dos Santos. 2022. Python Animation Tool for Simple Fluid Dynamics Simulation. https://www.linkedin.com/pulse/python-animation-tool-simple-fluid-dynamics-jedson-dos-santos?trk=articles_directory
[20]
D. Perez Garcia. 2018. Undecidability in physics. . . and its consequences. https: //www.youtube.com/watch?v=QG9Bueldok4&t=10s
[21]
Orit Hazzan. 2002. Reducing abstraction level when learning computability theory concepts (ITiCSE '02). ACM, New York, NY, USA, 156--160. https://doi. org/10.1145/544414.544461
[22]
Michio Kaku. 2008. Physics of the Impossible: A Scientific Exploration Into the World of Phasers, Force Fields, Teleportation, and Time Travel (1 ed.). Doubleday.
[23]
Maria Knobelsdorf, Christoph Kreitz, and Sebastian Bohne. 2014. Teaching Theo- retical Computer Science Using a Cognitive Apprenticeship Approach (SIGCSE '14). ACM Press, New York, NY, USA, 67--72. https://doi.org/10.1145/2538862. 2538944
[24]
Laura Korte, Stuart Anderson, Helen Pain, and Judith Good. 2007. Learning by Game-building: A Novel Approach to Theoretical Computer Science Education. In Proceedings of the 12th Annual SIGCSE Conference on Innovation and Technology in Computer Science Education (ITiCSE '07). ACM Press, New York, NY, USA, 53--57. https://doi.org/10.1145/1268784.1268802
[25]
Hans P. Langtangen. 2012. A Primer on Scientific Programming with Python (5th ed.). Springer Publishing Company, Incorporated.
[26]
Svein Linge and Hans P. Langtangen. 2016. Programming for Computations - Python: A Gentle Introduction to Numerical Simulations with Python (1st ed.). Springer Publishing Company, Incorporated.
[27]
Andrzej Maciejewski and Maria Przybylska. 2011. Non-integrability of the three- body problem. Celestial Mechanics and Dynamical Astronomy 110 (05 2011), 17--30. https://doi.org/10.1007/s10569-010-9333-z
[28]
Chiara Marletto. 2021. The Science of Can and Can't: A Physicist's Journey Through the Land of Counterfactuals. Allen Lane.
[29]
Moore. 1990. Unpredictability and undecidability in dynamical systems. Physical review letters 64 20 (1990), 2354--2357.
[30]
Markus P. Müller. 2021. Undecidability and Unpredictability: Not Limitations, but Triumphs of Science. Springer International Publishing, Cham, 5--16. https: //doi.org/10.1007/978-3-030-70354-7_2
[31]
Erik Neumann. 2016. Kinematics of the Double Pendulum. https://web.mit.edu/ jorloff/www/chaosTalk/double-pendulum/double-pendulum-en.html
[32]
T. N. Palmer. 2021. Bell's Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity. https://doi.org/10. 48550/ARXIV.2108.10902
[33]
Roger Penrose. 1989. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press, Inc., USA.
[34]
Bjorn Poonen. 2012. Undecidable problems: a sampler. (apr 2012), 28. http: //www-math.mit.edu/~poonen/papers/sampler.pdf
[35]
Daniel Richardson. 1968. Some undecidable problems involving elementary functions of a real variable. The Journal of Symbolic Logic 33, 4 (1968), 514--520. https://doi.org/10.2307/2271358
[36]
Bobby Richardst. 2021. A Computer Simulation of a Perpetual Motion Concept. https://www.youtube.com/watch?v=TZIQ4zSwjNo
[37]
Gabriel Robins. 1988. Teaching Theoretical Computer Science at the Undergraduate Level: Experiences, Observations, and Proposals to Improve the Status Quo. University of California. Computer Science Department 88, 63 (02 1988).
[38]
Marcus Du Sautoy. 2016. What We Cannot Know: Explorations at the Edge of Knowledge (1st ed.). 4th Estate.
[39]
Benjamin Schumacher. 2010. Impossible: Physics Beyond The Edge. The Great Courses.
[40]
Naoto Shiraishi and Keiji Matsumoto. 2021. Undecidability in quantum thermal- ization. Nature Communications 12, 1 (aug 2021). https://doi.org/10.1038/s41467- 021-25053-0
[41]
Michael Sipser. 2012. Introduction to the Theory of Computation.
[42]
Peter Smith. 2013. An Introduction to Gödel's Theorems (2nd ed.). Cambridge University Press.
[43]
Dave's Spacet. 2021. Thermodynamics in python (tutorial). https://www.youtube. com/watch?v=idwnFn2jJ94
[44]
John Stillwell. 2018. Yearning for the Impossible: The Surprising Truths of Mathe- matics (2 ed.). CRC Press.
[45]
Terence Tao. 2017. On the universality of potential well dynamics. (2017). https://doi.org/10.48550/ARXIV.1707.02389
[46]
Terence Tao. 2017. On the universality of the incompressible Euler equation on compact manifolds. https://doi.org/10.48550/ARXIV.1707.07807
[47]
Terence Tao. 2019. On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows. https://doi.org/10.48550/ ARXIV.1902.06313
[48]
Emmanuelle Tosel. 2000. Meromorphic Parametric Non-Integrability; the Inverse Square Potential. Archive for Rational Mechanics and Analysis 152 (06 2000), 187--205. https://doi.org/10.1007/PL00004233
[49]
Alexei Tsygvintsev. 2000. The meromorphic non-integrability of the three-body problem. Journal für die reine und angewandte Mathematik (Crelles Journal) 2001 (10 2000). https://doi.org/10.1515/crll.2001.061
[50]
Noson S. Yanofsky. 2016. The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us. The MIT Press

Cited By

View all
  • (2025)Introducing Theoretical Computer Science in High School Physics Courses from Impossibility and Undecidability ProblemsProceedings of the 56th ACM Technical Symposium on Computer Science Education V. 210.1145/3641555.3705207(1433-1434)Online publication date: 18-Feb-2025

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SIGCSE 2023: Proceedings of the 54th ACM Technical Symposium on Computer Science Education V. 1
March 2023
1481 pages
ISBN:9781450394314
DOI:10.1145/3545945
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 March 2023

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. impossibility
  2. physics
  3. theoretical computing
  4. undecidability

Qualifiers

  • Research-article

Conference

SIGCSE 2023
Sponsor:

Acceptance Rates

Overall Acceptance Rate 1,787 of 5,146 submissions, 35%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)37
  • Downloads (Last 6 weeks)6
Reflects downloads up to 03 Mar 2025

Other Metrics

Citations

Cited By

View all
  • (2025)Introducing Theoretical Computer Science in High School Physics Courses from Impossibility and Undecidability ProblemsProceedings of the 56th ACM Technical Symposium on Computer Science Education V. 210.1145/3641555.3705207(1433-1434)Online publication date: 18-Feb-2025

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media