Lecture 2: "An Impossible Program: from Turing to Strachey"


October 2019

My second video lecture on "History of Computer Science (and much more)" consists of two parts:

I recall people throwing the words "impossible," "undecidable," and "halting problem" at me when I was a Ph.D.student in the early 2000's. ... I hope 2020 or 2021 will become the year in which my work, entitled "The Halting Problem and Security's Language Theoretic Approach: Praise and Criticism from a Technical Historian", is published. While my article undergoes a second round of peer reviewing (after having been rejected without peer review on two prior occasions) I have video recorded my research findings and placed the two-part video lecture online.

Main sources

  • R. Crowell and R. Fox. Introduction to Knot Theory. Boston: Ginn and Co., 1963.
  • C. Strachey. An Impossible Program. The Computer Journal, Vol. 7, No. 4, p.313, 1965.
  • S. Shapiro. Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press, 2000.
  • J.E. Hopcroft, R. Motwani, J.D. Ullman. Introduction to Automata Theory: Languages, and Computation. Addison Wesley / Pearson Education, 2007.
  • E.A. Lee. Plato and the Nerd: The Creative Partnership of Humans and Technology. MIT Press, 2017.
  • R. Turner. Computational Artifacts: Towards a Philosophy of Computer Science, Springer, 2018.


More related work 

 "The machines we have considered here, the combination of the Euclidean straightedge and compasses, Descartes' machine and the Turing machines, have all of them had something to do with the foundations of mathematics. I have insisted upon the fact that those machines have had a theoretical function and that there was no need to materially construct them for them to be operational from that point of view. Furthermore, I said that in reality they cannot be constructed. Now, I can add that it is precisely as "machines impossible to materially construct" that they give rise to impossible problems."

Quoted from page 121 in Paul Henry's chapter `Mathematical Machines,'  appearing in the book `The Machine as Metaphor and Tool,' edited by H. Haken, A. Karlqvist, U. Svedin, Springer-Verlag, 1993.


Future work 

While the present lecture is primarily about "conflating the mathematical model and the modeled artefact" in the context of the Halting Problem, I have yet to explicate the link between this form of blending and the conflation of "descriptions" and "prescriptions." The latter, which surfaces 13 minutes into the second part of my lecture, is all over the place in the history of science and technology, e.g., in quantum mechanics:

"The wavefunction is not a description of the quantum object. It is a prescription for what to expect when we make measurements on that object." -- quoted from Philip Ball's on-line video, 8 minutes and 2 seconds into his talk.


[Last updated on 21 March 2021]