Running a Backtrace on the Lambda Calculus

This is part 0 in a multi part series. I’ll start my count from 0, like a computer scientist or an elevator designer in France, where the floors start from 0 instead of 1.

This is a project about the lambda calculus. The lambda calculus defines the atomic structure of all programming languages, being made of the most basic/elemental modular components. As prime numbers are to integers, the lambda calculus is to programming languages. It is the bones of the skeleton, the frame of the house.

This is certainly not the first attempt to catalogue the history and origins of the lambda calculus, nor is it by any means definitive or exhaustive. Rather it offers an introduction to the lambda calculus through the oft-forgotten quatrifocal lens — wherein the component disciplines are computer science, linguistics, philosophy, visual art. It is perhaps, what one might consider, if one were so inclined, an “avant-garde” approach to discussing such a foundational tenet of computer science. Dare I say, the reader may in fact enjoy the experience — though I can make no promise of such an outcome.

This project adopts a tone of informality only insofar as to better elucidate concepts which may benefit from such a flexibility of language, though such an informality is not evidenced by this very sentence announcing it (unless, of course, the reader considers words like “elucidate” and “insofar” as informal speech. In which case, I implore you to close your web browser with great haste, because it only gets more colloquially abysmal from here.)

It is with my deepest condolences that I inform the reader that humor may be employed as a rhetorical device throughout the project, albeit sparingly. I do apologize for this inconvenience.

There will also be pictures(!) throughout this project. If it is any consolation to the reader, I will refer to the pictures as capital-A Art and not lowercase-a art, so as to maintain an air of curatorial distance from such works and avoid collateral emotional resonance on my part. I accept no responsibility for the emotional state of the reader at the conclusion of this project (or for that matter, at any temporal point). If you are a person who is so inclined to be moved to tears reading about the intricacies of process calculi, then arm yourself with tissues. For anyone else, I would advise the same. Human emotional reactions are never as neatly inductively defined as the rules for function application, so I would encourage you to anticipate edge cases.

All parts of this project will be posted in the coming weeks.

A table of contents is listed below.

Table of Contents (subject to change)

  • 1. Methodology and motivations
  • 2. Definitions
  • 3. Logic
  • 4. Zeno’s paradox
  • 5. Calculus - Leibniz and Newton
  • 6. Georg Cantor
  • 7. Gödel’s Incompleteness Theorem
  • 8. Alan Turing and Alonzo Church - the Church-Turing Thesis
  • 9. Structuralism
  • 10. Post-structuralism
  • 11. Postmodernist thought
  • 12. Derrida and language
  • 13. Marshall McLuhan and the Medium of Language