This is a fanfic of aphyr's "Foobaring the Technical Interview" series, though with less literary flair: https://aphyr.com/tags/interviews
I hadn't heard of Barendregt numerals before; the reference seems to be to Barendregt, H.P. (1976). A global representation of the recursive functions in the lambda calculus, Theoretical Computer Science 3, pp. 225–242. https://repository.ubn.ru.nl/bitstream/handle/2066/17239/132.... The bit about numerals starts in §4.1 on p. 238 (p. 15/19), so you can just skip there if you don't need an introduction to the λ-calculus and Schönfinkel/Curry combinatory logic.
I wonder if the academic literature would be more enjoyable to read if it were still structured as dialogues, the way it originally was—Hofstadter and Galileo were just calling back to Plato. I think aphyr and Moody fall somewhat short of the standards they set, since the antagonists of their dialogues never raise any real objections, serving only as flimsy, symbolic opposition to the Invincible Hero Mary Sue protagonists, who never make any mistakes or change their minds about anything. As I wrote yesterday in https://news.ycombinator.com/item?id=45669385, narratives are central to how the humans understand anything; even adept, experienced programmers often anthropomorphize parts of their programs, indulging in the "this guy talks to that guy" metaphor that Dijkstra so famously deplored, on the perhaps reasonable grounds that it led to illogical thinking.
You noticed the thing about my article I'm the least comfortable with: the idea of a "Barendregt numeral."
The number encoding scheme I use in the article is from To Mock a Mockingbird. Near the end of the book, a character says: "Oh, there are many other [number encodings] that would work... but this particular one is technically convenient. I have adopted this idea from the logician Henk Barendregt."
But I couldn't find any other source that claims Barendregt invented it. Thanks for finding another source, I'll take a look at it and update the article!
For me, it was the thing about the article I found most interesting!
I'm not sure Barendregt is claiming to have invented it, and in your quote, Smullyan doesn't either. I've only skimmed the paper, but the paper is framed as an introduction to the λ-calculus and SKI-combinators, not as a presentation of novel results in the field. Its section "0. Preliminaries" (♥) does claim to present a novel representation of recursive functions, but doesn't bother to mention the numerals. In a journal paper published today, the absence of an endnote there would amount to a claim that the representation of numerals was novel, but I don't think that was necessarily true in that less-bibliometrics-plagued time. Though Barendregt does cite 18 sources in his endnotes, so maybe so.
I hadn't heard of Barendregt numerals before; the reference seems to be to Barendregt, H.P. (1976). A global representation of the recursive functions in the lambda calculus, Theoretical Computer Science 3, pp. 225–242. https://repository.ubn.ru.nl/bitstream/handle/2066/17239/132.... The bit about numerals starts in §4.1 on p. 238 (p. 15/19), so you can just skip there if you don't need an introduction to the λ-calculus and Schönfinkel/Curry combinatory logic.
I wonder if the academic literature would be more enjoyable to read if it were still structured as dialogues, the way it originally was—Hofstadter and Galileo were just calling back to Plato. I think aphyr and Moody fall somewhat short of the standards they set, since the antagonists of their dialogues never raise any real objections, serving only as flimsy, symbolic opposition to the Invincible Hero Mary Sue protagonists, who never make any mistakes or change their minds about anything. As I wrote yesterday in https://news.ycombinator.com/item?id=45669385, narratives are central to how the humans understand anything; even adept, experienced programmers often anthropomorphize parts of their programs, indulging in the "this guy talks to that guy" metaphor that Dijkstra so famously deplored, on the perhaps reasonable grounds that it led to illogical thinking.