May 14, 2026
Pretty graphs, petty comments
Extraordinary Ordinals
Math art drops, comments panic, and everyone argues what to even call it
TLDR: Marvin Borner published a hand-drawn visual tour of strange ways to represent numbers in advanced math notation. Readers split between awe and confusion, with some praising it as art, others begging for an explanation, and one instantly launching a naming dispute over “ordinals” versus “numerals.”
A delightfully brain-melting post called “Extraordinary Ordinals” tried to show how numbers can be drawn as hand-made graph diagrams inside a very abstract corner of math and computing. The author walks through several families of number representations—basically, different ways to write numbers using tiny symbolic structures instead of normal digits—and proudly notes the diagrams were made by hand, not AI. That detail alone feels like a wink at the internet: yes, the lines are weird, yes, they’re gorgeous, and yes, a lot of readers immediately treated the whole thing like gallery art with homework attached.
And the comments? Instant identity crisis. One camp was openly lost: “I didn’t understand that notation” and “I lack context” became the mood of the room. Another camp was pure appreciation, calling it “beautiful art” and admiring the line graphs even while admitting they had no clue what was happening. Then came the classic comment-section swerve: a terminology nitpick. One reader bluntly declared this should be “numerals,” not “ordinals,” injecting a tiny burst of pedantic drama into an already intimidating post.
The closest thing to a community hero was the commenter who stepped in to translate the article for civilians, explaining that it’s really a tour of famous ways to represent counting numbers, sorted by how often the symbols get reused. So the vibe was half “stunning, frame it” and half “someone please explain this wizard scroll.” In other words: peak internet academia, where the prettiest post is also the one making everyone confess they’re confused.
Key Points
- •The article organizes lambda-calculus numeral encodings into three categories: linear, affine, and non-linear.
- •It introduces a compact syntax for variables, abstractions, applications, and numbers, and states that every presented encoding can be used for arithmetic.
- •The Linear section defines application, abstraction, and β-reduction graphically, then presents Mackie and Parigot numeral systems.
- •The Affine section presents Scott numerals and a Bruijn system attributed to Borner, each with explicit definitions for initial numerals and successor forms.
- •The Non-Linear section discusses explicit duplication and presents Church, Mogensen, and two Wadsworth numeral-system definitions, including Mogensen’s arbitrary-base representation.