08-13-2026, 05:09 PM
The Largest Tweetable Number
Summary
In this lecture titled "The Largest Tweetable Number," mathematician Joel David Hamkins explores how astronomically large numbers can be described within Twitter's 280-character limit. Starting with basic digit fills and progression into factorials, googolplexes, and Knuth's up-arrow notation, he demonstrates how compact mathematical notation allows tiny character counts to express massive quantities.
He then presents the "paradox of the largest tweetable number"—a variation of Barry's paradox—noting that because only finitely many tweets are possible, there must exist a largest tweetable number, yet writing "the largest tweetable number plus one" immediately creates a contradiction.
By examining concepts like Kolmogorov complexity, Turing's halting problem, and Tarski's theorem on the non-definability of truth, Hamkins resolves the paradox by showing that "tweetability" and mathematical definability cannot be internally defined within the tweet itself without relying on an external axiomatic system.
LECTURE
Summary
In this lecture titled "The Largest Tweetable Number," mathematician Joel David Hamkins explores how astronomically large numbers can be described within Twitter's 280-character limit. Starting with basic digit fills and progression into factorials, googolplexes, and Knuth's up-arrow notation, he demonstrates how compact mathematical notation allows tiny character counts to express massive quantities.
He then presents the "paradox of the largest tweetable number"—a variation of Barry's paradox—noting that because only finitely many tweets are possible, there must exist a largest tweetable number, yet writing "the largest tweetable number plus one" immediately creates a contradiction.
By examining concepts like Kolmogorov complexity, Turing's halting problem, and Tarski's theorem on the non-definability of truth, Hamkins resolves the paradox by showing that "tweetability" and mathematical definability cannot be internally defined within the tweet itself without relying on an external axiomatic system.
LECTURE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘