Could a TRILLION Monkeys Write Shakespeare Before the Universe Ends?

The video explores the Infinite Monkey Theorem, using the 2002 real-world experiment with six macaques—which produced only random letters and toilet use—to show that actual monkeys fail, but the underlying mathematics of randomness makes the idea theoretically sound. It explains that with completely random keystrokes on a 44-key keyboard, every possible sequence has some probability, meaning even Hamlet could eventually be typed, but the odds are astronomically small: a single monkey would need around 10^328,688 years. The creator then demonstrates that even scaling up to one monkey per atom (about 10^80 monkeys) typing until the heat death of the universe falls hundreds of thousands of orders of magnitude short. However, using the Borel–Cantelli lemmas, the video concludes that with truly infinite time and independent attempts, the probability sums diverge, so the monkey would almost surely type Hamlet infinitely many times. The video closes with a personal update from the creator, explaining their year-long absence due to having two babies and promising more frequent content going forward.

• ▶ 0:24 The thought experiment was actually tried in 2002 with six Salawi crested macaques at a UK zoo; after nearly two months they produced no real words, mostly the letter S, with some specimens using the computer as a toilet.
• ▶ 1:12 The key point isn't real monkeys but randomness: since every key has some chance of being pressed, every word and sequence of words has some probability, making Shakespeare's works theoretically possible.
• ▶ 1:42 The idea extends beyond existing literature—if random typing can produce Shakespeare, it could also generate entirely new literary works or undiscovered scientific ideas.
• ▶ 2:03 The model assumes completely random, independent keystrokes on a 44-key keyboard, so any exact sequence of length n has probability (1/44)^n.
• ▶ 3:08 Typing “hello” has probability (1/44)^5 ≈ 1 in 165 million, meaning an average wait of over 26 years at one key per second.
• ▶ 5:08 Scaling up, a full Hamlet (~200,000 characters) would take roughly 10^328,688 years—making it essentially impossible for a single monkey, though more monkeys might change the picture.
• ▶ 6:12 Scaling up to one monkey per atom gives ~10⁸⁰ monkeys, setting up the question of whether random typing until the heat death of the universe could produce Hamlet.
• ▶ 7:32 The sponsor segment uses Artemis 2 coverage to show how 500+ sources frame the same story differently by political bias, introducing Ground News and its Blind Spot Feed.
• ▶ 9:41 The math kills the idea: even with 10⁸⁰ monkeys typing for the universe’s lifetime, they’d produce only ~10¹⁸⁷ letters—hundreds of thousands of orders of magnitude short of the needed ~10³²⁸,⁶⁹⁵.
• ▶ 12:10 The first Borel–Cantelli lemma: when probabilities shrink fast enough that their sum converges, an event almost surely occurs only finitely many times.
• ▶ 13:29 The second Borel–Cantelli lemma: for independent events, when the sum of probabilities diverges, the event almost surely occurs infinitely many times.
• ▶ 14:59 Since each attempt to type Hamlet has the same tiny positive probability, the sum diverges—so with infinite time, the monkey types Hamlet infinitely many times.
• ▶ 15:45 The creator explains their year-long absence: they had two babies, the pregnancy was rough, and the babies are now 4 months old.
• ▶ 15:53 One of the babies is introduced by name, Isaac.
• ▶ 16:00 The creator is back to making videos part-time and promises viewers they will see more of them than last year.

• ▶ 0:00 The Infinite Monkey Thought Experiment (0:00 - 2:03) - Poses the random-typing question, covers the real-life monkey test, and sets up the real question about randomness.
• ▶ 2:03 Mathematical Setup and Waiting Times (2:03 - 6:15) - Builds the 44-key probability model and estimates how long a single monkey would take to type "hello", Shakespeare, and Hamlet.
• ▶ 6:15 Scale, Sponsor Break, and Heat Death (6:15 - 10:13) - Expands to one monkey per atom, includes the sponsor segment, and asks whether Hamlet appears before heat death.
• ▶ 10:13 Infinity, Borel–Cantelli, and the Infinite Monkey Theorem (10:13 - 15:45) - Uses dartboard games to explain finite vs infinite probabilities and applies the results to the monkey–Hamlet problem.
• ▶ 15:45 Personal Update (15:45 - 16:15) - Briefly explains the creator's hiatus and introduces their two babies.