Could a TRILLION Monkeys Write Shakespeare Before the Universe Ends?

Could a TRILLION Monkeys Write Shakespeare Before the Universe Ends?

by Up and Atom

Formal & Physical Sciences Mathematics PBMathematicsPBTProbability and statistics
🎙 Up and Atom 👥 855K 📅 April 28, 2026 ⏱ 16 min 👁 50K 📄 science communication 🧭 2026-08-03
Available in: English (current) Français

Keywords

infinite monkey theoremprobabilityBorel-Cantelli lemmaShakespeareheat death

Summary

The video explores the famous infinite monkey theorem, which posits that a monkey randomly typing on a keyboard could eventually produce the works of Shakespeare. The presenter, Jade, begins by referencing a real-world experiment in 2002 where six macaques were given a keyboard, but they only produced a few letters and used the computer as a toilet. She then formalizes the problem by assuming a keyboard with 44 keys (26 letters, 10 digits, punctuation, and space) and independent key presses. She calculates the probability of typing ‘hello’ as 1/44^5, requiring about 165 million attempts on average. For a 50-character phrase, the time needed is about 10^76 years, far exceeding the age of the universe (1.38e10 years). For a 1000-character paragraph, it would take 10^1638 years, vastly exceeding the estimated heat death of the universe (10^100 years). For the entire Hamlet, with about 200,000 characters, the time required is 10^328,688 years. Even with a monkey for every atom in the universe (10^80 monkeys), typing at one key per second until heat death, they would produce only 10^187 characters, a negligible fraction. The video then considers infinite time, where the event becomes inevitable. It introduces the Borel-Cantelli lemma to analyze whether the monkey produces a finite or infinite number of Hamlets. Using a dartboard analogy, she explains that if probabilities decrease fast enough (summing to a finite number), the event occurs only finitely often. For the monkey typing, the probability of typing Hamlet in a block of 200,000 characters is 1/44^200,000, and the sum over infinite blocks converges, so with probability 1, the monkey types Hamlet only finitely many times. The video concludes that while the theorem is theoretically true, the timescales are so vast that it is practically impossible within the universe’s lifetime.

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Critical Evaluation

The video provides a thorough and mathematically rigorous analysis of the infinite monkey theorem, a classic thought experiment. The presenter clearly defines the assumptions, such as a finite keyboard with 44 keys and independent key presses, which are essential for the calculations. The step-by-step derivation of probabilities and timescales is well-structured and accessible, making complex concepts understandable. The use of the Borel-Cantelli lemma is particularly insightful, as it addresses a subtle question about the frequency of the event in infinite time, which is often overlooked in popular discussions. The video also incorporates a real-world experiment with macaques, adding empirical context and highlighting the gap between theoretical and practical outcomes. The scientific content is accurate, and the presenter acknowledges the limitations of her explanations when dealing with extremely large numbers, which is honest. The sources cited are not explicitly listed in the video, but the presenter mentions fact-checkers and references the 2002 experiment, which adds credibility. The sponsored segment about Ground News is clearly marked and does not detract from the scientific content, though it does interrupt the flow. The video’s title is catchy and accurately reflects the content, though it slightly overstates the ’trillion monkeys’ scenario, as the video considers up to 10^80 monkeys. Overall, the video is an excellent educational resource that balances entertainment with scientific rigor, making it suitable for a general audience interested in mathematics and probability.

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Title / Content Match

The title is catchy and accurately reflects the core question addressed in the video, which explores the probability of monkeys typing Shakespeare within cosmic timescales.

Quality & Reliability

8/10

The video presents a rigorous probabilistic analysis of the infinite monkey theorem, with clear assumptions and calculations. It cites the Borel-Cantelli lemma and references the 2002 real-world experiment with macaques. The content is fact-checked by multiple experts, and the mathematical reasoning is sound. However, the video includes a sponsored segment (Ground News) which is clearly marked, and the presenter's personal commentary on the news tool is subjective. Overall, the scientific content is reliable and well-explained.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

Concurring Sources

Contribution & Novelties

The video provides a clear and rigorous mathematical treatment of the infinite monkey theorem, including a novel application of the Borel-Cantelli lemma to determine that, in infinite time, the monkey will type Hamlet only finitely many times with probability 1. This goes beyond the common statement that it is ‘inevitable’ and offers a deeper probabilistic insight. The video also contextualizes the timescales with cosmic events like the heat death of the universe, making the numbers tangible.

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Radar Profile

The radar profile shows high scores in information quantity and quality, with a moderate technical level and high reliability. This indicates a well-balanced video that is both informative and accessible, with strong scientific grounding.

Reliability 8/10

💬 Très positif. Sur les 30 commentaires analysés, la grande majorité exprime un accueil chaleureux et félicite la créatrice pour son retour et l'arrivée de ses jumeaux, avec quelques commentaires humoristiques sur le thème des singes.