Cosmic Time
The infinite monkey theorem is a thought experiment illustrating the relationship between probability and infinity. It proposes that a monkey randomly typing on a typewriter for an infinite amount of time would eventually produce any given text, including the complete works of Shakespeare. While the theorem is often presented as a paradox, it is mathematically sound: given infinite attempts and infinite time, even events with vanishingly small probability become certain to occur.
Practical Timescales
The theorem highlights a crucial distinction between mathematical infinity and practical reality. Producing Shakespeare’s complete works through random typing would require roughly 10^183,000 keystrokes—a number vastly larger than the number of atoms in the observable universe (approximately 10^80). Even if a monkey typed continuously at a rate of one character per nanosecond since the Big Bang 13.8 billion years ago, it would not come close to accomplishing this task. The experiment thus demonstrates how probability calculations, while mathematically valid over infinite timescales, become meaningless when applied to finite cosmic timescales.
Relevance to Cosmology
Within the context of cosmic time, the infinite monkey experiment serves as a useful illustration of the limits of probability in the physical universe. It underscores why certain extremely improbable events—even those theoretically possible under the laws of physics—will never occur within the lifetime of the cosmos. This principle has applications in cosmology, thermodynamics, and discussions of what outcomes are genuinely achievable versus merely mathematically conceivable.
Source Notes
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- 2026-04-29: Infinite Monkey Experiment: Shakespeare Probability and Cosmic Time · ▶ source