To be, or not to be, that is the Question: Exploring the pseudorandom generation of texts to write Hamlet from the perspective of the Infinite Monkey Theorem

This article explores the theoretical and computational aspects of the Infinite Monkey Theorem, investigating the number of attempts and the time required for a set of pseudorandom characters to assemble and recite Hamlets iconic phrase, To be, or not to be, that is the Question. Drawing inspiration from Emile Borel’s original concept (1913), the study delves into the practical implications of pseudorandomness using Python. Employing Python simulations to generate excerpts from Hamlet, the research navigates historical perspectives and bridges early theoretical foundations with contemporary computational approaches. A set of tests reveals the attempts and time required to generate incremental parts of the target phrase. Utilizing these results, growth factors are calculated, projecting estimated attempts and time for each text part. The findings indicate an astronomical challenge to generate the entire phrase, requiring approximately $2.68\times {10}^{69}$ attempts and $2.95\times {10}^{66}$ seconds - equivalent to $8.18\times {10}^{62}$ hours or $9.32\times {10}^{55}$ years. This temporal scale, exceeding the age of the universe by $6.75\times 10e^{45}$ times, underscores the immense complexity and improbability of random literary creation. The article concludes with reflections on the mathematical intricacies and statistical feasibility within the context of the Infinite Monkey Theorem, emphasizing the theoretical musings surrounding infinite time and the profound limitations inherent in such endeavors. And that only infinity could write Hamlet randomly.