Articles containing proofs | Statistical randomness | Probability theorems | Infinity | Random text generation
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the entire observable universe would type a single complete work, such as Shakespeare's Hamlet, is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). The theorem can be generalized to state that any sequence of events which has a non-zero probability of happening will almost certainly eventually occur, given enough time. In this context, "almost surely" is a mathematical term meaning the event happens with probability 1, and the "monkey" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the "monkey metaphor" is that of French mathematician Émile Borel in 1913, but the first instance may have been even earlier. Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. Jorge Luis Borges traced the history of this idea from Aristotle's On Generation and Corruption and Cicero's De Natura Deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, up to modern statements with their iconic simians and typewriters. In the early 20th century, Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics. (Wikipedia).
Here's a re-enactment of the famous paradox known as the "infinite monkey theorem."
From playlist Cosmic Journeys
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Epsilon delta limit (Example 3): Infinite limit at a point
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From playlist Calculus
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There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
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Infinite Limits With Equal Exponents (Calculus)
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From playlist Calculus
Duality Theorem In this video, I use a neat little trick to show that the limit as n goes to infinity of 2^n is infinity, by using the fact (shown before) that the limit of (1/2)^n is 0. Exponential Limit: https://youtu.be/qxlSclbmh-w Other examples of limits can be seen in the playlis
From playlist Sequences
BM9.2. Cardinality 2: Infinite Sets
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From playlist Math Major Basics
Set Theory (Part 20): The Complex Numbers are Uncountably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will establish a bijection between the complex numbers and the real numbers, showing that the complex numbers are also uncountably infinite. This will eventually mean that the cardinal
From playlist Set Theory by Mathoma
Are there Infinite Versions of You?
PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Sign up for the mailing list to get episode notification
From playlist Many Worlds and the Multiverse Explained!
What's the Monkey number of the Rubik's cube?
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9.x: Genetic Algorithms and Evolutionary Computing - The Nature of Code
This video covers genetic algorithms and looks at how they are applied in 3 scenarios. 1: search problems where brute force is an impossibility (infinite monkey theorem). 2: physics-based systems 3: Interactive selection (i.e. user behavior driven fitness). This video is excerpted
From playlist The Nature of Code: Simulating Natural Systems
The most powerful (and useless) algorithm
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A Mathematical Journey through Scales - Martin Hairer
Oxford Mathematics Public Lecture The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty orders of magnitude. As we move from one to the other, the laws of nature can behave in drastically different ways, sometimes obeying quantum
From playlist Oxford Mathematics Public Lectures
Nexus Trimester - Alexander Shen (LIRMM, Montpellier) 2/2
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From playlist 8ECM Public Lectures
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Eva Miranda: Geometric quantization of toric and semitoric systems
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From playlist Topology
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