# math

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Given enough time, a hypothetical monkey typing at random would, as part of its output, almost surely produce all of Shakespeare's plays. 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 a given text, such as the complete works of William Shakespeare . In this context, "almost surely" is a mathematical term with a precise meaning, 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. The relevance of the theory is questionable —the probability of a monkey exactly typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time even a hundred thousand orders of magnitude longer than the age of the universe is extremely low (but not zero).

## Parable of the Monkeys

A.k.a. The Topos of the Monkeys and the Typewriters Borel, 1913 ... Concevons qu'on ait dressé un million de singes à frapper au hasard sur les touches d'une machine à écrire et que, sous la surveillance de contremaîtres illettrés, ces singes dactylographes travaillent avec ardeur dix heures par jour avec un million de machines à écrire de types variés. Les contremaîtres illettrés rassembleraient les feuilles noircies et les relieraient en volumes.

## Infinite

Infinity, in Western culture, means endless or immeasurable. Infinity commonly inspires feelings of awe, futility and fear. The symbol for infinity is called the lemniscate:

## PAP209tarnai

The greatest pleasures of mathematics and science are in understanding. Here is an example. Much too often science and mathematics are presented as Gee Whiz, or as the ability to perform calculations, or to answer Jeopardy-style questions, or even to feel superior to those of lesser knowledge. The enjoyment of these things soon palls and becomes stale. The real fascination is in understanding the world, not just describing it. As one example, consider the five Platonic solids, the convex regular polyhedra.

## Polyhedra Index Page

What's new For regular visitors, here is a handy reference to what has changed over the last year or so. 29 May 2011. Ditela, polytopes and dyads A new name for closed line segments completes the pantheon of names for polytopes - updated to 9 dimensions and other minor revisions/corrections. 27 March 2011.
Introduction Introduction (2003-12-23) Introduces the concept of the 4th dimension. The adventures of Fred, Bob and Emily From the 2nd to the 3rd dimension (2003-01-13)

## Uniform Polychora

Welcome to my new and improved polychoron web site. Uniform polychoron count still stands at 1849 plus many fissaries, last four discovered are ondip, gondip, sidtindip, and gidtindip. Most of the graphics was done using Pov-Ray . Last updated August 12, 2012. 2012 August 12 - Small corrections to Category B and Scaliform sector.

## Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal

Opening Pandora's Box For the Second Time ur story starts with a guy named Rudy Rucker , an American mathematician, computer scientist and science fiction author (and in fact one of the founders of the cyberpunk science-fiction movement). Around 20 years ago, along with other approaches, he first imagined the concept behind the potential 3D Mandelbulb (barring a small mistake in the formula, which nevertheless still can produce very interesting results - see later), and also wrote a short story about the 3D Mandelbrot in 1987 entitled " As Above, So Below " (also see his blog entry and notebook ).