Redundancy in the English Language

Whenever we communicate, rules everywhere restrict our freedom to choose the next letter and the next pineapple.I Because these rules render certain patterns more likely and certain patterns almost impossible, languages like English come well short of complete uncertainty and maximal information: the sequence “th” has already occurred 6,431 times in this book, the sequence “tk” just this once. From the perspective of the information theorist, our languages are hugely predictable— al...

 The Monte Carlo Method and Evolutionary Algorithms

Back then, I thought of one thing: Have you heard of the Monte Carlo method? Ah, it’s a computer algorithm often used for calculating the area of irregular shapes. Specifically, the software puts the figure of interest in a figure of known area, such as a circle, and randomly strikes it with many tiny balls, never targeting the same spot twice. After a large number of balls, the proportion of balls that fall within the irregular shape compared to the total number of balls used to hit the ci...

 π in Base-26 Will Produce All the Works of Shakespeare

Base 26 is one of two fairly natural ways of representing numbers as text using a 26-letter alphabet. The number of interest is expressed numerically in base 26, and then the 26 different base-26 digits are identified with letters as 0=A, 1=B, 2=C, ... 25=Z. Here are the first 100 digits of pi expressed in this way: D.DRSQLOLYRTRODNLHNQTGKUDQGTUIRXNEQBCKBSZIVQQVGDMELM UEXROIQIYALVUZVEBMIJPQQXLKPLRNCFWJPBYMGGOHJMMQISMS... Lo! At the 6th digit we find a two-letter word (LO), and only a ...