A Comprehensive Summary Of The Benford's Law Phenomenon: On The Unequal Spread Of Digits Within Scientific And Typical Data

Numbers are written in our digital language system by conveniently and efficiently utilizing the ten digits 0 to 9 in much the same way as sentences and books are written in the English language system by conveniently utilizing the 26 letters A to Z. Surprisingly, and against all common sense or intuition, the spread of these ten digits within numbers of random data is not uniform, but rather highly uneven. Benford's Law predicts that the first digit on the left-most side of numbers is proportioned between all possible digits 1 to 9 approximately according to LOG(1 + 1/digit), so that occurrences of low digits such as {1, 2, 3} in the first position are much more frequent than occurrences of high digits such as {7, 8, 9}. Remarkably, Benford's Law is found to be valid in almost all real life statistics, from data relating to physics, astronomy, chemistry, geology, and biology to data relating to economics, accounting, finance, engineering, and governmental census information. Therefore, Benford's Law stands as the only common thread running through and uniting all scientific disciplines!This book represents an intense and concentrated effort by the author to narrate this digital, numerical, and quantitative story of the Benford's Law phenomenon as briefly and as concisely as possible, while still ensuring a comprehensive coverage of all its aspects, results, causes, explanations, and perspectives. The most recent research results and discoveries in this field are included within this book in such a way as to be comprehensible and engaging to readers of all proficiencies.