The Markov Process
November 17, 2010
In the Beginning The Markov Process
"Did you bring me a man who cannot number his
fingers?".................... The Book of the Dead.
In the beginning math was thought to be directly related to the world of sense experience. According to Carl B. Boyer in his book, A History of Mathematics; archaic definitions suggest that mathematics is a science of number, magnitude, and form, which can be traced to the beginning of man along with some vague indications that mathematical design was found in life forms that predated the human race by several million years. It's valid to say that early man used mathematics to develop concepts of numbers in relation to counting; such as one bird as opposed to many birds, magnitude in relation to size; for instance the grand size of a buffalo in contrast with the small size of a mouse, and similarities and uniqueness in form [Boyer, 1968]. From the foundation of these basic mathematical principals many new processes came about. Man used his fingers and toes as well as objects to count which in turn led to the identification of numerical patterns. Such calculating practices evolved into observing the capability to count by twos, threes, fours, fives, and so on. The organization of placing objects into sets, and commingling number, magnitude, and form to realize basic patterns and series which led to complex sequences and chains. These impressions led to mathematical equations that predict the future based upon the present. Early mathematical concepts gave each new generation of mathematicians the ability to build and integrate sophisticated intellectual activity which has birthed algebra, geometry, deductive reasoning, trigonometry, measurement, logarithms, infinite series, probability, transversals, quantum physics, space travel, and the computer age, respectively.
Andrei Andreevich Markov played a very important role in the...