First, let us examine the definition of random by the Merriam-Webster Dictionary:
Etymology: Middle English, succession, surge, from Anglo-French randun, from Old French randir to run, of Germanic origin; akin to Old High German rinnan to run —more at run. Date: 1561. A haphazard course— at random : without definite aim, direction, rule, or method <subjects chosen at random>
Hence, randomness is unpredictability. Random numbers are, therefore, unpredictable numbers, elusive numbers that are always "on the run". Number that occur without any way of knowing how they came about. But how, within the domain of mathematics —the queen of sciences— can appear "numbers" that are unpredictable?
Random behavior is common in everyday physics; the radioactive decay, the falling drops in the rain, the noise pattern we see when the TV is not tuned to a specific station, the behavior of a desktop lava lamp.
Random numbers are usually compiled into tables; they are arranged in rows and columns in the "natural" order in which they appear.
There are no mathematical operation —like addition, multiplication, etc— that can produce random numbers (RN). They are generated by what is called "rules" or algorithms. On such rule is the one called "the middle terms" begin with any number that appears to your mind, square it, and take the middle digits to form the first RN, square again this middle number, use again the middle digits as the second RN, and keep repeating the process for as many RNs needed. This process is clumsy and maybe not so reliable; for in case the first number you take is the 101, its square is 10201, 020 squared is 400, etc.
The search for "good" and "reliable" RNs is endless, end each day the demand for them is increasing because they are used in messages encryption, telephone surveys, political polls, computer communications, etc. Another use for numeric randomness is online computer gambling and card shuffling like in Poker or Casino.
The problem with computers is that computer behavior is always programmed, hence, predictable, and violates the initial definition of randomness. So, maybe, computers are the less likely instrument to test for randomness. To compensate for this fact, the source, or seed of ``randomness'' is usually external, like a Geiger counter, atmospheric behavior, electron noise, desktop lava lamps, etc. The great benefit of computers is their speed they have to manipulate numbers and events.
Computer tables of random numbers are paradoxical: they are supposed to represent the order within the chaos; but this chaos must be generated in an orderly way.
The online gambling industry make extensive use of the random numbers, using programmed algorithms, that should instantly generate the numbers numbers for deals, but most of those routines are for generating what is called "pseudo-random" numbers.
Readers interested in the security of gambling online should read: How We Learned to Cheat at Online Poker: A Study in Software Security and Connoisseurs of Chaos Offer a Valuable Product: Randomness
Another method of obtaining random digits is to use digits of the decimal expansion of particular irrational and transcendental numbers like e and \/2. For example, the first 65 decimals of the square root of this number are,
√2 = 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799..
but at first glance it can be noticed that within this short segment of digits, there is an unusual occurrence of the digits 7 and 8 (11 and 8 respectively) while the occurrence for the digits 2 and 3 are 4 and 6 respectively. To be truly random, the distribution of digits must be fair among all 10 digits, but, at the same time, this condition requires that the sample of digits be great enough. The decimal expansion of √2 is infinite, a never ending, never repeating decimal, therefore, in that infinite sample it can be expected that all the digits be equaled distributed. However, even when the digits doesn't seem to be fairly distributed, given one digit at some specified position, it is impossible to determine which one will the next digit be.
In 1955, the Rand Corporation published a bizarre book titled A Million Random Digits with 100,000 Normal Deviates. The digits were produced electronically, in a long application of the first computers to this type of tasks. The Rand programmers devised an "electronic roulette wheel" that generated the output that was later compiled in a heavyweight book with that strange title.
For a handful of the so-called "book reviewers", this book is some kind of joke, something to laugh at, without taking into consideration the effort of producing such a work in the time when the computers were manipulated via punched cards.
The ``One Million Random Numbers'' published by the Rand Corporation in 1955 is not a novel, it has no characters, it has no plot. The RAND corporation has no monopoly of the RANDom numbers.
To summarize, for those that haven't understood the significance of the "rambling" numbers, keep in mind that in tables random numbers are usually presented in groups of five digits, like, but this has nothing to do with the five fingers of our hands, much less than palmistry. Finally, please understand that random numbers tables:
cannot be used in conjunction with the periodic table of elements to produce new elements.
are not produced by sympathizers of evolutionists, Einsteinists, Big-Bangers, old-earth geologists and most other elitist scientists.'
You can start reading it at any place, an jump to the end of the book without loosing anything ... you will not ruin your surprise factor. Numbers can be read in any order: upward, downward, or diagonally, but be consistent.
Random numbers tables can be exported to any country in spite that for people they are considered ``a national treasure''.
You can randomly ``read'' any portion of a random numbers table and still obtain the same random message.
RN tables are particularly symmetrical between base 10 an the hexadecimal system; you can "read" them in any of both "languages".