# Dictionary Definition

randomness

### Noun

1 (thermodynamics) a thermodynamic quantity
representing the amount of energy in a system that is no longer
available for doing mechanical work; "entropy increases as matter
and energy in the universe degrade to an ultimate state of inert
uniformity" [syn: entropy, S]

# User Contributed Dictionary

## English

### Pronunciation

- SAMPA: /"r

# Extensive Definition

Randomness is a lack of order, purpose, cause, or predictability in
non-scientific parlance. A random
process is a repeating process whose outcomes follow no
describable deterministic pattern, but follow a probability
distribution.

The term is often used in statistics to signify well
defined statistical properties, such as lack of bias or correlation. Monte
Carlo Methods, which rely on random input, are important
techniques of computational
science. Random selection is an official method to resolve
tied
elections in some jurisdictions, and is even an ancient method of
divination, as in
tarot, the I Ching, and
bibliomancy.

## History

Humankind has been concerned with random physical processes since pre-historic times. Examples are divination (cleromancy, reading messages in casting lots), the use of allotment in the Athenian democracy, and the frequent references to the casting of lots found in the Old Testament.Despite the prevalence of gambling in all times
and cultures, for a long time there was little inquiry into the
subject. Though Gerolamo
Cardano and Galileo wrote about
games of
chance, the first mathematical treatments were given by
Blaise
Pascal, Pierre de
Fermat and Christiaan
Huygens. The classical version of probability
theory that they developed proceeds from the assumption that
outcomes of random processes are equally likely; thus they were
among the first to give a definition of randomness in statistical
terms. The concept of statistical
randomness was later developed into the concept of information
entropy in information
theory.

In the early 1960s Gregory
Chaitin, Andrey
Kolmogorov and Ray
Solomonoff introduced the notion of algorithmic
randomness, in which the randomness of a sequence depends on
whether it is possible to compress
it.

## Randomness in science

Many scientific fields are concerned with randomness:### In the physical sciences

In the 19th century scientists used the idea of random motions of molecules in the development of statistical mechanics in order to explain phenomena in thermodynamics and the properties of gases.According to several standard interpretations of
quantum
mechanics, microscopic phenomena are objectively random. That
is, in an experiment where all causally relevant parameters are
controlled, there will still be some aspects of the outcome which
vary randomly. An example of such an experiment is placing a single
unstable atom in a
controlled environment; it cannot be predicted how long it will
take for the atom to decay; only the probability of decay within a
given time can be calculated. Thus quantum mechanics does not
specify the outcome of individual experiments but only the
probabilities. Hidden
variable theories are inconsistent with the view that nature
contains irreducible randomness: such theories posit that in the
processes that appear random, properties with a certain statistical
distribution are somehow at work, behind the scenes, determining
the outcome in each case.

### In biology

The theory of evolution ascribes the observed diversity of life to random genetic mutations some of which are retained in the gene pool due to the improved chance for survival and reproduction that those mutated genes confer on individuals who possess them.The characteristics of an organism arise to some
extent deterministically (e.g., under the influence of genes and
the environment) and to some extent randomly. For example, the
density of freckles
that appear on a person's skin is controlled by genes and exposure
to light; whereas the exact location of individual freckles seems
to be random.

Randomness is important if an animal is to behave
in a way that is unpredictable to others. For instance, insects in
flight tend to move about with random changes in direction, making
it difficult for pursuing predators to predict their
trajectories.

### In mathematics

The mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events, originally in the context of gambling but soon in connection with situations of interest in physics. Statistics is used to infer the underlying probability distribution of a collection of empirical observations. For the purposes of simulation it is necessary to have a large supply of random numbers, or means to generate them on demand.
Algorithmic information theory studies, among other topics,
what constitutes a random
sequence. The central idea is that a string of bits is random if and only if it is
shorter than any computer program that can produce that string
(Kolmogorov
randomness) — this basically means that random strings are
those that cannot be compressed.
Pioneers of this field include Andrey
Kolmogorov and his student Per
Martin-Löf, Ray
Solomonoff, Gregory
Chaitin, and others.

### In information science

In information science irrelevant or meaningless data is considered to be noise. Noise consists of a large number of transient disturbances with a statistically randomized time distribution.In communication
theory, randomness in a signal is called noise and is opposed
to that component of its variation that is causally attributable to
the source, the signal.

### In finance

The random walk hypothesis considers that asset prices in an organized market evolve at random. Other so called random factors intervene in trends and patterns to do with Supply and Demand distributions. As well as this, the random factor of the environment itself results in fluctuations in stock and broker markets.### Randomness versus unpredictability

Randomness is an objective property. Nevertheless, what appears random to one observer may not appear random to another observer. Consider two observers of a sequence of bits, only one of whom has the cryptographic key needed to turn the sequence of bits into a readable message. The message is not random, but is unpredictable for one of the observers. One of the intriguing aspects of random processes is that it is hard to know whether the process is truly random. The observer can always suspect that there is some "key" that unlocks the message. This is one of the foundations of superstition and is also what is a driving motive, curiosity, for discovery in science and mathematics.Under the cosmological hypothesis of determinism there is no
randomness in the universe, only unpredictability, since
there is only one possible outcome to all events in the universe.
No event under determinism can be defined as having probability since again
there is only one universal outcome.

Some mathematically defined sequences, such as
the decimals of pi, exhibit
some of the same characteristics as random sequences, but because
they are generated by a describable mechanism they are called
pseudorandom. To an
observer who does not know the mechanism, a pseudorandom sequence
is unpredictable.

Chaotic systems are unpredictable in practice due
to their extreme dependence on initial conditions. Whether or not
they are unpredictable in terms of
computability theory is a subject of current research. At least
in some disciplines of computability theory the notion of
randomness turns out to be identified with computational
unpredictability.

Randomness of a phenomenon is not itself
'random'. It can often be precisely characterized, usually in terms
of probability or expected value. For instance quantum mechanics
allows a very precise calculation of the half-lives of atoms even
though the process of atomic decay is a random one. More simply,
though we cannot predict the outcome of a single toss of a fair
coin, we can characterize its general behavior by saying that if a
large number of tosses are made, roughly half of them will show up
"Heads". Ohm's law and
the kinetic theory
of gases are precise characterizations of macroscopic phenomena which
are random on the microscopic level.

## Randomness and religion

Randomness has been associated closely with the notion of free will in a number of ways. If a person has free will (as defined by incompatibilists), then his actions will be unpredictable by other people and will contain an element of irreducible indeterminacy. By religious or supernatural conceptions of incompatibilist free will, such human actions may be the only source of randomness in the universe. (According to the naturalistic conception, by contrast, incompatibilist free will arises from pre-existing indeterminacy in physical laws and is not necessarily a unique feature of humans. According to the compatibilist conception, there is no randomness and humans are merely too complex to be easily predicted).Some theologians have attempted to resolve the
apparent contradiction between an omniscient deity, or a first cause,
and free
will using randomness. Discordians
have a strong belief in randomness and unpredictability. Buddhist
philosophy states that any event is the result of previous events
(karma) and as such there
is no such thing as a random event nor a 'first' event.

Martin
Luther, the forefather of Protestantism,
believed that there was nothing random based on his understanding
of the Bible.
As an outcome of his understanding of randomness he strongly felt
that free will was limited to low level decision making by humans.
Therefore, when someone sins against another, decision making is
only limited to how one responds, preferably through forgiveness
and loving actions. He believed based on Biblical scripture that
humans cannot will themselves, faith, salvation, sanctification, or
other gifts from God. Additionally, the best people could do
according to his understanding was not sin but they fall short and
free will cannot achieve this objective. Thus, in his view absolute
free will and unbounded randomness are severely limited to the
point that behaviors may even be patterned or ordered and not
random. This is a point emphasized by the field of behavioral
psychology.

These notions and more in Christianity often lend
to a highly deterministic worldview and that the concept of random
events is not possible. Especially, if purpose is part of this
universe then randomness, by definition, is not possible. This is
also one of the rationales for religious opposition to Evolution, where,
according to theory, (non-random) selection is applied to the
results of random genetic variation.

Donald
Knuth, a Stanford computer scientist and Christian commentator,
remarks that he finds pseudo-random numbers useful and applies them
with purpose. He then extends this thought to God who may use
randomness with purpose to allow free will to certain degrees.
Knuth believes that God is interested in people's decisions and
limited free will allows a certain degree of decision making.
Knuth, based on his understanding of quantum
computing and entanglement, comments that God exerts dynamic
control over the world without violating any laws of physics
suggesting that what appears to be random to humans may not, in
fact, be so random.

C. S.
Lewis, a 20th century Christian philosopher, discussed free
will at length. On the matter of human will, Lewis wrote: "God
willed the free will of men and angels in spite of His knowledge
that it could lead in some cases to sin and thence to suffering:
i.e., He thought freedom worth creating even at that price." In his
radio broadcast Lewis indicated that God "gave [humans] free will.
He gave them free will because a world of mere automata could never
love…" Lewis, believing in free will, had an indirect belief in
randomness by setting up a dependency of love on free will.

In some contexts, procedures that are commonly
perceived as randomizers - drawing lots or the like - are used for
divination, e.g. to reveal the will of the gods; see e.g. Cleromancy.

## Applications and use of randomness

In most of its mathematical, political, social
and religious use, randomness is used for its innate "fairness" and
lack of bias.

Political: Greek
Democracy was based on the concept of isonomia (equality of political
rights) and used complex allotment machines to ensure that the
positions on the ruling committees that ran Athens were fairly
allocated. Allotment is now
restricted to selecting jurors in Anglo-Saxon legal systems and in
situations where "fairness" is approximated by randomization, such as
selecting jurors and
military
draft lotteries.

Social: Random numbers were first investigated in
the context of gambling, and many randomizing
devices such as dice,
shuffling
playing cards, and roulette wheels, were first
developed for use in gambling. The ability to fairly produce random
numbers is vital to electronic gambling and, as such, the methods
used to create them are usually regulated by government Gaming
Control Boards. Throughout history randomness has been used for
games of chance and to select out individuals for an unwanted task
in a fair way (see drawing
straws).

Mathematical: Random numbers are also used where
their use is mathematically important, such as sampling for
opinion
polls and for statistical sampling in quality
control systems. Computational solutions for some types of
problems use random numbers extensively, such as in the Monte
Carlo method and in genetic
algorithms.

Medicine: Random allocation of a clinical
intervention is used to reduce bias in controlled trials (e.g.
Randomized controlled trials).

Religious: Although not intended to be random,
various forms of divination such as cleromancy see what appears
to be a random event as a means for a divine being to communicate
their will. (See also Free will and
Determinism).

### Generating randomness

It is generally accepted that there exist three
mechanisms responsible for (apparently) random behavior in systems
:

- Randomness coming from the environment (for example, Brownian motion, but also hardware random number generators)
- Randomness coming from the initial conditions. This aspect is studied by chaos theory, and is observed in systems whose behavior is very sensitive to small variations in initial conditions (such as pachinko machines, dice ...).
- Randomness intrinsically generated by the system. This is also called pseudorandomness, and is the kind used in pseudo-random number generators. There are many algorithms (based on arithmetics or cellular automaton) to generate pseudorandom numbers. The behavior of the system can be determined by knowing the seed state and the algorithm used. These methods are quicker than getting "true" randomness from the environment.

The many applications
of randomness have led to many different methods for generating
random data. These methods may vary as to how unpredictable or
statistically
random they are, and how quickly they can generate random
numbers.

Before the advent of computational random
number generators, generating large amounts of sufficiently
random numbers (important in statistics) required a lot of work.
Results would sometimes be collected and distributed as random
number tables.

### Randomness measures and tests

There are many practical measures of randomness for a binary sequence. These include measures based on frequency, discrete transforms, and complexity or a mixture of these. These include tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.### Links related to generating randomness

## Misconceptions/logical fallacies

Popular perceptions of randomness are frequently wrong, based on logical fallacies. The following is an attempt to identify the source of such fallacies and correct the logical errors.### A number is "due"

This argument says that "since all numbers will eventually appear in a random selection, those that have not come up yet are 'due' and thus more likely to come up soon". This logic is only correct if applied to a system where numbers that come up are removed from the system, such as when playing cards are drawn and not returned to the deck. It is true, for example, that once a jack is removed from the deck, the next draw is less likely to be a jack and more likely to be some other card. However, if the jack is returned to the deck, and the deck is thoroughly reshuffled, there is an equal chance of drawing a jack or any other card the next time. The same truth applies to any other case where objects are selected independently and nothing is removed from the system after each event, such as a die roll, coin toss or most lottery number selection schemes. A way to look at it is to note that random processes such as throwing coins don't have memory, making it impossible for past outcomes to affect the present and future.### A number is "cursed"

This argument is almost the reverse of the above, and says that numbers which have come up less often in the past will continue to come up less often in the future. A similar "number is 'blessed'" argument might be made saying that numbers which have come up more often in the past are likely to do so in the future. This logic is only valid if the roll is somehow biased and results don't have equal probabilities — for example, with weighted dice. If we know for certain that the roll is fair, then previous events have no influence over future events.Note that in nature, unexpected or uncertain
events rarely occur with perfectly equal frequencies, so learning which events are
likely to have higher probability by observing outcomes makes
sense. What is fallacious is to apply this logic to systems which
are specially designed so that all outcomes are equally likely —
such as dice, roulette wheels, and so on.

## References

## Books

- Randomness by Deborah J. Bennett.Harvard University Press, 1998. ISBN 0-674-10745-4
- Random Measures, 4th ed. by Olav Kallenberg. Academic Press, New York, London; Akademie-Verlag, Berlin (1986). MR0854102
- The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth, Reading, MA: Addison-Wesley, 1997. ISBN 0-201-89684-2
- Fooled by Randomness, 2nd ed. by Nassim Nicholas Taleb. Thomson Texere, 2004. ISBN 1-58799-190-X
- Exploring Randomness by Gregory Chaitin. Springer-Verlag London, 2001. ISBN 1-85233-417-7
- Random, by Kenneth Chan, includes a "Random Scale" for grading the level of randomness

## See also

## External links

- Random.org generates random numbers
- HotBits generates random numbers from radioactive decay
- Yuzoz.com generates random numbers from live space events
- Chaitin: Randomness and Mathematical Proof
- A Pseudorandom Number Sequence Test Program (Public Domain)
- Dictionary of the History of Ideas: Chance
- Philosophy: Free Will vs. Determinism
- RAHM Nation Institute
- History of randomness definitions, in Stephen Wolfram's A New Kind of Science.
- Computing a Glimpse of Randomness

randomness in Arabic: عشوائية

randomness in Catalan: Atzar

randomness in Czech: Náhoda

randomness in Danish: Tilfældighed

randomness in German: Zufall

randomness in Spanish: Azar

randomness in Esperanto: Hazardo

randomness in French: Hasard

randomness in Ido: Hazardo

randomness in Latin: Fors

randomness in Dutch: Toeval

randomness in Japanese: ランダム

randomness in Polish: Losowość

randomness in Portuguese: Aleatoridade

randomness in Russian: Случайное событие

randomness in Simple English: Random

randomness in Slovak: Náhodnosť

randomness in Swedish: Slump

randomness in Turkish: Rastlantısal

randomness in Chinese: 随机

# Synonyms, Antonyms and Related Words

aimlessness, capriciousness, causelessness, chance, chanciness, changeableness, derangement, designlessness, disarrangement, disarray, disarticulation,
discomfiture,
discomposure,
disconcertedness,
disharmony, dishevelment, disintegration, disjunction, disorder, disorderliness, disorganization,
disproportion,
disruption, disturbance, dysteleology, entropy, erraticism, erraticness, fickleness, haphazardness, hesitancy, hesitation, incalculability,
incertitude,
incoherence,
indecision, indecisiveness, indemonstrability,
indeterminacy,
indetermination,
indeterminism,
indiscriminateness,
inharmonious harmony, irregularity, irresolution, luck, most admired disorder,
nonsymmetry,
nonuniformity,
perturbation,
promiscuity,
promiscuousness,
purposelessness,
suspense, suspensefulness,
turbulence, unaccountability,
uncertainness,
uncertainty,
uncertainty principle, undecidedness, undeterminedness,
unforeseeableness,
unpredictability,
unprovability,
unsureness, unsymmetry, ununiformity, unverifiability,
upset, vacillation, whimsicality