Randomness

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Randomness is the lack of pattern or predictability in the event. The random sequence of events, symbols or steps has no sequence and does not follow a clear pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different results over a large number of events (or "trials") can be predicted. For example, when throwing two dice, the yield of any particular roll is unpredictable, but the number 7 will occur twice more often than 4. In this view, randomness is a measure of yield uncertainty, not arbitrary, and applies to the concept of opportunity, and entropy information.

Mathematics, probability, and statistics fields use the formal definition of randomness. In statistics, a random variable is a task of numerical value for every possible outcome of the event space. This association facilitates the identification and calculation of probability events. Random variables can appear in random order. A random process is a sequence of random variables whose results do not follow a deterministic pattern, but follow the evolution described by the probability distribution. These and other constructs are very useful in probability theory and various randomness applications.

Randomness is most often used in statistics to signify well-defined property statistics. The Monte Carlo method, which relies on random inputs (such as from random number generators or pseudorandom number generators), is an important technique in science, such as, for example, in computational science. By analogy, the quasi-Monte Carlo method uses a quasirandom number generator.

Random selection , when narrowly attached to a simple random sample, is an item selection method (often called a unit) of a population where the probability of selecting a particular item is the proportion of the item in the population. For example, with a bowl containing only 10 red marbles and 90 blue marbles, a random selection mechanism will select red marble with a probability of 1/10. Note that a random selection mechanism that selects 10 marbles from this bowl does not always produce 1 red and 9 blue. In situations where a population consists of distinguishable goods, a random selection mechanism requires the same probability for each item to be selected. That is, if the selection process is such that every member of the population, from saying the subject of research, has the same probability to choose then we can say the selection process is random.

Video Randomness

Histori

In ancient history, the concept of coincidence and randomness intertwined with fate. Many ancient people throw dice to determine their fate, and this then evolves into a coincidence game. Most ancient cultures use various methods of prediction to try to avoid randomness and destiny.

The Chinese from 3000 years ago were probably the earliest people to formalize opportunities and opportunities. The Greek philosophers discussed randomness at length, but only in a non-quantitative form. It was not until the 16th century that Italian mathematicians began to inaugurate the opportunities associated with various coincidences. The invention of calculus has a positive impact on the formal study of randomness. In the 1888 edition of his book The Logic of Chance John Venn wrote a chapter on Randomized Conception which included his view of the digit randomness of pi numbers by using them to create random paths in two dimensions.

The early part of the 20th century saw rapid growth in formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. In the mid to late 20th century, the idea of ​​algorithmic information theory introduced a new dimension to the field through the concept of algorithmic randomness.

Although randomness is often viewed as a barrier and disruption for centuries, in the 20th century computer scientists began to realize that the introduction of deliberate random into calculations can be an effective tool for designing better algorithms. In some cases, the random algorithm outperforms the best deterministic method.

Maps Randomness

In science

Many scientific fields pay attention to randomness:

In physics

In the 19th century, scientists used the idea of ​​a random motion of molecules in the development of statistical mechanics to explain phenomena in thermodynamics and gas properties.

According to some standard interpretations of quantum mechanics, microscopic phenomena are objectively random. That is, in an experiment that controls all relevant parameters causally, some aspects of the results still vary randomly. For example, if an unstable single atom is placed in a controlled environment, it can not be predicted how long it will take for atomic decay - only the probability of decay in a given time. Thus, quantum mechanics does not determine the outcome of individual experiments but only the probability. Hidden variable theory rejects the view that nature contains irreducible randomness: such a theory presupposes that in randomly generated processes, properties with certain statistical distributions work behind the scenes, determining outcomes in each case.

In biology

The synthesis of modern evolution links the diversity of life observed with random genetic mutations followed by natural selection. The latter retains some random mutations in the gene pool as it systematically increases the chance of survival and reproduction that the mutated gene gives to the individual who has it.

Some authors also claim that evolution and sometimes development require a certain form of randomness, that is the introduction of new behaviors qualitatively. Rather than the choice of one possibility among some that have been given before, this randomness corresponds to the formation of new possibilities.

The characteristics of an organism appear to some extent in a deterministic way (eg, under the influence of genes and environment) and to some extent randomly. For example, the density of spots that appear on a person's skin is controlled by genes and exposure to light; while the exact location of the individual spots appears random.

As far as behavior is concerned, randomness is important if an animal behaves in ways unpredictable to others. For example, insects in flight tend to move with random changes in direction, making it difficult to pursue predators to predict their trajectories.

In math

The mathematical theory of probability arises from attempts to formulate a mathematical description of accidental events, originally in the context of gambling, but later in relation to physics. Statistics are used to infer the probability distribution underlying the empirical observation collections. For the purposes of simulation, it is necessary to have a large inventory of random numbers or means to produce them on demand.

The study of information theory algorithms, among other topics, what constitutes a random sequence. The main idea is that string bits are random if and only if shorter than a computer program that can generate strings (Kolmogorov randomness) - this means that random strings are those that can not be compressed. The pioneers of this field include Andrey Kolmogorov and his disciples Per Martin-LÃÆ'¶f, Ray Solomonoff, and Gregory Chaitin. For the notion of infinite sequence, it usually uses the Per Martin-LÃÆ'¶f definition. That is, the infinite sequence is random if and only it holds all enumerable recursive zero sets. Other notions of random order include (but are not limited to): recursive randomness and Schnorr randomness based on computable computable martingales. It was shown by Yongge Wang that the idea of ​​randomness is generally different.

Randomness occurs in numbers such as log (2) and pi. The decimal number of pi forms an infinite sequence and "never repeats itself in cyclical mode." The numbers like pi are also considered to be normal, meaning their numbers are random in a certain statistical sense.

Pi seems to behave like this. In the first six billion decimal places pi, each number from 0 to 9 appears about six hundred million times. Yet such results, accidentally by accident, do not prove normality even in basis 10, let alone normality in other number numbers.

In statistics

In statistics, randomness is typically used to create simple random samples. This enables a truly random group survey of people to provide realistic data. Common methods of doing this include drawing names from caps or using random number graphs. Random number chart is just a large table of random numbers.

In information science

In information science, irrelevant or meaningless data is considered noise. Noise consists of a large number of transient disturbances with statistically random time distribution.

In communication theory, randomness in a signal is called "noise" and opposes that its causal variation component is caused by source, signal.

In the case of random network development, the randomness of communication rests on two simple assumptions of Paul Erd? S and Alfrà © à © d RÃÆ'  © nyi which says that there are a fixed number of nodes and this number remains to live off the network, and that all nodes are equal and connected randomly to each other.

In finance

A randomly running hypothesis assumes that the price of an organized market asset evolves randomly, in the sense that the expected value of their change is zero but the actual value may change to positive or negative. In general, asset prices are influenced by unexpected events in the general economic environment.

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In politics

Random selection can be the official method for completing elections bound in some jurisdictions. Its use in politics is very old, because the holder of office in Ancient Athens was chosen by many people, there was no vote.

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Randomness and religion

Randomness can be seen as contrary to the deterministic ideas of some religions, such as where the universe was created by an omniscient god who is aware of all past and future events. If the universe is considered to have a purpose, then randomness can be considered impossible. This is one of the reasons for the religious opposition to evolution, which states that non-random selection is applied to the result of random genetic variation.

Hindu and Buddhist philosophy states that every event is the result of previous events, as reflected in the concept of karma, and thus no random event or first event.

In some religious contexts, the procedure generally regarded as randomisation is used for divination. Cleromancy uses bone castings or dice to reveal what is seen as the will of the gods.

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Apps

In most mathematical, political, social and religious uses, randomness is used for innate "justice" and lack of bias.

Politics : Athens's democracy is based on the concept of isonomia (equality of political rights) and uses a complex designation machine to ensure that positions on the ruling committee running Athens are equitably allocated. The present designation is restricted to selecting jurors in the Anglo-Saxon legal system and in situations where "justice" is predicted by randomization, such as selecting jurors and mandatory lotteries.

Games : The random numbers were first investigated in the context of gambling, and many random devices, such as dice, playing cards, and roulette wheels, were first developed for use in gambling. The ability to generate random numbers fairly is essential for electronic gambling, and, as such, the methods used to make it are usually governed by the government's Gaming Control Agency. Random images are also used to determine the lottery winner. Throughout history, randomness has been used for chance games and to select individuals for unwanted tasks in a fair manner (see the picture of straws).

Sports : Some sports, including American football, use a coin toss at random the initial conditions for a game or a superior team to play postseason. The National Basketball Association uses weighted lotteries to order teams in its design.

Maths : Random numbers are also used where their use is mathematically important, such as sampling for polls and for sampling statistics in a quality control system. Computing solutions for some types of problems use random numbers extensively, as in the Monte Carlo method and in genetic algorithms.

Treatment : Random allocations of clinical interventions are used to reduce bias in controlled trials (eg, randomized controlled trials).

Religion : Although not intended to be random, various forms of prediction such as cleromancy see what appears to be random events as a means for divine beings to communicate their will. (See also free will and Determinism).

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Generation

It is generally accepted that there are three mechanisms responsible for random behavior (apparently) in the system:

1. Randomness coming from the environment (for example, Brownian motion, but also a random number generator set)
2. Randomness originating from initial conditions. This aspect is studied by chaos theory and observed in systems whose behavior is very sensitive to small variations in initial conditions (such as pachinko and dice machines).
3. Randomness is intrinsically generated by the system. This is also called pseudorandomness and the type used in the pseudo-random number generator. There are many algorithms (based on arithmetic or cell automaton) to generate pseudorandom numbers. The behavior of the system can be determined by knowing the state of the seed and the algorithm used. This method is often faster than getting "true" randomness from the environment.

Many random applications have caused many different methods to generate random data. These methods can vary as to how predictable or random it is statistically, and how quickly they can generate random numbers.

Before the emergence of random number generator calculations, generating a large number of sufficient random numbers (important in statistics) requires a lot of work. Results are sometimes collected and distributed as random number tables.

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Size and test

There are many practical measures of randomness for binary sequences. These include measurements based on frequency, discrete transformation, and complexity, or this mixture. These include tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Epoch.

Quantum Non-Locality has been used to authenticate the presence of original randomness in a certain set of numbers.

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Misconceptions and logic errors

Popular perceptions of randomness are often mistaken, based on faulty reasoning or intuition.

Number is "due"

This argument is, "In the selection of random numbers, since all numbers finally appear, those who have not appeared are 'because', and thus more likely to appear immediately." This logic is only true if applied to the system where the emerging numbers are removed from the system, such as when the playing cards are pulled and not returned to the deck. In this case, once the jack is removed from the deck, the next draw is likely to be a jack and more likely for some other cards. However, if the jack is returned to the deck, and the deck is completely direshuffle, the jack may be pulled like any other card. The same is true in other processes where objects are independently selected, and nothing is deleted after every event, such as roll dice, coin toss, or lottery lottery scheme. A completely random process like this does not have memory, making it impossible for past results to affect future results.

A number is "damned" or "blessed"

In the order of random numbers, a number can be said to be condemned because the number is less frequent in the past, and therefore it is expected that it will rarely occur in the future. A number can be considered blessed because it has happened more often than others in the past, and therefore is expected to appear more often in the future. This logic only applies if the randomness is biased, for example with a loaded die. If the dice is fair, then the previous scrolls do not give an indication of future events.

In nature, events rarely occur with equally perfect frequencies, so observe the results to determine which events are more likely to make sense. It is a mistake to apply this logic to systems designed to make all the results with the same possibilities, such as shuffled cards, dice, and roulette wheels.

Opportunities are never dynamic

At the beginning of the scenario, one might calculate the probability of a particular event. The fact is, as soon as people get more information about the situation, they may need to recalculate the probability.

Let's say we are told that a woman has two children. If we ask whether one of them is a woman, and is told yes, what is the probability that the other child is also a woman? Considering this new child independently, one might expect the possibility that another child is a female is ½ (50%). But by building a probability chamber (illustrating all possible outcomes), we see that the real probability is only 1/3 (33%). This is because space is likely to illustrate the four ways of having these two children: boys, girls, boys, girls and girls. But we were given more information. Once we were told that one of them was female, we used this new information to eliminate the boys scenario. Thus the space of probability reveals that there are still 3 ways to have two children where one is female: boy, girl, girl. Only 1/3 of these scenarios make other children too women. By using the probability space, we tend not to miss any possible scenarios, or ignore the importance of new information. For more information, see Paradox boy or girl.

This technique provides insight into other situations such as Monty Hall issues, game scenarios where cars are hidden behind one of three doors, and two goats hidden as a booby gift behind the other. After the contestant chooses a door, the host opens one of the remaining doors to reveal a goat, removing the door as an option. With only two doors remaining (one with the car, the other with the other goats), the player must decide to keep making decisions, or change and choose another door. Intuitively, one might think the player chooses between two doors with the same probability, and the opportunity to choose another door makes no difference. But the probability space reveals that contestants have received new information, and can increase their chances of winning by turning to another door.

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See also

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References

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Further reading

• Randomness by Deborah J. Bennett. Harvard University Press, 1998. ISBNÃ, 0-674-10745-4.
• Random Action, 4th ed. by Olav Kallenberg. Academic Press, New York, London; Akademie-Verlag, Berlin, 1986. MR0854102.
• Computer Programming Arts. Vol. 2: Seminumeric Algorithm, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997. ISBNÃ, 0-201-89684-2.
• Fooled by Randomness, second edition. by Nassim Nicholas Taleb. Thomson Texere, 2004. ISBNÃ, 1-58799-190-X.
• Exploring Randomness by Gregory Chaitin. Springer-Verlag London, 2001. ISBNÃ, 1-85233-417-7.
• Random by Kenneth Chan includes "Random Scale" to assess the degree of randomness.
• The Drunkard's Walk: How Randomness Regulates Our Lives by Leonard Mlodinow. Pantheon Books, New York, 2008. ISBNÃ, 978-0-375-42404-5.

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External links

• QuantumLab Quantum random number generator with single photon as an interactive experiment.
• HotBits generate random numbers from radioactive decay.
• Quantum Random Quantity QRBG Generator
• Quick Quantum QRNG Quick Quiz Gasoline
• Chaitin: Randomness and Mathematical Proof
• Pseudorandom Number Sequence Testing Program (Public Domain)
• Historical Dictionary : Opportunity
• RAHM Nation Institute
• Counting Overview Paralysis
• Chance versus Randomness, from Stanford Encyclopedia of Philosophy

Source of the article : Wikipedia