随机
维库，知识与思想的自由文库
一个随机的过程是一个不定因子不断产生的重复过程，但它遵循一个概率分布(en:probability distribution)。 术语随机经常用于统计学中，表示一些定义清晰的、彻底的统计学属性，例如偏差(en:bias)或者交互作用(en:correlation)的缺失。随机与任意不同，因为“一个变量是随机的”表示这个变量遵循概率分布。而任意在另一方面又暗示了变量没有遵循可限定概率分布。
[编辑] HistoryHumankind has been concerned with random physical processes since prehistoric times. Examples are divination (cleromancy, reading messages in random patterns) and gambling. Despite the prevalence of gambling in all times and cultures, for a long time there was little western 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. [编辑] 科學與隨機許多科學領域與隨機有關： [编辑] 物理科學在19世紀，科學家使用分子的不規則行動的概念去發展統計力學，以解釋熱力學和氣體定律的現象。 根據一些量子力學的標準解釋，微觀現象是客觀地隨意。換句話說，在一個所有相關的參量受控的實驗中，也會出現任意變化的情況，例如我們無法預計在受控環境中放置一粒不穩定的原子衰敗的時間，只能計算在指定的時間內衰敗的可能性，所以量子力學計算的是機會率而非單一實驗的結果。Hidden variable theories嘗試避開大自然包含不能降低的隨機性，這樣的理論假定在看上去任意的過程中，有些符合統計分佈而暗藏的特性在幕後運作以得出結果。 [编辑] 生物學進化論將觀察到的多樣性歸因於隨幾突變。由於一些突變的基因帶給了擁有它們的個體更高的存活與繁衍的機會，隨機突變保留在了基因庫中。 生物體的特徵在某种程度上是確定性地發生的（例如：在基因和環境的影響下），在某种程度上是隨機發生的。例如，基因與曝光量僅僅支配著人體皮膚上出現的色斑密度；而單個色斑的精確位置看來是隨機決定的。 [编辑] 數學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 (Chaitin-Kolmogorov randomness) - this basically means that random strings are those that cannot be compressed. Pioneers of this field include Andrey Kolmogorov, Ray Solomonoff, Gregory Chaitin, Anders Martin-Löf, and others. [编辑] 通訊理論在通訊理論中，一個信號的隨機性稱作噪聲，它對立於由源（信號）所引起的那一部分變化。 [编辑] In financeThe random walk hypothesis considers that asset prices in an organized market evolve at random. [编辑] Randomness versus unpredictabilityRandomness 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 which who has the cryptographic key needed to turn the sequence of bits into a readable message. The message is not random, but is for one of the observers unpredictable. 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. Under the cosmological hypothesis of determinism there is no randomness in the universe, only unpredictability. Some mathematically defined sequences exhibit some of the same characteristics as random sequences, but because they are generated by a describable mechanism they are called pseudo-random. To an observer who does not know the mechanism, the pseudo-random 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. It is important to remember that phenomena that are random in some respects may be precisely characterizable in other respects. Quantum mechanics allows a very precise calculation of the half-lives of atoms even though the process of atomic decay is a random one. Ohm's law and the kinetic theory of gases are precise characterizations of macroscopic phenomena which are random on the microscopic level. Random is not truly random in the sense of the word. For a random outcome to occur there must be at least one variable which changes each time the event is repeated or else the same outcome will always occur. However variables influence the outcome of an event and the more variables there are the more contorted the end result will be. Random is applied to a situation where the end result cannont accurately be guessed because of the number of influencing variables. [编辑] Randomness and religionSome theologians have attempted to resolve the apparent contradiction between an omniscient deity, or a first cause, and free will using randomness. Discordianists have a strong belief in randomness and unpredictability. [编辑] Applications and use of randomnessRandom 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. Random numbers are also used for non-gambling purposes, both where their use is mathematically important, such as sampling for opinion polls, and in situations where "fairness" is approximated by randomization, such as selecting jurors and military draft lotteries. Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms. [编辑] Generating randomnessIn his book A New Kind of Science, Stephen Wolfram describes three mechanisms responsible for (apparently) random behavior in systems :
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 amount of sufficiently random numbers (important in statistics) required a lot of work. Results would sometimes be collected and distributed as random number tables. One of the most well known advocates of randomness is Kenneth Chan, the author of the highly referenced book simply titled Random, which explores the many concepts associated with the term itself and includes the Random Scale, for grading the level of randomness and which was awarded the coveted "Adam Milligan Award for Excellence" at the 2006 International Psychology Conference in Miami. [编辑] Links related to generating randomness
[编辑] Misconceptions/logical fallaciesPopular perceptions of randomness are frequently wrong, based on logical fallacies. Following is an attempt to identify the source of such fallacies and correct the logical errors. For a more detailed discussion, see Gambler's fallacy. [编辑] A number is "due"This argument says that "since all numbers will eventually come up 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's 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. [编辑] 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. [编辑] Books
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