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randomness.md

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 Randomness means unpredictability, lack of patterns, and/or behavior without cause. Random events can only be predicted imperfectly using [probability](probability.md) because there is something present that's subject to chance, something we don't know; events may be random to us either because they are inherently random (i.e. they really have no cause, pattern etc.) or because we just lack knowledge or practical ability to perfectly predict the events. Randomness is one of the most basic, yet also one of the most difficult concepts to understand about our [Universe](universe.md) -- it's a phenomenon of uttermost practical importance, we encounter it every second of our daily lives, but it's also of no lesser interest to science, philosophy, art and religion. Whole libraries could be filled just with books about this topic, here we will be able to only scratch the surface of it by taking a look at the very basics of randomness, mostly as related to [programming](programming.md) and [math](math.md).
 
-As with similarly wide spanning terms the word *randomness* and *random* may be defined in different ways and change meaning slightly depending on context, for example sometimes we have to distinguish between "true" randomness, such as that we encounter in [quantum mechanics](quantum.md) or that present in nondeterministic mathematical models, and [pseudorandomness](pseudorandomness.md) (what as a programmer you'll be probably dealing with), i.e. imitating this true randomness with [deterministic](determinism.md) ("non-randomly behaving") systems, e.g. sequences of numbers that are difficult to [compress](compression.md). Other times we call random anything at all that just deviates from usual order, as in "someone started randomly spamming me in chat". Let's briefly review a few terms related to this topic:
+As with similarly wide spanning terms the word *randomness* and *random* may be defined in different ways and change meaning slightly depending on context, for example sometimes we have to distinguish between "true" randomness, such as that we encounter in [quantum mechanics](quantum.md) or that present in nondeterministic mathematical models, and [pseudorandomness](pseudorandomness.md) (what as a programmer you'll be probably dealing with), i.e. imitating this true randomness with [deterministic](determinism.md) ("non-randomly behaving") systems, e.g. sequences of numbers that are difficult to [compress](compression.md). Other times we call random anything at all that just deviates from usual order, as in "someone started randomly spamming me in chat". Sometimes there are slight nuances in the meaning, for example by the word "random" we can mean "generated by a randomly behaving process", but also for example "data having statistical properties the same as if they were generated by a random process". Sometimes the distinctions don't matter too much, sometimes they do. Let's briefly review a few terms related to this topic:
 
 - **randomness**: The wide term meaning great unpredictability, which may be inherent or just apparent. We usually divide it to:
   - **true randomness**: Randomness that is caused by inherently unpredictable behavior of a system, i.e. behavior that truly has no cause and is decided purely by chance, without ever being able to be perfectly predicted, even just theoretically; this is contrasted with pseudorandomness. A typical example given is [quantum physics](quantum.md) in which true randomness seems to be present in things such as some properties of elementary particles of the Universe -- though in fact this can never be proven with certainty, there is so much evidence of us not being able to predict quantum phenomena that we just mostly take it for the closest thing to true randomness in real world. However we can also see some purely mathematical models to have true randomness, simply because they define it so, e.g. a nondeterministic [Turing machine](turing_machine.md) is simply defined to sometimes make purely random decisions.