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When we say that something is random, it simply implies that the occurrence under observation does not have any cause or at least that cause cannot be determined beforehand in layman's language. For a scientific mind, every occurrence has to have a cause and must follow some algorithm in order to happen (please correct me here if I am wrong). I wonder could any occurrence in nature be random in the first place? Could any observation may occur without any cause?

In the case of Atmospheric Noise, we do not know what causes it precisely or simply what frequency of atmospheric noise occurs due to what cause or reason is unknown(please update me here if I am wrong). And even then if the cause is "unknown", what really makes statisticians to claim that frequencies of atmospheric noise are purely random?

Here is the official link of the website that uses the service of atmospheric noise for generating random numbers: Random.org

Please explain and justify. Thank you

Muhammad Maqsoodur Rehman
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    Who exactly does claim that this is the **only** source of randomness?! How do *you* define "*purely* random"? [Random.org](https://www.random.org/randomness/) itself says that there are "endless" sources of randomness that can be used... – Tim Aug 06 '18 at 07:57
  • @Tim I know that for a fact that atmospheric noise is not only source for generating random numbers. The popularity of the website random.org (researchers claim that the site generates pure random numbers using atmospheric noise) in the classrooms just made me to put my question that way. And again what is "purely random" is a question that researchers are still trying to answer. Computer programs nowadays generate pseudo-random numbers. – Muhammad Maqsoodur Rehman Aug 06 '18 at 08:04
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    So what is your question, as you seem to already know the answer to it? – Tim Aug 06 '18 at 08:05
  • @Tim Here is an interesting video on generating random numbers: https://www.youtube.com/watch?v=SxP30euw3-0 – Muhammad Maqsoodur Rehman Aug 06 '18 at 08:05
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    I am not asking about interesting videos, but asking you to clarify what is your question, since you seem to know the answer? – Tim Aug 06 '18 at 08:07
  • @Tim I just cannot convince myself that anything in nature could be random. Please bear with me as I am not a statistician but a novice student of Mathematics, Statistics and Computer Science. My knowledge is quite limited. – Muhammad Maqsoodur Rehman Aug 06 '18 at 09:31
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    As the documentation on Random.org says, the site does not claim that the results are "purely random". They are chaotic and highly unpredictable, i.e. what we mean by "random" (see answer below). The philosophical discussion on if there is anything in the nature that is "purely random" is out of scope of this site. – Tim Aug 06 '18 at 09:34
  • This question reads like it belongs on a philosophy or physics site rather than here. – whuber Aug 06 '18 at 12:33
  • Quantum random number generators. See the intro here https://www.nature.com/articles/s41598-019-56706-2 – Daddy Kropotkin May 21 '21 at 19:10

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Quoting the RANDOM.ORG site itself:

. . . Another suitable [for generating random numbers] physical phenomenon is atmospheric noise, which is quite easy to pick up with a normal radio . . . As long as you are careful, the possibilities are endless . . .

. . . You could argue that the atmospheric noise used as a source for the RANDOM.ORG numbers can be viewed as a chaotic but deterministic system. Hence, if you knew enough about the processes that cause atmospheric noise (e.g., thunderstorms) you could potentially predict the numbers generated by RANDOM.ORG.

However, to do this, you would probably need knowledge of the position and velocity of every single molecule in the planet's weather systems. This is of course infeasible, and the inaccuracy of weather forecasts is a good example of how difficult it is to give even a rough estimate of the behaviour of weather systems. For this reason, it is impractical to predict random numbers from RANDOM.ORG, even for a determinist.

Tim
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Perhaps, there's no such thing as pure randomness. So, any pure randomness might be just our lack of information about the system. So, our best shot in search for pure randomness is to look for complex enough systems whose randomness is very difficult or impractical (as Tim said) to predict.

If we take, for example, the probability of electron appearing in certain position, it will depend on previous data.

DmytroSytro
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