# What is Randomness: Definition and 133 Discussions

In common parlance, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.
The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.
Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, particularly in the field of computational science. By analogy, quasi-Monte Carlo methods use quasi-random number generators.
Random selection, when narrowly associated with a simple random sample, is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, say research subjects, has the same probability of being chosen, then we can say the selection process is random.According to Ramsey theory, pure randomness is impossible, especially for large structures. Mathematician Theodore Motzkin suggested that "while disorder is more probable in general, complete disorder is impossible". Misunderstanding this can lead to numerous conspiracy theories. Cristian S. Calude stated that "given the impossibility of true randomness, the effort is directed towards studying degrees of randomness". It can be proven that there is infinite hierarchy (in terms of quality or strength) of forms of randomness.

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1. ### I Rough approximation of the number of different games for the card game "Commander"

I play magic the gathering in a format called commander. Each player start with a deck of card that has 99 cards in it, for simplicities sake, I'll give very simple rules. Each card is different, we have 4 players, each shuffling their deck of cards and drawing 7. Roll for who goes first...
2. ### A Concrete examples of randomness in math vs. probability theory

A recent question about interpretations of probability nicely clarified the role of the Kolmogorov axioms: [... some excursions into QM, negative probabilities, and quasiprobability distributions ...] Conclusion: the Kolmogorov axioms formalize the concept of probability. They achieve this by...
3. ### B QM randomness vs chaotic determinism?

Can you swap out the RNG that is the wave function collapse with a suitable deterministic chaotic process that matches the wave function (squared)? I can picture a multi leg pendulum swinging around drawing out the wave function. The point where you measure is the point the pendulum was at. Is...
4. ### I Does chaos amplify inherent quantum level randomness?

Does chaos amplify inherent quantum level randomness/uncertainty to macroscopic level?
5. ### I New papers on randomness and QM, need insight please

Hi,new college guy here,previewing next year's work. Been seeing these articles,written by reputed physicists. 1. https://www.mdpi.com/1099-4300/23/5/519 this one claims that quantum randomness is false.does this argument be strong enough to rule out QM's so-called randomness?I understand that...
6. ### B Is an experiment planned to discern determinism and randomness in QM

I can remember reading something about a future experiment which alledgely could decide if there is an underlying deterministic layer governing quantum phenomena or if pure, empty chance rules suppreme (which I can't imagine). It had something to do with arrival times but I can't imagine how...
7. ### Exploring the Illusion of Randomness: The Truth Behind Algorithms and Chaos

I've been learning a lot about algorithms in my AI class, senior year of my computer science degree. Some of the algorithms we talk about involve randomness. Does true randomness even exist in reality? Wouldn't everything random, have an explanation by some physical process? Is chaos random...
8. ### I Models and theories of laws of physics emerging from chaos?

Some physicists (like John A Wheeler, Holger B Nielsen or Ilya Prigogine) have proposed that all the laws of physics (including the most fundamental ones) emerged from a primordial chaos (for example, in the case of Wheeler, he proposed that laws of physics emerged from an initial random and...
9. ### B Randomness in electron position

So from what I understand the position of an electron at any given time is based on a probability model. My question is how does gravity play a role in this model? Can we say the position of the electron is truly random? What if this "randomness" is caused gravitational forces pulling it in...
10. ### I Exploring Randomness and Chaos in Classical & Quantum Physics

Note: This question involves both classical and quantum physics, so I didn't know where to put it. I'll start with the coin flip: People often compare electron spins to a coin flip, citing that coin flips are random. I am wondering if that is a true analogy, or just another faulty analogy...
11. ### Is randomness real or the inability to perceive hyper complex order?

How did you find PF?: random Brownian motion Is randomness real or is it simply defined as such due to our inability to perceive hyper complex order? Randomness is a troublesome word. I'd feel better if I knew it was an objective phenomenon and not merely a placeholder description of...
12. ### I What does it mean to influence a quantum measurement's outcome?

This just occurred to me and I don't expect to be the first one to address it: It is said that in a specific measurement basis, the outcome of a measurement in this basis is determined by chance. But in how far is this the case, since if the eigenvectors are for example ##\overrightarrow{A}##...
13. ### A Understanding Kolmogorov-Smirnov Test Results for Random Number Generators

Hi all, I have some doubts regarding the Kolmogorov test: I made a simple c++ program generating two samples of random numbers following a Landau distribution (I used the "hit and miss" method). I made the Kolmogorov test, in order to check the randomness of the generator, but I'm having some...
14. ### I The Mystery of Atomic Decay: Is it Truly Random or is There More at Play?

Moderator's note: This is spin-off from https://www.physicsforums.com/threads/why-randomness-means-incomplete-understanding.975227 Reading this thread I would like to point out one aspect that makes me wonder personally and has also been mentioned here by other users. The decay of atoms...
15. ### I Why randomness means incomplete understanding

Summary: We lack a fundamental understanding of the measurement process in quantum mechanics. Actually ever programming language has such a function, and it is executed to everyone's satisfaction. Suppose we want to create a device that faithfully simulates some aspect of Nature. To do so...
16. ### Exploring Chaos & Randomness in Deterministic Dynamics

For myself is horrible to imagine that indeterministic randomness can appear in deterministic, absolutely known and visible dynamics. I have briefly look on the mathematics behind it and understand almost nothing... Well I have a very basic knowledge in mathematics. There is so-called "Rannou's...
17. ### Is the 'Randomness' of Evolution Really Random?

(In order to ask my question, I need to explain a little bit. But I don't have a background in biology, so I may make some mistakes along the way. corrections are welcome.) Recently I've been thinking a lot about evolution. Its really fascinating. The random exploration of the life "phase...
18. ### A Uncertainty vs Randomness in Quantum Physics

In Quanta Magazine there is article on this link...
19. ### I Random Unit Vector Angle Difference

I am simulating random angles from 0 to 2π with a uniform distribution. However, if I take the differences between random angles, I get a non-uniform (monotonically decreasing) distribution of angles. In math speek: Ai = uniform(0,2π) dA = Ai - Aj dA is not uniform. Here is a rough image of...
20. ### B Thought experiment -- A radioactive decay detector and randomness

Take one radioactive element and put a detector all around it so that you can immediately detect whenever it will undergo radioactive decay. Have a clock connected to the detector to note the "exact" instant at which the atom decays. Let's say that after 3min after the clock started counting the...
21. ### I Would this experiment prove or disprove quantum randomness?

I was told of a thought experiment by a friend of mine who says that his thought experiment will either prove or disprove randomness in quantum mechanics, and this was in fact verified by several other physicists, who said that if this experiment was ever successfully carried out it would either...
22. ### B Is Radioactive Decay Truly Random?

How can radioactive decay be random if we can calculate aproximately when it will happen . For example we know that an isotope will decay every 2 years by calculating the half life . Doesnt that mean that the decay is systematic rather than random because we can calculate when its guna happen ...
23. A

### B Is Randomness in Quantum Mechanics Truly Non-Deterministic?

Consider this a layman's question. I am not an expert on deeper aspects of probability. I simply rely on Kolmogorov's axioms and the calculation methods I learned as a student. To me it's just a bit of mathematics and it makes perfect sense as mathematics. When it comes to actually...
24. ### I Can something be caused and be ontologically random?

Or does ontological probability exist? I was reading an article that came up in my google searches ( https://breakingthefreewillillusion.com/ontic-probability-doesnt-exist/ ) ignore the free will philosophy stuff. But the author makes the claim that ontological probability simply does not...
25. ### I Deterministic chaos and randomness

The term "deterministic chaos" emphasizes that chaotic behavior is random in-practice but deterministic in-principle. But does this even make sense in a finite universe where computation is physical? There ain't no such thing as a Turing machine with an infinite tape. If computing the behavior...
26. ### Randomness of quantum mechanics and Pi

Just a thought I had one day, but the general idea I've heard is that quantum mechanics has a random property to it. The number Pi is apparently a number without any sort of apparent pattern to it either, seemingly random? Could these two things somehow be related? For example somehow...
27. ### B Why do scientists claim that there's true randomness?

When we look at the cars on the road, it appears like where they are driving is random, their directions appear as random. But the drivers don't drive into random directions. It appears random to us because we don't know the thoughts and intentions of the drivers. If we knew almost everything...
28. ### I Projection Postulate vs Quantum Randomness

The Wikipedia article Quantum Indeterminacy discusses the measurement problem and possible reasons why measurement values are inherently random. In the section labeled "Measurement", the Projection Postulate is briefly discussed. After explaining the Projection Postulate, in the second...
29. ### B Is there a definition of randomness?

Is there a definition of "random(ness)"? Is it defined?
30. ### I Photosynthesis and quantum randomness

Some studies suggest that during photosynthesis, electrons travel all possible paths simultaneously, and then always collapse at the reaction center. My question is, doesn't that contradict quantum randomness? Shouldn't the location of the electron after the collapse be predictably random?
31. ### Higher Dimension and Randomness

I often here claims that higher dimensions such as the 5th and 6th dimensions deal with different possible realities, be it branching off or from different start conditions. I find this confusing and would like to have it cleared up how it is possible for different so called realities to occur...
32. ### A Exploring Randomness vs Chaos: Decoding the Nature of the Universe

The universe is random or chaotic?
33. ### B Examples of quantum randomness?

hope I am not totally lost here but can someone give specific examples of randomness re quantum mechanics. in my view any well constructed identical experiments that are repeated 1000 times yield the same well defined very sharp distribution of results within the precision of the experimental...
34. ### B Does quantum physics imply the existence of randomness?

So, I am not an expert in quantum physic, I just watched a lot of videos about it. If I understand correctly, particles do not have a particular position as long as you don't observe them. With a certain equation, we can draw a cloud of probabilities which describes how likely the particle is...
35. ### A Does true randomness exist in nature?

Does randomness exist in nature? We say every event must abide by the laws of nature, including QM probability/uncertainty. QM says outcomes are uncertain. Does uncertainty imply both randomness and probability? It seems that randomness is superfluous to the uncertainty principle, and it makes...
36. ### B Entanglement, correlation and randomness

I was wondering. In this example I use polarized photons, but maybe it is applicable to electrons and spin also. We can prepare two completely unentangled polarized photons, and send them in opposite directions to two detectors preceded by a filter at particular angles. Both of them will show a...
37. ### I Randomness as a function of the observer's knowledge

I found a couple of closed threads related to the definition of randomness, but my question is slightly different. Is there a mathematical way to express the fact that randomness is the eye of the beholder? For example, if I give a sequence of 1000 numbers such that you cannot predict the...
38. ### B Begining of time, cause and effect and quantum randomness

Hi Everyone. This thread relates to the ongoing debate as to whether or not time has a beginning and other related debates. As I see it, a beginning of time would imply the past existence of a very first cause which was not the effect of a previous cause. Who agrees and who disagrees with this...
39. ### I Parallel universes and randomness

As you might know there is no such thing as true randomness, which means everything happens for a reason. Let's say everything with the exactly same input will always return the exactly same output if you repeat it, no matter if there is a computer or a human being. Much might seem random, but...
40. ### Are photons passing a polarization filter randomly?

This may be a dumb question, but maybe someone can help me out: Consider a pair of entangled photons A and B, fired at respectively Alice and Bob who both let it go through a polarisation filter at different angles. Now Alice establishes that half of the photons get through her filter, and half...
41. ### Absolute compression = true randomness?

So I've read from various places that maximal compression produces a truly random output. But suppose you were going to apply compression to a truly random series of numbers with something like LZW. Well wouldn't it be the case that since randomness often produces sequences which do not appear...
42. ### Elementary particles and randomness

From the elementary particles that science has been able to identify until now, are there any that appear to be useless, at least as far as we know? Or do all the identified particles play a role in the grand scheme of the universe?
43. ### Can the following explain randomness in quantum events?

Hi, I was just wondering if the following can be viewed as an explanation for randomness in quantum events. My knowledge of quantum physics is not all that good. I've got a bit of philosophical bent, which is the source of my interest. Anyways... Assume that when particles interact, what...
44. ### Clarifying the Meaning of "Random" in Quantum Physics

This might be a silly question but when people say that something on the quantum level is completely "random," (except for general probability) does that mean, according to theory at least, if you were to go back in time and repeat an experiment exactly that the results could just as easily be...
45. ### Tracking states of randomness with three states

I know that matter can only exist in one state at a time; however at the quantum level knowing what state it is in at a set time is impossible to know for sure until you look at the system. Like with how Schrodinger cat is in a state of randomness between the two states of dead and alive until...
46. ### References for Randomness & Pseudorandomness

I wish to understand something about randomness and Pseudorandomness. In particular, given a set of "seemingly-random" numbers, what can one do to analyse as to whether they are randomly generated numbers or just a pseudorandom sequence. Can somebody point me to Good, pedagogical Referances in...
47. ### Randomness in time reversal case

I have dice whit starting temperature of 0 K in vacuum and its displaying number 1 ,after drop it displays number 6 (for example) . Now if we reverse time, will dice sitting still on surface return to original position (displaying number one ) or it will display different random number ?
48. ### How to tell the difference between randomness and chaos?

Found this question while think of determine&random. If a system if very complex, it may looks like random. Even GUT is found, it is still impossible to tell what a determined system will be after a long period because of Heisenberg's uncertainty principle. An error in initial conditions, even...
49. ### Randomness of radioactive decay

Hi everyone! I have two questions about radioactive decay that some of you might be able to answer (I'm a mathematician and no physicist by the way). The first one is very general: As I understand it the time at which a single instable atom decays is believed to be a truly random process. But...
50. ### Testing Randomness in a Set of 200+ Data Points

Hi everyone. It's been years since I've done any stats, so I need a bit of help, please. I want to include it in a blog post I'm going to do (not here on PF), so I don't want to give away too many details :p I apologise for my terrible understanding of stats, please be patient! Anyway, over...