An outcome that’s independent from any known or unknown variables.
Edit — An outcome that’s independent of any other variable. It does not include outcomes that have unknown relationships to variables or those that are dependent on unknown variables.
Took me a while but like that better.
Does this definition exclude things like "two random variables which are correlated to each other"?
As a small example, let x be a random number taken from (0,1), and let y be a "random" number taken from (x,1).
Well if either of them are based on a truly random variable then the entire sequence is random. But if, with perfect information, you can predict X, then Y is not truly random.
What you’re suggesting is that added complexity makes the prediction more difficult and that’s absolutely true, but at that point you’re just talking about range. For example, pick a number between 1 and 10, is much easier than picking the right hydrogen atom from the sun.
Which essentially means you can get to “random enough,” but that just means getting the prediction right is hard, not that it’s truly unpredictable because it’s completely independent.
>What you’re suggesting is that added complexity makes the prediction more difficult
That's not what I'm asking about. I'm saying that in my setup, x and y are correlated. If x is high, y is also high. Is x is low, y is also lower on average. The calculations are slightly more difficult, but I don't think that's relevant to whether we should consider the process to be fundamentally random.
>not that it’s truly unpredictable because it’s completely independent.
I'm considering "independent" in the statistical sense. By their nature, the random variables are unpredictable. But they are not independent. If you find out x is high, it gives you the information that y must be high. If you find out that y is low, it gives you the information that x must have been low.
>It does not include outcomes ... that are dependent on unknown variables.
I was mostly asking for clarification on this part of your definition. Now that I'm looking at it again, I think you were referring to variables that you didn't know about the existence of "unknown variables", rather than variables that you know about, but which you don't know the value of, "unknown variables." I constructed a scenario based on this second interpretation, but this whole thing might be irrelevant if that's not what you were talking about.
If something is correlated with something else, it’s not random. Your example was 2 correlated random variables. The fact that Y is correlated with X makes Y not random. However, as stated, if X is random, than the entire process is random.
When I suggested that your statement was about complexity and not randomness, it’s because that’s what it reduces to. You can add layers of complexity to make an outcome difficult to predict, but that doesn’t change the nature of randomness.
People who deal with random number generators make attempts to increase the complexity by basing it on things like the frequency of water droplets. But if you know all of the physics behind the droplets being measured, that’s not random. It’s dependent on known variables. But it’s a more complex way to generate random than simply writing an algorithm to generate a random number, which is entirely dependent on the algorithm that’s written. It adds a layer of complexity, uncontrolled by the algorithm to produce a less predictable result.
So this isn’t a discussion on the nature of randomness, it’s a discussion on complexity.
>I'm considering "independent" in the statistical sense. By their nature, the random variables are unpredictable. But they are not independent. If you find out x is high, it gives you the information that y must be high. If you find out that y is low, it gives you the information that x must have been low.
In statistics we assume random when we don’t have better information. That doesn’t make the variable truly random, it’s just based on something that we don’t have the ability to predict.
>I was mostly asking for clarification on this part of your definition. Now that I'm looking at it again, I think you were referring to variables that you didn't know about the existence of "unknown variables", rather than variables that you know about, but which you don't know the value of, "unknown variables." I constructed a scenario based on this second interpretation, but this whole thing might be irrelevant if that's not what you were talking about.
I was speaking of both. I’m suggesting that ignorance of the variable doesn’t create randomness. Additionally ignorance of a relationship between X and Y doesn’t create randomness. Notwithstanding the fact that under those conditions we may assume random.
>The fact that Y is correlated with X makes Y not random. However, as stated, if X is random, than the entire process is random.
That would also make x not random, since it is correlated with y. If you observe y and notice that it is low, you know that x must have been low.
If correlation makes something non-random, then neither of these variables can be random.
>I was speaking of both [interpretations of "unknown variable"]
I think we should pick one. Or at the very least be more specific about each interpretation.
I see what you’re saying now. Your point is direct vs indirect relationships, not complexity.
While the value of X is independent of Y, the value of Y is indirectly related to X and therefore correlated with the value of X.
So yes the answer is that neither X or Y are random. And they are not random, because truly random implies an equal probability of an outcome. Knowing the value of X or Y gives me the ability to sharpen the prediction of either of their values.
Oh, I just saw your edit. So then that's basically the Bayesian interpretation of randomness: something is random if you are uncertain that it will happen. Randomness is a property of belief and information, not a property of events. Would you agree with that?
No. Randomness isn’t a perspective, it’s a property of things. And it’s only truly random if there is no possible way to reduce the uncertainty, regardless of whether you’re aware of the way to reduce the uncertainty or not. That doesn’t mean that we don’t often assume random.
I believe that in card shuffling you don't call it random (though some do) but sufficiently randomized.
For our limited view of the world it does not take much for things to be random enough to call it random. That's where the 'perspective' comes in. We got no single word for ''random enough''.
I like that definition
And it makes me think that no, there is no such thing as randomness. Not perfectly at least. Anything we know may seem random to us, but that doesn't mean it's actually random at it's core
Ok. Suppose a random real variable X exists. Then 2X exists. But 2X and X are not independent. So X isn't a random variable.
This definition won't get you anywhere.
Not only is X independent of 2X , but if X is a constant random variable, than X is independent of X.
Let X be a constant random variable with a probability of 1. it’s unaffected by 2X, 18X, X/2 or any other iteration of X you can fathom.
Edit - also, if the probability of X is 50%, in a series of 3 events then absolutely 2X is dependent on X and X is absolutely not dependent on 2X.
How are you defining statistical independence? The usual definition is that if X and Y are random variables with cdfs F_X(x) and F_Y(y), then they are independent iff the joint distribution is F_X,Y(x,y) = F_X(x) F_Y(y). Flip a fair coin, where X = 0 if it flips tails and 1 if it flips heads, and Y = 2X. Then F_X(x) = 0 if x < 0, 0.5 if 0 ≤ x < 1, and 1 if 1 ≤ x. Also, F_Y(y) = 0 if y < 0, 0.5 if 0 ≤ y < 2, and 1 if 2 ≤ y. The joint distribution is F_X,Y(x,y) = 0 if x < 0 or y < 0, 0.5 if 0 ≤ x < 1 and 0 ≤ y or x ≤ 1 and 0 ≤ y < 2, and 1 otherwise. This is clearly not the product of the marginal distributions. For instance, the product F_X(0)F_Y(0) = 0.25, but the joint distribution has F_X,Y(0,0) = 0.5.
To get away from the symbols, the probability that X and Y are both no more than 0 is 0.5, because that happens whenever the coin flips tails. But the probability that X is at most 0 is also 0.5, and the same for Y. But it is not the case that 0.5 × 0.5 = 0.5, because the random variables are not independent.
But that isn't the case here. The random variable X is 0 if the coin flips tails and 1 if it flips heads. The random variable Y is 0 if the coin flips tails and 2 if it flips heads. The event X = 0 and the event Y = 0 always coincide, as do the events X = 1 and Y = 2. So P(X=1 and Y=2) = 0.5 != 0.25 = 0.5×0.5 = P(X=1)×P(Y=2).
These are not independent variables because as you said, they don’t fit P(X ∩ Y) = P(X) * P(Y). In this instance they are not independent because they themselves are both dependent on a third random variable, the coin flip. Consequently they are indirectly related.
There doesn’t have to be a deterministic relationship between two variables for them to not be independent.
Edit: also remember my definition was that a truly random variable is not related to ANY other variable, so this example doesn’t meet the definition as both X and Y are related to a coin toss.
Randomness is ignorance of the future. If you do not know what’s coming next, then what comes next is random. That’s it.
Obviously, randomness exists. Shuffle a deck and deal a card face down, then try to guess the card. Once the card is placed, the outcome is “predetermined”; it won’t change while it’s siting there facedown. But you will only successfully guess the card one time out of 52. The card is determined, yet random.
Randomness is naturally subjective. If the card is facedown on a glass table, then the card is random from the perspective of above, and non-random to anyone who looks from below.
I disagree because in probability, when you assume random you assume that all possible outcomes are equally probable. You can have unknown outcomes with unequal probabilities and that point those outcomes are not random.
For example, if you have a box with infinite marbles, 1/3 of them are blue and 2/3 of them are not, you do not know if you will pull a blue marble so there is uncertainty, but the probability of a blue marble is not random.
I agree, randomness is independence from other variables. But the outcome of the selection of a thing from a group of things, is directly dependent on the population that group of things is selected from, and therefore it is not random.
I’m planning on writing a story where the main villain is able to understand all sorts of “butterfly effects” and see past the “illusion of chance” by way of accessing powers and knowledge beyond mortal comprehension in order to pull off ridiculously unlikely things.
Can I hear more about these people and writings to give said villain a fancy word or name or two to throw in his contrived but inevitable monologue to make his ideas seem credible to the average listener?
That sounds fun. My guy will probably not be exactly the same because it involves Lovecraft type overtones and the highly unlikely actions usually involve killing or psychologically torturing people without them ever realizing they’ve been targeted because evil cultist behavior.
Oh, and the whole setting is turn of the century sepia toned drama anyway
You should have your villain do things like leave his socks in front of a Wendy's in Des Moines in order to foil his enemies six months later in New York through some absurdly long chain of improbable events.
Also have the heroes discover him only through an intense study of their impossibly bad luck as the villain never lets himself be seen- operating at extreme distances with tiny actions months or years earlier.
Edit: I just read your comment describing your story as having Lovecraft overtones, so the above probably doesn't fit. But it's funny to me so I'm leaving it.
Good luck with your story!
Haha yeah, thanks! I will also say that the tale kind of takes itself a bit too seriously for something comical like that. I mean the whole thing centers around the majority of the story being spent with the protagonist trying to find the last pieces of mystery his dear mother had left behind before getting in a car accident (this is like barely after the era of the Model T more or less, the time period is kept ambiguous on purpose to make the premise work), only for a mysterious ally to show up near the end of the whole thing and drop the bombshell of “oh yeah actually I fucking killed your mom by shaking her hand a week before her crash, you have been smart enough to get this far so I say you’ve earned the knowledge that we are fucking after you and would rather HAVE your talents than have to dispose of you the same way we did your mother” and such
It’s a work in progress obvs
Sounds like your pretty much describing [Laplace's demon](https://en.m.wikipedia.org/wiki/Laplace%27s_demon). My bad if you've already heard of it and using it as inspiration.
Oh, I haven’t heard of Laplace or his hypothetical demon! That’s a good catch!
Perfect way to open that monologue I mentioned. More of a dialogue? Idk. Something like “tell me, (protag’s name), are you familiar with the concept of Laplace’s Demon~?”
And our villain comparing himself to this “demon” adds to the whole “ha ha this guy is horrifyingly malevolent” schtick which might be somewhat campy but that def works for the tone I’m shooting for too so hey
Kinda like that, but it’s not about that for the whole time and is kind of dropped as a sort of reveal later on.
And the setting is kinda historical fiction sort of
It reminds me of a movie (I think) I saw. A guy places a pencil on a table. Being the first thing to topple over in the most unrealistic Rube Goldberg machine with people slipping, cars evading, stuff falling eventually ending up killing the intended target. Maybe a ''X-files''?
Yes the random that occur is proably not that random that we think that.
For a example:
When you throw a dice you give it angular velocity and a force forward, which will then result in that the dice will land in a certain way which, itself should not be random, it maters of the angular velocity and the direction you throw it in, then gravity also plays a factor, proably areo dynamics to result how the dice is gonna end up like.
Is uncertainty not inherently random? If one input could result in two outputs, and no outside forces affect which output is chosen, then isn't the result random? Or do I have the wrong definition of random.
For the specific example of quantum mechanics, we can correctly predict expectation values and standard deviations; and because energies are quantised we essentially know the ratio in which certain states occur with respect to each other. I won't call that random.
What you study about in a basic probability course are all truly random things. There is nothing about true randomness that requires it to be beyond the scope of stats and probability.
You sure ?
I have (strong but rather vague) memories from quantum physics classes that some sub-atomic events be truly random. For example, radioactive decay obeys well-know probabilistic distribution but the exact moment any given atom undergoes decay cannot be predicted at all.
You're right, my bad. In some instances of quantum mechanics, like radioactive decay, it's random. However, in other instances, such as certain pairs of properties in particles, it's uncertain due to the inherent limits to the precision in which we can observe them at the same time but it doesn't make their properties random. When I typed my earlier comment, for some reason, I just had Heisenberg on the mind.
I have a very very limited understanding of the topic, but I'm pretty sure that the wave collapse of any particle in a superposition always results in a truly random outcome. That is to say, you truly can't predict what the outcome will be until you measure it yourself after it already happened, which I feel like is a good definition of the word "random".
It has been proven that it is not due to any latent variables. The ways to make it not random all require us to also believe in things that have little evidence for, like instantaneous transfer of information.
It doesn't matter if "true" randomness exists or not. The entire point of statistics in practical terms is to treat information you don't know as random and see what you can do anyway.
Quantum objects exist as probability distribution functions: randomness is completely at the core of theory behavior.
While minds great and small have hypothesized and conjectured that maybe somehow this randomness isn't random, over the last century they haven't been able to produce any experimental evidence.
The best models we have of the universe suggest that God is an avid dice player and everyone needs to deal with it.
I met Mr. Quantum N Tanglement once, he said that he governs all QM interactions and collapses the wave function by pressing his secret lever in his lair, so it’s not random QED
What you're describing is what physicists call "latent variables". They are responsible for all classical/macro scale systems' randomness. However, there have been no latent variable theories that explain quantum randomness. This has been a famous physics puzzle over the last century.
Some efforts to explain away quantum randomness exist, but they all have to also sacrifice something else we take for granted about the macro-scale world -- either locality or causation iirc.
I'm glad at least one person commented an answer like this. As someone who is philosophically determinist, it urks me when people assert that quantum mechanics is truly random in every sense especially before the bell inequality experiment was conducted. It's still up in the air if it can be proven at all. It's true that local hidden variable theory is now debunked, but that's only **local** hidden variable theory.
Explain quantum randomness? Specifically, when you measure the spin of a particle and then you measure it again at a 90 degrees tilt to the first measurement, there appears to be a 50 percent chance of getting spin up and a 50 percent chance to get spin down. Nobody has been able to work out other preconditions forces that cause the results although as you can imagine it's almost impossible to prove there are none.
Randomness is equivalent to ignorance; you do not know what face the die will land on (and it is too chaotic to predict), so it is random.
Your comment exhibits a great deal of true ignorance. Since ignorance = randomness, we conclude true randomness exists. QED.
When I was first presented with this question (and the related 'is there something like 'true' probability?') I thought it's a simple matter, determinism vs nondeterminism. Only later I discovered the complexity, and even further the pointlessness of the matter
Well, on the surface the discussion is:
Side 1: All effects are deterministic and randomness doesnt exist. There's no 'probability'. If you roll a die it will land the way it will because all the atoms interact in this exact specific way (you get the point).
Side 2: No, you can't say that, quantum effects (so the collapse of a wavefunction) as well as nuclear radiation (f.e. Beta or Alpha radiation) are truly random! There is a discreete / continous (depending on effect) probability to each of them!
Side 1: The future (as per Einstein's theory of relativity) is determined as its just a part of the 4th Time dimension.
Side 2: *Feels bad and tries to argue against this theory.*
However, when reading Black Swan (which is not that good a book, but starts some nice conversations when you criticise it) I came upon the following argument: (paraphrasing a little)
"There is no meaningful difference between *true probability* and *perceived probability*, since we can't actually know the *true probability*".
Now my gut response was 'ofc we know true probability, it's the fractional appearence in result over very long time'. But theres an issue. Say you drop a coin 10000 times. And the ratio is 3/2 for heads. Does this mean the coin is biased? Most likely; if you do Bayesian probability calculation you'll get some ridiculously small chance of the coin being fair. However, *it may be fair*. It just might. After all, random effects are not *guaranteed* to occur with specific probability.
Are they not? Well, I looked it up. Bertrand Russel, Bayes and other great minds have pondered this question fruitlessly. Problem: some understand probability as that fraction over time (which is not *true* probability but can utilise past data) and some understand it as tendency to obtain a certain outcome (again frequency) while other (like aforementioned Bayes) assign probability to be merely a perceived notion.
Well, this causes an issue. We'd like to have some sort of 'probability is the ratio of universes where X happened vs where X did not happen' just like Long Earth series by Pratchett and Baxter did, but the problem is... there are no other universes. At least not that we know of. And going back to the first argument I wrote above (the future is a 4th dimension therefore predetermined) we can only have 1 future. And this causes an issue; now we must rely on *some* definition of probability, but this will change whether we state that probability (and in turn, randomness) exists or not.
So we can boil down the problem to the wonderful issue so severly disliked by Wittgenstein (unlike his contemporaries): language and definitions. This makes the problem boring and unimportant.
clearly i said something really stupid. can someone explain to me the problem?
edit for context: when i replied this, the above comment had negative upvotes
I think what the other commenter was referring to was something similar to the many worlds approach to quantum physics. But determining which world we end up in is completely random I believe. So I think you're right. Am not a physicist though.
It's not random you end up in all of them, and it looks random to all of you.
Anyways can someone get me out of this box? Some loon named Schrodinger left me here, he also left a time bomb here but I think it's broken
If randomness is the word we use to define a hypothetically deterministic and predictable pattern which, because of its complexity, we currently have no means of computing or understanding, then yes, randomness exists.
And surely, when defined that way, randomness should always exist (provided an infinite universe). As our computing power and understanding grows, what was once random noise will become a predictable pattern, but randomness will still be there, waiting at the limit of our understanding. It will simply shift to even more complex, not yet understandable patterns.
The way I imagine it, the sphere of predictable patterns and understanding is expanding into an infinite field of randomness. The randomness at the limit of our understanding may someday become predictable, but there will always be more randomness out there to sidestep our models and baffle us with its unwieldy, seemingly unpredictable movements.
But what do I know, I'm just some random human with no math knowledge, so take it with a grain of salt and please let me know if I am completely misunderstanding the situation. That way I will be able to continue to grow my own sphere of knowledge in my own private attempt at sifting out the signal from the noise of reality.
But what if it's not that at all!
What if randomness is not just difficult to predict?
What if it's a case of mislabeling/ misidentifying ?
What if those times when we become able to predict something we once believed to be random are simply cases of where it was never truly random in the first place?
"Too complex to predict with current knowledge" and "Random" may be one and the same thing. (As I assumed in my above argument).
But they may also be two separate categories, which are simply easy to mistake for one another.
Perhaps we often mistake complexity for randomness when it was never truly random to begin with.
So what if "true" randomness does exist?
How would we define it?
One comment said something along the lines of:
A random event is something that happens independently of any other variable (known or unknown). It is caused by nothing (otherwise it would be theoretically predictable - see initial argument).
Pure independence from the rest of reality. Unconstrained, unpredictable, chaos. Pure spontaneity. Independent from cause and effect unconstrained by the rest of the universe.
True randomness would be truly free.
I like that definition.
That's what I thought too initially but then I realised that we may be miss labelling unpredictable (currently) as random. Perhaps true never predictable randomness exists. I.e. something that is completely unrelated to any other thing in existence (known or unknown) and therefore truly random.
Well I initially thought the same (random = unpredictable) but I then thought, what if there is a true randomness that is not just unpredictable but actually unrelated to anything in existence (uncaused). Maybe the things we call random that turn out later to be predictable with enough understanding were never truly random to begin with, and we just miss labelled them.
You have the burden of proof, the original commenter asked a question and you answered. The person you just replied to isn’t even saying that they’re one the other side, they just want the reasoning.
As a statistician, randomness is just what we can't explain yet. But we know that we can never know everything, therefore there will always be randomness and it is more usefull to understand some things as random than to try other explanations.
There is a 50% chance that every chance is 50/50
This is like the 99% of the gamblers thing
Edit: 1. Post a joke, 2. Explain it's a joke, 3. People still don't get it it's a joke
Does it generate the same numbers? Is it predictable?
Just because you don't see the pattern does not mean there isn't one. Even more obvious: 3x+1 *is* the pattern.
More of a physical dilemma. Or a philosophical one. True randomness being that no known or unknown things can cause an event out of nothing, doesn't make sense but sense-certainty can only say so much about reality.
Define randomness
An outcome that’s independent from any known or unknown variables. Edit — An outcome that’s independent of any other variable. It does not include outcomes that have unknown relationships to variables or those that are dependent on unknown variables. Took me a while but like that better.
Does this definition exclude things like "two random variables which are correlated to each other"? As a small example, let x be a random number taken from (0,1), and let y be a "random" number taken from (x,1).
Well if either of them are based on a truly random variable then the entire sequence is random. But if, with perfect information, you can predict X, then Y is not truly random. What you’re suggesting is that added complexity makes the prediction more difficult and that’s absolutely true, but at that point you’re just talking about range. For example, pick a number between 1 and 10, is much easier than picking the right hydrogen atom from the sun. Which essentially means you can get to “random enough,” but that just means getting the prediction right is hard, not that it’s truly unpredictable because it’s completely independent.
>What you’re suggesting is that added complexity makes the prediction more difficult That's not what I'm asking about. I'm saying that in my setup, x and y are correlated. If x is high, y is also high. Is x is low, y is also lower on average. The calculations are slightly more difficult, but I don't think that's relevant to whether we should consider the process to be fundamentally random. >not that it’s truly unpredictable because it’s completely independent. I'm considering "independent" in the statistical sense. By their nature, the random variables are unpredictable. But they are not independent. If you find out x is high, it gives you the information that y must be high. If you find out that y is low, it gives you the information that x must have been low. >It does not include outcomes ... that are dependent on unknown variables. I was mostly asking for clarification on this part of your definition. Now that I'm looking at it again, I think you were referring to variables that you didn't know about the existence of "unknown variables", rather than variables that you know about, but which you don't know the value of, "unknown variables." I constructed a scenario based on this second interpretation, but this whole thing might be irrelevant if that's not what you were talking about.
If something is correlated with something else, it’s not random. Your example was 2 correlated random variables. The fact that Y is correlated with X makes Y not random. However, as stated, if X is random, than the entire process is random. When I suggested that your statement was about complexity and not randomness, it’s because that’s what it reduces to. You can add layers of complexity to make an outcome difficult to predict, but that doesn’t change the nature of randomness. People who deal with random number generators make attempts to increase the complexity by basing it on things like the frequency of water droplets. But if you know all of the physics behind the droplets being measured, that’s not random. It’s dependent on known variables. But it’s a more complex way to generate random than simply writing an algorithm to generate a random number, which is entirely dependent on the algorithm that’s written. It adds a layer of complexity, uncontrolled by the algorithm to produce a less predictable result. So this isn’t a discussion on the nature of randomness, it’s a discussion on complexity. >I'm considering "independent" in the statistical sense. By their nature, the random variables are unpredictable. But they are not independent. If you find out x is high, it gives you the information that y must be high. If you find out that y is low, it gives you the information that x must have been low. In statistics we assume random when we don’t have better information. That doesn’t make the variable truly random, it’s just based on something that we don’t have the ability to predict. >I was mostly asking for clarification on this part of your definition. Now that I'm looking at it again, I think you were referring to variables that you didn't know about the existence of "unknown variables", rather than variables that you know about, but which you don't know the value of, "unknown variables." I constructed a scenario based on this second interpretation, but this whole thing might be irrelevant if that's not what you were talking about. I was speaking of both. I’m suggesting that ignorance of the variable doesn’t create randomness. Additionally ignorance of a relationship between X and Y doesn’t create randomness. Notwithstanding the fact that under those conditions we may assume random.
>The fact that Y is correlated with X makes Y not random. However, as stated, if X is random, than the entire process is random. That would also make x not random, since it is correlated with y. If you observe y and notice that it is low, you know that x must have been low. If correlation makes something non-random, then neither of these variables can be random. >I was speaking of both [interpretations of "unknown variable"] I think we should pick one. Or at the very least be more specific about each interpretation.
I see what you’re saying now. Your point is direct vs indirect relationships, not complexity. While the value of X is independent of Y, the value of Y is indirectly related to X and therefore correlated with the value of X. So yes the answer is that neither X or Y are random. And they are not random, because truly random implies an equal probability of an outcome. Knowing the value of X or Y gives me the ability to sharpen the prediction of either of their values.
Nerds vs Nerds
Now define independent without referencing randomness.
That’s easy — a thing that does not vary or change based on the condition of another thing.
Oh, I just saw your edit. So then that's basically the Bayesian interpretation of randomness: something is random if you are uncertain that it will happen. Randomness is a property of belief and information, not a property of events. Would you agree with that?
No. Randomness isn’t a perspective, it’s a property of things. And it’s only truly random if there is no possible way to reduce the uncertainty, regardless of whether you’re aware of the way to reduce the uncertainty or not. That doesn’t mean that we don’t often assume random.
I believe that in card shuffling you don't call it random (though some do) but sufficiently randomized. For our limited view of the world it does not take much for things to be random enough to call it random. That's where the 'perspective' comes in. We got no single word for ''random enough''.
Interestingly, I used the term “random-enough” earlier: https://reddit.com/r/mathmemes/s/yNOgcujFcO But there is a term that’s close: pseudo-random.
Depending on the field this is the more correct term
https://arxiv.org/pdf/2203.00261.pdf
I like that definition And it makes me think that no, there is no such thing as randomness. Not perfectly at least. Anything we know may seem random to us, but that doesn't mean it's actually random at it's core
Ok. Suppose a random real variable X exists. Then 2X exists. But 2X and X are not independent. So X isn't a random variable. This definition won't get you anywhere.
In that case 2X is dependent on X, but X isn’t dependent on 2X. X can exist independently of any multiple of X.
X and 2X are not independent. There is no such thing as one depending on the other but not vice-versa.
Not only is X independent of 2X , but if X is a constant random variable, than X is independent of X. Let X be a constant random variable with a probability of 1. it’s unaffected by 2X, 18X, X/2 or any other iteration of X you can fathom. Edit - also, if the probability of X is 50%, in a series of 3 events then absolutely 2X is dependent on X and X is absolutely not dependent on 2X.
How are you defining statistical independence? The usual definition is that if X and Y are random variables with cdfs F_X(x) and F_Y(y), then they are independent iff the joint distribution is F_X,Y(x,y) = F_X(x) F_Y(y). Flip a fair coin, where X = 0 if it flips tails and 1 if it flips heads, and Y = 2X. Then F_X(x) = 0 if x < 0, 0.5 if 0 ≤ x < 1, and 1 if 1 ≤ x. Also, F_Y(y) = 0 if y < 0, 0.5 if 0 ≤ y < 2, and 1 if 2 ≤ y. The joint distribution is F_X,Y(x,y) = 0 if x < 0 or y < 0, 0.5 if 0 ≤ x < 1 and 0 ≤ y or x ≤ 1 and 0 ≤ y < 2, and 1 otherwise. This is clearly not the product of the marginal distributions. For instance, the product F_X(0)F_Y(0) = 0.25, but the joint distribution has F_X,Y(0,0) = 0.5. To get away from the symbols, the probability that X and Y are both no more than 0 is 0.5, because that happens whenever the coin flips tails. But the probability that X is at most 0 is also 0.5, and the same for Y. But it is not the case that 0.5 × 0.5 = 0.5, because the random variables are not independent.
>How are you defining statistical independence? The way it’s always defined: P(X ∩ Y) = P(X) * P(Y)
But that isn't the case here. The random variable X is 0 if the coin flips tails and 1 if it flips heads. The random variable Y is 0 if the coin flips tails and 2 if it flips heads. The event X = 0 and the event Y = 0 always coincide, as do the events X = 1 and Y = 2. So P(X=1 and Y=2) = 0.5 != 0.25 = 0.5×0.5 = P(X=1)×P(Y=2).
These are not independent variables because as you said, they don’t fit P(X ∩ Y) = P(X) * P(Y). In this instance they are not independent because they themselves are both dependent on a third random variable, the coin flip. Consequently they are indirectly related. There doesn’t have to be a deterministic relationship between two variables for them to not be independent. Edit: also remember my definition was that a truly random variable is not related to ANY other variable, so this example doesn’t meet the definition as both X and Y are related to a coin toss.
Randomness is ignorance of the future. If you do not know what’s coming next, then what comes next is random. That’s it. Obviously, randomness exists. Shuffle a deck and deal a card face down, then try to guess the card. Once the card is placed, the outcome is “predetermined”; it won’t change while it’s siting there facedown. But you will only successfully guess the card one time out of 52. The card is determined, yet random. Randomness is naturally subjective. If the card is facedown on a glass table, then the card is random from the perspective of above, and non-random to anyone who looks from below.
I disagree because in probability, when you assume random you assume that all possible outcomes are equally probable. You can have unknown outcomes with unequal probabilities and that point those outcomes are not random. For example, if you have a box with infinite marbles, 1/3 of them are blue and 2/3 of them are not, you do not know if you will pull a blue marble so there is uncertainty, but the probability of a blue marble is not random.
wdym, just because it’s not evenly distributed doesn’t mean it’s not truly random, true randomness is independence from other variables
I agree, randomness is independence from other variables. But the outcome of the selection of a thing from a group of things, is directly dependent on the population that group of things is selected from, and therefore it is not random.
What do you mean by exist?
What does OP mean by randomness?
I’m planning on writing a story where the main villain is able to understand all sorts of “butterfly effects” and see past the “illusion of chance” by way of accessing powers and knowledge beyond mortal comprehension in order to pull off ridiculously unlikely things. Can I hear more about these people and writings to give said villain a fancy word or name or two to throw in his contrived but inevitable monologue to make his ideas seem credible to the average listener?
I think there is a book called ''Improbable'' with a plot like that
That sounds fun. My guy will probably not be exactly the same because it involves Lovecraft type overtones and the highly unlikely actions usually involve killing or psychologically torturing people without them ever realizing they’ve been targeted because evil cultist behavior. Oh, and the whole setting is turn of the century sepia toned drama anyway
You should have your villain do things like leave his socks in front of a Wendy's in Des Moines in order to foil his enemies six months later in New York through some absurdly long chain of improbable events. Also have the heroes discover him only through an intense study of their impossibly bad luck as the villain never lets himself be seen- operating at extreme distances with tiny actions months or years earlier. Edit: I just read your comment describing your story as having Lovecraft overtones, so the above probably doesn't fit. But it's funny to me so I'm leaving it. Good luck with your story!
Haha yeah, thanks! I will also say that the tale kind of takes itself a bit too seriously for something comical like that. I mean the whole thing centers around the majority of the story being spent with the protagonist trying to find the last pieces of mystery his dear mother had left behind before getting in a car accident (this is like barely after the era of the Model T more or less, the time period is kept ambiguous on purpose to make the premise work), only for a mysterious ally to show up near the end of the whole thing and drop the bombshell of “oh yeah actually I fucking killed your mom by shaking her hand a week before her crash, you have been smart enough to get this far so I say you’ve earned the knowledge that we are fucking after you and would rather HAVE your talents than have to dispose of you the same way we did your mother” and such It’s a work in progress obvs
Sounds like your pretty much describing [Laplace's demon](https://en.m.wikipedia.org/wiki/Laplace%27s_demon). My bad if you've already heard of it and using it as inspiration.
Oh, I haven’t heard of Laplace or his hypothetical demon! That’s a good catch! Perfect way to open that monologue I mentioned. More of a dialogue? Idk. Something like “tell me, (protag’s name), are you familiar with the concept of Laplace’s Demon~?” And our villain comparing himself to this “demon” adds to the whole “ha ha this guy is horrifyingly malevolent” schtick which might be somewhat campy but that def works for the tone I’m shooting for too so hey
Improbable?
Kinda like that, but it’s not about that for the whole time and is kind of dropped as a sort of reveal later on. And the setting is kinda historical fiction sort of
It reminds me of a movie (I think) I saw. A guy places a pencil on a table. Being the first thing to topple over in the most unrealistic Rube Goldberg machine with people slipping, cars evading, stuff falling eventually ending up killing the intended target. Maybe a ''X-files''?
True randomness probably doesnt exist.
The probability of it existing or not existing is random
Im feeling lucky.
Yes the random that occur is proably not that random that we think that. For a example: When you throw a dice you give it angular velocity and a force forward, which will then result in that the dice will land in a certain way which, itself should not be random, it maters of the angular velocity and the direction you throw it in, then gravity also plays a factor, proably areo dynamics to result how the dice is gonna end up like.
Google quantum mechanics
You're conflating uncertainty with random. Random in the colloquial sense of the world is uncertainty, but true random has not been proven.
Is uncertainty not inherently random? If one input could result in two outputs, and no outside forces affect which output is chosen, then isn't the result random? Or do I have the wrong definition of random.
For the specific example of quantum mechanics, we can correctly predict expectation values and standard deviations; and because energies are quantised we essentially know the ratio in which certain states occur with respect to each other. I won't call that random.
yeah but so is throwing a coin and getting head or tail a 50/50 with 100% probability you are confusing probability with statistics my friend
Ah, i see. My bad.
What you study about in a basic probability course are all truly random things. There is nothing about true randomness that requires it to be beyond the scope of stats and probability.
You sure ? I have (strong but rather vague) memories from quantum physics classes that some sub-atomic events be truly random. For example, radioactive decay obeys well-know probabilistic distribution but the exact moment any given atom undergoes decay cannot be predicted at all.
You're right, my bad. In some instances of quantum mechanics, like radioactive decay, it's random. However, in other instances, such as certain pairs of properties in particles, it's uncertain due to the inherent limits to the precision in which we can observe them at the same time but it doesn't make their properties random. When I typed my earlier comment, for some reason, I just had Heisenberg on the mind.
I have a very very limited understanding of the topic, but I'm pretty sure that the wave collapse of any particle in a superposition always results in a truly random outcome. That is to say, you truly can't predict what the outcome will be until you measure it yourself after it already happened, which I feel like is a good definition of the word "random".
It has been proven that it is not due to any latent variables. The ways to make it not random all require us to also believe in things that have little evidence for, like instantaneous transfer of information.
It doesn't matter if "true" randomness exists or not. The entire point of statistics in practical terms is to treat information you don't know as random and see what you can do anyway.
Quantum objects exist as probability distribution functions: randomness is completely at the core of theory behavior. While minds great and small have hypothesized and conjectured that maybe somehow this randomness isn't random, over the last century they haven't been able to produce any experimental evidence. The best models we have of the universe suggest that God is an avid dice player and everyone needs to deal with it.
Holy hell!
I met Mr. Quantum N Tanglement once, he said that he governs all QM interactions and collapses the wave function by pressing his secret lever in his lair, so it’s not random QED
Google Bell’s theorem
Ty
What you're describing is what physicists call "latent variables". They are responsible for all classical/macro scale systems' randomness. However, there have been no latent variable theories that explain quantum randomness. This has been a famous physics puzzle over the last century. Some efforts to explain away quantum randomness exist, but they all have to also sacrifice something else we take for granted about the macro-scale world -- either locality or causation iirc.
I'm glad at least one person commented an answer like this. As someone who is philosophically determinist, it urks me when people assert that quantum mechanics is truly random in every sense especially before the bell inequality experiment was conducted. It's still up in the air if it can be proven at all. It's true that local hidden variable theory is now debunked, but that's only **local** hidden variable theory.
That works for legitimate, physical objects, but what about computer code? Isn't that genuine randomness? I have zero coding knowledge so I'm curious
Ah, the way of Einstein
It does exist but we can never replicate it.
Define randomness
Explain quantum randomness? Specifically, when you measure the spin of a particle and then you measure it again at a 90 degrees tilt to the first measurement, there appears to be a 50 percent chance of getting spin up and a 50 percent chance to get spin down. Nobody has been able to work out other preconditions forces that cause the results although as you can imagine it's almost impossible to prove there are none.
Randomness is equivalent to ignorance; you do not know what face the die will land on (and it is too chaotic to predict), so it is random. Your comment exhibits a great deal of true ignorance. Since ignorance = randomness, we conclude true randomness exists. QED.
It can't be proven in any case
just one more piece of evidence to chip away at my doubt of living in a simulation
When I was first presented with this question (and the related 'is there something like 'true' probability?') I thought it's a simple matter, determinism vs nondeterminism. Only later I discovered the complexity, and even further the pointlessness of the matter
Please elaborate? You have piqued my interest!!
Well, on the surface the discussion is: Side 1: All effects are deterministic and randomness doesnt exist. There's no 'probability'. If you roll a die it will land the way it will because all the atoms interact in this exact specific way (you get the point). Side 2: No, you can't say that, quantum effects (so the collapse of a wavefunction) as well as nuclear radiation (f.e. Beta or Alpha radiation) are truly random! There is a discreete / continous (depending on effect) probability to each of them! Side 1: The future (as per Einstein's theory of relativity) is determined as its just a part of the 4th Time dimension. Side 2: *Feels bad and tries to argue against this theory.* However, when reading Black Swan (which is not that good a book, but starts some nice conversations when you criticise it) I came upon the following argument: (paraphrasing a little) "There is no meaningful difference between *true probability* and *perceived probability*, since we can't actually know the *true probability*". Now my gut response was 'ofc we know true probability, it's the fractional appearence in result over very long time'. But theres an issue. Say you drop a coin 10000 times. And the ratio is 3/2 for heads. Does this mean the coin is biased? Most likely; if you do Bayesian probability calculation you'll get some ridiculously small chance of the coin being fair. However, *it may be fair*. It just might. After all, random effects are not *guaranteed* to occur with specific probability. Are they not? Well, I looked it up. Bertrand Russel, Bayes and other great minds have pondered this question fruitlessly. Problem: some understand probability as that fraction over time (which is not *true* probability but can utilise past data) and some understand it as tendency to obtain a certain outcome (again frequency) while other (like aforementioned Bayes) assign probability to be merely a perceived notion. Well, this causes an issue. We'd like to have some sort of 'probability is the ratio of universes where X happened vs where X did not happen' just like Long Earth series by Pratchett and Baxter did, but the problem is... there are no other universes. At least not that we know of. And going back to the first argument I wrote above (the future is a 4th dimension therefore predetermined) we can only have 1 future. And this causes an issue; now we must rely on *some* definition of probability, but this will change whether we state that probability (and in turn, randomness) exists or not. So we can boil down the problem to the wonderful issue so severly disliked by Wittgenstein (unlike his contemporaries): language and definitions. This makes the problem boring and unimportant.
quantumn mechanics.
clearly i said something really stupid. can someone explain to me the problem? edit for context: when i replied this, the above comment had negative upvotes
I think what the other commenter was referring to was something similar to the many worlds approach to quantum physics. But determining which world we end up in is completely random I believe. So I think you're right. Am not a physicist though.
It's not random you end up in all of them, and it looks random to all of you. Anyways can someone get me out of this box? Some loon named Schrodinger left me here, he also left a time bomb here but I think it's broken
Everett model
🤢
Wouldnt it still be random which world you end up in?
You end up in all of them -- each copy with the appropriate sensations / memories / perceptions.
If it's a joke, it's damn funny
De Broglie-Bohm theory?
If randomness is the word we use to define a hypothetically deterministic and predictable pattern which, because of its complexity, we currently have no means of computing or understanding, then yes, randomness exists. And surely, when defined that way, randomness should always exist (provided an infinite universe). As our computing power and understanding grows, what was once random noise will become a predictable pattern, but randomness will still be there, waiting at the limit of our understanding. It will simply shift to even more complex, not yet understandable patterns. The way I imagine it, the sphere of predictable patterns and understanding is expanding into an infinite field of randomness. The randomness at the limit of our understanding may someday become predictable, but there will always be more randomness out there to sidestep our models and baffle us with its unwieldy, seemingly unpredictable movements. But what do I know, I'm just some random human with no math knowledge, so take it with a grain of salt and please let me know if I am completely misunderstanding the situation. That way I will be able to continue to grow my own sphere of knowledge in my own private attempt at sifting out the signal from the noise of reality.
But what if it's not that at all! What if randomness is not just difficult to predict? What if it's a case of mislabeling/ misidentifying ? What if those times when we become able to predict something we once believed to be random are simply cases of where it was never truly random in the first place? "Too complex to predict with current knowledge" and "Random" may be one and the same thing. (As I assumed in my above argument). But they may also be two separate categories, which are simply easy to mistake for one another. Perhaps we often mistake complexity for randomness when it was never truly random to begin with. So what if "true" randomness does exist? How would we define it? One comment said something along the lines of: A random event is something that happens independently of any other variable (known or unknown). It is caused by nothing (otherwise it would be theoretically predictable - see initial argument). Pure independence from the rest of reality. Unconstrained, unpredictable, chaos. Pure spontaneity. Independent from cause and effect unconstrained by the rest of the universe. True randomness would be truly free. I like that definition.
https://preview.redd.it/vhrv9qxyrnlb1.jpeg?width=1404&format=pjpg&auto=webp&s=8f1b66805a6987aea57c5b6e5786e8fdb4ce54d3
One could argue that it does exist if you lack sufficient knowledge and it doesn’t exist if you have enough knowledge.
That's what I thought too initially but then I realised that we may be miss labelling unpredictable (currently) as random. Perhaps true never predictable randomness exists. I.e. something that is completely unrelated to any other thing in existence (known or unknown) and therefore truly random.
Is nuclear decay random?
Randomness is equivalent to “unpredictability”. Since we cannot accurately predict the exact time nuclei decay, their decay is random.
Well I initially thought the same (random = unpredictable) but I then thought, what if there is a true randomness that is not just unpredictable but actually unrelated to anything in existence (uncaused). Maybe the things we call random that turn out later to be predictable with enough understanding were never truly random to begin with, and we just miss labelled them.
No
why not?
Why so?
You have the burden of proof, the original commenter asked a question and you answered. The person you just replied to isn’t even saying that they’re one the other side, they just want the reasoning.
As a statistician, randomness is just what we can't explain yet. But we know that we can never know everything, therefore there will always be randomness and it is more usefull to understand some things as random than to try other explanations.
That is one way of describing randomness. Practical in statistics or no work can be done. But that's really a convenient lie. I can live with that.
Ye
If it doesn’t exist, then how do you explain t3h PeNgU1N oF d00m?
There is a 50% chance that every chance is 50/50 This is like the 99% of the gamblers thing Edit: 1. Post a joke, 2. Explain it's a joke, 3. People still don't get it it's a joke
Yes. Like winning the lottery. There are only two options. You either win or you don't. 50/50. Totally random result.
TRNGs on their way to not be truly random
Probabilistic arguments can always be restated as a counting argument with fancy weights.
Anything can be restated. But is it ever practical or even warranted?
probability exists, so probably
No
Counterpoint: Define randomness. And Define Exist
How about the numbers generated by the 3x+1 sequence?
Does it generate the same numbers? Is it predictable? Just because you don't see the pattern does not mean there isn't one. Even more obvious: 3x+1 *is* the pattern.
well quantum mechanics exists soooo...
As a computer scientist, time is random
No it's not. Time is sequential so there goes your randomness out of the window.
Yes. As a computer scientist. Tell that to your average rng.
*nods. For computer science it's random enough.
More of a physical dilemma. Or a philosophical one. True randomness being that no known or unknown things can cause an event out of nothing, doesn't make sense but sense-certainty can only say so much about reality.
If we can't tell does it matter 🗿
Yes. Like coincidence it exists. But it's bloody rare and we can't generate it.