If @0celo7 had chutzpah he'd tack them to a public bulletin board with a note saying "I can't remember your name, but I thought you'd want these back".
@DanielSank Okay, I dunno how it works in 'Murica, but here all garbage cans have wheels, and the people filling them are responsible for pushing them to the street
Is there are term for the most random thing possible?
Suppose we have a bunch of lights A,B,C,D,E,F
A blinks every 2 seconds B blinks when A blinks 2 times C dims and brightens according to the function sin^2(wt) D blinks randomly in a way such that on average the probability of it is light follows a gaussian distribution E blinks in a pattern that resembles a random walk F blinks in a way that depends chaotically to A and B
Can there exists a lamp G such that it blinks so randomly that even when one tries to
My mind have the tendency to wonder about the most extreme example of any knowledge I came across
Well, the gist of the question is trying to ask about the mathematical term for some event (which can be either 0 or 1) that is so random that even when trying to do a time average of the number of 1 you see, you always get a different probability distribution each time (so that it cannot be say to follow something nice like a normal distribution, or even a probability distribution that change with time
That is, I am trying to find the name for a concept that represent the most extreme version of no correlation, that has no conceivable pattern, because even a random walk has dependence on …
The lamps A-F are just emphasising that G has to be so random that it does not behave like what A-F does (not even a random walk or chaos)
Put it in another way, I often heard that when people mentioned about something is random and statistical, they often form normal distributions
I am trying to look for something that is the extreme version of random such that it cannot be described by any probability distribution, and I am wondering what's the math concept that describes that
user54412
A random variable is nothing more than a plain old variable with an attached probability distribution. There is no mathematical theory of any other type of random variable; in particular there is no theory of random variables with undefined distributions, just as there is no theory of Euclidean triangles with undefined interior angles.
hmm, I see, looks like I don't understand the concept "random" well enough. I always thought true random = unpredictable even in the context of probabilities
In that case, what does it mean in mathematical terms when we say the random variables X and Y have no correlation?. How to write such result in the form of expressions?
(previous previous message)I am not sure, I think I am thinking along the lines of "that it is so unpredictable that even if you measure it multiple times, the probability that it happens cannot be determined even in principle, other than it is nonzero"
(Acuriousmind's message just above) Ok, I guess the reason I am not aware of it is I am new to that term ( I have learnt variance, but covariance is kinda new to me), thus I don't know the term to look it up myself, but thanks, should give that a read
@ACuriousMind Btw for that double slit question that we discussed earlier, is my thinking on why the speed is ~c correct? (that because $H_{int}$ (and hence all terms > 0th order) will vanish in the expansion once $t\geq t_{switch}$ therefore the time evolution will not be changed until $t=t_{switch}$)
@Acuriousmind What machinery I need in order to compute the propagation speed. Is relativistic QM sufficient or I have to go full blown QFT? (I am interested in that because the feymann lecture notes inspired me a guess on something, that I believe I can check whether my understanding make sense by calculating the propagation speed)
if I have an outgoing null congruence $l^a$ and an ingoing null congruence $k^a$ normalized so that $l^ak_a = -1$ and both $l^a, k^a$ are normal to a one-parameter family of 2-spheres
then is there a physical or geometric quantity associated with $k^a \nabla_a l_b$?
"Unfortunately Professor Hawking is unable to respond to specific scientific enquiries, or theories. Please do not email these as although they may be valid, we simply do not have the resources to comment on them."
