Ahh. I could very well be wrong.
Trying to understand this; visualization-wise, are you saying that instead of visualizing the point moving around, with the green circles fixed, we should be visualizing the green circles moving around, with the point fixed?
Since this is lesswrong let me try to explain with probability.
If you have a random variable X then you have an associated measure:
measure(A) = probability that X is in A.
If X has a probability density function f then:
measure(A) = integral over A of f = probability that X is in A
If you measure has an associated density then you can visualize it by visualizing the probability density function.
You get the Dirac measure if X is constant. Your random variable X always returns the same result. The associated pdf is the Dirac delta ‘function’. Sometimes people visualize the Dirac delta as an infinitely tall and infinitely thin Gaussian.
Ahh. I could very well be wrong. Trying to understand this; visualization-wise, are you saying that instead of visualizing the point moving around, with the green circles fixed, we should be visualizing the green circles moving around, with the point fixed?
Alternate explanation:
dirac_x(A) is a function of A, x is fixed.
Yeah, this makes sense. Hmm. I’ll think about this more then edit the post. Thanks
Since this is lesswrong let me try to explain with probability.
If you have a random variable X then you have an associated measure:
measure(A) = probability that X is in A.
If X has a probability density function f then:
measure(A) = integral over A of f = probability that X is in A
If you measure has an associated density then you can visualize it by visualizing the probability density function.
You get the Dirac measure if X is constant. Your random variable X always returns the same result. The associated pdf is the Dirac delta ‘function’. Sometimes people visualize the Dirac delta as an infinitely tall and infinitely thin Gaussian.
Does this make sense?