you can’t actually have a continuous distribution in reality
The crushing majority of evidence suggests that continuous distributions are what reality is built on.
The problem with integrating 0 to get P(anything) = 0 is that you can’t switch the order in which you take limits—the limit that gives you P(X=x) = 0 is outside the integral, and the integral itself behaves like a limit (remember Riemann sums?). So if you switch the order of the limits by integrating 0, you have committed an illegal operation.
I am familiar with the idea. I just don’t see where the evidence is. Sure, quantizing space fits well with there being a maximum entropy of space, but this seems like a classical solution to a very non-classical problem, and it eliminates relativity in the process.
You are the one claiming that “the crushing majority of evidence” opposes discrete theories.
My position is more that we can barely see anything down that far, and so we have very little experimental evidence about whether the universe is continuous or discrete.
In the absence of evidence, assuming uncomputable physics seems to be counter-intuitive to me. We don’t know of anything else that is uncomputable.
We don’t know of anything else that is uncomputable.
We’re talking about the entire universe here, so it would be just as valid to say we don’t know of anything else that is (discretely) computable.
And yeah, there is always some level of discreteness that would have no impact on our observations, just like there is some level of teapots in the asteroid belt that would have no impact on our observations. You’re right that that sort of thing isn’t ruled out by the evidence, so my statement was wrong.
Teapots in the asteroid belt are contrary to Occam’s razor. The situation with discrete physics is very different. Science has a long history of showing that apparently-continuous phenomena actually turn out to be grainy on a smaller scale.
The crushing majority of evidence suggests that continuous distributions are what reality is built on.
The problem with integrating 0 to get P(anything) = 0 is that you can’t switch the order in which you take limits—the limit that gives you P(X=x) = 0 is outside the integral, and the integral itself behaves like a limit (remember Riemann sums?). So if you switch the order of the limits by integrating 0, you have committed an illegal operation.
Augh, my mistake. This is why I am currently doing a math refresher. Thank you :)
Yeah, it makes all sorts of sense to just set things to values, but once you start using limits that breaks things. Stupid limits.
Not really. Lots of discrete things look continuous—if you stand far enough back.
Alright, I’m curious. Are you claiming that the probability distributions that come out of quantum mechanics are discrete?
If you are not familiar with the idea, perhaps, see: http://en.wikipedia.org/wiki/Digital_physics
I am familiar with the idea. I just don’t see where the evidence is. Sure, quantizing space fits well with there being a maximum entropy of space, but this seems like a classical solution to a very non-classical problem, and it eliminates relativity in the process.
You are the one claiming that “the crushing majority of evidence” opposes discrete theories.
My position is more that we can barely see anything down that far, and so we have very little experimental evidence about whether the universe is continuous or discrete.
In the absence of evidence, assuming uncomputable physics seems to be counter-intuitive to me. We don’t know of anything else that is uncomputable.
We’re talking about the entire universe here, so it would be just as valid to say we don’t know of anything else that is (discretely) computable.
And yeah, there is always some level of discreteness that would have no impact on our observations, just like there is some level of teapots in the asteroid belt that would have no impact on our observations. You’re right that that sort of thing isn’t ruled out by the evidence, so my statement was wrong.
Teapots in the asteroid belt are contrary to Occam’s razor. The situation with discrete physics is very different. Science has a long history of showing that apparently-continuous phenomena actually turn out to be grainy on a smaller scale.