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How long does it take to become Gaussian?

Surprised no one has brought up the Fourier domain representation/characteristic functions. Over there, convolution is just repeated multiplication, so what this gives is . Conveniently, gaussians stay gaussians, and the fact that we have probability distributions fixes . So what we're looking for is how quickly the product above squishes to a gaussian around , which looks to be in large part determined by the tail behavior of . I suspect what is driving your result of needing few convolutions is the fact that you're working with smooth, mostly low frequency functions. For example, exp, which is pretty bad, still has a  decay. By throwing in some jagged edges, you could probably concoct a function which will eventually converge to a gaussian, but will take rather a long time to get there (for functions which are piecewise smooth, the decay is .

 

One of these days I'll take a serious look at characteristic functions, which is roughly the statisticians way of thinking about what I was saying. There's probably an adaptation of the characteristic function proof of the CLT that would be useful here.

Two reasons to expect a peaceful change of power in the US

There's generally a simpler explanation in this case that Trump and the Joint chiefs of staff have had a rocky relationship, so the military has no interest in assisting a coup attempt, even if they are willing to renounce democratic norms (they are sworn to protect the constitution, after all). Without cooperation from the military a coup is a non-starter.

The allegory of the hospital
What needs to be assumed when reasoning about existential risk, and how are the high stakes responsible for forcing us to assume it?

I guess I opted for too much brevity. By their very nature, we don't* have any examples of existential threats actually happening, so we have to rely very heavily on counterfactuals, which aren't the most reliable kind of reasoning. How can we reason about what conditions lead up to a nuclear war, for example? We have no data about what led up to one in the past, so we have to rely on abstractions like game theory and reasoning about how close to nuclear war we were in the past. But we need to develop some sort of policy to make sure it doesn't kill us all either way.

*at a global scale at least. There are civilizations which completely died off (Rapa Nui is an example), but we have few of these, and they're only vaguely relevant, even as far as climate change goes.

The allegory of the hospital

Writing well is really hard. Thanks for sharing.

Non offensive word for people who are not single-magisterium-Bayes thinkers

I believe the term you are looking for is a fox, in the sense of Tetlock. But honestly, as someone who is generally pro-toolboxism, I don't understand why that's offensive. The whole point is that you have a whole toolbox of different approaches

The allegory of the hospital

Often the issue is that what you're trying to predict is sufficiently important that you need to assume *something*, even if the tools you have available are insufficient. Existential risks generally fall in this category. Replacing the news with an upcoming cancer diagnosis, and telepathy with paying very careful attention to that organ, and whether Sylvanus is being an idiot is much less clear.


On the other hand, if someone is taking even odds on an extremely specific series of events, yeah, they're kind of dumb. And I wouldn't be surprised to find pundits doing this.

Are Humans Fundamentally Good?

not at all, and especially not for subjects with intro textbooks. That said, it's just a starting place, and it's almost worth as much as a source of references as an actual overview.

SlateStarCodex deleted because NYT wants to dox Scott
There is a power imbalance in place.

this is precisely the argument that cancel culture often makes, often with good reason, with outside actors piling on what may have started as a parochial dispute.

Are Humans Fundamentally Good?

So for something interactive which helps build intuition, this is a great game about the prisoner's dilemma (goes in the same direction as what greylag linked actually, but with much cuter animations, and can serve as intro). If you want something with more substance, I don't think I can beat a thorough reading of the wikipedia page followed by choosing a book from their further reading section which matches what you're comfortable with.

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