This is actually what I expected to read: "The standard deviation is useful because with the average and the standard deviation, one can fully characterize a normal distribution. However, the standard deviation is less useful a statistical summary the farther away from 'normal' you get, and in reality, there is no such thing as a normal distribution, as a true normal distribution is defined on the entire real number line from negative infinity to positive infinity. Reality always provides some bound, and it's often quite distorted from Guassian. For instance, a 'normal' distribution averaging 2 with a standard deviation of 1.4, bounded by 0, is quite non-Gaussian in many important ways! (Not least of which is that you're going to have to do something to replace the missing probability...)
"People rarely check how closely their data conform to the standard distribution; indeed, many people blindly apply the standard deviation to their data regardless of its distribution! The resulting number is often more obfuscatory than helpful, to the extent that it crowded out more useful summaries.
"It's a useful metric when treated carefully, but it is rare to encounter it treated carefully. Science courses would be well-served to stop teaching it in favor of a stronger emphasis on multiple distributions. (Multiple distributions are usually touched upon, but implicitly our curricula overfavor the Gaussian distribution and end up accidentally implicitly convincing students its the only one.)"
But... it doesn't. You ever hear about the hypothetical possibility of your atoms lining up and falling through the floor?
It's hypothetical in the sense that it's really ridiculously unlikely, but there is no bound preventing it.
Now the central point about different probability curves stands, but that's not what Taleb was talking about--he seems to think that it's the tool's fault if people are using it wrong--and it's also not what Homunculiheaded argued.
"But... it doesn't. You ever hear about the hypothetical possibility of your atoms lining up and falling through the floor?"
A bad example; that's a very, very large sample space, such that deviations from mathematical perfection are irrelevant. They do exist, if you're precise enough (for instance, the universe is not modeled by perfectly continuous space), but I'm not inclined to argue them, because it's too easy to argue that they're irrelevant. So instead consider something more human-sized: Match a normal distribution to the height of human beings.
It works very well, except in real life, the probability of a negative-height human being is zero. This is not what the Gaussian model predicts.
Unfortunately, rather more science takes place in the second domain than the first.
"that's not what Taleb was talking about"
I'm quite aware. The fact that I commented on how I got something other than what I expected rather suggested that, I thought... The fact that this isn't precisely what Homunculiheaded said is also why I posted, rather than just upvoting....
>The fact that this isn't precisely what Homunculiheaded said is also why I posted
Ah. I misread the following...
>>This is actually what I expected to read:
as agreement ("This is actually what I expected to read."). My mistake.
>Unfortunately, rather more science takes place in the second domain than the first.
As I said to Homunculiheaded, this is because of the relative utility of the models, which we understand--and even those that do not understand it do not make the tool's use invalid.
What are we bemoaning, here, but actual misunderstanding itself?
"People rarely check how closely their data conform to the standard distribution; indeed, many people blindly apply the standard deviation to their data regardless of its distribution! The resulting number is often more obfuscatory than helpful, to the extent that it crowded out more useful summaries.
"It's a useful metric when treated carefully, but it is rare to encounter it treated carefully. Science courses would be well-served to stop teaching it in favor of a stronger emphasis on multiple distributions. (Multiple distributions are usually touched upon, but implicitly our curricula overfavor the Gaussian distribution and end up accidentally implicitly convincing students its the only one.)"
But that's just me.