Imho the whole “person’s wealth vs small country’s GDP” comparison is probably at least as much about people not understanding what GDP is as about confusing stocks and flows
It's amazing how far the banning lab meat coalition has made it given that they have no real arguments, and they usually don't even bother pretending to have any.
We usually repeat that correlation doesn’t imply causation, which is true. But the reverse, causation doesn’t imply correlation, is ALSO true.
Let X~N(0,1) and Y=X^2. In this example, X causes Y.
But the correlation between X and Y is Corr(X,Y)=Corr(X,X^2)=Cov(X,X^2)/(σ_X*σ_(X^2))=(E[X*X^2]-E[X]*E[X^2])/(σ_X*σ_(X^2))=0. Why?👇
The function h(x)=x^3 is odd:
(-x)^3=-x^3
and the distribution is symmetric around 0, f is even:
f(x)=f(-x)
Thus (x^3)*f(x) is odd (odd*even=odd function) and the integral of an odd function over a symmetric interval is 0.
Thus E[X^3]=∫X^3*f(x)dx=0
(the integral is from -♾️ to ♾️)
The same occurs with the function g(x)=x because g(-x)=-x=-g(x) (it’s odd).
So E[X]=∫X*f(x)dx=0
(the integral is again from -♾️ to ♾️)
Thus Corr(X,Y)=0 because Cov(X,X^2)=0.
Thus we have proven that causation DOES NOT IMPLY correlation.
Q. E. D. ▪️
Why aren't the kids playing outside anymore?
Because half the country considers anything other than sitting quietly in your home watching Netflix or playing video games to be third world behaviour.
I wish billionaires were the owner-managers of companies that won a market by supplying something new. I also wish they consumed basically none of their wealth, and instead saved at abnormally high rates.