Why I hate Universe
Is this clickbaity?
A very deep seated in me is, a philosophy, that be good or bad, success or failure, happiness or sadness, or any dichotomous pair you can find is equally likely. Infact, this is not just limited to pairs. I want (if that’s too strong), I expect everything to be equally likely. I am not going to rant here about my philosophy. I will we ranting pretty strongly about why this Universe goes against my philosophy and doing so high key pisses me off.
There is Central Limit Theorem which says (if my memory serves) if you have a set of observations which come from an unknown distribution and you know that they have finite mean and variance, then in the infinity limit, the distribution tends to Gaussian. I think I butchered the theorem here. I am not at all mathematically rigourous here. But whatever, I think I captured the esssense of it.
The thing that pisses me off is this: “CLT says distributions tend to Gaussian”. We all know Gaussian is not uniform. It’s got an exponential tail and buldge around the mean. It’s not like uniform distribution. It’s not flat everywhere (well it can’t be everywhere, so let’s just say finite support)
I like uniform distribution because of my philosophy. All the probabilities are same. In a class of 100 students, 10 would have perfect score of 10/10, another 10 would have 9/10, and so on. But this Gaussian dude messes it up, this dude drops majority of students around the mean and very few at the top and very few at the bottom. Why would anyone call this perfect? In a perfect world, there should be 10 really smart dudes not just one or two.
Now that I have written this, (so, in retrospect) it kind of makes sense why Universe does what it does. Uniform distribution although is uniform, all probabilities are the same, and it’s nice and comforting, has to have a finite support. It can’t park itself over the entire Real line. The normalization kills it. But this Gaussian dude can survive the Normalization and still be on the entire real line. Nature probably chooses the entirity of the entire things for itself. Greedy nature. But, I guess, by doing so, it pays the price of finite variance.
Both the uniform and the normal distributions are like brothers. They belong to the maximum entropy family. Uniform has no restrictions and Normal has finite variance and finite mean. So, Nature wanting maximum freedom chooses Normal over Uniform and makes us dream about our perfect worlds with Uniform distributions. But, hey what about our exponential brother/sister? S/He’s got maximum entropy and lives over the entire field why doesn’t Universe choose that. Exponential is no better. Is it because our CLT uses “finite variance” and if we relax that condition we go to exponential? TBH, I am not aware of such a rule.
So, yea, then why Gaussian, why “normal” is normal and not uniform? Why does Univserse want two parameters finite? Isn’t our dimension 3D?