Stop Telling People Nature Has Gaussians. It Does Not.
“A fundamental part of statistics” is not a fundamental part or nature. The reason something approaches a Gaussian is because one CHOOSES to interact pieces as a sum, making them independent and identically distributed.
The fact that the sum of a large number of independent, identically distributed random variables will tend to follow a normal distribution has absolutely nothing to do with natural systems, it has to do with the way statistics chooses to define a group.
Complexity BY DEFINITION achieves emergence through its component interactions. Nature does not ADD its pieces together. You will not find a single example in nature where the group is formed by addition and independence; the pieces ALWAYS interact in nature.
If you grab a bunch of people and add their heights together and calculate an average based on a normal distribution this has NOTHING to do with nature. There is no phenomenon in nature that adds heights together to solve a problem using what statisticians call an average. Ever.
You cannot apply math and statistics to the real world without understanding natural phenomena. If you choose to apply mathematics and statistics to the natural world your allegiance is to an understanding of phenomena, not blind adherence to the disconnected internal consistencies of your little stats toolbox.
The central limit theorem is not a reflection of something occurring in nature, it is a reflection of what happens with a human chooses to artificially define component interactions in a mathematically convenient way.
The interactions in nature are far more akin to multiplication, within and between virtually infinite sets of codependent “variables.” They are not little isolated pieces in a vacuum of non-interaction.
Thinking nature follows the fictitious machinations of a statistician’s convenient little bell curve is peak scientific illiteracy.
Postscript
No, this has nothing to do with the fact that “models are imperfect.” This has to do with the fact that any model is a lens by which you choose to view reality through.
