How Nature Preorders Random mathematical Outcomes To those individuals pointing out the difference between Statistics and Probability Distributions and those presenting abstract mathematical thinking—I counter with the fact that "statistically speaking" is a term that most people will understand whether or not they have any fundamental understanding of mathematics or not. The original post is designed in such a way that the common person, laymen or average student (or anyone who watches the news) will be able to engage in the conversation without having to impression upon them the differences between things like Statistical Analysis, Probably Distributions, Discrete and Continuous Data, Discrete Probability, Analog and Digital, Fractals.... so on and so on and so forth.
The reason why I have presented this in this way (in the simplest and most widely understandable terms) is to help the laymen engage in the conversation. Why? Because the common person presumes that when they fill the jar they will get a mix of colored marbles. They presume this because billions of years of evolution has programmed their intuition through a process of natural selection. That being said, how old is the language of math--Babylon maybe? That is but a minuscule fraction of time in comparison. Let us remember that mathematics is a language that human beings have created. We designed it and implement it in our attempts to describe the workings of the physical universe... it is however not in actually the physical universe. It is our attempts to describe and understand it. There is a difference.
In math, if you plug in the wrong values (or if you leave something out) you get a result that appears to be true but in the actual physical universe it ends up being untrue because your math was incomplete. Let me point out the obvious: it is not actually provable that you can eventually end up with a jar filled with only white marbles given the physical conditions that I described. The math that you are using may tell you that it is so, but you cannot actually prove it experimentally in the real and physical world. That means it requires faith on your part to believe that it is true and thus the math you chose to use was complete and you didn't overlook anything. You have to believe that you have accounted for everything when you say “sure... you can end up with a gallon size jar filled with only white marbles if you have infinite tries” even though the average person (who knows nothing about the language of math) knows this to be and untrue statement.
To Summarize: what I am pointing out here is that when you calculate the outcome you may not be putting all of the "math" into the equation. You may not be calculating all the variables. You may just be measuring what is likely to happen as little colored balls fall out of a hole, falsely presuming that the origin of said colored balls is a pure and total random process. In the example above... it is not. The paint analogy presented by Metaphysician Undercover is actually a very good one. If you put a can of paint into a paint mixer you may expect to see a streak of unmixed paint at the top when you opened the lid. But it is not possible for the paint to remain separated after the mixer is done with its work. It does not matter if you have infinite paint cans in infinite universes and infinite tries. If the paint is paint and if the paint mixer does it's job then the paint will be mixed.
This is the way that the actual physical world works and this thread is an attempt to describe how the various physical phenomena of our underlining reality preorders random outcomes.