No it is not, as we are now talking about chemistry. Marbles are not small enough to fall in that category and behave very differently. — Jeremiah

You are fundamentally incorrect. The laws of physics do not change between a can of paint and a gigantic clambering vat of swirling marbles. The change only occurs in your mind and the unfinished math that you employ as a result reflects an unfinished answer.

I kind of think this discussion is at its end, Ergo's "hypothesis" has been shown to have many flaws. — Jeremiah

It is my thinking that this particular discussion about randomness is among the most important debates in science, physics, mathematics and philosophy. I must also now point out that you have not actually presented any evidence to show that my original hypothesis has many flaws. You only concluded, that it does, offering no real world representations to support you opinion only more unfinished math.

But in the end, that's how these things tend to unfold. Challenging a principle often yields the same result as challenging someones faith or strongly held opinion, because some principles are simply opinions taken on faith and are not provable experimentally.

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.

Here is the thing...

Although the math says that infinite jars and infinite chances will "almost certainly" result in a jar filled with only one color of marbles eventually the math that tells us this is not taking into account the inherent nature of the mechanism in question. In order for a jar to be filled with only one color of marbles you would have to violate the complex mathematics governing the chaotic and dynamic processes inside of the vat.

Observe: the same statistical math that leads you to believe that you will eventually "have to" result in a jar filled with only one color of marble (if given infinite tries) also tells us that inside of the dynamic, turbulent, swirling mass of the vat the colors of the marbles will tend to be evenly distributed inside the mass

That means that by the time that the marbles fall out of the funnel located at the bottom of the vat statistically they HAVE to already be distributed by statistical laws. As a result, it would actually defy statistical laws if at any time the statistical distribution of the colored marbles inside of the vat were as such that they would yield an entire jar's worth of marbles of only one single color. It's not just extremely unlikely that such a thing would happen, it is actually a violation of the most fundamental statistical principles.

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• So the math says "yes" (almost certain) you can/should get a jar filled with only one color of marbles when it is only looking at the end result of marbles falling out of a hole.

• But the same math says "no" (would be in violation) when you take into account the total dynamic processes that are taking place prior to the marbles falling out of the bottom. This is one example of how nature preorders random mathematical outcomes.