The paint analogy presented by Metaphysician Undercover is actually a very good one. — Ergo

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. I know statistics, maybe someone who knows chemistry can comment on the paint, but I do know marbles are not paint.

I noticed how you didn't try to defend any of your supposed statistical "laws". Could you tell us what those laws are?

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. — Ergo

Perhaps you could extend some sympathy to those poor souls, lacking your deep statistical intuition, who are condemned to think abstractly about such situations? A simplified example might be useful:

Say your jars could only hold 3 marbles. How often could you expect to find a jar with only one colour in it, and why?

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. — Ergo

There is reliance on what is called "the principle of plenitude". This principle states that if something is possible, then if given an infinite amount of time, that possibility will necessarily be actualized. That is why, even if it is provable that a jar of only white marbles is possible, it is still not provable that this will actually occur, because it assumes an infinite amount of time. So we have an unprovable relationship between the finite and the infinite, which is simply assumed here. Each time we fill a jar, we have a definite (finite) occurrence. We are assuming that "time" is such that if we continue with finite occurrences, time will give us the capacity for infinite repetition.

So we must make a particular assumption about the nature of time in order to support the principle of plenitude. There is a relation between time and numbers, such that numbers are an order, two comes "after" one, and three comes "after" two. We assume that one could theoretically keep counting forever and therefore numbers are infinite. But we could use the principle of plenitude against itself. We could say that it is possible that time will end. Therefore if given an infinite amount of time, it is necessary that we will reach the end of time, and this negates the infinite amount of time, in a paradoxical way.

But we can put the principle of plenitude aside because it only comes into play after the possibility is established. I believe that it is Ergo's claim that a jar of all one colour is not even possible under the described circumstances. And Jeremiah claims that it is possible. I have a question for Jeremiah. If slight variances in the mixture, from one jar to another are observable, what leads you to the conclusion that a jar of all one colour is possible?

If slight variances in the mixture, from one jar to another are observable, what leads you to the conclusion that a jar of all one colour is possible? — Metaphysician Undercover

And where did you establish that only slight variations can occur over an infinite number of jars? If we say something can happen outside normal distribution then we are saying an occurrence that is not a slight variation can occur. I already went over this.

And this is where Ergo's mistake is: He is assuming that given the null is true we will always get an even distribution [This does not mean exactly even.], because in a fair test after all the math is done we will fail to reject the null; either 90, 95, or 99.95 (typical standards) percent of the time, but there is no always. Yes, we can use the math to approximate a normal distribution but it is called "normal" for a reason.

Here is a simple rundown of the Empirical Rule: http://www.statisticshowto.com/empirical-rule-2/ — Jeremiah

And where did you establish that only slight variations can occur over an infinite number of jars? If we say something can happen outside normal distribution then we are saying an occurrence that is not a slight variation can occur. I already went over this. — Jeremiah

What would constitute something happening "outside the normal distribution"?

http://www.statisticshowto.com/empirical-rule-2/

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts:

68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.

Something that happens outside the third standard deviation.

Something that happens outside the third standard deviation. — Jeremiah

I gave a formula earlier for the density of occurrences of jars of a single colour. By definition, when this happens, it is well outside many standard deviations for moderate sized jars.

The normal distribution does not end at 3 standard deviations.

Technically it is a bell curve, so it really does not have an end. My point being due to the low probability you will likely fail to reject the null and it will look like the math is proving an even distribution of the marbles. So I think the math is being misunderstood to mean you will always be within 3 SDs, when that is just not true.

I have to also point out, we are all just assuming there will be roughly an even distribution of the marbles in the jar, but this is not something that has been proven. The only way to get reliable answers would be to actually do the experiment.

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” — Ergo

This right here vs. this:

"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 -Ergo"

Have you accounted for everything? Did your Godly brain uncover all confounding variables? I am sorry, but until you actually run the experiment you don't really know how they will distribute.

You cannot prove they will be distributed on the "statistical law" alone. In fact you are violating a few rules of statistics by making your claim without any data to back it up.

I'll agree with the point: that there may be something unconsidered which will prevent a jar of all colors (which would mean we don't have randomization); however, that also applies to the assumption they will be evenly distributed.

The truth is we are working a hypothetical, and what is needed to get real answers is to actually do the experiment.

I'll agree with the point there may be something unconsidered which will prevent a jar of all colors, however that also applies to the assumption they will be evenly disturbed. — Jeremiah

The only assumption is that the marbles are well-mixed.

He is also making an assumption about even distribution. I am not sure if that is what you are referring to with "well-mixed".

colors of the marbles will tend to be evenly distributed inside the mass — Ergo

To be honest, I can't believe I over looked that detail, guess I was not paying close enough attention. We don't actually know if the marbles will be evenly distributed.

And where did you establish that only slight variations can occur over an infinite number of jars? — Jeremiah

As I said, we should drop the possibility of an infinite number of jars, because this is an appeal to the principle of plenitude, which in this case, establishes an unreal relation between the finite and the infinite. It assumes the possibility of an infinite number of jars, without demonstrating how this is a real possibility. I believe that due to the nature of time, and physical existence, this is not a real possibility. This is the weakness of Ergo's op, it asks about infinite jars. When you ask unreal questions you get unreal answers.

If we say something can happen outside normal distribution then we are saying an occurrence that is not a slight variation can occur. — Jeremiah

A slight variation in the proportions of coloured marbles is the normal distribution, just like when you flip coins, a slight variation in the number of heads and number of tails, is the normal. You appear to be arguing that the existence of such a slight variation indicates the possibility of a large variation, if given enough repetitions. On what principle do you argue this? Consider the example I gave already:

"Say you flip a coin 19 times, with 10 heads and 9 tails. Does this suggest to you that if you flip the coin 19,000,000 times you'll end up with 10,000,000 heads and 9,000,000 tails?"

The question is, how do you get from the continued observance of small variations, which would be your premise, that there is not exactly the same number of each coloured marble in each jar, to the conclusion that a large variation (one much larger than any observed variation), is possible? What would be the premise which you would apply to give you this conclusion?

Math will allow us to calculate the probability of it happening. Does this prove it will happen? Not necessarily, but it does suggest it is a possibility, even if it is a very slim one. And the math is making a far more convincing argument than your words.

One of the reasons I study math is so I can philosophize in mathematics as well as words.

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

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.

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. — Ergo

Isn't there an important difference between "tending to be evenly distributed" and "necessarily being evenly distributed"?

It sounds as if you've taken the general tendency and turned it into a universal law of nature admitting of no exceptions. I'm not sure that's how "statistical laws" are supposed to work.

The laws of physics do not change between a can of paint and a gigantic clambering vat of swirling marbles. — Ergo

Yes, they do. Liquids behave differently than solid marbles.

Saturation is the point at which a solution of a substance can dissolve no more of that substance. This point of maximum concentration, the saturation point, depends on the temperature of the liquid as well as the chemical nature of the substances involved. If a change in conditions (e.g. cooling) means that the concentration is higher than the saturation point, the solution has become 'supersaturated'.
In organic chemistry, a saturated chemical compound has no double bond or triple bond or ring. In saturated hydrocarbons, every carbon atom is attached to two hydrogen atoms, except those at the ends of the chain, which have three hydrogen atoms.
In biochemistry, the term saturation refers to the fraction of total protein binding sites that are occupied at any given time. Applies to enzymes, and molecules like haemoglobin.
In organometallic chemistry, an unsaturated complex has fewer than 18 valence electrons and thus is susceptible to oxidative addition or coordination of an additional ligand. Unsaturation is characteristic of many catalysts because it is usually a requirement for substrate activation.

https://simple.wikipedia.org/wiki/Saturation_(chemistry)

It is my thinking that this particular discussion about randomness is among the most important debates in science, physics, mathematics and philosophy. — Ergo

References? If it is such an important debate surely you can manage that.

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. — Ergo

Let me get this straight you are now using unfalsifiability to justify your claim? You do realize that a hypothesis must be falsifiable in order for it to actually be a valid hypothesis, right? It is becoming more and more clear that you do not know much about science or statistics.

I think this is an ulterior motive behind this thread.