Can you ever achieve a jar filled only with only one single color of marbles in it? — Ergo

Not impossible. but extremely unlikely.

On an infinite timeline with infinite jars it is inevitable.

The chance of winning the Power Ball Lottery is something like one in 175 million, and it still happens.

We will take this into the realm of enormous numbers. What if you filled a trillion jars? Would the outcome be different? A Centillion jars? A Trillion Centillion jars? Would the outcome be different then? — Ergo

As long as the proportion of marbles is the same and each color has a fair and equal chance of dropping into the jar, then filling more jars would not change anything. The probability of each outcome will remain the same from jar to jar. The only way that probability would change is if the proportion of the marbles changed or if the randomization broke down.

So if we have 5 favorable combinations out of a total of 153,478,146 possible combinations (assuming it is a standard size mason jar holding 115 marbles; just a very rough guess) then we have a 3.257835217E-8 chance of a solid color jar. Hopefully my memory on calculating probability is correct.

Now what happens when we make the jar bigger? Every time we increase the size of the jar the probability gets smaller and smaller.

So if we keep increasing the size of the jar can the probability ever get so small it is 0? It would have to be so big that it could never be filled.

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.

it is actually a violation of the most fundamental statistical principles. — Ergo

We are not really talking about statistic, we are talking about probability. While statistics does incorporate probability mathematics, it itself is a science. The "most fundamental statistical principles" are not actually all that mathematical in nature.

"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"

I didn't realize this as all on a some type of time release, but we can start multiplying probabilities.

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. — Ergo

Once again we are talking about probability, not statistics; and no it won't. Unless the vat is smaller than the jar, and well vats are not smaller than jars, in fact they are typically very big. Big enough to easily fill a funnel and a jar with a single color.

"

This is one example of how nature preorders random mathematical outcomes. — Ergo

"

You are talking about a human made factory.

Excellent statement about the perplexities of nature. I often wondered myself about the embedded intelligence of nature.

The fact that he does not know the difference between probability and statistics is something of a concern.

I expected your post to simply say, "It has an app for it."

Re your thought experiment, there doesn't seem to be anything random about it, by the way.

It would be practically impossible to predict the exact number of each color that would end up in a given jar, but as long as everything is set up so that marbles are being fed in a steady stream from each color room to the final mix, there's nothing random about that.

I'm with Ergo on this. The manufacturing process, conveyors, and mixing mechanism are designed to continually produce a consistent mixture of colour. Therefore you will never get a jar of all the same colour marbles unless there is a failure in the mechanism of the factory.

I am sorry, but if you have randomization then you are going to have deviation. There will be a normal distribution which will be based on proportion of the colors, but if we are claiming randomization, then there will be deviation from that distribution. If there is no possibility of deviation then it is not random.

Well of course it's not random in any absolute sense. The op describes a very specifically, organized mechanical system, therefore the outcome (the filling of the jars) is not random in the sense which you are using "random". The use of the word "random" in the op title is somewhat mischievous, if not downright deceptive, because there is nothing random about the described arrangement.

Personally, I would like to know the source of his information and I would not mind seeing the math, as I feel we may not be getting a fair representation of it here. The way he uses the terminology makes me suspicious.

The op describes a very specifically, organized mechanical system, therefore the outcome (the filling of the jars) is not random in the sense which you are using "random". — Metaphysician Undercover

Not really; there is no system that could account for this: " They all converge and pour into a large vat where the marbles are mixed together in a torrent of bouncing, clambering mass that flows like fast moving water."

Unless I see something more academic, I am standing by the position: If the out put to the jars is randomized then you can get a full jar of solid colors.

The outcome isn't randomized though. Ergo uses "random" in the title to throw you off. Nothing in the description of the factory indicates that there is any randomness. Evenly sized, shaped, and weighted marbles are produced, of different colours. They are brought together in even proportions and mixed evenly. The outcome can be nothing other than an even mixture. The system is designed to produce an even mixture.

If the vat is the same size of the jar, but vats are not the same size as jars. Vats are typically much bigger than jars. At any rate, it is sounds more like a word game than one of math.

If you are mixing the vat then there is a probability you'll have pockets of same color marbles.
We can put marbles in a jar and mix them all about and see with our own eyes the distribution. If you are mixing them, then you are randomizing them.

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

This right here is what we would call a normal distribution, but it is possible to see an event outside the normal distribution.

Weird thread.

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

When you say 'statically xxx' you are saying that some situations/events/etc are more likely than others. Also it's a description not a normative statement. It's weird to hypostatize statistics as if there is some statistical force acting on the marbles.

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.

But does the maths say this?
Your trying to play off two mathematical claims against each other, but if you flesh it out more there is not conflict at all.
1. If there is a the possibility of a jar filling up with a certain color then infinite jars will almost certainly have at least one in which there is only one color.
2. If it's impossible - lets say I set my machine to place one of each color in each jar and it never fails to do this - then even with infinite jars there will not be any with one color in a jar.

The mixing machine is analogous to the mixing of tinctures in a can of paint. If every time you open a can of paint, the colours are well mixed, then the mixing machine has been applied to the parameters necessary for the job. But if sometime you open a can to find a streak of unmixed colour, then the mixing machine hasn't done it's job, and has not been properly designed.

But does the maths say this?
Your trying to play off two mathematical claims against each other, but if you flesh it out more there is not conflict at all.
1. If there is a the possibility of a jar filling up with a certain color then infinite jars will almost certainly have at least one in which there is only one color. — shmik

The issue here is modelling a deterministic physical system as a stochastic process. If we agree that randomness is an appropriate model, then the probability of finding a jar filled with a single colour would be something like 1 in 4^(n-1) where n is the number of marbles in the jar.

So, if n=101, then you should get a jar full of a single colour every ~1.6x10^60 jars, by which time you will have used up the matter in the universe and created a super-massive black hole.

Look this is simple; take a jar fill it with various colored marbles then shake it around and see if any of the colors are not evenly distributed.

The idea that every single time you mix the marbles you are always going to get an even distribution is just not realistic, and it is not support by the math. A probability distribution always has an element of uncertainty.

by which time you will have used up the matter in the universe and created a super-massive black hole. — tom

Unless the operators of the factory are environmentalist.

The jar is basically a random sample of of the vat.

So what Ergo is suggesting is that the proportion in the jar will be always be even.

In statistic we would never make an absolute claim like that, because statistic is the science of uncertainty, but we would create a null hypothesis:

Po: P1=P2=P3=P4=P5

Versus an alternative hypothesis

Pa: At least one of the proportions is different.

We would then have to take a jar and measure the results against a null distribution to figure out the probability of the observed results given the null distribution is true. We would then use this p-value or test statistic, to make a conclusion about the hypothesis.

And this is where Ergo's mistake is: He is assuming that given the null is true we will always get an even distribution, 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/

The process includes an element of uncertainty, and in statistics the conclusion will never be the null is true, it will always be there is strong/weak evidence for (or against) the null (or the alternative which ever may be). And we would make that conclusion based on the probability of the observed results given the null is true.

Statistics does not measure certainty, it measure uncertainty.

So what Ergo is suggesting is that the proportion in the jar will be always be even. — Jeremiah

I don't think Ergo is suggesting that the proportion will always be perfectly even. The question is, how does the reality of a minor variance in proportion translate, for you, into the possibility of a major variance in proportion? 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?

I think I identified his mistake. Hypothesis testing will likely support an even distribution. Which to the untrained eye can look like math is proving there will be an even distribution. So I feel he may be misunderstanding that process.

Now we all agree the probability of an all color jar is incredibly low, but that is different then what he was saying.

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.