Comments

  • How Nature Preorders Random mathematical Outcomes
    I kind of think this discussion is at its end, Ergo's "hypothesis" has been shown to have many flaws.
  • How Nature Preorders Random mathematical Outcomes
    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 then your words.

    One of the reasons I study math is so I can philosophize in mathematics as well as words.
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes


    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 massErgo
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes


    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.
  • How Nature Preorders Random mathematical Outcomes


    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.
  • A question about English expressions for martial arts
    "Jones threw a punch."

    You don't actually have to say threw a, as you could just say, "Joe punches" or "Joe punched". Or you even just say "Joe punched his opponent." You can add a prepositional phrase if you like, "Joe punched his opponent in the face." Some other examples: "Joe smacked Mark", "Joe beat Mark with his fist.", "Joe cracked his knuckles across Mark's jaw, and Mark swallowed a tooth." "Joe gave Mark a fat lip."

    "Mark go fed up, and hammered Joe with a crowbar."

    There are so many possible combinations, so just be creative.
  • How Nature Preorders Random mathematical Outcomes
    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
  • How Nature Preorders Random mathematical Outcomes
    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?
  • How Nature Preorders Random mathematical Outcomes


    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.
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes


    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.
  • How Nature Preorders Random mathematical Outcomes
    colors of the marbles will tend to be evenly distributed inside the massErgo

    This right here is what we would call a normal distribution, but it is possible to see an event outside the normal distribution.
  • How Nature Preorders Random mathematical Outcomes
    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.
  • How Nature Preorders Random mathematical Outcomes


    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.
  • How Nature Preorders Random mathematical Outcomes
    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.