• Perfection and Math

Probability ranges 0 to 1 because you can never have something with a higher probability of 100% or a probability lower then 0%

Statistically probability is the proportion of possible outcomes from the repeated exercise of a random event.

Categorical differences can be a number of things from colors, does a medicine make your feel better, is it night or day, etc.

So I am not entirely sure what you mean by "measured relatively", as it might depend on what you are trying to find out. But for an example if I wanted to know if flowers grow more in day or night, then I would have to compare the two, and that would actually be a study that used both categorical and quantitative variables.
• Perfection and Math

It is categorical (or sometimes called qualitative) because things such a like and dislike are categories. There are no objective standards to measuring degrees of likeness. Even though you can assign numbers to the categories, they are still categories.

Here is the text book definition, pulled from one of my statistics course books.

Quantitative variables are made of numerical measurements that have meaningful units attached to them. Categorical variables take on values that are categories or labels.

Like and dislike as far as math is concerned are categorical labels and not numerical measurements. If I say I like something more than something else then that is its label; that is not a numerical measurement.
• Perfection and Math
That's quantification if ever I saw one.

No, it is not. That is qualitative.
• Perfection and Math
I think no other human invention has that much depth and breadth of application as mathematics.

Spoken language and written language. Even math depends on these two.
• Argument Against the Existence of Animal Minds
Homo sapiens are just one of millions of extant species of conscious animals. If you rank these species in descending order of overall intelligence, human beings rank at the very top of the list--out of millions, we're number one. As a human being, it seems like I got very lucky, when it's conceivable that I could have been a bat, cicada, giraffe, cow, rat, spider, salmon, kangaroo, etc.jdh

A probability model is only useful if it can be fitted to the real world. The probability of a species when a new life is actually born is not determined by a ranking system. It is determined by the species of the parents. You model is fictitious and worthless in determining the probability of your species. The fact is since both your parents were humans you had a 100% chance of being human.

You can make up fictitious probability models all day long but just thinking them up will not make them an accurate approximation of real world probability. The only way to do that is by collecting real samples.

Also, you would not rank the probability of a random life sample from Earth by intelligence, you would rank it by the proportion of human life out of all life on Earth.
• The Coin Flip
That's just what we mean when we say that the probability of a coin toss outcome is 50%. So the answer to your question in the OP: it doesn't matter whether the coin toss has occurred or not - as long as you haven't looked.

No, it is not.
• The Coin Flip
If I flip the coin 10 more times each time I flip it, the coin can land on heads or tails, but after it has landed it does not matter how many times I go to look at the coin, it will not change from heads to tails or vice versa.

So what this shows us is that in order for something to have probability there has to be a chance mechanism of some kind involved. After the coin lands probability is no longer a relevant question. We can guess what it might be, and you may have a 50% chance of being right but that chance pertains to your guess and not the coin.
• How Nature Preorders Random mathematical Outcomes
I think this is an ulterior motive behind this thread.
• How Nature Preorders Random mathematical Outcomes
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.
• 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 than 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?

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

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