By suggesting God has a chance to exist you are actually claiming that God currently does not exist but that a future event will give God a chance to exist.

As such, we can determine that there are six possibilities about our cause and the existence of a God. Thus, we can deduce the probabilities of these outcomes (assuming they are all equally probable).
That no God exists has a 1 in 2 (1/2) chance.
That a God exists has a 1 in 3 (1/3) chance.
That a Semi-God exists has a 1 in 6 (1/6) chance — Javants

That is not probability.

Probability is the proportion of possible out comes under the repeat exercise of a random event. You didn't exercise a random event, you made up a bunch of stuff and assigned values to it.

Also there is no probability for the existence of something; it either exist or it doesn't. God doesn't have a 33% chance of existing, that is just stupid. Either God is there or God is not. Something can have a chance to come into existence but once it is here it is no longer a question of probability.

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.

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.

That's quantification if ever I saw one. — TheMadFool

No, it is not. That is qualitative.

I think no other human invention has that much depth and breadth of application as mathematics. — TheMadFool

Spoken language and written language. Even math depends on these two.

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.

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. — SophistiCat

No, it is not.

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.

I think this is an ulterior motive behind this thread.

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

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.

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.

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

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.

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 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.

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.

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.

"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.

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

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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

" It's to the degree that philosophy deals with precisely this 'wider' subject matter that I call it a poor - or maybe rather limited - philosophical tool."

Sorry, I just can't get fully on boat with that one. Consider this famous quote:

“Give me but a firm spot on which to stand, and I shall move the earth.”
― Archimedes, The Works of Archimedes

Science provides the firm spot on which philosophy can stand. I don't think we are too far off in our ways of thinking, I just don't argue with the notion it is a "poor" philosophical tool.