geckopelli
07-05-2004, 10:49 PM
Statistical Anyalsis, Short Term Unpredictability, and the Occurance of Low Probability Sequences.
Let’s consider a deck of cards. 52 cards, 13 each of 4 different suits, 2,3,4,5,6,7,8,9,10,J,Q,K,A.
A newly opened deck comes out of the pack, Spades, Hearts, Clubs, Diamonds- we know the order of the cards, in other words.
So I can say, “the 22nd to 26th cards in the deck are a royal flush (10,J,Q,K,A of the Spades suit), and so are the 9th to 13th, 35th to 39th, and 48th to 52nd cards groups.
So we can say, “There are four royal flushes in a deck of 52 cards”.
Or can we?
What if we run the deck through a series of 1,000,000 automatic shuffling machines?
The cards are still there, but what are the chances of even one royal flush being in there?
Well, with out spending time working it out, the card books say it’s only one chance in 250,000.
That means, if we repeat the million shuffles with 250,000 decks, we’ll get 1 royal flush among them.
Even if this holds rigidly, than the question is: in which of the 250,000 decks will the royal flush occur? Will it be the 50th? Or the 222,514th deck?
The deck began in a simple order. A million random shuffles later we have no way of knowing the order of the cards because it’s too complex to follow what happens. Chaos.
It’s beyond our math to provide an equation. We know what’s happening, but only in a very general way.
Standard statistical analysis says there are factorial 52 ways to mix the cards. That’s 52 x 51 x 50 x 49…..x 3 x 2 x 1. A number to big to post.
Now repeat the experiment 1,000,000 times.
This gives you 250,000,000,000 decks, which theoretically contain 1,000,000 Royal flushes.
What if they don’t?
Well, repeat the experiment a billion times. Or a trillion-trillion times. In the long run, those odds will hold.
But how long is the long run?
Our two hundred and fifty thousand- million (250 billion) decks are nothing compared to a trillion-trillion -; 1,000,000,000,000,000,000,000,000- that’s 1,000,000,000,000,000 times more.
So what if none of our 250,000 decks is a royal flush? And we do it again, and still don’t get one. The odds didn’t hold in the short run.
So how can they hold in the long run?
Well, lo and be hold, we did it again and we got 3 royal flushes! That makes us 3 for 3! Overall, the odds held- but the royal flushes came in a “Cluster”, not in a predictable manner.
It was a low probability cluster in a high probability chain of events.
Chaos Theory is an attempt to understand how such clusters occur.
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The so-called bible codes are apparent clusters of low probability combinations found among a chain of words using high probability combinations of letters and grammar.
Just like our out of order royal flushes. They could’ve randomly occurred.
Life formation from chemical/biological energy is a low probability event occurring among higher probablility events. Compared to all the energy use in the Universe, there’s virtually no statistical chance of energy forming Life.
The same can be said for the earth and the stars and EVERYTHING we think is substantial.
The conclusion is that Uncertainty of Probability Rules. Statistical Analysis may indicate the overall direction, but it does not prove anything. Such is the nature of the fundamental laws of the Universe.
Uncertainty rules Reality, ultimately. If there is a god, I suspect the proof lies in the correct application of the principle behind Uncertainty.
Let’s consider a deck of cards. 52 cards, 13 each of 4 different suits, 2,3,4,5,6,7,8,9,10,J,Q,K,A.
A newly opened deck comes out of the pack, Spades, Hearts, Clubs, Diamonds- we know the order of the cards, in other words.
So I can say, “the 22nd to 26th cards in the deck are a royal flush (10,J,Q,K,A of the Spades suit), and so are the 9th to 13th, 35th to 39th, and 48th to 52nd cards groups.
So we can say, “There are four royal flushes in a deck of 52 cards”.
Or can we?
What if we run the deck through a series of 1,000,000 automatic shuffling machines?
The cards are still there, but what are the chances of even one royal flush being in there?
Well, with out spending time working it out, the card books say it’s only one chance in 250,000.
That means, if we repeat the million shuffles with 250,000 decks, we’ll get 1 royal flush among them.
Even if this holds rigidly, than the question is: in which of the 250,000 decks will the royal flush occur? Will it be the 50th? Or the 222,514th deck?
The deck began in a simple order. A million random shuffles later we have no way of knowing the order of the cards because it’s too complex to follow what happens. Chaos.
It’s beyond our math to provide an equation. We know what’s happening, but only in a very general way.
Standard statistical analysis says there are factorial 52 ways to mix the cards. That’s 52 x 51 x 50 x 49…..x 3 x 2 x 1. A number to big to post.
Now repeat the experiment 1,000,000 times.
This gives you 250,000,000,000 decks, which theoretically contain 1,000,000 Royal flushes.
What if they don’t?
Well, repeat the experiment a billion times. Or a trillion-trillion times. In the long run, those odds will hold.
But how long is the long run?
Our two hundred and fifty thousand- million (250 billion) decks are nothing compared to a trillion-trillion -; 1,000,000,000,000,000,000,000,000- that’s 1,000,000,000,000,000 times more.
So what if none of our 250,000 decks is a royal flush? And we do it again, and still don’t get one. The odds didn’t hold in the short run.
So how can they hold in the long run?
Well, lo and be hold, we did it again and we got 3 royal flushes! That makes us 3 for 3! Overall, the odds held- but the royal flushes came in a “Cluster”, not in a predictable manner.
It was a low probability cluster in a high probability chain of events.
Chaos Theory is an attempt to understand how such clusters occur.
-------
The so-called bible codes are apparent clusters of low probability combinations found among a chain of words using high probability combinations of letters and grammar.
Just like our out of order royal flushes. They could’ve randomly occurred.
Life formation from chemical/biological energy is a low probability event occurring among higher probablility events. Compared to all the energy use in the Universe, there’s virtually no statistical chance of energy forming Life.
The same can be said for the earth and the stars and EVERYTHING we think is substantial.
The conclusion is that Uncertainty of Probability Rules. Statistical Analysis may indicate the overall direction, but it does not prove anything. Such is the nature of the fundamental laws of the Universe.
Uncertainty rules Reality, ultimately. If there is a god, I suspect the proof lies in the correct application of the principle behind Uncertainty.