Right: the monkey banging on a keyboard claim is wildly misleading. Wikipedia is correct on this: “However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time the results are reversed. If there were as many monkeys as the number of atoms in the universe typing extremely fast for trillions of times the age of the universe, the probability of the monkeys replicating even a single page of Shakespeare is unfathomably small.” Of course, infinite monkeys and infinite time is another matter https://en.wikipedia.org/wiki/Infinite_monkey_theorem
If these highly improbable events occur all the time, then what does the math actually tell us? It's not telling us that these highly improbably events are rare so I'm struggling to understand the value.
Also, understanding probabilities is one of the most important features in helping discern reality. It helps you understand if your beliefs are wildly improbable—or likely true.
If highly improbably events like card shuffles and sentence structures are occurring multiple times a day, what value does an improbability calculation bring to our understanding? Something is highly improbable but happening all the time - what do I do with that information?
What is highly improbable is the exact ordering of the cards in the deck after the shuffle. That exact ordering never occurs multiple times a day. Every shuffled deck is unique—and brings a brand new ordering that has never occurred before in the history of the universe. Same with every non-trivial sentence we write or speak. Grasping the uniqueness of something as simple as the order of a freshly shuffled deck forces you to confront the basic probabilities of events unfolding in the world —an awareness that sharpens judgment, shapes intuition, and keeps you from being misled by appearances.
I realize that. The highly improbable events are happening all the time. It's as if the improbability calculation tells you nothing about how often they show up - but that doesn't seem right either. I'm genuinely stumped.
Okay, I see what you are saying. Importantly, a shuffled deck is *not* highly improbable. Shuffled decks occur all the time. That's not what we are saying. What is highly improbable --essentially impossible--is a particular ordering of those cards. What is highly improbable is a shuffled deck that ends up with the ace of hearts on top, followed by the king of hearts, queen of hearts, jack of hearts.. etc. down to the two of Hearts, then ace of diamonds, king of diamonds .... etc. ... then ace of spades ... etc., then ace of clubs ... down to the last card, the 2 of clubs. That has never occurred before--and will never occur after a thoroughly shuffled deck in the history of the human race.
*Any possible ordering* of a deck of cards *must* occur after the deck is shuffled. That's 100%. What won't happen is a particular ordering of all 52 cards that you call out beforehand.
EVERY particular ordering has the same high improbability. All are essentially impossible as you say, and yet, the statistically impossible happens all the time.
After thinking about it for a while, the statistics tell us how difficult it will be to PREDICT in advance which highly improbable outcome will occur. An "impossible" ordering of the cards will occur when a shuffle occurs, but good luck predicting what the ordering it will be.
Well, with the birthday situation, the math tells you it is not as improbable as it may seem—and you can test it yourself next time you’re in a room with 23 or more people. Just yell out: “Let’s see if anyone shares a birthday: whoever is born in January, what day of the month? Okay, February … “ And so on.
With the astronomical number of variations in ordering a deck of cards or creating a sentence, this helps show how improbabilities multiply and gives you a sense of how unlikely it is to hit the lottery or that all the lines shared between North and Shakespeare might be coincidental.
So a monkey banging at a keyboard will never compose the complete works of Shakespeare. Settled.
Also, settled: I cannot be conversant in a new language by memorizing the first 10 pages of a phrase book.
Right: the monkey banging on a keyboard claim is wildly misleading. Wikipedia is correct on this: “However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time the results are reversed. If there were as many monkeys as the number of atoms in the universe typing extremely fast for trillions of times the age of the universe, the probability of the monkeys replicating even a single page of Shakespeare is unfathomably small.” Of course, infinite monkeys and infinite time is another matter https://en.wikipedia.org/wiki/Infinite_monkey_theorem
If these highly improbable events occur all the time, then what does the math actually tell us? It's not telling us that these highly improbably events are rare so I'm struggling to understand the value.
Also, understanding probabilities is one of the most important features in helping discern reality. It helps you understand if your beliefs are wildly improbable—or likely true.
If highly improbably events like card shuffles and sentence structures are occurring multiple times a day, what value does an improbability calculation bring to our understanding? Something is highly improbable but happening all the time - what do I do with that information?
What is highly improbable is the exact ordering of the cards in the deck after the shuffle. That exact ordering never occurs multiple times a day. Every shuffled deck is unique—and brings a brand new ordering that has never occurred before in the history of the universe. Same with every non-trivial sentence we write or speak. Grasping the uniqueness of something as simple as the order of a freshly shuffled deck forces you to confront the basic probabilities of events unfolding in the world —an awareness that sharpens judgment, shapes intuition, and keeps you from being misled by appearances.
I realize that. The highly improbable events are happening all the time. It's as if the improbability calculation tells you nothing about how often they show up - but that doesn't seem right either. I'm genuinely stumped.
Okay, I see what you are saying. Importantly, a shuffled deck is *not* highly improbable. Shuffled decks occur all the time. That's not what we are saying. What is highly improbable --essentially impossible--is a particular ordering of those cards. What is highly improbable is a shuffled deck that ends up with the ace of hearts on top, followed by the king of hearts, queen of hearts, jack of hearts.. etc. down to the two of Hearts, then ace of diamonds, king of diamonds .... etc. ... then ace of spades ... etc., then ace of clubs ... down to the last card, the 2 of clubs. That has never occurred before--and will never occur after a thoroughly shuffled deck in the history of the human race.
*Any possible ordering* of a deck of cards *must* occur after the deck is shuffled. That's 100%. What won't happen is a particular ordering of all 52 cards that you call out beforehand.
EVERY particular ordering has the same high improbability. All are essentially impossible as you say, and yet, the statistically impossible happens all the time.
After thinking about it for a while, the statistics tell us how difficult it will be to PREDICT in advance which highly improbable outcome will occur. An "impossible" ordering of the cards will occur when a shuffle occurs, but good luck predicting what the ordering it will be.
Well, with the birthday situation, the math tells you it is not as improbable as it may seem—and you can test it yourself next time you’re in a room with 23 or more people. Just yell out: “Let’s see if anyone shares a birthday: whoever is born in January, what day of the month? Okay, February … “ And so on.
With the astronomical number of variations in ordering a deck of cards or creating a sentence, this helps show how improbabilities multiply and gives you a sense of how unlikely it is to hit the lottery or that all the lines shared between North and Shakespeare might be coincidental.