Combinations of 52 cards (52 factorial)

Summary

This video script explores the staggering concept of 52 factorial, which represents the number of unique ways a deck of 52 cards can be arranged. The narrator highlights the enormity of this number, explaining that it's so vast that even with the universe's age and continuous shuffling, not all possibilities could be achieved. Using vivid analogies, such as walking around the Earth and removing drops from the Pacific Ocean, the script emphasizes the sheer scale of 52 factorial. It also touches on the concept of human uniqueness, pondering how many possible versions of a person exist, making each life precious.

Takeaways

• 😀 52 factorial (52!) represents the number of unique ways a deck of 52 cards can be arranged.
• 😀 There are 52 possibilities for the first card, 51 for the second, 50 for the third, and so on, leading to 52! unique arrangements.
• 😀 52 factorial is an astronomically large number: 8.0658 × 10^67.
• 😀 Even if you shuffled a deck every second since the beginning of the universe (13.7 billion years ago), you wouldn’t cover all possible arrangements.
• 😀 The observable universe is only about 10^18 seconds old, which is tiny compared to the number of seconds in 52! (10^67).
• 😀 A visual metaphor to understand 52! involves walking around the Earth at a rate of one step every billion years while removing drops of water from the Pacific Ocean.
• 😀 After emptying the Pacific Ocean and stacking paper to reach the Sun, there would still be 52! seconds left on the timer.
• 😀 Even if you repeated the walking and water-dropping process 256 more times, you’d only be one-third of the way done with 52! seconds.
• 😀 An alternative analogy involves dealing a royal flush every billion years, buying lottery tickets, filling the Grand Canyon with sand, and leveling Mount Everest.
• 😀 By the time Mount Everest is leveled, the timer would have barely moved toward reaching zero, illustrating the enormity of 52! and the time scale involved.
• 😀 52! is so large that the number of possible humans (or people that could have existed) is even larger, emphasizing the rarity and uniqueness of individual human existence.

Q & A

What does 52 factorial represent?

52 factorial (52!) represents the number of different ways a deck of 52 playing cards can be arranged. It is the product of all integers from 1 to 52.

Why is 52 factorial such a large number?

52 factorial is an extraordinarily large number because it involves multiplying 52 numbers together. This leads to a result of approximately 8.0658 × 10^67, which is vastly larger than the age of the universe in seconds.

How many seconds is the observable universe old?

The observable universe is about 10^18 seconds old, which is a tiny fraction of the number 52 factorial, showing how large 52 factorial is.

How many possible card arrangements have occurred in the history of the universe?

Even if you had been shuffling a deck of cards every second since the beginning of the universe, you would still not have come close to assembling all the possible arrangements of 52 cards.

What is a visualization used to demonstrate how large 52 factorial is?

A visualization by Scott appeals to walking around the Earth, taking one step every billion years, and removing a drop of water from the Pacific Ocean each time. This process would take longer than 52 factorial seconds to complete, even after refilling the ocean and walking around the Earth repeatedly.

What happens when the Pacific Ocean is emptied in the visualization?

Once the Pacific Ocean is emptied by removing a drop every time you walk around the Earth, the next step involves placing a sheet of paper on the ground, refilling the ocean, and continuing until the paper stack reaches the Sun. At this point, a vast amount of time remains on the timer, illustrating the enormity of 52 factorial.

How does Scott suggest passing the time in the visualization?

Scott suggests dealing yourself a royal flush every billion years, buying a lottery ticket, and performing various other tasks like filling the Grand Canyon with sand and removing rock from Mount Everest. Even after completing these tasks over 250 times, you would still not have reached the end of 52 factorial seconds.

What is the implication of the size of 52 factorial for human life?

The enormity of 52 factorial suggests that there are vastly more possible combinations of humans than there are humans who could ever exist. This implies that many possible people, including those with extreme intelligence, humor, or other traits, will never be born or die in the way we experience life.

How does the concept of 52 factorial compare to human existence?

The concept of 52 factorial emphasizes that while each person's life is unique, there are so many possible combinations of humans that most potential people, even those with extraordinary qualities, will never come into existence.

What is the main takeaway from the visualization of 52 factorial?

The main takeaway is that 52 factorial is an incredibly large number, far beyond human comprehension, and even simple actions like shuffling a deck of cards create a nearly infinite number of possible outcomes, some of which may never have occurred in the entire history of the universe.