Game Theory Scene | 21(2008) | Now Playing

Summary

In this engaging lecture, the professor explains Newton's method for solving non-linear equations, highlighting its connection to Joseph Raphson, who developed the same technique earlier but received less credit. The discussion then transitions into a fun game show analogy where Ben Campbell answers a probability-based problem. When asked whether to stick with his initial choice or switch doors after the host reveals a goat, Ben applies statistical reasoning and chooses to switch, increasing his chances of winning. The lecture emphasizes the importance of understanding variable change and avoiding emotional biases in decision-making.

Takeaways

• 😀 Newton's method is used to solve non-linear equations.
• 😀 Although Newton is credited with the method, Joseph Raphson published the same method 50 years earlier.
• 😀 The success of Newton's method depends on the start value being close to the true zero.
• 😀 Ben Campbell humorously suggests that Joseph Raphson was the original author of Newton's method, pointing out Newton had a better publicist.
• 😀 After 1700, very little is known about Raphson, except his discovery of Kabbalah 300 years before Madonna.
• 😀 A 'game show host problem' is introduced to demonstrate statistics and variable change.
• 😀 In the game show problem, a contestant is given the chance to choose between three doors, one hiding a car and the other two hiding goats.
• 😀 After the host opens a door revealing a goat, the contestant can switch their choice to increase the odds of winning the car.
• 😀 Statistically, switching the door increases the chances of winning the car from 33.3% to 66.7%.
• 😀 Ben Campbell applies mathematical reasoning and switches his choice, securing the car instead of a goat.
• 😀 The takeaway from the game show problem is that understanding statistical probabilities can overcome emotional biases and lead to better decisions.

Q & A

What is Newton's method used for?

Newton's method is used to solve non-linear equations.

Who is suggested to be the original author of Newton's method, and why?

Joseph Raphson is suggested to be the original author of Newton's method because he published the same method 50 years earlier than Newton. However, Newton gained more credit due to better publicity.

Why didn't Joseph Raphson get credit for Newton's method?

Joseph Raphson didn't get credit because Newton had a better publicist, and after 1700, there was little known about Raphson except for his discovery of the Kabbalah.

What is the 'game show host problem' discussed in the transcript?

The 'game show host problem' refers to the Monty Hall problem, where a contestant must decide whether to stick with their initial choice of a door or switch after the host reveals a goat behind another door.

What was Ben's initial choice in the game show problem?

Ben initially chose door number one.

What happens after the host opens a door in the game show problem?

After the host opens door number three, revealing a goat, the contestant is given the option to switch their choice to door number two.

Why is it in Ben's best interest to switch doors in the game show problem?

It is in Ben's best interest to switch doors because the probability of winning the car increases from 33.3% to 66.7% if he switches, based on the statistics of the game.

What is meant by 'variable change' in the game show problem?

'Variable change' refers to the shift in probabilities after the host reveals a goat behind one of the doors, altering the chances of winning the car.

What emotional factor often prevents people from switching doors in the game show problem?

Most people are reluctant to switch doors due to paranoia or fear, often influenced by emotions, even though statistics suggest it is better to switch.

What does Ben's decision in the game show problem illustrate about decision-making?

Ben's decision illustrates the importance of ignoring emotions and using simple math and statistics to make decisions, leading to a better outcome, in this case, winning a car.