How Good Is Our Intuition ?

Below are some examples related to our intuition. The answers to the first two examples are provided.

(1)  A rope and the earth

Suppose you tie a rope tightly around the Earth's equator (note: circumference of earth at equator is about 25,000 miles, i.e., about 132,000,000 ft.). You add an extra 3 feet to the length of the rope. All around the Earth the rope is raised up uniformly as high as is possible to make it tight again. How high is that?

The circumference of earth at equator is about 132,000,000 ft. Thus 3 feet is very, very, small compared to the circumference. Intuition tell us that the rope probably rises up very slightly, if at all.

Well, that is wrong. According to mathematics, the rope will rise up about 5.7 inches (almost half a foot). 

So, if a stranger tells us the correct answer, we likely think that the person is lying because it is so improbable, according to our intuition.

(2)  Books

There are 20 books on a bookshelf. What are the approximate number of ways to arrange the books?

Watch this video for an answer:   Books on a Shelf

(3)  Flight Training

Takeoff and landing are often referred to as the "critical phases" of flight because the majority of accidents occur during these two stages. Thus, flight schools require student pilots to receive rigorous takeoff/landing training together with numerous drills. An airplane flight instructor was hired to train student pilots. He believed in giving verbal feedback to trainees immediately so they can improve their skills. When trainees had an exceptional smooth landing, he praised the trainees lavishly. When trainees had a rough landing, he criticized them harshly. Soon he noticed that praise for an exceptional smooth landing is typically followed by a poor landing. On the other hand, criticism for a rough landing is often followed by an improvement on the next try. After seeing this pattern of behavior many times, he came to the conclusion that verbal rewards are detrimental to learning while verbal punishments are beneficial.

Is the conclusion correct?