In 1989 democratic movements were making progress in Eastern Europe and the communist leader in East Germany had to resign. The pressure was so great that the current East German government had decided to allow some restricted passage through the Berlin Wall. The person who was assigned the job of announcing this decision was not given the exact orders and he was asked when this would occur. He did not know so he said it would be open completely and ‘immediately’. People started gathering at the wall and the guards, who were also not informed of what was happening laid down their weapons and opened the gates to all. The genie was out of the bottle and the wall came tumbling down in the next day.

(The Great Courses – Turning Points in American History)

It is not a surprise that the number of integers (1,2 3, 4, etc…) has an infinite number of numbers. The number of irrational numbers is also infinite but it is a larger number of infinite numbers. And any list of numbers has a ‘Power Set’ which consists of all possible combination of numbers in that list. That power set will always have more numbers than the original list so the power set of irrational numbers is a larger infinite number than the original list. And you can then take the power set of the power set and so on. This means that there are an infinite number of different sizes of infinite numbers.

(The Great Courses – Zero to Infinity: A History of Numbers)

Astronomers are required but a US congressional mandate to track all asteroids which are over 1 kilometer in length. There has already been a situation where a small asteroid was discovered and then correctly predicated to hit the earth in Sudan a week before it happened. This allowed people to be ready to pick up some of the pieces after the impact.

(The Great Courses – Life in Our Universe)

Any number can be raised to another number. Example 2 to the power of 3, designated here as 2 ** 3 is the same as 2 * 2 * 2. The number Pi is well known as an irrational number (no repeating digits) and is part of the ratio between the radius and the circumference of a circle.  The number e is Euler’s number and it is also an irrational number and is used in equations describing growth. The square root of -1, designated i is called an imaginary number since it cannot be described using any ‘real’ numbers, but it also has applications in our real world as it is used in equations describing electrical fields. It would seem that these two irrational numbers and the imaginary i could not have anything in common but in one of the most incredible formulas in math it has been proven that e ** (Pi * i) = -1. That is e raised to the power of (Pi times the square root of -1) equals -1. Mathematicians still do not know how to interpret this amazing correlation between three of the most fundamental numbers we know about.

(The Great Courses – Zero to Infinity: A History of Numbers)

The Rough Riders under Teddy Roosevelt are famous for their exploits in the Spanish-American War in Cuba. They are credited for winning the Battle of San Juan Hill. While they did take a nearby hill, the important San Juan Hill was actually taken by the 10th Negro Calvary.

(The Great Courses – Turning Points in American History)

The Soviet Union tried to do everything possible to make the west look bad so they approved the showing of the movie ‘The Grapes of Wrath’ to show poor people in the United States. However, the people watching the movie were impressed that even poor people had cars so when the officials realized that was impressing its citizens they had the movie pulled from their theaters.

(The Great Courses – Turning Points in American History)

Dice made from fired clay date back to around 3000 BCE. Since there were no ‘number’ symbols they used number of dots to represent the numbers on each side. We still use that today!

(The Great Courses – Zero to Infinity: A History of Numbers)

On September 5 , 1882 the first Labor Day parade was held in New York City. By 1886 it became a national event and in 1894 it was made a Federal Holiday. In 1888 labor organizers had called for a general strike on May 1st and in unity countries all around the world recognized the date. Therefore Labor Day in the United States is in September but around the rest of the world it is May 1st even though it was inspired by labor in the United States.

(The Great Courses – Turning Points in American History)