Chapter 50: Six Sensational Discoveries

We take many things for granted nowadays. We have solved many equations and discovered many things. Obviously it has not always been that way. Chapter 50 of The Colossal Book of Mathematics section 12 is entitled Six Sensational Discoveries and it focuses on six discoveries, predictions, and solutions found in 1974.

                  The first discovery listed has to do with the four-color-map conjecture. Before, it was proven that 5 colors are needed for coloring all planar maps so that no 2 regions that border each other in any way have the same color. In November 1974 William McGregor, who was a graph theorist out of Wappingers Falls, New York, created a map that contains 110 regions that cannot be colored with fewer than 5 colors. Though this report was published in the Journal of Combinational Theory, some mathematicians still believe that the theorem will be proved later on.

                 

                  The next discovery was quoted as “the most exciting discovery of 1974” was the discovery that the number e when raised to the power of Õ times the square root of 163 comes out to be an integer. A mathematician from India, Srinivasa Ramanujan, solved the equation by hand and found the value to be 262537412640768743.99999999 and so on. A French program in 1972 went as far as two million 9’s. No one was able to prove that the sequence of 9’s went on forever therefore disproving that it is an integer but rather that is an integral fraction. In May 1974, John Brillo proved that the number is an integer and that the equation equals exactly 62537412640768744. It is still not fully understood how 163 being that it is a prime number makes the expression an integer.

                  In 1973, Richard Pinkleaf of MIT designed a chess-playing program that would learn from its own and its opponents mistakes called MacHic. Pinkleaf would make MacHic play against itself and found that games would be completed in 1.5 seconds on average. After running for 7 months, the program established that pawn to king’s rook 4 is a win for white. Although it could not solve all possible outcomes and situations, it did extend the “game tree” branches so that every branch of the tree would have a position where black should resign. Pinkleaf received a lot of negativity in the chess community to destroy MacHic and its records since it could ultimately win against anyone. The discovery was controversial to the grand masters but also set us on a path for computers in the future.

                  Another controversial discovery was that the special theory of relativity contains a flaw. The theory is described as a meter stick flying horizontally while a plate with a hole in the middle that is parallel to the sticks path and it is moving vertically. The stick and the hole in the plate will eventually coincide. Assumed that the plate has a fixed inertial frame and the stick is moving relatively fast. The result is that the stick will pass through the hole in the plate easily. But when explained from the sticks point of view, in the end, there’s no way a 10 cm stick by 1 m hole will move past without a collision of some sorts. Therefore, the assumption of special relativity is violated.

                  Two lost books written by Leonardo da Vinci were found and published in 1974. Both contained depictions of inventions and tools not previously known to have been created by da Vinci. One was a system of mechanics that we now use for clocks and chains on bicycles. The other was a drawing of a full working sewage and toilet system with da Vinci drawn using the invention as well. The drawings contained an idea for a valve flush toilet, a water closet with continuously running water, and a folding seat.

                  Lastly, there was the discovery/ invention of a simple motor that runs on psi energy. The motor is so simple that even individuals at home could make it. In 1973, Robert Ripoff originally came up with the idea but later passed it on to Henrietta Birdbrain. The steps of creating the motor are as follows, directly from the chapter:

1.         Cut a 3-7-inch rectangle from paper

2.         Make a tiny slot in the paper toward the top center, it must be 3/8^th inches long and 1/8^th from the top

3.         Bend the paper into a cylinder and glue together

4.         Cut a second slot in the center of the overlap, opposite of the first one

5.         Cut a strip of paper 3/8^th inch by 3 inches

6.         Insert a pointed needle twice through the center of the strip no more than 1/4^th in. below the bottom edge of the strip

7.         Push the ends of the strip through the cylinder’s two slots

8.         Balance the needle on top of a narrow bottle at a minimum of 4 inches high. (bottle should be glass of a hard plastic)

9.         Place the motor on a book with the books spine running north and south

10.   Sit in front of the motor

11.   Cup hand on the side of the motor close but to a point where you are not touching it.

12.   Focusing on the motor will make it slowly rotate either clockwise or counterclockwise

Having a clear mind while focusing on the motor is key to the experiment. But psi effects as said in the chapter are “elusive, skittish, and unpredictable” (page 681).

                  Although the chapter focuses on discoveries made in 1974 or around that time, all the findings were across different fields of study. It shows how one little thing can have an impact across multiple fields including science, math, and even art. It may not be apparent now but back then it was a big deal and everyday there are discoveries to be made that will have the same impact us now as the ones mentioned in chapter 50 had on the people in the early 1970s.