First, some background.
Samuel Morse was born in 1791. He attended Yale, graduating in 1810. He aspired to be a painter. I didn't realize he did of this other career until I read about his paintings in David McCollough's book, The Greater Journey: Americans in Paris. Here is his portrait of President James Monroe.He lost his wife and both parents in a three year span. As an escape, he went to Europe. During this time he made some contacts that led to led to the invention of Morse Code.
It didn't catch on for a few years. A U.S. congressman showed interest and a test was done with a wire stretching from Washington D.C. to Baltimore. He successfully asked, "What hath God wrought" and the rest is history.
It relies on a series of dots and dashes. They can be communicated with electronic impulses or light impulses. It was very important, but began to fall out of favor with the invention of Bell's telephone in which actual words could be used instead of a code for spelling out words. It is still used in various areas, including signal lamps by the coast guard. Those without speech can use the tapping of Morse code to communicate. But for the most part, it is found in history books.
SOS, for example, is ...---... How many are combinations of dots and dashes are needed to cover the alphabet? This could be found use the fundamental counting principal (If there are "m" ways to do one thing, and "n" ways to do another, there are "m x n" ways to do both.)
- Using one symbol means a dot or a dash could be used - two choices.
- Two symbols means there are 2 x 2 = 4 ways.
- Three symbols means there are 2 x 2 x 2 = 8 ways.
- Four symbols means there are 2 x 2 x 2 x 2 = 16 ways.
Since there are 26 letters in our alphabet, this still isn't enough. We could use five symbols, but that makes it more cumbersome. I can be done, though, by using one, two, three, or four symbols. Since 2+4+8+16 = 30. That is plenty to cover the whole alphabet.
If we need more that just words - digits, or symbols like ? and ;, we are going to need more. So for them, we need to use 5 symbols. How many possibilities would that give us?
Two to the fifth power is 32, and that means we have 2+4+8+16+32 = 62 possibilities. That gives us enough for 26 letters, 10 digits, and 26 more symbols beside.
