I had just given an evening program for families at a school in Berkeley when a parent named Steven Birenbaum came up to tell me something remarkable. During the presentation I had introduced my book G Is for Googol: A Math Alphabet Book by projecting this inequality on the screen. (The slashed equal sign means "does not equal.")
No one who has tapped a computer keyboard in the past ten years needs an explanation of the word on the right. The less-known word on the left is the name for the number one followed by one hundred zeros and it appears in the title of my book. Googol, the number, is of enduring interest to myself, to many children and adults who love thinking about big numbers, and to Steven Birenbaum. He is the great-great nephew of Edward Kassner, the mathematician in the story I had told about how this un-numberlike name had been invented:
"A mathematician wrote a one with a hundred zeros after it and showed it to his nine-year old nephew. 'What do you think we should call this number?' he said. The nephew thought a minute and said, 'Googol!" I have no idea why the mathematician asked the question or why the boy answered the way he did, but his name stuck and ever since then we've called this giant number 'googol.'"
After speaking with Mr. Birenbaum I now know why the storied mathematician was seeking a fanciful name for this enormous number and I have a pretty good idea of why the winning name was "googol."
The mathematician was Edward Kasner, who taught at Columbia University for 39 years during the first half of the 20th Century. He was looking for a striking way to make a point about all whole numbers, no matter how large, because he had been irked by the way people (even scientists) used the words "infinite" and "infinitely" as synonyms for "enormous" or "numerous." In a published lecture, Kasner observed ruefully that people commonly said things like, "It is so large that it is infinite."
Kasner wanted the world to know that no matter how large something may be, "large" cannot mean infinite!
I am reminded of my sixth grade teacher who said, "Tell me any number and I'll tell you one bigger." Whatever number we proffered, he just appended "and one" to it, and he had a bigger number. If you thought the biggest number was "gazillion," he would ask, "What about gazillion and one?" His point was that there is no such thing as the biggest number. Infinity, on the other hand, is not countable and is not a number. As I sometimes tell upper elementary kids in presentations, "Infinity is not a number but numbers are infinite."
Back to Kasner. He wanted an easily-remembered monicker for a gigantic number so he could talk about it. He presented the challenge of naming it to his two young nephews Milton and Edwin Sirotta during a walk in Palisades Park, near Manhattan. As the story goes, Milton blurted out "Googol!"
A few years ago, when the internet company Google* was holding its initial public stock offering, the Wall Street Journal ran a profile of Kasner by Carl Bialik. (You can read it here.) From the article I learned that some of Kasner's living relatives believe that the two brothers should be given equal credit for a collaborative effort. (A number that big can stand to have two namers, I guess.) Denise Sirotta, daughter of Edwin, not only makes that case based on family lore, but she sheds light on the question of why "googol"? She says her father told her that Kasner wanted "a word with a sound that had a lot of O's in it."
Think about it: "googol." Not only is the sound rich with O's but so is the look. Notice those letters. Every one of them except the "l" has an "O" in it (yep, even the "g's").
So, thanks to the serendipity of my encounter with Steven Birenbaum, both of my public musings earlier in the evening—why did Kasner want a name for this basically useless number and why did the boy(s) say "googol"?— have been answered.
I have to mention one other thing about Kasner, which I learned from the Wall Street Journal article. The mathematician never had children but he was adored by his nieces and nephews. It is said that on a walk with some of them in the Palisades, the party encountered tea kettles and matches that he had hidden under rocks and teabags that he had hung from trees. They stopped to make tea!
No wonder Kasner was described by Time magazine in 1940 as a mathematician who was "distinguished but whimsical." What a noble combination!