What is the highest known numerical value

What is a googol?

There is something seductive about large numbers. The trillion comes off our lips as easily as the million, and we hardly notice the difference between a quadrillion and a trilliard.

There is a good reason for this. Because our decimal system has the enormous advantage that we can write numbers of any size with minimal effort. More precisely, we get by with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 and can use them to write any number. The size of the economic stimulus program, the gross national product of Germany, the number of atoms in the universe or the largest known prime number: our 10 digits are sufficient for everything.

It cannot be taken for granted. For example the Romans: They also used numbers, but no decimal system or something similar. Its largest number was M, which meant 1000. There were also additional characters, such as a framed M, which meant 100,000, but these were more artificial continuations. If the Romans wanted to write a million, they would have had to write 1000 "M" s. And with a billion it should already be a million "M" s or 10,000 framed "M" s. In other words: no Roman bank could have paid out or transferred a billion - simply because the number could not have been written. That means: Our current financial crisis would not have been possible with the Romans for mathematical reasons!

On the other hand, how easy it is for us to rise to ever larger numbers: thousand, million, billion, trillion, trillion and so on. There are just three zeros added to it, so for example a trillion is a 1 with 12 zeros. We can write such numbers without any problems, and in principle it is not much more difficult to transfer 100 billion euros to someone than just 100 euros. As we now know: an extremely dangerous possibility!

The decimal system originated around the 8th century AD. in India. The decisive factor was the invention of zero. The decimal system began its triumphant advance with the spread of Islam and came to Western Europe via Spain. In 1202 the mathematician Leonardo of Pisa, alias Fibonacci, published a book that began with the programmatic sentence: “The nine Indian figures are 9 8 7 6 5 4 3 2 1. With these nine figures and the symbol 0, which represents the Arabs Zephirum name, any number can be written. "

By the way: after a quadrillion comes the trillion, a number with 18 zeros. 6 more zeros each have Quadrillion, Quintillion, Sextillion, Septillion, Octillion, Nonillion.

One can of course exaggerate: In 1938, the American mathematician Edward Kasner asked his then nine-year-old nephew Milton Sirotta how he would call a huge number, namely the number 10100 (written out a 1 with 100 zeros). Little Milton invented the word "googol".

A googol is much larger than the number of atoms in the universe, which is “only” about 1078.

Kasner went one better and defined "Googolplex" as the number 10 to the power of Googol. This is a truly unimaginably large number, but easy to describe: a 1 followed by Googol (i.e. 10100) zeros. It cannot be written down in numbers, because it has more numbers than there are atoms in the universe. This means that even if you were to use every atom as storage space for a digit, you would not be able to write this number!

The response to the search engine “Google” is by the way not accidental: The name was intended to express the endeavor to cover a huge number of Internet pages. Consistently, the company headquarters of Google is called “Googleplex”.

January 19, 2010

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