What is a Googolplex?

A googolplex is an extremely large number that has been referred to several times in popular culture. Fans of the Back to the Future trilogy will recall that Emmett "Doc" Brown refers to a googolplex in Back to the Future III. But few people are aware that a googolplex is not just a piece of Hollywood imagination but an actual number that has been given this name by mathematicians. What follows is a brief discussion about the quantity of a googolplex itself, followed by a discussion of some interesting trivia relating to a googolplex.

To understand what a googolplex is, one must first understand what a googol is. A googol is defined by the number ten raised to the 100th power (10¹⁰⁰). This would be written out as a 1 followed by 100 zeros. Needless to say, a googol itself is already a larger number than the average person can relate to in ordinary experience. But a googolplex takes this incomprehensibility to exponential proportions.

A googolplex is defined by the number ten raised to the power of a googol. For those unfamiliar with exponents and powers, this would be the number ten multiplied by itself a googol number of times. Needless to say, this results in a staggeringly large number that defies human comprehension in anything other than abstract mathematical terms.

To give an idea of the staggeringly large number called a "googolplex," consider that a googolplex is greater than the number of atoms in the known universe. This means that one could not write out the number itself non-exponentially, since first of all there would not be enough time to do so, but more fundamentally there would not be enough atoms available to make the ink or pencil marks from! Thus the only way to represent a googolplex is through scientific or exponential notation. By convention, a googolplex is often represented via the combination of numerals and the word "googol" in superscript. For example, one could indicate a googolplex in the following manner: 10^googol.

In addition to the popular culture references to the googol and the googolplex, the term "googol" is the basis for the name of the company "Google," albeit with a modified spelling. The modified spelling may have been necessary due to the difficulties in registering the name of a number as a trademark. In any case, the company Google has made the terms "googol" and "googolplex" ubiquitous in popular culture.

In conclusion, a googolplex is a ming-bogglingly huge number that exists for our human-sized intellects only in the mathematical abstract. Outside of this abstract thought and representation, a googolplex exists only in Plato's heaven, the realm of pure and abstract forms.