What is a Googol and why is it such a giant number?

For those who are not fans of numbers, a googol is basically the number 10¹⁰⁰, or in decimal notation, it is written as the digit 1 followed by one hundred zeros.

The term googol was coined in 1938 by Milton Sirotta, a nine-year-old boy, nephew of the American mathematician Edward Kasner. Kasner announced the concept in his book "Mathematics and the Imagination." Isaac Asimov once said about it: "We will have to endure forever a number invented by a baby."

The googol is not of particular importance in mathematics and has no practical uses either. Kasner created it to illustrate the difference between an unimaginably large number and infinity, and it is sometimes used this way in teaching mathematics.

The googol machine

Daniel de Bruin decided to build a machine with a gear system that visualizes this number, which according to him is greater than the sum of all the atoms in the known universe.

It consists of 100 interconnected gears, which when the gear at one end turns, slowly turns the gear behind it at a speed of 1 to 10.

For example, when it completes 10 full rotations on the first gear, it will cause the second gear to turn only once.

This means that to turn the second gear 10 times, the first gear would have to turn 100 times, turning the third gear only once.

«For the last gear to turn once, the first must turn a googol of times.

Or rather, it will need more energy than all the known universe has to do that. That blows my mind.»

The version in the video is a prototype and cannot run for long, but I am making a version that could work for years/decades.

A googol is approximately equal to the factorial of 70¹, and its prime factors are 2 and 5. In the binary system, it would take 333 bits.

A googolplex is a 1 followed by a googol of zeros, that is, 10 raised to the googolth power:

1 googolplex = 10googol = 10¹⁰¹⁰⁰

A piece of paper large enough to explicitly write all the zeros of a googolplex could not fit within the universe (luckily, scientific notation simplifies this). A googolplex is still finite, and therefore, a googol and a googolplex are the same distance from infinity as 1.

One of the largest named numbers is the googolduplex, which is a 1 followed by a googolplex of zeros. If a piece of paper large enough to write all the zeros of a googolplex is larger than the universe, a piece of paper large enough to write a googolduplex would be larger than a googolplex of universes, like ours, combined.

The regular geometric figure with a googol of faces is called a googoledron. This figure would practically be a sphere, due to the immense number of faces. It should be noted that it is equally impossible to construct it, as there are not enough particles on Earth.

Fun fact: The search engine Google was named after this number. The original founders of Google were going to call it Googol, but ended up with Google due to a spelling mistake by Larry Page.