Numbers are weird. You deal with tens, hundreds, and thousands every single day while checking your bank account or looking at your speedometer. Maybe you even wrap your head around a billion when thinking about tech moguls or government spending. But then there’s the googol.
It’s a value so staggeringly large that it basically breaks the human brain.
Most people know the name because of a certain search engine, but the history of the word and the sheer scale of the math behind it is way more interesting than a corporate branding story. We are talking about a number that is literally larger than the number of atoms in the known, observable universe. It isn't just a "big" number. It is a mathematical boundary that helps us understand how limited our physical reality actually is.
The Nine-Year-Old Who Named the Infinite
The origin story of the googol isn't some stuffy academic breakthrough in a lab. In 1920, an American mathematician named Edward Kasner was taking a stroll in the New Jersey Palisades. He was hanging out with his nephews, Milton and Edwin Sirotta. Kasner, who was a professor at Columbia University, wanted a name for a specific, incredibly large number: 1 followed by 100 zeros.
He asked nine-year-old Milton to come up with a name.
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Milton suggested "googol."
Kasner liked the whimsical, nonsense feel of it. He later introduced the concept to the world in his 1940 book, Mathematics and the Imagination, co-authored with James R. Newman. Kasner's goal wasn't just to be cute; he wanted to illustrate the difference between an incredibly large number and infinity. A googol is finite. It has an end. But for any practical purpose in our physical lives, it might as well be endless.
Visualizing the Scale: Why Your Brain Fails
Let's look at the math. In scientific notation, a googol is expressed as $10^{100}$. If you wrote it out by hand, it would look like this:
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
That looks manageable on a screen, right? It's just a bunch of zeros. But try to find a physical comparison, and everything falls apart.
Consider the atoms in your body. There are roughly $7 \times 10^{27}$ atoms in an average human. That’s a massive amount. Now, look at the entire Earth. Scientists estimate there are about $10^{50}$ atoms making up our entire planet. We aren't even halfway to a googol yet.
If you take the entire observable universe—every star, every galaxy, every black hole, and every speck of cosmic dust—estimates suggest there are between $10^{78}$ and $10^{82}$ atoms. Even if you count every single subatomic particle in existence, you are still billions of times short of reaching a single googol.
Think about that. If every atom in the universe was its own universe, and you counted all the atoms in those universes, you’d finally be getting close.
The Google Connection (and the Typo)
You can't talk about what is a googol without talking about Larry Page and Sergey Brin. Back in 1996, the Stanford grad students were working on a search engine they originally called "Backrub." Thankfully, they realized that was a terrible name for a global tech giant.
They wanted a name that represented the vast amount of information they were trying to index. They settled on "googol."
However, when Sean Anderson, a fellow graduate student, searched to see if the domain name was available, he accidentally typed "https://www.google.com/search?q=google.com" instead of "https://www.google.com/search?q=googol.com." Page liked the misspelling better. It was shorter, looked cleaner, and the domain was available. They registered it on September 15, 1997.
The irony is that Google has never actually indexed a googol of pages. Even with the trillions of URLs currently in their index, they are still light-years away from hitting that $10^{100}$ mark. In a way, the company name is a permanent tribute to an impossible goal.
Googol vs. Googolplex: It Gets Worse
If a googol wasn't enough to make your head spin, Kasner’s nephew Milton also suggested a name for an even larger number: the googolplex.
A googolplex is 1 followed by a googol of zeros.
You literally cannot write this number down. Not because it would take a long time, but because there isn't enough space in the universe to hold the ink. If you tried to write a googolplex on small slips of paper, there wouldn't be enough matter in the observable universe to create the paper, nor enough space to store it.
Even if you could write zeros at a rate of three per second, it would take you vastly longer than the current age of the universe to finish writing a googolplex. We are talking about time scales that make the 13.8 billion years since the Big Bang look like a fraction of a second.
Why Do Mathematicians Even Use It?
Honestly, a googol doesn't have much "utility" in standard engineering or physics. NASA doesn't need a googol to land a rover on Mars. Most of our most complex calculations in quantum mechanics or astrophysics stay well under the $10^{50}$ range.
However, the googol is incredibly useful in probability and combinatorics.
If you have a deck of 52 cards, the number of ways you can shuffle them is $52!$ (52 factorial). This comes out to roughly $8.06 \times 10^{67}$. That’s huge, but still less than a googol. But if you start looking at the possible moves in a game like Chess or Go, you blow past the googol very quickly.
The Shannon Number, which represents the conservative lower bound of the game-tree complexity of chess, is $10^{120}$. In this context, a googol is actually a "small" reference point. It serves as a benchmark for mathematicians to categorize the complexity of systems.
The Heat Death of the Universe
There is one place in science where "googol" sized numbers show up naturally: the very, very distant future.
In the theory of the Heat Death of the Universe, we look at the lifespan of black holes. According to Stephen Hawking’s theories on Hawking Radiation, black holes eventually evaporate. But they don't do it quickly.
A massive black hole (the size of a galaxy's core) might take roughly $10^{100}$ years to fully evaporate. This is often called the "Googol Era" of the universe. At this point, the stars have all burnt out, the galaxies have drifted apart, and the only things left are these slowly decaying pits of gravity. When the last black hole evaporates after a googol of years, the universe enters a state of ultimate entropy where no more work can be performed.
It’s a bit bleak, but it’s the only time in "real life" where the number 100% matters.
How to Wrap Your Head Around Huge Numbers
If you're trying to use these concepts in your own life or work, it helps to understand the logarithmic nature of growth. Most of us think linearly. If I give you ten dollars, and then ten more, you have twenty.
But with powers of ten, every step is a massive leap.
- $10^6$: A million (seconds in 11 days).
- $10^9$: A billion (seconds in 31 years).
- $10^{12}$: A trillion (seconds in 31,000 years).
By the time you get to $10^{100}$, you have left the realm of human experience entirely.
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Actionable Takeaways for the Curious:
- Check your scale: Whenever you hear a giant number in the news (like the national debt or corporate valuations), remember that "trillion" is only $10^{12}$. It feels infinite, but it’s nothing compared to the mathematical concepts used in computing and physics.
- Explore Combinatorics: If you want to see "googol-sized" problems in action, look into the "Traveling Salesman Problem" or encryption algorithms. Modern 256-bit AES encryption uses a key space of roughly $1.1 \times 10^{77}$, which is why it’s currently unhackable by brute force—there simply isn't enough time in the universe to try every combination.
- Use the correct terminology: Next time someone says a task is "infinitely hard," you can annoy them by pointing out it’s probably just "googol-level hard." There’s a big difference.
The googol reminds us that while our physical world is limited, our ability to conceive of things beyond it is not. Milton Sirotta’s nonsense word gave a name to the unthinkable, proving that even a nine-year-old can help define the boundaries of the universe.
To dig deeper into the math of the extremely large, research Graham’s Number or Tree(3). If you thought a googolplex was big, those will truly make your head explode. They make a googol look like zero.