Ever feel like your to-do list is infinite? It isn't. Not even close. If you want to talk about something that actually approaches the limits of the physical universe, you have to talk about ten to the power of 100.
Mathematically, we call it a googol.
It’s a 1 followed by a hundred zeros. It looks 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.
Writing it out is honestly a bit of a gimmick because the human brain is pretty much hardwired to fail at grasping this scale. We’re great at counting apples. We’re okay at visualizing a stadium full of people. But once we hit the cosmic scale, we just shut down and label it "big."
That’s a mistake.
Understanding ten to the power of 100 isn't just a math nerd's hobby. It’s a boundary marker. It tells us where the physical world ends and where pure, abstract mathematics takes over.
The 9-Year-Old Who Named the Google Monster
Most people think "Googol" was some corporate branding brainstormed in a Silicon Valley boardroom. Nope. It was actually a kid. Specifically, Milton Sirotta, the nine-year-old nephew of American mathematician Edward Kasner.
Back in 1920, Kasner was looking for a name for this staggering number. He asked Milton. The kid blurted out "googol," and it stuck. Kasner later featured it in his book Mathematics and the Imagination.
The irony? Larry Page and Sergey Brin actually meant to name their search engine "Googol" to represent the vast amount of information they were indexing. They misspelled it. History was made because of a typo.
But let's be real—even a search engine indexing every grain of sand on Earth wouldn't come close to this number.
Putting Ten to the Power of 100 in Perspective (If That’s Possible)
To understand how massive this is, you have to look at the universe.
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The number of atoms in the entire observable universe is estimated to be between $10^{78}$ and $10^{82}$. Think about that for a second. Every single atom in every star in every galaxy we can see doesn't even get us to 1% of a googol.
Actually, it doesn't even get us to 0.0000000000000001% of a googol.
Because of the way exponents work, ten to the power of 100 is $10^{18}$ times larger than the number of atoms in the universe. If you wanted to fill the universe with a googol of anything, you’d need to take every single atom and turn each one of those atoms into its own entire universe. Then you’d have to count all the atoms in those universes.
Only then would you be getting close.
It’s a number that exists almost entirely in the realm of theory. In the "real" world, there is nothing to count that requires it. Even the number of seconds since the Big Bang is only about $4.3 \times 10^{17}$.
It makes the national debt look like pocket change.
Why Physicists Actually Care About It
You might think scientists would just ignore a number this big because it's "useless." But they don't. Especially not when they talk about the end of everything.
Enter the "Heat Death" of the universe.
In a few trillion years, the stars will stop shining. Eventually, black holes will be the only things left. But even black holes don't last forever. Thanks to something called Hawking Radiation—named after Stephen Hawking—black holes slowly "leak" mass and eventually evaporate.
How long does it take for a massive black hole to disappear?
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Roughly $10^{100}$ years.
That is the approximate timeframe for the ultimate "expiration date" of the universe as we know it. When you hear a physicist mention ten to the power of 100, they aren't usually talking about counting things; they’re talking about the terrifyingly long stretches of time that dominate the far future of cosmology.
The Difference Between a Googol and a Googolplex
If you think a googol is big, wait until you meet its older brother.
A googolplex is ten to the power of a googol.
$10^{(10^{100})}$
Edward Kasner (the uncle of the kid who named the googol) described it as a number so large that if you tried to write it out, you would literally run out of space in the universe. You couldn't even write it in "fine print" on every atom. There simply isn't enough matter to hold the ink or enough space to hold the paper.
It’s basically a mathematical middle finger to the concept of physical reality.
Cryptography and the Googol Barrier
Why does this matter in technology today? Encryption.
When you use 256-bit AES encryption to protect your bank account or your private messages, you are relying on the sheer impossibility of counting. A 256-bit key has $2^{256}$ possible combinations.
To give you an idea of that size: $2^{256}$ is roughly $1.1 \times 10^{77}$.
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Wait. That’s actually smaller than a googol.
But even though it’s smaller, it’s still "astronomically" large. If you had a billion computers testing a billion keys every second, it would still take longer than the age of the universe to crack that code.
The fact that we haven't even reached ten to the power of 100 in our strongest encryption tells you just how much "room" there is in mathematics. We are barely scratching the surface of what these numbers allow us to do with data security.
Common Misconceptions About Big Numbers
People often confuse "infinity" with numbers like a googol.
A googol is not infinity. In fact, compared to infinity, a googol is effectively zero.
Mathematically, a googol is finite. It has a beginning and an end. You can add 1 to it. You can divide it by 2. This is a crucial distinction in calculus and set theory. When we talk about $10^{100}$, we are talking about a specific point on the number line, even if it’s a point we will never physically reach.
Another weird one? The "Chessboard" problem.
People think the number of possible games of chess might be around a googol. It’s actually much larger. The Shannon Number, which represents the conservative estimate of the game-tree complexity of chess, is $10^{120}$.
Chess is literally more complex than the number of years it takes for the universe to die.
Actionable Insights: How to Use This Knowledge
You aren't going to use ten to the power of 100 to balance your checkbook, but understanding its scale changes how you view data and probability.
- Audit Your Passwords: Now that you know 256-bit encryption is roughly $10^{77}$, realize that a simple 8-character password is tiny by comparison. Use a password manager to get closer to those "cosmic" numbers of entropy.
- Perspective on Probability: When someone says there’s a "one in a million" chance, that's $10^{-6}$. When they say "impossible," they usually mean something approaching $10^{-100}$. Understanding this helps you filter out hyperbole in news and science reporting.
- Embrace the Abstract: Use the concept of a googol to teach kids (or yourself) about the difference between "physical reality" and "mathematical reality." One is limited by atoms; the other is limited only by imagination.
The next time you see the word Google, remember the nine-year-old kid and the hundred zeros. We live in a world defined by these hidden giants. Even if we can't see a googol, we are definitely living in its shadow.
If you're interested in the math of the extremely large, your next step should be looking into Graham's Number or Tree(3). If you thought a googol was big, those will make it look like the number 1. Seriously. Give them a search. The rabbit hole goes much, much deeper than a hundred zeros.