You’ve probably heard the word "googol" before. It sounds like a character from a children's cartoon or, more obviously, the slightly misspelled namesake of a trillion-dollar search engine. But the actual value of 10 to the power of 100 is so staggeringly large that our human brains—evolved to count berries and mammoths—basically short-circuit when we try to visualize it. It’s a 1 followed by 100 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.
Think about that for a second.
Most people assume this number has some deep, mystical significance in physics. Honestly? It doesn't. It was actually "invented" in 1920 by a nine-year-old boy named Milton Sirotta. His uncle, the American mathematician Edward Kasner, asked him to come up with a name for a truly giant number. Milton said "googol." Kasner later popularized it in his 1940 book Mathematics and the Imagination. The goal wasn't to solve a formula. It was to show the difference between "infinite" and "really, really big."
The Problem With Visualizing 10 to the Power of 100
We like to think we understand big numbers. Million? Sure, that’s a few luxury houses. Billion? That’s a tech mogul’s net worth. Trillion? That’s a national debt. But 10 to the power of 100 isn't just bigger; it’s physically impossible to represent within our known reality.
Here is the kicker: there aren't even a googol of atoms in the entire observable universe.
Current estimates from cosmologists suggest there are roughly $10^{80}$ atoms in the observable universe. If you took every single atom in every star, every galaxy, and every speck of dust across billions of light-years, you’d still be 20 orders of magnitude short of a googol. In math terms, you would need 100 quintillion more universes just to have enough atoms to match the value of 10 to the power of 100.
It’s hollow. It’s a vacuum of scale.
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When people search for this number, they often think it’s the biggest number there is. It’s not. Not even close. Mathematicians deal with things like Graham's Number or TREE(3), which make a googol look like a rounding error. But a googol sits in that "uncanny valley" of mathematics where it’s small enough to write down on a single line of paper but too big to ever exist in the physical world.
Why the Tech Giants Stole the Name
In 1996, Larry Page and Sergey Brin were working on a search engine at Stanford. They originally called it "BackRub"—which, let's be real, is a terrible name. They wanted a name that represented the vast amount of information they were trying to index. They landed on "Googol."
Legend has it (and this is backed by Stanford's own archives) that a fellow graduate student, Sean Anderson, checked if the domain "https://www.google.com/search?q=google.com" was available. He accidentally misspelled it. Page liked the misspelling better.
But there’s a deeper irony here. Google doesn’t index a googol of pages. Not even close. There aren't a googol of websites. There aren't even a googol of distinct thoughts ever had by humanity. The name is an aspiration, a nod to the fact that the digital universe is expanding faster than we can track. Using 10 to the power of 100 as a brand wasn't about the math; it was about the vibe of overwhelming scale.
The Googolplex: Making 10 to the Power of 100 Look Tiny
If you think a googol is a headache, wait until you meet its older sibling: the googolplex. This is 10 to the power of a googol.
Edward Kasner famously described a googolplex by saying that if you tried to write it out—literally writing zeros on a piece of paper—you would run out of room in the entire universe. Even if you wrote zeros on every single atom, you wouldn't have enough atoms to finish the number.
There is actually a serious debate in physics about the "Poincaré recurrence time." This is the theoretical amount of time it would take for a system (like our universe) to eventually return to its initial state through pure quantum fluctuations. Some physicists estimate this time could be measured in googolplexes of years. It’s the kind of math that makes you want to go lay down in a dark room.
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Physics and the Heat Death of the Universe
While a googol doesn't count physical objects well, it does a great job of counting time in the very, very far future.
The era of black holes is where 10 to the power of 100 actually becomes useful. In about $10^{40}$ years, protons are expected to decay. After that, the only major "citizens" of the universe will be black holes. But even black holes don't last forever. Thanks to Hawking Radiation, they slowly leak mass.
A supermassive black hole with the mass of a galaxy will take roughly $10^{100}$ years to completely evaporate.
That is the "Googol Era." It is a cold, dark, and incredibly lonely point in the timeline of our cosmos. At this point, the universe has basically "run out" of things to do. The value of 10 to the power of 100 represents the final breath of the stars. It’s the ultimate timer.
Common Misconceptions About Large Powers
People often get confused between $10^{100}$ and $100^{10}$.
$100^{10}$ is just a 1 followed by 20 zeros. That’s a hundred quintillion. It’s huge, but it's "real world" huge. You can count that high with a supercomputer in a reasonable amount of time.
But $10^{100}$? You can't compute that. If you had a computer that could perform a trillion operations per second, and you started it at the moment of the Big Bang, it would have only completed about $10^{30}$ operations by now. It wouldn't even be 1% of the way to a googol. It wouldn't be 0.00000000001% of the way there.
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Exponential growth is deceptive. It’s not a ladder; it’s an explosion.
Practical Ways to Understand the Scale
Since we can't use atoms, let's try something else. Imagine a grain of sand.
Now imagine a beach made of that sand.
Now imagine every beach on Earth.
Total grains of sand on Earth: roughly $7.5 \times 10^{18}$.
Now imagine every grain of sand on Earth is actually its own entire Earth, also covered in beaches. And every grain of sand on those beaches is another Earth. Even after doing this multiple times, you are nowhere near 10 to the power of 100.
This is why mathematicians use scientific notation. Standard numerals are a waste of ink when you’re dealing with the infinite or the near-infinite.
Next Steps for the Curiously Minded
If you want to actually "see" the scale of these numbers without your brain melting, there are a few things you can do right now:
- Check out the "Scale of the Universe" interactive tools. Websites like Scale of the Universe 2 allow you to scroll from the Planck length all the way to the observable universe ($10^{27}$ meters). It helps put the "smaller" big numbers in perspective.
- Read "Mathematics and the Imagination" by Edward Kasner. It’s the source material. It’s surprisingly readable for a book written by a math genius in the 40s.
- Use a scientific calculator to play with exponents. Try calculating $2^{100}$ versus $10^{100}$. You'll see how changing the base slightly changes the outcome by trillions of orders of magnitude.
- Look into the "Wait But Why" blog's series on big numbers. Tim Urban does a fantastic job of breaking down the "Graham's Number" and other monstrosities that make a googol look like a toddler's toy.
Ultimately, 10 to the power of 100 exists to remind us that our physical reality is just a tiny, tiny slice of what is mathematically possible. We live in a world of small numbers. But the universe thinks in much, much larger ones.