Venturing into the Vastness: A Humorous Jaunt Through Large Numbers, Infinity, and Bowser’s IQ
Ever felt small? Like, existentially small? Buckle up, because we’re going on a journey through really, really big numbers. We’re talking about numbers that make your student loan debt look tiny. And yes, we’ll ponder Bowser’s surprisingly high IQ. Why not?
The Big Number Brigade: From Googol to Utter Oblivion
Googol: The Number That Inspired a Search Engine (Thank You, Misspelling!)
Let’s begin with a classic: the googol. What is it? Picture writing 1 and following it with 100 zeros. That’s a googol. In shorthand, it’s 10^100. Pretty big, right? Fun fact: this number inspired a search engine you might know – Google. The founders wanted “Googol,” but a misspelling gave us “Google.” What luck!
Googolplex: When Big Just Isn’t Big Enough
Think a googol is impressive? Hold my drink. Meet the googolplex. This giant is 10 to the power of a googol (10^googol). Or, a 1 followed by a googol of zeros. Writing it out? Don’t bother. You’d run out of ink and paper. It dwarfs the atoms in the observable universe. Practical uses? None. It’s just for flexing.
Googolplexian (or Googolduplex): Are We There Yet? Nope.
Just as you think we’ve maxed out, someone yells “Hold my juice!” Enter the googolplexian, or googolduplex. It’s 10 to the power of a googolplex (10^googolplex). Writing that is impossible. Thinking too hard might cause a crisis. And yes, there’s a “googolplexianth,” which is 10^(10^(10^100)). It never ends!
Graham’s Number: Beyond Comprehension, But We Know the Last Digits!
Now we’re in true abstract territory with Graham’s number. Mathematician Ronald Graham invented this colossal number. It’s larger than all atoms in the observable universe. We can’t write it fully, even in scientific notation. We define it with Knuth’s up-arrow notation, which means “really, really big.” Quirkily, we know the last 20 digits: 04,575,627,262,464,195,387. And its practical use? Just upper bound in theoretical math.
Skewes’ Number: Even Bigger Than a Googolplex (Obviously)
You might think we hit the limit of large numbers. Wrong! Enter Skewes’ number. While a googolplex is huge, Skewes’ number laughs at it. It’s hard to explain without complex math, but it’s way bigger than a googolplex. It’s true in number theory since even mathematicians want bragging rights.
TREE(3): The Tree-Building Titan
Get ready for TREE(3). This isn’t defined by basic exponentiation, but through constructing trees. Yes, trees. Mathematical trees, not leafy ones. This number, from the tree process, is finite but extremely large. It exceeds Graham’s number significantly. It’s mind-boggling and shows that even games can spawn incomprehensible numbers.
Rayo’s Number and BIG FOOT: Pushing the Boundaries of Naming Numbers
Now we’re seeing numbers defined by their own definitions. Rayo’s number is “the smallest positive integer larger than any finite integer named in first-order set theory with googol symbols or less.” Confused? Everyone is. Then came BIG FOOT, made by a Googology Wiki user to surpass Rayo’s number. It’s numerical one-upmanship at its finest. Not useful for your checkbook.
Infinity: The Concept, Not the Number
After these huge numbers, let’s discuss infinity. It’s not a number, but a concept of unboundedness. Different “sizes” of infinity exist. Countable infinity (like natural numbers) is smaller than uncountable infinity (real numbers). Mathematicians use transfinite numbers like aleph-0 (א0) and aleph-1 (א1) to represent these infinities. And “infinity minus infinity”? It’s indeterminate. Math loves showing off.
Comparing the Giants: Infinity Still Wins (Obviously)
How do these massive numbers compare with infinity? Graham’s number is finite, despite being huge. Infinity is infinitely larger than any finite number, no matter how absurdly large. Graham’s number outstrips a googolplexian and TREE(3) dwarfs both. But infinity? It’s in its own league. The ultimate mic drop in math.
Other Numerical Oddities: Googoltriplex, Robloxplex, and Minecraftplex
Just when you think you’ve seen it all, here come more oddities. There’s googoltriplex, which is 10^10^100 + 1 digits long. Then, internet-born numbers like Robloxplex and Minecraftplex. Robloxplex comes from a YouTuber at 10^4,778,815,304. Minecraftplex appears in another video at 10^215. These are large and highlight our urge to quantify everything on the internet.
Salad Numbers and Utter Oblivion: When Definitions Get… Messy
Then there are the less serious contenders, like a salad number. It’s a “mishmash of existing numbers or functions.” Think of it as numerical randomness. Lastly, there’s Utter Oblivion, crafted to exceed BIG FOOT. It’s more of a thought experiment than a true number. Large numbers can get nebulous.
Marioplex: Game Theory Gets Gigantic
Marioplex: Powered by Game Theory (and Mario)
Let’s shift from abstract math to something pixelated: the marioplex. Coined by MatPat from Game Theory, it’s defined as 10 to the power of 12,431. While not as huge as some past numbers, it’s still massive. Pursuant to Game Theory lore, it’s larger than atoms in the universe. Marioplex Mario has “more energy in one atom than all the universe.” That’s a lot of energy.
Bowser, Mario, and Statistically Significant Silliness
Bowser’s Ever-Shifting Size and Surprisingly High IQ
Speaking of Mario, let’s discuss Bowser. His size varies wildly per game. In Bowser’s Fury, he stands at 120 meters tall. In most games, he’s around 10 feet 2 inches, twice Mario’s height. But here’s the shocker: Bowser’s IQ is allegedly 9,800, as per DEATH BATTLE Wiki. Yes, really: 9,800. This begs the question: if Bowser is so smart, why does he keep losing to a plumber?
Mario Game File Sizes: From Tiny to… Less Tiny
From Bowser’s brainpower to bytes! The first Super Mario Bros.? A mere 32KB file size. Super Mario 3D Land? A hefty 512 MB (4,096 blocks). Super Mario Galaxy? A significant 3.3GB. Super Mario 3D World? A slimmer 1702 MB. Game file sizes have inflated over time, much like these large numbers.
Super Mario Maker and Mario Lore Tidbits
If you’re feeling creative, there’s Super Mario Maker, released in 2015 as a game creation system. Aiming for 100% in Super Mario 3D Land requires about 221⁄2 hours. And did Bowser ever beat Mario? Yes! Once he lifted Peach’s Castle and ordered Kammy Koopa to keep Peach locked up. Bowser’s competence can surprise you.
Super Mario 64: Building
a 3D World
Ever wonder about Super Mario 64? The graphics used N-World, a toolkit from Silicon Graphics. Developers first focused on Mario’s movement. They tested and refined his animations on a grid. They did this before they created levels. Priorities mattered.
Other Numbers and Sizes: Just Because We Can
One Billion, One Trillion, and Beyond (Informally Speaking)
Back to large numbers. One billion is written as 1 followed by nine zeros (1,000,000,000). One trillion has twelve zeros (1,000,000,000,000). Then comes quadrillion, quintillion, sextillion, etc. For informal numbers, we have zillion, bazillion, gazillion. These terms are enthusiastic and not precise.
Nybble: A Bite-Sized Unit of Information
For a small information unit, there is the nybble (or nibble). It represents half a byte or four bits. Cute, right?
1 Followed by 500 Zeros: Just to Reiterate “Large”
To show how large numbers can be, a 1 followed by 500 zeros is written as 10^500. This number remains smaller than a googol. You understand the concept.
Mathematical Miscellany: Omega, Infinity, and Scientific Notation
Real Numbers, Scientific Notation, and the Omega Constant
A billion (1,000,000,000) is a real number. It is a natural number. In scientific notation, a 1 followed by 500 zeros is 1 x 10^500. The Omega Constant (Ω) is about 0.567143290409783872999968662210. It satisfies the equation Ω * eΩ = 1. Math surprises us.
The Infinity Symbol: ∞ and ♾
The symbol for infinity is ∞. If you prefer, ♾ is the infinity symbol in a circle. Infinity can look stylish.
Sizes of Actual Objects: Relativity Check
Ecozilla Watch, Rexcelsior LEGO Spaceship, Viperwolf, and Hyalella azteca: Grounding Ourselves in Reality
After discussing numbers, let’s check real-world sizes. The Citizen Promaster Dive “Ecozilla” watch measures 48mm wide and 18.6mm thick. The Rexcelsior LEGO spaceship stands 7” high, 15” long, and 8” wide. A Viperwolf (from Avatar) is about 6.5 feet long and 3 feet high. The tiny Hyalella azteca, a type of amphipod, measures 3–8 millimeters in length. From microscopic to macroscopic numbers, it’s all relative.
Here it is. A brief look at large numbers, infinity, and complex stats of Super Mario. You might feel more informed. You may feel slightly bewildered. Perhaps you feel less existentially small. Or you may just feel hungry for pizza. Either way, you’re welcome.
