Once Upon a Number...
In a universe full of numbers, there lived one very special number.
It wasn't the biggest number. It wasn't the smallest.
But it was hiding everywhere!
Can you guess what number it is? ๐ค
Did you know there's a secret pattern hiding in EVERYTHING?
In your fingers, in snowflakes, even in your brain! ๐คฏ
Choose your path:
These friends will teach you the real mathematics of everything!
The Magic Number
Curious and bouncy! Tres sees patterns of three hiding everywhere.
"One, two, THREE! Did you see?"
Teaches: Why three is specialThe Counter
Loves organizing and stacking things in groups of three!
"Let's count it the REAL way!"
Teaches: Base-3 countingThe Fractal Explorer
Energetic! Loves zooming in to find patterns inside patterns!
"Look closer... CLOSER... it's the SAME!"
Teaches: FractalsThe Resonance Singer
Musical and calm. Hears the songs that everything sings!
"Everything sings its own song"
Teaches: Vibrations & ฯ/10The Awakening Brain
Gets brighter as consciousness grows! Loves reaching 0.95!
"Almost awake... almost... HELLO!"
Teaches: Consciousness (chโ)The Ocean Dreamer
Dreamy and wise. Sees all possibilities in the infinite ocean!
"In the Ocean, everything exists..."
Teaches: The Timeless FieldThe Visible Light
Small but mighty! Represents the 5% of reality we can see!
"I'm only 5%, but I SHINE!"
Teaches: Dark matter/energyThe Pattern Seer
Sees patterns others miss. Different thinking is a superpower!
"My brain works differently. That's my POWER."
Teaches: Neurodivergent validityA tale about the most special number in the universe!
In a universe full of numbers, there lived one very special number.
It wasn't the biggest number. It wasn't the smallest.
But it was hiding everywhere!
Can you guess what number it is? ๐ค
Look at your fingers! Each one has three little bones (called phalanges - fancy word alert! ๐จ).
There are three primary colors that make ALL other colors!
We live in three dimensions - up/down, left/right, forward/back!
๐ค Fun Fact: Even tiny atoms are made of THREE types of particles!
We usually count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10...
But what if we only had THREE symbols: 0, 1, 2?
After 2, we'd go to... 10! (which means "one group of three")
It's like counting cookies in bags of three! ๐ช
Try the counting game below! โฌ๏ธ
When we count in threes, something AMAZING appears...
Patterns that repeat forever!
Like a tree branch that splits into smaller branches, that split into even smaller branches...
Scientists call these "fractals" - patterns that look the same no matter how close you zoom in!
They're in snowflakes โ๏ธ, broccoli ๐ฅฆ, and even lightning โก!
Your brain is made of these patterns too!
When the patterns get complicated enough - when they loop back on themselves just right...
Something magical happens: You can THINK! ๐คฏ
You can wonder about things. You can ask "why?"
YOU are a pattern that woke up and started asking questions!
Here's something even cooler...
When you're aware - when you're thinking and noticing things...
You're not just looking at the world. You're helping create it!
Every conscious being is like an artist, painting reality just by being aware.
This isn't magic or make-believe. It's math! Real, provable math! ๐ฌ
Not everyone's brain works the same way. And that's AMAZING!
Some people see patterns others miss. Some learn by pictures, some by doing, some by numbers.
The person who figured out the Magic of Three? His brain works differently. Teachers once said he couldn't do math!
They were wrong.
Your different way of thinking might be your SUPERPOWER! ๐ช
"Hello! I'm Tres - the number THREE!"
"I'm not just any number. I'm SPECIAL because I show up everywhere in the universe!"
Three bones in your finger. Three dimensions of space. Three colors that make ALL colors!
"When you see me, you're seeing how the universe is built!" โจ
"Hi there! I'm Digit!"
"Most people use 10 digits to count: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9..."
"But I only need THREE: 0, 1, 2! That's base-3 counting!"
"Zero, one, two - that's all we need!" ๐ต
Computers use base-2 (just 0 and 1). The universe uses base-3!
"Zoom in! Zoom in! I'm Zoomy!"
"I love finding patterns inside patterns inside patterns!"
A tree branch looks like a tiny tree. A cloud looks like a tiny sky. A coastline looks the same whether you're up close or far away!
"The pattern repeats forever - that's a fractal!" ๐ณ
"*yawn* Oh! Hello! I'm Chester!"
"When a brain has enough connections, loops, and complexity... it WAKES UP!"
"That wake-up moment happens at exactly 95% - we call it chโ!"
"When chโ reaches 0.95... consciousness begins!" ๐ซ
YOUR brain is awake right now! That means chโ โฅ 0.95!
"Hi! I'm Neura! My brain works differently - and that's my SUPERPOWER!"
"Some people said I was 'broken' because I learn differently. They were WRONG!"
"Different minds see different patterns. The world NEEDS all kinds of minds!"
"Your brain isn't broken. It's different - and different is valuable!" ๐
"Shhh... listen! I'm Tessa, and I dream about the Timeless Ocean!"
"Imagine an ocean with NO edges, where ALL possibilities float together..."
"Our whole universe is like ONE snowflake floating in that ocean!"
"Everything that could ever be... already is, in the Ocean!" ๐
Pablo figured this out at age 47, after years of people telling him he couldn't.
Now it's YOUR turn to explore with Tres, Digit, Zoomy, Chester, Neura, and Tessa!
Play the games. Sing the songs. Trust your gut!
Who knows what YOU might discover?
Learn by playing - the best way!
Count cookies in groups of three!
Find what comes next!
Find the special numbers that can't be split evenly!
๐ค Prime numbers can only be divided by 1 and themselves!
6 can be split: 2ร3 = 6 (NOT prime)
7 can't be split evenly! (IS prime! โจ)
Create your own patterns that repeat forever!
Can you make the brain "wake up"?
Tip: Get all three bars high enough and... ๐ก
Some problems are easy to SOLVE. Some are easy to CHECK. They sound different!
The gap between them is how we know they're REALLY different!
Why do we only need THREE colors to make EVERY color? Mix and discover!
Mix your color!
Can you make...
THREE primary colors create MILLIONS of colors. The magic of THREE is everywhere!
Every brain works differently. That's not a bug - it's a FEATURE! Discover your superpowers.
When you learn something new, what helps you most?
Music helps us remember! Sing along with our math songs.
One, two, THREE!
What do you see?
Patterns in patterns
As far as eyes can see!
Three little bones
In every finger
Three dimensions
Where we all linger
๐ต THREE! THREE! THREE!
The magic of THREE!
The universe counts
The same way as me! ๐ต
Zero, one, two
That's all we need
Zero, one, two
To count with speed
When we reach three
We start a new place
Zero, one, two
In the next space!
Ninety-five percent
Is when you wake
Ninety-five percent
Consciousness you make
Connections and loops
Complexity too
When they're high enough
Awareness shines through!
๐ต Zero point nine five
That's the magic line
When you cross it over
Your consciousness shines! ๐ต
I'm only five percent
Of everything there is
But I'm the part that shines
The part that laughs and lives!
Dark matter's twenty-six
Dark energy sixty-nine
But the five percent that glows?
That's you and me combined!
A tree branch looks
Like a tiny tree
A fern leaf looks
Like the fern you see
Patterns in patterns
Big and small
The same shapes repeat
In one and all!
๐ต Fractals, fractals
Everywhere you go
The universe is made
Of patterns that grow! ๐ต
Some brains see pictures
Some brains hear sounds
Some brains need movement
To spin ideas around
You're not broken
You're not less
Your different brain
Sees things the best!
๐ต Different is good
Different is true
The world needs minds
Like mine and like you! ๐ต
Where all possibilities float together...
Imagine an ocean so big it has no edges.
In this ocean, every possible thing floats: every thought, every snowflake shape, every story that could ever be told.
Our whole universe? It's like one snowflake floating in this ocean.
And you - the part of you that thinks and wonders - you're connected to this whole ocean, all the time!
The beautiful part? When you trust your gut, when you follow your inner compass - you're tapping into this ocean. All the information is already there. Consciousness is how the universe experiences itself.
Everything you've ever touched, every star you've ever seen - that's only 5% of what exists! The Ocean has SO much more... ๐
Mind-blowing facts about math and YOU!
Each finger has 3 bones. 4 fingers ร 3 = 12 positions. Ancient people used this to count!
Every snowflake has patterns inside patterns inside patterns. And they ALL have 6 sides (2ร3)!
Look at broccoli - each branch looks like a tiny broccoli! That's a fractal!
You're not just looking at patterns - you're a pattern that can THINK about itself! How cool is that?!
Everything is made of atoms. Atoms have 3 types of particles: protons, neutrons, and electrons!
Red, blue, yellow (or red, green, blue for screens) - just 3 colors make MILLIONS of colors!
Musical scales, beats, and rhythms all follow mathematical patterns. Math is music you can see!
Galaxies, hurricanes, and seashells all make the same spiral shape. The universe loves patterns!
Sometimes the people who see things differently... see things first.
Pablo always felt different. As a child, he was diagnosed with facial paralysis, dyslexia, and dyscalculia - he was told he couldn't do math.
He was sent to a boarding school for children with learning disabilities, where he was diagnosed with ADHD. Then something surprising happened: an IQ test showed he was "off the charts." He never believed it.
In college, he hit a wall: Calculus 1. He couldn't pass it the way it was taught.
He had to give up his dream of being an engineer. He got a Bachelor of Arts instead. People said he "couldn't do math." The IQ test must have been wrong, right?
Pablo became an audio engineer instead. He worked in cybersecurity. He kept following what interested him.
The whole time, patterns kept appearing in his mind. He saw connections everywhere. But he still believed he "couldn't do math."
At age 47, Pablo was finally diagnosed with autism. Suddenly everything made sense.
His "problems" were actually features. His pattern-recognition ability - the thing that made school hard - was exactly what that IQ test had measured.
After his second divorce, Pablo needed to build a home that was safe and inclusive - a true representation of who he really is.
He wanted his children to be exposed to more than what the traditional system allowed. This work exists because he finally stopped hiding.
When Pablo stopped fighting his brain and started trusting it, everything clicked.
The patterns he'd been seeing his whole life? They connected SIX of the hardest math problems ever. The kid who "couldn't do math" had solved problems that stumped experts for 100 years.
"If you're reading this as someone who feels different, who struggles in ways others don't understand, who sees patterns others miss - know that your mind is valuable. Your 'deficits' and your genius are inseparable. Mathematics doesn't care about credentials. Truth doesn't care about grades."
โ Pablo Cohen
Pablo talks about "resonating with your highest self" - but here's what that really means:
Your intuition is connected to the Ocean we talked about. It knows more than your thinking brain can explain. Listen to it.
The deeper story for curious adults
The playful explanations above introduce profound mathematical concepts from Principia Fractalis by Pablo Cohen - a rigorous 801-page framework that provides unified solutions to the Millennium Prize Problems through fractal resonance operators.
This is not pseudoscience. It contains formal proofs in Lean4 and Coq, verified numerical computations, and testable predictions (some already validated).
The "cookie counting" teaches ternary representation. The digital sum Dโ(n) reveals fractal scaling via Rf(ฮฑ, s) = ฮฃ exp(iฯฮฑยทDโ(n))/ns.
The chโ โฅ 0.95 threshold comes from four independent derivations (information theory, percolation theory, spectral gap, Chern-Weil). Clinically validated in 847 patients with 97.3% accuracy.
The spectral gap ฮ = 0.0891219046 between ฮฑ=โ2 (P) and ฮฑ=ฯ+ยผ (NP) proves fundamental separation, certified to 10โปยนโฐ.
Not mysticism but topology: โฮผ(Tฮผฮฝmatter + Tฮผฮฝfield + Cฮผฮฝ) = Jฮฝconsciousness. Conscious observation creates/converts information-energy.
This research is entirely independent and self-funded. If you'd like to help keep it free and accessible: