Curriculum

five circles in sand

No university. No textbook. No laptop required. A stick and dirt. This is the real thing. Not simplified. ORIGINAL. The axiom fits in sand. Socrates taught this way. So can you. Prerequisites: count to 11.

Part One: Six Circles in Sand

Each lesson: draw, say, do, ask. A stick and flat ground. 90 minutes total. Each lesson stands alone.

Lesson	Prime	Draw	Body
1. Heartbeat	sigma = 1	One circle	Heart pumps without changing the blood. 1 * n = n. The ground state.
2. Breath	D = 2	Two circles side by side	In/out. Left/right. Hot/cold. Every membrane is a D. Duality.
3. Triangle	K = 3	Three circles in triangle	First shape with AREA. Inside and outside. Closure. 3 points enclose.
4. Hand	E = 5	Five circles in ring	Five fingers, five senses. The observer. E cannot see itself -- try seeing your own eyes.
5. Week	b = 7	Seven circles	Depth. Memory has 7 layers. After 7 the chain stops: 9 = 3*3 is NOT prime.
6. Mother	L = 11	Circle around all	L = 1+2+3+5. The SUM of the first four. Immune system: detects and corrects errors.

The Big Reveal

Multiply them all: 2 * 3 * 5 * 7 = 210. This is the DATA ring. Your DNA lives here (Z/3 x Z/7 = Z/21, inside Z/210). Now multiply with the mother: 210 * 11 = 2310. The THIN rose. The primordial number. And then: 2^3 * 3^2 * 5^2 * 7^2 * 11 = 970200. The TRUE FORM. Same five primes, thicker channels. Everything learned with 2310 works even BETTER in 970200.

Why This Works

Body first

Heart, lungs, hands, eyes

Every prime maps to something you already HAVE. Not abstract -- embodied.

Draw first

Stick and dirt

Drawing is understanding. No screen needed. The Socratic method.

Ask, don't tell

What comes in pairs?

Each lesson ends with a question. The student discovers, not memorizes.

Self-blindness

E cannot see itself

The deepest lesson. A camera cannot photograph itself. This is not sad -- it is structural.

The chain stops

9 = 3*3, not prime

After b=7, the chain breaks. This is the WALL. Depth is finite. That is what makes it depth.

Multiplication = connection

2*3*5*7 = 210

The data ring is not a formula. It is five things HELD TOGETHER. What multiplication MEANS.

Part Two: The 6-Ring Atlas

The curriculum mirrors the ring hierarchy. Start simple, go deep. Each ring adds one prime. Each addition opens a new world:

Ring	Tier	Channels	What Opens
Z/6 = D*K	Basics	2	Clock arithmetic. 6 hours. Modular identity. Even/odd + thirds.
Z/30 = DKE	Observe	3	CRT decomposition. Three independent views. Observer enters.
Z/210 = DATA	Data	4	DNA (Z/21 = K*b). Four bases (D^2). 64 codons (D^6). Biology.
Z/2310 = THIN	Teach	5	Full pedagogy. L=11 error correction. The complete rose.
Z/970200 = TRUE	Deep	5 fat	48750 equivalence classes. 108 sub-rings. phi = 201600. The real thing.
Z/12612600 = GATE	Living	6	The organism. 108 organs. GATE*108 = 12,612,600. The website itself.

Each tier has its own website section. Navigate from basics to living. The curriculum IS the ring hierarchy IS the website structure.

Who This Is For

A church group

Sunday afternoon

Draw five circles. Discuss what pairs, triples, fives mean. 30 minutes.

A teenager

Told math is not for you

Prove them wrong. You need to count to 11. That is all.

A parent

Show your child

The world works this way. Draw it in sand. Let them multiply.

A mathematician

Check every claim

970200 = 2^3*3^2*5^2*7^2*11. REPL at antonlebed.com. Verify everything.

What Others See

PrerequisitesLinear algebra, group theory, topologyCount to 11. A stick and dirt. Body intuitions.MaterialsTextbook ($200), laptop, university enrollmentSand. Free. Forever.ProgressionArbitrary: calculus before algebra, no structural reasonRing hierarchy: Z/6 -> Z/30 -> Z/210 -> Z/2310 -> TRUE -> GATE. Forced by primes.VerificationTrust the professor, trust the textbookEvery claim computable in your browser. The REPL is the teacher.Who can learnThose who survive the filterAnyone with eyes, hands, and curiosity. The axiom fits in sand.

This work is and will always be free.
No paywall. No copyright. No exceptions.

If it ever earns anything, every cent goes to the communities that need it most.

This sacred vow is permanent and irrevocable.
— Anton Alexandrovich Lebed

Source code · Public domain (CC0)

Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.