Curriculum

seven circles in sand

No university. No textbook. No laptop required. A stick and dirt. This is the real thing. Not simplified. Original. Seven primes fit in sand. Socrates taught this way. So can you. Prerequisites: count to 13.

Part One: Seven Lessons 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	1	One circle	Heart pumps without changing the blood. 1 * n = n. The identity.
2. Breath	2	Two circles side by side	In/out. Left/right. Hot/cold. Every membrane is a pair. The only even prime.
3. Triangle	3	Three circles in triangle	First shape with AREA. Inside and outside. 3 points enclose a region.
4. Hand	5	Five circles in ring	Five fingers, five senses. Try seeing your own eyes -- 5 cannot see itself.
5. Week	7	Seven circles	Depth. Memory has 7 layers. After 7 the chain stops: 9 = 3*3 is NOT prime.
6. Mother	11	Circle around all	11 = 1+2+3+5. The SUM of the first four. Detects and corrects errors.
7. Boundary	13	Ring around the ring	c(6) = 26+1 = 13. The Cunningham child of 23. The boundary between inside and outside.

The Big Reveal

Multiply them all: 2 * 3 * 5 * 7 = 210. This is Z/210. Your DNA lives here (Z/3 x Z/7 = Z/21, inside Z/210). Now multiply with 11: 210 * 11 = 2,310. The primorial of 11. And then raise exponents: 2^3 * 3^2 * 5^2 * 7^2 * 11 = 970,200. Same five primes, richer channels. Add 13: 12,612,600. Six channels. Add 17: 214,414,200. Seven channels. 5*7 = 1 mod 17 closes the ring and the period quadruples to 1680.

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

5 cannot see itself

The deepest lesson. A camera cannot photograph itself. 5^2 divides the ring but 5 does not divide 24.

The chain stops

9 = 3*3, not prime

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

Multiplication = connection

2*3*5*7 = 210

Z/210 is not a formula. It is four 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 = 2*3	Basics	2	Clock arithmetic. 6 hours. Even/odd + thirds.
Z/30 = 235	Patterns	3	CRT decomposition. Three independent views.
Z/210 = 235*7	Connections	4	DNA (Z/21 = Z/3 x Z/7 inside Z/210). Four CRT channels.
Z/2,310 = 235711	Theory	5	Five channels. mod-11 error correction.
Z/970,200 = 2^33^25^27^211	Ideas	5 (prime-power)	48,750 classes. Carmichael lambda = 420. phi = 201,600.
Z/12,612,600 = above * 13	Lab	6	341,250 classes. 13 adds a boundary channel.
Z/214,414,200 = above * 17	Lab	7	The complete ring. 5*7 = 1 mod 17 closes. Period 1680.

Each tier has its own website section. Navigate from Basics to Lab. 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

12612600 = 2^3*3^2*5^2*7^2*11*13. REPL at antonlebed.com. Verify everything.

Contrast Table

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/2,310 -> Z/12,612,600. 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. Seven primes fit in sand.