School of Tomorrow / MartianMath
Kirby Urner's two interlocking curricula for teaching synergetics through Python and computational geometry — the most active effort to translate Fuller's geometry into executable, standards-aligned STEAM education.
School of Tomorrow
A cross-disciplinary K-16 framework that weaves synergetics with Transcendentalism, Pragmatism, Wittgenstein, and Quaker tradition. The curriculum positions Fuller's geometry not as an isolated subject but as a thread through philosophy, mathematics, and design science. It uses Python as the medium of instruction — students learn geometric concepts by writing and running code rather than by reading prose.
The framework covers:
- Synergetics philosophy — synergy, system, Universe as operational definitions
- Polyhedra as graphs — vertices, edges, faces as data structures
- Sphere packing — closest-packing simulated computationally
- Concentric hierarchy — computing whole-number tetravolumes in Python
- Quadray coordinates — a 4-axis coordinate system native to the tetrahedron, offered as an alternative to both Cartesian XYZ and Fuller's own vector notation
- Synergetics Constant (S3) — the conversion factor between IVM and XYZ volumes
MartianMath
The Python-based teaching sequence, structured as Jupyter notebooks. The playful name ("Martian") signals that this geometry comes from outside the Euclidean/Cartesian tradition — an alien coordinate system that happens to model physical reality more directly.
The pedagogical sequence: synergetics philosophy → polyhedra as graphs → sphere packing → concentric hierarchy → synergetics constant → quanta modules. Students progress by computing, not by memorizing.
Distinctive Approach
Where Amy Edmondson explains synergetics through geometric exposition and C. J. Fearnley's FAQ guides readers through the texts, Urner embeds synergetics in executable code. The three approaches are complementary:
| Pedagogue | Medium | Strength | |
|---|---|---|---|
| people/amy-edmondson | Edmondson]] | Book (geometric exposition) | Rigorous, complete, followable |
| people/cj-fearnley | Fearnley]] | FAQ (reading guide) | Concise map of the territory |
| people/kirby-urner | Urner]] | Code (Python notebooks) | Hands-on, executable, verifiable |
All three independently converge on the same concept backbone and dependency order, which lends confidence to any proposed synergetics curriculum.
Significance
School of Tomorrow / MartianMath is the most sustained effort to make synergetics teachable in a modern educational context. By translating Fuller's concepts into Python, Urner makes them testable: students can verify the concentric hierarchy's whole-number ratios by computation, not by faith. The curricula also demonstrate that synergetics aligns with STEAM education standards, answering the objection that Fuller's work is too idiosyncratic for formal instruction.
See Also
- Kirby Urner — author and maintainer
- A Fuller Explanation — Edmondson's book-length pedagogical introduction
- Fuller FAQ: Synergetics — Fearnley's reading-based learning guide
- Synergetics — the primary text all three curricula teach from
- Design Science — the applied frame
- Concentric Hierarchy — core concept taught computationally
- Vector Equilibrium — core structure explored through code
Sources
- School of Tomorrow (GitHub) — curriculum repository
- MartianMath / DigitalMathematics (GitHub) — Python-based teaching sequence
- grunch.net/synergetics — Urner's synergetics web hub
- Fuller FAQ: Synergetics (raw) — references Urner's work