One number, one code
No two integers within the supported domain share the same underlying geometry. Distinguish mathematical uniqueness from visual confusion after projection.
EXPERIMENTAL MATHEMATICS / OCTOBER 2026
Make number
spatial.
What if the geometry of a number could reveal how to transform it? Begin with Cistercian numerals. Then investigate three new, exactly decodable number systems designed for graphical arithmetic.
FIG 001 · CANONICAL NOTATION
1,993 — ONE FIGURE / FOUR PLACES
01REFERENCE SYSTEM
The historical baseline.
One vertical stem, four decimal places. This is a notation, not a historically established arithmetic machine.
Ready
The bare stem denotes zero here as a modern interface convention. Historical forms varied.
CISTERCIAN · 1993
Open the nine-stroke alphabet
Upper right = ones; upper left = tens; lower right = hundreds; lower left = thousands. Shapes are reflected into the other quadrants.
02GENERATIVE NOTATIONS
The number becomes a form.
Rotate a transparent 3D object. The depth and structure are mathematical channels—not arbitrary decoration. Every mark has an inverse decoding rule.
GEOMETRY CONTROL
Four transparent planes
The number has four decimal floors. Each digit is encoded by a count of luminous radial marks. Ten marks normalize to one on the next floor.
digit d → d radial marks · Σ dᵢ10ⁱ = n
Projection is 2.5D on a regular screen; orbiting reveals the 3D structure. Screen visibility depends on camera angle and overlap.
03OPERATORS / EXACT INVARIANTS
Calculate by transformation.
One operation, two geometries: compare Cistercian stroke union against canonical arithmetic, then inspect the rules that actually preserve numerical value.
A / BASELINE STROKE UNION
B / EXACT RESULT
12 + 18 = 30
Arithmetic checked.
Stroke overlap alone does not in general perform addition.
EXHAUSTIVE LOCAL SCAN
How often does plain overlay work?
Test every ordered operand pair from 0 through 99. No sampling, no generative claims: compare literal line sets against exact results.
Press “Run” to measure.
04HUMAN READABILITY LAB
Can a person learn to see the number?
Train ordinal sequence and quantity associations. Then test symbol recognition without decimal labels, recording your own trial accuracy and time. This is a self-experiment, not a validated population study.
Mnemonic scaffold
LEARNING CARD6
For Cistercian: up-right is ones; up-left tens; down-right hundreds; down-left thousands. Learn the nine strokes, then combine places.
Recognition test
Choose a training notation, inspect examples, then start a recognition test.
No trials completed.
Trials are stored only in this browser until you clear them or export them. The experiment makes no claim of cognitive improvement.
05RESEARCH PROGRAM
Design principles and falsifiable tests.
Complex encoding is not valuable by itself. A useful mathematical writing system must survive exact decoding, ambiguous viewpoints, realistic memory limits and arithmetic tests.
Operations preserve meaning
Operations on codes must map to arithmetic operations after decoding. Every rewrite is checked with an exact numerical oracle, including carry and zero.
Make symbols discriminable
Measure confusions, latency, delayed retention and generalization to unseen combinations. Elegance without learnability is insufficient.
Test 3D, do not assume
Compare locked 2.5D projections against free rotation. Depth can carry structure, but foreshortening and occlusion can also bury it.
Evidence and boundaries
Research on artificial number-symbol learning supports training with order and quantity cues. Symbol recognizability and memorability depend on visual design and conceptual distinctiveness. These findings motivate experiments; none demonstrates that this particular geometry improves arithmetic.
- Weiers, Inglis & Gilmore (2023): learning artificial number symbols with ordinal and magnitude information
- Merkley & Scerif (2015): continuous visual properties in new numerical symbols
- Reverse engineering what makes a symbol memorable (2026)
- Creating ad hoc graphical representations of number (2023)
- On visually-grounded reference production: 2D versus 3D (2019)
Cistercian historical reading: David A. King, The Ciphers of the Monks (2001). Geometry systems A, B and C on this page are newly constructed experimental notation proposals.