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Two Mesoamerican systems that count in twenties and are built on opposite principles.
Both count in twenties, which is why they are constantly conflated. The Maya system is positional: a cell's value depends on its height in a vertical column, and it has a sign for zero to hold an empty place. The Aztec system is additive: each power of twenty has its own sign and a quantity is written by repeating those signs, so it needs no zero and a large number takes a large area of the page.
Both are Mesoamerican base-twenty systems; this one is positional and the Aztec one additive.
Drawn from the visual attributes recorded for each symbol. Only traits the two records disagree about are listed.
| Trait | Maya bar-and-dot numerals | Aztec numerals |
|---|---|---|
| Built from | lines and dots, number like | abstract and number like |
| Maya bar-and-dot numerals | Aztec numerals | |
|---|---|---|
| Principle | Positional. | Additive. |
| Zero | Has one, written as a shell. | Needs none. |
| Space a large number takes | Fixed by the number of positions. | Grows with the quantity. |
| Relationship (from Symbolwise's records) | Commonly confused with Aztec numerals — Both are Mesoamerican base-twenty systems; this one is positional and the Aztec one additive. | Commonly confused with Maya bar-and-dot numerals — Both are Mesoamerican base-twenty systems, but the Maya notation is positional and the Aztec one additive. |
Mesoamerican calendrical and numerical notation
University of Texas Press and comparable scholarly editions · retrieved 2026-08-27
Scholarly treatment of Maya and related notation. Cited for the identity and reading of a sign; decipherment is an active field and a reading that is contested is recorded as contested.
Alpha is a Greek letter and stands for a quantity — an angle, a coefficient, a significance level. The proportionality sign is an operator and stands between two quantities to say they keep a constant ratio. The drawings differ in that the proportionality sign's right-hand stroke runs out in an open curve rather than closing into the letter's tail.
Look at the left-hand edge. A straight flat back is an AND gate: the output is true only when every input is. A curved concave back is an OR gate: true when any input is. Everything else about the shapes is similar, which is why the back edge is worth checking deliberately rather than at a glance.
Look at what follows. A prefix never stands alone — it is glued to a unit symbol, as in kW or kg. A constant stands by itself in an equation. Careful physical writing subscripts the constant as k_B for exactly this reason, and the kelvin's capital K is a third claimant to the same letter.
Length is the tell. A crescendo hairpin is drawn long, below a stave, and spans the passage it applies to — its extent *is* the instruction. A less-than sign is one character wide and sits between two values. If it stretches, it is music; if it fits between two numbers, it is mathematics.