Chapter 11: The Symbol Shortage
The commodity-counter theory claims each token shape represented a specific commodity. This interpretation has a fatal mathematical flaw: there are not enough shapes.
Counting the Shapes
Plain tokens come in approximately sixteen basic types:
- Cones
- Spheres
- Flat disks
- Lenticular disks
- Cylinders
- Tetrahedrons
- Ovoids
- Triangles
- Rectangles
- And a few others
Of these, only five to seven are common. The others are rare.
Counting the Commodities
Neolithic economies involved many commodities:
Grains: Wheat, barley, emmer, einkorn, millet
Animals: Sheep, goats, cattle, pigs, donkeys
Animal Products: Milk, cheese, butter, wool, leather, bone, horn
Fish: Multiple species depending on region
Plant Products: Flax, vegetables, fruits, nuts
Manufactured Goods: Pottery, baskets, textiles, rope
Tools: Blades, scrapers, axes, needles
Materials: Clay, ochre, obsidian
Services: Labor, transport, construction
Dozens of commodity types. Maybe hundreds.
The Math
Seven common shapes cannot represent dozens of commodities.
If cone means grain, what represents wool? What represents pottery? What represents labor?
The conventional response: different sizes meant different things. A small cone for one commodity, a large cone for another.
But sizes were not standardized. "The size of the counters varies from artifact to artifact and from site to site." (p. 11)
Another response: combinations represented complex commodities. But no combinatorial syntax is attested. How would "two cones plus one sphere" convey specific meaning?
The commodity-counter theory simply cannot work with the available token vocabulary.
Money Works with Few Denominations
Currency requires only a few denominations.
The United States uses about fourteen: seven coin types and seven bill types. With fourteen denominations, we price everything in the economy.
Token shapes functioning as authentication data require even less. The shapes do not represent values at all. They represent random patterns—shared secrets.
Three cones, two spheres, one disk. That is not a price. That is a password.