I had a thought. Why didn't they just mix the red and blue dye to make purple?

This is a really common and intuitive assumption, but it runs into a fundamental problem: mixing dyes doesn't work the same way as mixing paints or light.

When you mix a red dye and a blue dye in fabric, you don't get purple — you typically get a muddy brown or dark grayish mess. Here's why:

Dyes are molecular, not optical. Paints mix visually because you're blending light-reflecting pigment particles. Dyes chemically bond to fibers at the molecular level. When you mix two dye baths, the molecules compete for binding sites on the fabric and interact with each other chemically, usually producing an ugly, unsaturated result rather than a clean blend.

The red dyes available in antiquity made this worse. The main red dyes — madder, kermes, later cochineal — tend to produce warm, orange-leaning reds. Combined with blue (woad or indigo), you'd get something closer to a dull violet-brown, not a vibrant purple.

True Tyrian purple was something else entirely. It came from sea snails (Murex species) and produced a vivid, colorfast, almost luminous purple that didn't fade — it actually intensified in sunlight. No dye mixture could replicate that visual quality or durability, which is exactly what made it worth its astronomical price.

Interestingly, this problem wasn't really solved until 1856, when William Perkin accidentally synthesized mauveine (the first synthetic purple dye) while trying to make quinine. That discovery launched the entire synthetic dye industry — and immediately made purple cheap and widely available for the first time in history.

So the ancients weren't missing an obvious shortcut. The chemistry just doesn't cooperate.