No one could see the colour blue until modern times
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Also, the argument that 'they didn't have the name for this color' is flimsy: maybe they had the name, we just don't know it.
This isn't something special about ancient greek. Even in several modern languages like Japanese, the word for blue also applies to colors that in english would be described as shades of green. The color spectrum is continuous, and where a culture decides to delineate one color from another is arbitrary. For example I would call rgb 60,220,240 a sky blue, while 60,240,220 would be a mint green, but these colors are way closer to one another than either is to rgb 0,255,0 or 0,0,255, which I could just as easily call dark mint or dusk sky.
And it's not like english is even the most extreme example. In english, cyan is a shade of blue, for example russian has 7 primary colors, with what we'd call blue split up into a light azure (goluboy) and an ultramarine (siniy). It would be absurd to say that english speakers can't see these colors simply because we refer to both of them as blue.
How do we know the Egyptians had a word for blue, if the Greeks didn't?
What did everyone call the dyes and carvings made Lapis Lazuli? And what about dyes produced from woad and indigo?
How did people describe the color of sapphires?
That doesn't seem consistent with the Wikipedia entry on woad dye [0] (blue [1]), which mentions woad-dyed textiles found, e.g. at a German site dated to 530 BCE. (?)
edit: Also Herodotus uses words that were translated as "blue" (accurately?), for example describing a palace in Media (in modern Iran) [2]:
>"On this wall the battlements are white, of the next black, of the third scarlet, of the fourth blue, the fifth orange; all these colors with paint."
(I wonder is this was the same blue chemistry as the Ishtar Gate of Babylon, which survives today and is in fact blue, very blue, extremely, shockingly blue [3]).
edit edit: Herodotus' wording of the above is "τετάρτου δὲ κυάνεοι" [4], which is an inflection of "κυάνεος" [5], which is glossed as "dark", "dark-blue"; and in the references section "azure", "blue", and "cerulean". The etymology links to "κύανος", which going forwards is the etymological root for "cyan"; and going backwards is possibly the same word ancient Hitties used for "precious stone" and "copper". (Note the extremely ancient blue pigment azurite [7] is simply a natural copper ore).
[0] https://en.wikipedia.org/wiki/Isatis_tinctoria#Ancient_use
[1] https://duckduckgo.com/?q=woad+dye&iax=images&ia=images
[2] https://en.wikipedia.org/wiki/Ecbatana#Historical_descriptio...
[3] https://en.wikipedia.org/wiki/Ishtar_Gate
[4] https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext...
[5] https://en.wiktionary.org/wiki/κυάνεος
http://www.perseus.tufts.edu/hopper/searchresults?la=greek&p...