I'm not an expert on the ancient Greeks, but the last I heard there wasn't much evidence of a written language during the Greek Dark Ages. But to jump from what we know of Greek culture from written remnants (plays and poetry) it would seem to place a great deal of emphasis on "linearity".
Take the Method of Loci used to, ahem, memorize the "linear" points of a speech or argument. While it's true that you can access points at random, that doesn't take away from the fact that they are staged and memorized in a specific order for presentation.
Bottom line, I think you're accepting the Sapir-Whorf hypothesis uncritically. It seems so reasonable, but when you get down to specifics -- like the actual number of words for snow in English and Innuit -- it just doesn't pan out. Similarly, I think anyone who's read Adler and Van Doren's pre-Internet "How to Read a Book" would scoff at Carr's notion that books can't be an interactive medium. People can be mentally lazy using any media.