"Midan" (Classical Maydan) had an older meaning before it became the usual word for a public square: it meant a large field for sporting events, such as a polo field or a hippodrome. (It's used from Central Asia westward and is probably originally Persian or Turkish rather than Arabic, but I'm prepared for commenters to correct me on that.) And one of the meanings of "tahrir," besides "liberation," is "editing." A muharrar is an Editor; the ra'is al-tahrir is the Editor in Chief. I like to think we aim to "liberate" the author's meaning from the text, but for whatever reason, that's one of the meanings. (And of course there's the old saying that every Arabic word has at least four meanings: a) its usual meaning; b) the direct opposite of its usual meaning; c) a meaning related to sex; and d) a meaning related to camels. It's an exaggeration. But not by much.)
But I'm glad that the Field of Editing has, at least for Google Translate, become the symbol of the Egyptian Revolution.
UPDATE: Well, I did say commenters should correct me. Commenter JP runs rings around me:
I do not think that Maydan is of Persian origin, and it certainly is not of Turkish - words indigenous to the latter seldom, if ever, begin with "m".JP for the win.
A scan of Hans Wehr for cognates produces a few other Arabic words that look as if they might be related to "maydan" because they carry meanings similarly relative to a wide, open expanse such as a square or a field:
mîdâ2 - measure, amount, length, distance
mâ2ida - table
madâ - extension, expanse, stretch, etc.
With -ân/-ôn being a common Semitic suffix connoting full or utmost possession, I see not to reason to conclude from the existence of M-Y-D and M-D words with related meaning, that maydân is of Arabic origin. I would reference the theory that proto-Semitic had bilateral roots from which the later trilateral roots evolved and also connect M-D-D - a root in both Arabic and Hebrew that connotes physicality and flat space.
However, until this moment, I had always assumed the word was related to madîna - perhaps in a morphed fu3ayl form. Though in post-Quranic Arabic madîna means city, as I think you have noted before, its etymological ancestors in Hebrew and Aramaic have larger geographic meanings of country or province. The common denominator here perhaps being jurisdictions, as it had always been put to me the ultimate derivation of madîna was the root D-Y-N "to judge".