Heya! I'm writing an academic paper (network science / social network analysis) that proposes a new measure of *polarization* \- roughly, how strongly a network splits into opposed, internally-agreeing camps. Since "polarization" has Greek roots, I thought it'd be fitting to name the measure with a Greek letter rather than a boring Latin one, and I want to make sure I don't embarrass myself with the etymology or the spelling. Also, (hot take) Greek letters used in formulas just look cooler than the Latin ones.

Here's my thinking, and I'd love someone who knows their Greek to let me know if I am correct here:

The formula combines two ingredients, and I noticed both have Greek names:

* **extremeness-** how far out toward the poles the opinions sit- which, I understand, relates to **ἄκρον** (ákron, "extremity/peak," as in acropolis, acrobat)
* **homogeneity-** how internally alike a group is - which is basically already Greek: **ὁμοιογένεια** (ὅμοιος "same" + γένος "kind")

So I landed on **Ω (omega)** as the symbol, with the idea that it evokes both ὁμοιογένεια *and* the "alpha and omega / the whole span" idiom -extremeness at the α end, homogeneity at the ω end. (I know the literal first letter of ὁμοιογένεια is omicron, not omega but it looks basically the same as latin O, so I'm leaning on the α–ω "totality" idiom rather than a strict initial, but tell me if that's a stretch that'll make a classicist wince.)

My questions:

1. **Etymology of "polarization":** I *think* it's from **πόλος** (pólos, "axis/pole") via Latin *polus,* i.e. "having to do with poles" — and specifically **not** from πολύς ("many," the poly- in polygon). Am I right that it's pólos, not poly-? I really don't want to write "from Greek pólos" and have it be wrong.
2. **Spelling/accents:** are these written correctly, breathing marks and all? ἄκρον, ὁμοιογένεια, πόλος.
3. **A word for "fairness":** part of the paper is about the measure being *fair* across different groups (behaving the same regardless of which subgroup you look at, so impartiality more than "justice"). I've seen **ἀμεροληψία** (amerolipsía, "impartiality"?) and **ἰσότητα** (isótita, "equality/parity"). Which better captures "impartial / doesn't take a side"? And is ἀμεροληψία spelled right?

Not trying to write the whole paper in Greek, just a symbol or two and maybe a one-line footnote where I won't misspell anything. Any corrections (or better suggestions) very welcome. Σας ευχαριστώ!

Sociologist/network-scientist writing a paper - want to name a measure with a Greek letter and get the etymology right before it's in print