How did the Greeks represent fractions?

Ptolemy, at least, expressed them somewhat clumsily, by adding reciprocals. There were dedicated symbols for half: [math]unicode{x10175}, unicode{x10176}[/math], two thirds: [math]unicode{x10177}[/math], and three quarters: [math]unicode{x10178}.[/math] Outside of those, fractions were expressed by using double prime for reciprocals, ″.

So Ptolemy used ιβ″ = 1/12 a lot for geographical coordinates; and he would also use expressions like γ″ιβ″ = 1/3 + 1/12 = 5/12 or [math]unicode{x10175}[/math]ιβ″ = 1/2+1/12 = 7/12.

EDIT: For those without font support for Ancient Greek Numerals:

How can this Rilke translation be improved?

So you seek to translate:

Ich möchte aus meinem Herzen hinaus
Unter den großen Himmel treten.

“I would like to step out of my heart,
And go walking beneath the enormous sky.”

I’ll start by putting in the missing accent marks 🙂

ἐκ τῆς καρδίας βούλομαι ἐκβαίνειν
ὑπὸ τῷ μεγάλῳ οὐρανῷ βαδίζειν

I am so, so not going to have anything to say about metre: never got the hang of it.

The Greek matches the English, but not the German. Notice that the Greek repeats ek– : “step out, out of my heart”; the German repeats the aus: “out of my heart, away”, but the verb isn’t there at all: it’s literally “I would out of my heart, away, beneath the great heaven to tread”. So I’d get rid of ἐκβαίνειν: the Greek should be as taut as the German.

The other problem is that ἐκ τῆς καρδίας sounds like “from my heart” (which in German would be von Herzen); in fact Aristophanes uses it in that meaning in Clouds 86 ἀλλ’ εἴπερ ἐκ τῆς καρδίας μ’ ὄντως φιλεῖς “but if you truly love me from your heart”.

Homeric/Poetic Greek is not something I’m in any way comfortable, but maybe ἑκάς ‘far away from’?

And for the ‘great heaven’, I’m thinking ‘broad’—cf. the Orthodox icon caption of the Virgin Mary as πλατυτέρα τῶν οὐρανῶν.

τῆς καρδίας ἑκάς βούλομαι
ὑπὸ τῷ πλατεῖ οὐρανῷ ἐκβαδίζειν

“away from the heart I wish
under the broad heaven to step out”

Someone else do the metre.

Does Quora frown upon cussing in one’s answers?

See links in Nick Nicholas’ answer to Why does Quora permit foul language?

It used to, five years ago: What is the guideline on the use of profanity on Quora?

See Marc Bodnick’s answer to What is the guideline on the use of profanity on Quora? [Originally Answered: Is profanity a violation of the Be Nice rule?] (2011, incorporated into Answer Wiki)

Users should avoid unnecessary profanity.

Tracey Bryan’s answer to Why aren’t rules guiding the use of profanity enforced more on Quora? (2012)

Quora has a policy against profanity: What is the guideline on the use of profanity on Quora?

The reviewers and admins will thus edit questions, or collapse answers, which are in contravention to this policy, but they can’t be everywhere.

Quora appears not to any more. As witnessed by all the Top Writers since 2013 answering questions like this with variations of “FUCK no, ahahahahahaha!!!!11!!!11”. Starting with:

Dan Holliday’s answer to What is the guideline on the use of profanity on Quora? [Originally Answered: Is it appropriate to use curse words in your answers in Quora?] (2013)

If not, then I’m in big fucking trouble.

Here’s an answer from seven years ago, on why using the Q&A format to publish Quora policy guarantees this kind of confusion when policy changes—or indeed policy at all:

Xianhang Zhang’s answer to What are some of the basic “Community Management 101” mistakes that Quora has made? (2010)

Dogfooding is all well and good but Quora deciding to put its charter documents in the same Q&A system as everything else means that they’re fragmented and may as well not exist for new users.

Do read the rest of that answer and weep, btw.

Are you happy with Quora’s decision to remove the “followed by X, Y, Z, and N other people you follow” from people’s profiles?

I am happy for one reason only:

I called it. Two months ago:

Nick Nicholas’ answer to What’s the next useful and perfectly good feature that Quora is going to do away with?

Wild speculation:

*touch wood* Blogs.


The current trend though, is away from social media functionality, and has been deemphasising your followers. So:

Less Wild speculation:

In the display of your followers, or the mouseover display of a user: the followers you have in common.

It’s the last piece of the puzzle: MVW badges and TW quills have already been taken away from the former.

EDIT: Yes, Quora has put the mutual followers field back.

For now.

Would you listen to a 5-hour symphony?

I sat through the 1992 revival of Einstein on the Beach, which goes for five hours, and which is much more static (as hardcore minimalist music) than a symphony would be. I had no problem sitting through the entire thing—even though the opera creators imagined you could walk in and out as you pleased. And I was proud to give them a standing ovation at the end of it.

(The audience was much more restless in the 1992 revival than the 1984 revival, apparently. There was booing in the bed scene. The people booing did not stick around for the standing ovation.)

The six hour TV version of The Mahabharata (1989 film)? Not a problem.

I’ve enjoyed Mahler’s Third, which is an hour and three quarters; I’ve been puzzled by where the hell Brian’s Gothic was going, and its length at an hour and three quarters was not the reason why.

As long as the symphony is any good, I’m up for it. Just gimme a La-Z-Boy and a coffee, and I’m good to go.

Why isn’t Susan James active on Quora anymore?

If you go through her log, you will notice that Susan’s activity is intermittent. She posts for a few days, then is absent for months. In fact, her latest period of posting was her most protracted, and the first in which she posted on more than one topic.

Her being absent, in any case, has plenty of precedent.

Why is there a disgusting new font on Quora?

You mean, the font announced with a literal gong within Quora?

Instagram post by Quora • Feb 11, 2017 at 2:28am UTC

quora: Ringing the gong! One of our oldest traditions for product launches–this time we’re celebrating our new custom typeface [math]unicode{x1F514}unicode{x1F514}unicode{x1F514} [/math]#quora

[Why yes, Quora does use emojis on Instagram—not em-dashes, though.]

Of course this has been covered off with great erudition by Martin Silvertant: Martin Silvertant’s answer to Why is there a disgusting new font on Quora?

In conclusion, Quora has not introduced a disgusting new typeface. Rather, they are using the typeface they chose incorrectly. Quora has done amazingly by using Tiempos Text for body text, but they need some guidance in establishing a harmonious, coherent typographic system for the website.

Quora Design Team. “Guidance in establishing a harmonious, coherent typographic system for the website Sold Separately.”

What is the origin of the scientific name of the apple tree “malus”?

This has been answered already, I’ll just answer it more anecdotally.

Indo-European has two words for apple, that show up in different daughter branches:

  • *h₂ébōl shows up in Germanic (… apple), Celtic, Balto-Slavic, and probably Hittite šam(a)lu- ‘apple tree’
  • *méh₂lom shows up in Greek (Doric mālon, Attic mēlon), Latin (mālum), Albanian (mollë), and Hittite maḫla ‘apple’

This has been a puzzle for Indo-Europeanists.

  • Some Indo-Europeanists have assumed the genuine Indo-European word was *h₂ébōl, and *méh₂lom was a pre-Greek loanword.
  • Some Indo-Europeanists have assumed that Indo-European had split up into northern and southern dialects, and dialects are allowed to have different words for the same thing—without one word being necessarily more Indo-European than the other.
  • This was news to me: Proto-Indo-European phonology – Wikipedia says that some Indo-Europeanists have tried to unify the two forms as *h₂eml-:
    • *h₂eml- > *h₂ebl- > *h₂ébōl
    • *h₂eml- > *meh₂l- > *méh₂lom
  • EDIT: And add the speculation by Guus Kroonen in On the origin of Greek μῆλον, Latin mālum, Albanian mollë and Hittite šam(a)lu- ‘apple’ that *méh₂lom, which he reconstructs as *smh₂l, is related to proto-Kartvelian (as in Georgian) *msxal- ‘pear’.

So much for apple. What’s the story with mălus ‘evil’?

As others have pointed out, the vowel in malus is short; so whatever it’s derived from, it’s not going to be derived from *méh₂lom (where the laryngeal h₂ serves to lengthen the preceding vowel).

malus – Wiktionary

From Proto-Italic, related to Oscan mallom and mallud (“bad”). Originally associated with Ancient Greek μέλας (mélas, “black, dark”), but support for this is waning. Perhaps from the same Proto-Indo-European root as Avestan [math]unicode{x10B28}unicode{x10B00}unicode{x10B0C}unicode{x10B2D}unicode{x10B0C}unicode{x10B0C}unicode{x10B00}[/math] (mairiia, “treacherous”).

Which means… we don’t know. All we do know is, it is indeed a coincidence. Although yes, it’s a coincidence mediaeval theologians have had a field day with. In fact, it’s likely the reason why Westerners assume the forbidden fruit was an apple: Forbidden fruit. De ligno autem scientiae boni et mali “of the tree of the knowledge of good and evil/apples”. Jewish tradition instead pointed to the fig, the grape, or wheat.

What is said at Greek funerals?

Constantinos Kalampokis’ answer to What is said at Greek funerals? covers everything that happens at a funeral; but I’m assuming the question is particularly after what the condolence formula is.

Both Greek and Turkish are notorious in linguistics for having a formulaic expression for just about every occasion; it’s part of good social behaviour that you’re expected to come up with the right formula for the right occasion. Hence the proverbial expression for someone tactless: Πάρ’ τονα στο γάμο σου να σου πει «και του χρόνου», “Take this guy to your wedding, and he’ll wish you ‘Many Happy Returns!’”

In funerals, the formulaic expression is ζωή σε λόγου σας “life to you” (where λόγου σας “your word” is an old circumlocution for “you”, cf. “your lordship”).… offers the alternatives ζωή σε σας “life to you”, and να ζήσετε/ζείτε να τον/τη θυμάστε “may you live/keep living, so that you can keep remembering him/her” (i.e. may his/her memory survive in you).

Τα συλλυπητήριά μου “my condolences” is a more formal, stiff expression; I doubt you’d use it with friends. Κουράγιο “(have) courage!” is also heard, to acknowledge the hardship of family members.

I have a lot of time for the expression Να είναι ελαφρύ το χώμα που θα τον σκεπάσει “may the soil that covers him be light”. But that’s not used at funerals, it’s a valediction typically used for famous people.