Maybe you can recognize the continuity as a native Greek speaker. As someone who has learnt Ancient Greek that didn't help at all when I visited Greece. I mean even the letters (some) are now used differently.

I know just Ancient Greek. When I was in the country, I was consistently blown away by how much I could understand, even without knowing Modern Greek.

A billboard for cigarettes contained their equivalent of the surgeon general's warning, using the word "βλάπτεται." βλάπτειν in Ancient Greek means "to injure." βλάπτεται is best read as a middle-voice form: "causes harm."

In a doctor's office in Athens I'd been waiting for a while, so I approached the nurse's station, and a visibly impatient nurse said to me before I could open my mouth "περιμένετε, παρακάλω."

"μένειν" in Ancient Greek means "wait." "μένετε" is a polite imperative, in the present tense ("do or keep doing something"). "περί" as a verbal prefix often means something similar to its meaning as a preposition: "around." "παρακάλω" means in this context exactly what it did 2,500 years ago: "I ask," i.e. "please." I could understand exactly the intended sense: "please continue to wait."

My jaw dropped. I was too dumbfounded to do anything but stare at her. She sighed, rolled her eyes, and switched to English: "Please wait!"

On my first morning in the country I bought a drink called μύθος, not realizing I'd purchased cheap beer (with a delicious tiropita). Same word, same sense: "mythos."

There are limits, definitely. The vocab, grammar, and syntax are different, often very different. The pronunciation letter by letter is broadly the same as it has been for millenia, though, since the changes that turned Ancient Greek into Koine, isn't it?

Still, the similarities and, to some extent, mutual intelligibility of Ancient and Modern Greek are mind-blowing, particularly for someone who grew up speaking English, which didn't even exist two thousand years ago, except, maybe, as some subtle quirk of proto-germanic on a weird little island off the coast of Europe proper.

The continuity is to some extent artificial, as there was a re-Hellenization effort in Greece after the expulsion of the Ottoman Empire. Even where the Ottoman Empire's cultural and linguistic influence were somewhat escapable, though, there's a shocking degree of linguistic continuity. Mani, an isolated, culturally distinct region of the deep Peloponnese, retains features of the Doric dialect that its residents spoke in Archaic Greece around the time the texts of Homer's Iliad and Odyssey were taking shape.

I've been reading Sacred Scripture in Greek these days, thanks to a free Bible study app with the approved translations. And it's extremely eye-opening to see the level of wordplay in the Gospels, that's sometimes hinted by modern homilists, but it goes to a depth you just wouldn't believe.

I thought I could "get by" in Greek just from my knowledge through medical and scientific terms, but there's a lot more to it!

One of the other exciting experiences was to attend a Greek Orthodox liturgy that was sung/chanted in Greek, too. I don't know exactly what variety of liturgical Greek is used, but speaking as someone who knows English and Spanish, and I can recognize many other languages, to hear the Greek chanted and pronounced so eloquently like that was transcendent, and sometimes surprisingly "foreign".

Whenever I see a film or TV of modern Greek signs, I try to sound out the words and decipher as much as possible. I feel like there is some "signal loss" since ancient times, with the musical tone, the rough breathing, etc. But it's definitely exciting to experience some comprehension across several millennia!

This is so nice to hear! I regret not spending more time with the New Testament when I had the opportunity (my time for Greek is essentially nil at this point). It's such a treat to run across people who savor the language the way you do, and it really is dumbfounding to hear those echoes across the milennia, isn't it?

The ways scripture intersects with more ancient literature is its own fascinating area of study, too. Take John 1:1: Ἐν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν, καὶ θεὸς ἦν ὁ λόγος. If you've read Hesiod's Theogony, the contrast could't be starker: ἦ τοι μὲν πρώτιστα Χάος γένετ᾽, αὐτὰρ ἔπειτα Γαῖ᾽ εὐρύστερνος. In Hesiod, the birth of the cosmos and the gods is physical. The first things that comes into being, Χάος, is just the absence of anything else. In the New Testament, by contrast, the beginning is not physical, nor is there any absence. It's something like an idea or something like rational intelligibility (ὁ λόγος). This is so wildly different from so-called Pagan religion: the universe not only makes sense; it makes sense in ways that human beings can access. Divinity isn't power and violence. It's intelligence. This reminds me, now that I mention it, of Augustine's view that evil is absence -- specifically the absence of good.

There's so, so much of this. I didn't know about the wordplay though! Wordplay has such a wonderful history in ancient literature. I distinctly remember a lightbuld moment, when I was reading Plato's Republic, where the god Wealth is described as a "blind (tuphlos) leader." In Plato's time, that "ph" is pronounced "p-h", not "f." And the word wealth, of course, is Plutos. So tuphlos is an phonetic anagram of Plutos.

Thanks for the substantial comment. So I guess your Ancient Greek is much better than mine. On the other hand when I learned the language I was suprised how many "foreign words" (in German) now started to make a lot more sense because I was able to decipher their constituents. Things like "telescope" or combinations with "peri" (as you said), "meta" and so on. Going to recap some things now :)