So this is just a generic question on why in HK and other 4x games, Babylon and Greeks are depicted as scientific cultures.

Knowing their historical achievement I imagine them much more as influential cultures rather than scientific. 

Babylon is famous for the first codified law wich in the game is very related to influence and civics.

Greek culture historically spread to all the middle east and to romans, which again is very related to influence in game. Also they were famous for filosophy, comedy, tragedy and art in general for which i dont see great justification for being depicted as scientists.

Strictly speaking, no culture before the scientific method (XVII century) can be called "scientific" by our contemporary standards. That being said, if you want to have ancient cultures with a scientific affinity (and you do, to make the game more varied and fun) then it makes perfect sense for these to be Babylon and Greece.

Babylonians had some elaborated mathematical system that was copied by many other ancient civilizations. Our time measurement, for example, comes from the fact that the Babylonian system was set in base 60 (hence 60 secounds in a minute, 60 minutes in an hour and so on). There's also evidence that they studied astronomy quite a lot, even if it was mostly for reasons related to mysticism.

Greeks had philosophy, of course. Even though nowadays we think of philosophy as mostly metaphysics and ethics, back then philosophy included the understanding of the natural world (including what we now call biology, physics...). There are many thinkers of classical Greece that advanced mathematics (we still study the Pythagoras theorem in school nowadays) and astronomy quite a lot. It took humanity more than a thousand years to start correcting the astronomical concepts that the ancient greeks studied. They may have been wrong about the sun circling around the Earth, and atoms being as small as matter can get, but at least they made an effort to study the universe.

Thank you for your answer, also very interesting I didnt know about babylonian mathematics.

What you say gameplay wise is true, still maybe the Zhou could have been a better picks as a scientific culture also given their Confucian school as EQ.

Also about the greeks, having the Anphiteatron as a scientific district is a bit anti-thematic for me but I think it is a matter of personal taste.

Archimedes was another great mathematician and had a great understanding of physics. The Archimedes' screw is something that is in use even today. The greek alphabet itself was used as the basis of the Latin and Cyrillic alphabets and a lot of the surrounding peoples sent their nobles and brightest to greek schools within Greece. Or in the case of the romans, they even bought greek slaves to work as private tutors.

The Amphitheater was not simply a stage where plays were displayed. It was used for political, philosophical and scientific debates, much like today we have various conferences. Sometimes they even held elections there (in case the polis was actually ruled by a democracy).

I can understand if you are not from Europe to have cursive knowledge about the Greek culture and civilization but for those in Europe the Greeks have a mythical renown for pushing a lot of the sciences and being the forerunners in multiple domains.

The pattern seems to be (apart from modern cultures) in rough order from most obvious to least:

Builder cultures are mostly known for giant monuments.  Egyptian pyramids, Taj Mahal, Angkor, etc.  Even industrial Siamese seem based on the big Buddha statues

Scientists cultures are often cultures known for philosophy, math, and other clear advances.  Greece and babylon are described here, Ummayads 9really, caliphate and related arab/early muslim empires) are known for lots of medical, astronomy, philosophy, etc. advances.  French in industrial may reference salons in the 1700's and people like Voltaire, Lavoisier, etc.

Merchant culturs are known for trade, obviously.  Phoenicians, Carthage, Ghana, Venice are pretty obvious here.

Expansionist cultures are known for their large empires.  Assyrians, Achaemenids, British, Rome, these are pretty obvious.

Militarist are mostly known for specific powerful soldiers.  Myceneans from trojan war stories, Mongols and huns with horse archers, Vikings generally known as fighters and raiders, Poles for cavalry, etc.  Hittites are the odd one here, they are normally just known for having an empire.  maybe trojan war stories or battle of Qadesh are the inspirations here.

Influence are a bit weirder, some are obviously known for artistic stuff like italy, but a good share of cultures seem here because they fit better than elsewhere.

Agrarian also seems to mostly be "known but not strongly for anything else and/or feels more agricultural", often the less developed ones (like Calts in classical) get pushed here.  OP superpower I wish i could grab them first occasionally Harrapans are actually known for irrigation, though the "don't know much else' applies very strongly here (they had well planned cities and very early sanitation systems and...that's about it, outside of generic ancient civilization stuff.  And they even are missing some of that.)

Of course, there are some cultures like Joseon and probably Persians that are what they are to fit enough cultures of all types into an era.