Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

Who runs the universal simulation? Another name for God. The eternal torment of Roko’s Basilisk? Another name for Hell. AGI will save us from ourselves with its incomprehensible intelligence? A cyber-Jesus. Moving your mind into a transhumanist body? Souls rising to Heaven. Etc.

That Greek knowledge and culture survived the collapse of their prominence? Similar to the Romans after them and Babylonians before them.

Greek had been a lingua franca in the major ports of future empires for centuries [1], and Greek remained a spoken and written language in the Byzantine empire (the same was not true of ancient Egyptian or Babylonian – which were supplanted by Greek or other Aramaic languages during the hellenistic period).

I think at least as much credit is owed to the inheritors of Greek culture (Romans, Byzantines, the various Arabic empires), for preserving source material and references.

But I think Greece was seen as the original "filter" for civilization because it was both "successful" and comparatively extroverted to the great civilizations that came before.

Basically, it's what you said in your middle paragraph – wide availability, accessibility of language and culture. In other words, "better dissemination". :)

[1]: https://en.wikipedia.org/wiki/Greek_colonisation

Why is that obvious? The ancient Egyptians & Mesopotamians had a concept of archaeology, why not the Greeks?

[1] https://www.brainyquote.com/quotes/shaquille_oneal_381872

> If you create a parallelogram

Parallelism requires affine geometry, which you can't get just with straight lines (and their meeting points). Here are couple of explanations:

- We can also get projective geometry by using great-circles on the surface of a sphere (e.g. "equators" at different angles around the Earth), instead of straight lines on a flat plane: both situations give rise to exactly the same theory. Parallelism doesn't exist on the surface of a sphere, since all great-circles will meet at two antipodal points, so projective geometry (which describes great-circles as well as straight lines) cannot be used to construct/ensure/check that two sides of a quadrilateral are parallel.

- Alternatively, consider that projective geometry is invariant to changes in perspective, whilst parallelism is not. For example, we can get two straight lines by tracing over a photo of train tracks. If the photo was taken top-down, then the lines we traced will be parallel; but if the photo was looking along the track then our traced lines will converge (in the photo, they "meet" at the horizon). Projective geometry (and hence straight lines) can't distinguish between these two scenarios, due to this invariance.

> And if you can determine that the diagonals are the same length

If we extend our straight-line setup with some way to determine parallelism, we still wouldn't be able to compare the lengths of the diagonals, since they go in different directions. Projective geometry + parallelism is affine geometry, which can only compare lengths in the same direction. Essentially, parallelism allows us to translate: we can use this to compare two line segments by translating one so they share a common starting point, then seeing whether the other end has landed closer or further than the first line's. The latter comparison only makes sense if all the points end up colinear (i.e. the original segments were parallel, unlike a pair of diagonals).

To compare the diagonals we also need some form of metric, e.g. like the distance between a pair of compasses.