The Greeks had the ability, for certain, but their spin on the scientific
method was such that they saw no purpose in experimental proof of theories.
After all, once you have figured Nature out in your mind, what point is
there in getting messy by proving the truth? I particularly enjoyed reading
Socrates' arguments for the existence of an immortal soul, based on his own
personal experiences alone. No wonder the rulers of the time sought his
death - he was as far from the pragmatic science of today as possible.
Their 'inventions' were mostly used as special effects for their temples,
to impress the common folk, or for toys. Persons who actually would dig
into the mess to prove things were looked down on as mere mechanics and
laborers.
The Egyptians, I don't have good information on. Now I will have to go to
the library again..
Chuck Kuecker