There is always the possibilty that this was a "one off" work of an ancient D'Vinci.  And let us not forget the knowledge lost with the burning of the Library of Alexandria, or destroyed by zealots.

As for abstract thinking, this is one reason AI will always be limited... the great power of the mind is the ability to imagine and wonder "What if..."

Unfortunately, our educational system (with exceptions) is not geared to be in sync with rapidly changing technology. By the time a technology has reached the textbook, it has matured and taught as "accepted practice". Tomorrow's great ideas are most likely to come from coop students who experience the "real world" and the "hallowed halls" more or less simultaineously.

The ancient Greeks' stories and achievements essentially taught the world how to think. That is, the Greeks recognized that there was probably a way to do something better, even if humans could currently not conceive of it.

• Aristotle predicted that industrialization, e.g. in the form of what we would now call robots, would abolish slavery by making it uneconomical. The Industrial Revolution proved this prediction accurate about 2000 years later.
• The Greek legend of Daedelus involved human-powered flight, and gave people the idea that they might indeed be able to fly one day. ("“The desire to fly,” wrote Wilbur Wright, “is an idea handed down to us by our ancestors who, in their grueling travels across trackless lands in prehistoric times, looked enviously on the birds soaring freely through space, at full speed, above all obstacles, on the infinite highway of the air.”")
• The legends of Hercules literally transformed the world through Alexander the Great, who cited Hercules as his role model (and who was even depicted as wearing Hercules' lion skin). Hercules often had to solve problems by thinking about them, and he altered geography by diverting two rivers to clean out the Augean Stables. Alexander later altered geograpy by building a causeway or isthmus to attack the fortress of Tyre, and similarly came up with a very innovative solution to the Gordian Knot.
• The Greek legend of Hephaestus said that the god of engineering and mechanical crafts created mechanical men (robots) to assist him in his work.
• Greeks showed that steam could do useful work, and also (Archimedes) the value of mechanical advantage; he purportedly used machines to destroy enemy warships and, according to some stories, used an array of mirrors to direct concentrated sunlight against enemy ships to set them on fire. Modern solar furnaces use exactly that approach today.

The Antikythera mechanism is particularly impressive because it must have been hand-made, without modern machine tools and without modern metrology methods, but nonetheless performed its intended function

The antikythera mechanism is actually an analog computer of the time.  Where to put it in the scale of complexity of instruments of 150 B.C. culture is difficult; perhaps a historian of science can tell us, but I imagine that it is near the best at that time.  It seems to be based on the geocentric solar system, and uses fairly basic geometric principles of that time.  But its engineering is tremendous.  We must be careful to not imbue it with our modern views of its purposes for them. I agree that since astrology was as real to them as automobiles are to us, a timekeeper for olympic events would naturally be folded in with astronomical events.

Progress was made in 1500 years after the antikythera despite the lack of power for devices, in disagreement with Marchant.  The astrolabe comes to mind, a cousin of the antikythera.  And William Oughtred's slide rule also, after the invention of logarithms by Napier.  Both of these are analog computers with no stored potential energy.  Machines that use potential energy, i.e., "engines," include the windmill (maybe 9th century A.D.) and the many military machines similar to the trebuchet.  Progress would have to be thought of in terms of the mere invention of these devices, for they weren't as sophisticated as the antikythera (the slide rule is the exception).

I agree that invention is the result of application of abstract ideas to the concrete world.  In addition to this, "chance favors the prepared mind," as Ben Franklin said.  And there is imagination.  It took the imagination of Richard Feynman to tell everyone that nanotechnology was possible, decades after the atomic theory of matter was confirmed.  But I cannot agree that music and the arts are somehow an essential ingredient to invention.  Certainly Einstein was an accomplished violinist, but he never said that this ability was essential for his imagination in physics.  It was a soothing avocation for him, period.  Science fiction clearly inspires the imagination, but it does not invent anything.  Isaac Asimov was an awesome author and popularizer of science, but he did not need his literary expertise in his study of chemistry. 

The STEM initiative is so important for the 21st century, but I fear for its dilution when arts get involved as a substitute.  I think the STEAM movement is anathema to science and technology (A = arts).  I disagree that scientists and artists are more alike than different, as a Scientific American article of some years ago posits.  Artists tag along and may make meaningful the advances of science to the common person, but they work with emotions and the common human experience.  Neither of these is the coin of the realm for science and technology.  In other words, no amount of expertise in Shakespeare could prepare one to construct the Brooklyn Bridge, but enjoying the theatre was probably a nice part of Washington Roebling's life.  Chance does not favor the mind prepared with Milton, Chaucer and Dickinson insofar as technological advance is desired.

Thank you for your inspiring column!

Last night as I considered this discussion, I came to the question, "Which is cause and which is effect?" Is art the catalyst or the byproduct in the process?