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Not to mention they were destroyed by mobs of barbarians, no offense to the French and Germans, and lacked much of the mathematics and scientific understanding to progress.

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No need to indicate when you can work millions to death as slaves.

Also, lead poisoning from plumbing can't have helped.

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I wonder what tragedy led to it being stashed there and never retrieved

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Beat me to it with that Machine Thinking link!

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Wouldn't it mostly have to do with the discovery of other energy sources. Think like coal, dynamite. Wouldn't be suprised if mining would be one of the major limits. And not forgetting their knowledge of metallurgy.

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I wonder how much all of that is worth now

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Have you read The Perfectionist's? It's a great book and covers the early history of precision.

Fantastic read!

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Romans didn’t need smartphones, they had smart servants

I'm no historian and this is a very off the cuff answer with next to no sources. But according to my history teacher. When you have slaves you don't need an industrial revolution. There's no impetus to bother with all the work of setting up the complicated logistics it requires.

Fascinating.

My question: how does this affect Drake's equation?

https://en.wikipedia.org/wiki/Drake_equation?wprov=sfla1

One of Drake's factors is

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

The article doesn't explicitly state it, but it's imaginable (since I've just imagined it) that the set of circumstances described as necessary for the invention and perfection of the steam engine could be so unlikely as to make our own planet the only one in the galaxy to have developed such technology.

Or maybe something of the kind is inevitable after a few thousand years of agrarian civilisation.

Who knows?

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There's a thin line between happy and horror