This question is worth revisiting because it hasn't been answered definitively. It's indeed one of those things over which we will continue to argue.
Peter Thiel is fond of noting the incredible technological progress the modern world experienced starting around 1800 and ending, in his opinion, 1969 (with the moon landing, and the field of information technology excepted). Niall Ferguson recently gave a Ted Talk on what he views as "6 Apps" that caused modernity's material progress. And most recently Deirdre McCloskey has written about this "great enrichment" that didn't start to take off until around 1800 and arguably continues to this day (even if Thiel and others argue we stopped progressing as we should in 1969).
The possibilities as to what caused such to happen when and where it did are endless. For instance, it could be that Providence simply willed it to start taking off around 1800. Or, that advanced aliens who seeded life on Earth decided that was the time to start filtering down to humanity more knowledge that would lead to such dramatic advances. The evidence for both of such cannot, alas, be falsified. So we need to look somewhere else.
My explanation is that it was the Enlightenment zeitgeist perfectly captured in the quotation below by Ben Franklin in a letter written to John Lathrop, May 31, 1788:
I have been long impress’d with the same Sentiments you so well express, of the growing Felicity of Mankind from the Improvements in Philosophy, Morals, Politicks, and even the Conveniencies of common Living by the Invention and Acquisition of new and useful Utensils and Instruments, that I have sometimes almost wish’d it had been my Destiny to be born two or three Centuries hence. For Inventions of Improvement are prolific, and beget more of their Kind. The present Progress is rapid. Many of great Importance, now unthought of, will before that Period be procur’d; and then I might not only enjoy their Advantages, but have my Curiosity satisfy’d in knowing what they are to be. I see a little Absurdity in what I have just written, but it is to a Friend who will wink and let it pass, while I mention one Reason more for such a Wish, which is that if the Art of Physic shall be improv’d in proportion with other Arts, we may then be able to avoid Diseases, and live as long as the Patriarchs in Genesis, to which I suppose we should make little Objection.This is for lack of a better term -- and I'm sure we can come up with better than this -- classically liberal, Enlightenment progressivism.
Yes, it's something scientifically based. But there's more to the story. These thinkers like Ben Franklin had a holistic view that every field of knowledge including politics and theology were sciences.
The problem I have with Jack Goldstone's essay, as it were, is that he's too particular in specifying and crediting engineering. Yes, of course engineering is important. But so too are the insights of economist Adam Smith and those who followed him. Economics is not engineering. As Niall Ferguson notes, it's not just one thing; it's a number of things. Thus, it's something more holistic than specific.
Look at how such thinkers as Franklin viewed the "science" of political theology. It's not necessarily traditional orthodox Christianity which had been established since 325 AD. But it's also not necessarily the strictly deist God of Spinoza. (One could argue, as Jason Kuznicki did in the original Cato series that the modern Enlightenment view would eventually grow into such, and perhaps then further towards agnosticism and atheism.)
And much of what they wrote was consistent with what's written in the Bible. Indeed, we see Franklin using biblical examples as inspiration for scientific advancements. But this approach is more free and forward thinking.
Many of these "scientists of everything" were like Franklin (electricity), Joseph Priestley (chemistry), Richard Price (finance), members of The Club of Honest Whigs. That's to whom I give chief credit for modernity's advances.
The period in which they operated was "the Enlightenment" of the late 18th Century. Ironically, the advances of modernity didn't start to take off until 1800, which marks the end of that period. So we can say that the late 18th Century Enlightenment is when the seeds were planted. To the extent that pre-Enlightenment periods caused the Great Enrichment, we would have to argue that they created the fertile soil for the fruits of which the seeds of the Enlightenment rightly take credit.