| | As you say, science and technology are inseparable. "Science deals with the principles that describe how an aspect of the world works, and technology is an application of some of those laws." And I agree that once a valid theory is available it suggests experiments (inventions) to be performed. The problem you and I (and our contemporaries broadly) face now is remaining clear on the actual details of the process.
The IEEE Global History Network has an article on the Early Applications of Electricity (here). Coulomb's Law (1785), Ohm's Law (1827), and Faraday's Law of Induction (c. 1831), did not follow in conceptual sequence. Ohm's Law was denied at first and not accepted for 20 or 30 years. Similarly, Faraday's research was rejected for not being mathematically stated; and scientists denied the reality of "lines of force."
Also, while we nicely say I = V/R (V = IR, etc.), in fact, Ohm originally included a thermocouple, explaining the changes in current according to the length of a resistive wire and along with changes in temperature. Today, we separate those. Also, by the same token, Faraday's Law is now recognized as two distinct phenomena.
Most clearly, however, I point out that these "early" electrical experimenters were the second generation following the electricians of Benjamin Franklin's time for whom electricity was a "fluid." That was the paradigm which Coulomb, Faraday, and Ohm inherited. Their work led to a new understanding, a better theory. As the "Early Applications" article shows, inventors built useful new machines without a clear theoretical understanding of what electricity "is." (We still may not know...)
In electricity, we have a mnemonic: ELI THE ICE MAN. E leads I in inductive circuits (L for induction) and I leads E in capacitive circuits. In the 21st century we still build things that work using 19th century paradigms. In any non-trivial circuit, both induction and capacitance are present. Like science and technology, they are inseparable, perhaps. But, for the purpose of analyzing a circuit, to build one or fix one, it makes a difference which leads in what wires. So, too, as you note, did some inventions come after a theory was accepted.
The rocket to the moon was not so much a matter of Newton's Law of Universal Gravitation as it was the Sadi Carnot's work in thermodynamics which made the fine design of powerful engines possible. As you note, theory allowed technology. However, I point out that James Watt built working steam engines to pump water from mines and then to strike beautiful merchant tokens before Carnot was born. Carnot had the Watt engines as the empirical evidence which his theory attempted to explain.
The local Objectivist group here is reading Leonard Peikoff's Understanding Objectivism. My copy arrives later this week, so this is not a good quotable citation, but early on, Peikoff says that to express knowledge, you must put it in some context, even if your understanding is incomplete and later amended. So, as you say, I agree, any inventor does not work purely empirically with no theory, by blind trial and error (despite Edison to the contrary), but has some theory, however wrong, to guide the work and its expected outcome.
But, pushed to its limits, that means that the work of Galileo came not from his own theory of motion, but as a result of the medieval idea of "impetus" upon which those seige engines and tower clocks were constructed. His familiarity with the wonderful new machines of the Middle Ages gave him the body of knowledge about which to contruct a broad theory.
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