i am reasonably certain a smart person could explain to ben franklin (a smart person and something of a polymath) the fundamental principles behind the operation of a smartphone down to a pretty precise level of detail, without too much trouble, except stopping to walk him through mathematical formalism and defining terms. maybe the biggest problem you'd encounter is the notion of a band gap and how it makes a transistor work--that's where you really have to make a big leap into the conceptual world of quantum physics, and either you'd have to black-box it or spend a long time explaining no really this is our best model for very small scale physics and it has enormous predictive power. one area he might get sidetracked on is initially conceiving of a multipurpose device as, in principle, a sort of aggregate of many smaller miniaturized devices: a radio and a library and a music player and a calculator etc all separately packed into one small machine. and this isn't a stupid intuition--on some level this intuition for imagining future technology persists in science fiction at least as late as the original Star Trek!--but it's also one that's easy to correct. i feel like ben franklin could understand the concept of general-purpose computation and symbolic manipulation: the popularization of this framework as a general approach to mathematics postdates him, but not by a lot.
the biggest hurdle honestly is probably just that at a certain point the rate of a device results in qualitatively different capabilities as you ascend the power-law curve. babbage could envision a general purpose computation device in the early 19th century, and the biggest conceptual leap from that to a cell phone is orders-of-magnitude improvement, but this gets you from "a way to speed up tedious by-hand computations for mathematics" to "a complete modern information-technology ecology," which is qualitatively fundamentally different. there are people who do grasp the Implications of that sort of thing intuitively (ray kurzweil predicting AI in the 2020s just based on increasing computational power) but there are a lot of smart people who have trouble with that sort of thing. and then of course "at a certain point of computing sophistication you can use statistical methods to train a machine on the whole corpus of human language and get a computer program that has enormous general-purpose capacities starting from nothing but blobs of random numbers" is also deeply counterintuitive. i still have trouble with it!
but i wonder how far back you can go and still find somebody smart you could Explain The Smartphone To. you would have to explain a lot more about the basic operation of electricity and magnetism to newton, hooke, and huygens; but they seem like they'd get there pretty quick. certainly newton would. and you don't have to delve into relativity here or anything that's really going to cause a philosophical headache: newton might be quite relieved that you can point to specific physical waves as your medium for electromagnetism, especially if you mention as an aside that that model works for gravity, too. i guess if you go back too far and you lose symbolic algebra--and concepts like "the square of the distance" become principally about geometry, and not a free-moving mathematical abstraction, you lose a major conceptual tool for the formalisms. and once you hit the 15th century you might lose inertia, momentum, and the idea that terrestrial and celestial matter all obey the same rules.
but where do you lose the idea of an ordered, mathematical universe in general, the idea that abstraction and empiricism, and the formulation of quantifiable natural laws (and not of natures and ends) is how you understand physics? is that a 17th century/enlightenment thing? are there individuals before that transition who would still get it, or how complete and limiting was that sort of Artistotlean worldview? this i don't know enough about the history of science to say.
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