I think you may be placing too much emphasis on curiosity as a terminal value here rather than a means of acquiring other terminal values--not that I think it has no value in and of itself, but that's not its only use and not its biggest in most respects.
If I know that a light switch/bulb's properties are fully explained by science and nothing else about it, that DOES tell me things I didn't know beforehand. It tells me that it is much less of a priority to figure out how the light bulb works than it would have been if nobody had a clue. If there is any situation in which knowledge of how it works is necessary there's already someone who knows, and if there is a situation in the future in which I decide it would be to my benefit to learn how it works I will have little trouble learning it at that time, rather than needing to arm myself with that knowledge well in advance because I can't predict how long it will take to acquire (this ignoring the issue of how long it would take for me to wrap my head around the concepts if I tried; it's easier to learn if it's already known, no matter where the baseline difficulty is set). And if there is some incredibly useful piece of low hanging fruit which could be derived from just knowledge about the light bulb, I could be confident that somebody else had found it (and if it's not low hanging fruit, well, others have at least had as much of a shot at it as I would; unless I have reason to believe that there is something I could learn from the knowledge that others would have missed so far, in which case skip to the next paragraph). Even knowing that the keyword involved is "electricity", which does not even begin to count as understanding, tells me SOMETHING (though not enough that a science teacher should feel justified stopping there)--it tells me which section in the phone book to look at if I need someone to fix my lightswitch, or which section of the library to look in to learn about it myself. The former is all some people will need to know about lightswitches for their entire lives.
Of course I know a good deal more about it than that, and in fact some of my knowledge will be useful to me in a real way in my real life. But the knowledge about what organ X does and where it is, is not directly useful to me in the same way--for all practical purposes it's good enough that I can ask a doctor or search certain trustworthy portions of the internet for the answer to any question about what I should do from a medical perspective in most situations. Yes, knowledge of medicine being more immediately on hand might help me react faster to a problem and a situation may come up where I personally ought to know CPR and don't, but my situation isn't as bad as if nobody knew this information. And I can teach myself most of the useful things that you can/must do immediately and with no equipment or pills, without ever needing to know how the inside of my body really looks.
This only applies to things unrelated to the fields you do care about. If you care about or expect to be involved in making AI, knowledge of all things computer and how electricity works and how modern computer chips are built and anything you can learn about existing intelligences is valuable. Knowledge of what your liver does, however, isn't just somebody else's problem; it's not a problem. If you feel curious about the liver that's great, but if not you don't really have to.
The example with the elephant isn't great, because that is a situation in which I would care about the knowledge, and would seek to either ask the person who knows about it to explain to me or, if the explanation turns out to be far more difficult and/or long than I am willing to accept, will ask him all the predictive questions I would've been able to answer if I knew about it, such as "Is this going to get worse if I ignore it until a more convenient time", "How do I make it leave", "Is my house in danger" or even the almighty "Is there anything else important I should know about this" (because it is a human being who knows about it, not a genie, and he can predict what facts I'd consider important even if I don't know what to ask for). Or if even that was too hard (or he was unwilling to tell me), at least to remove it from the room for me.
The example of you waving your hands to create light and calling it science would also not stop me until I became convinced that significantly more people than just you knew it and that some of these people would be willing to tell me if I asked. But that's because my curiosity about the light as a whole would stem as much from mistrust of another person to apply that knowledge to humanity's general benefit as from real curiosity. You can't hold out on me with the knowledge that that light can also cure cancer if I also understand what you do about the light, or if I know that a number of other people unlikely to share a stake with you in any enterprise know it.
The real danger would be if that elephant had been in my room since the day I was born and I didn't know enough to be curious about it.
Imagine that I, in full view of live television cameras, raised my hands and chanted abracadabra and caused a brilliant light to be born, flaring in empty space beyond my outstretched hands. Imagine that I committed this act of blatant, unmistakeable sorcery under the full supervision of James Randi and all skeptical armies. Most people, I think, would be fairly curious as to what was going on.
But now suppose instead that I don’t go on television. I do not wish to share the power, nor the truth behind it. I want to keep my sorcery secret. And yet I also want to cast my spells whenever and wherever I please. I want to cast my brilliant flare of light so that I can read a book on the train—without anyone becoming curious. Is there a spell that stops curiosity?
Yes indeed! Whenever anyone asks “How did you do that?” I just say “Science!”
It’s not a real explanation, so much as a curiosity-stopper. It doesn’t tell you whether the light will brighten or fade, change color in hue or saturation, and it certainly doesn’t tell you how to make a similar light yourself. You don’t actually know anything more than you knew before I said the magic word. But you turn away, satisfied that nothing unusual is going on.
Better yet, the same trick works with a standard light switch.
Flip a switch and a light bulb turns on. Why?
In school, one is taught that the password to the light bulb is “Electricity!” By now, I hope, you’re wary of marking the light bulb “understood” on such a basis. Does saying “Electricity!” let you do calculations that will control your anticipation of experience? There is, at the least, a great deal more to learn.1
If you thought the light bulb was scientifically inexplicable, it would seize the entirety of your attention. You would drop whatever else you were doing, and focus on that light bulb.
But what does the phrase “scientifically explicable” mean? It means that someone else knows how the light bulb works. When you are told the light bulb is “scientifically explicable,” you don’t know more than you knew earlier; you don’t know whether the light bulb will brighten or fade. But because someone else knows, it devalues the knowledge in your eyes. You become less curious.
Someone is bound to say, “If the light bulb were unknown to science, you could gain fame and fortune by investigating it.” But I’m not talking about greed. I’m not talking about career ambition. I’m talking about the raw emotion of curiosity—the feeling of being intrigued. Why should your curiosity be diminished because someone else, not you, knows how the light bulb works? Is this not spite? It’s not enough for you to know; other people must also be ignorant, or you won’t be happy?
There are goods that knowledge may serve besides curiosity, such as the social utility of technology. For these instrumental goods, it matters whether some other entity in local space already knows. But for my own curiosity, why should it matter?
Besides, consider the consequences if you permit “Someone else knows the answer” to function as a curiosity-stopper. One day you walk into your living room and see a giant green elephant, seemingly hovering in midair, surrounded by an aura of silver light.
“What the heck?” you say.
And a voice comes from above the elephant, saying,
“Oh,” you say, “in that case, never mind,” and walk on to the kitchen.
I don’t know the grand unified theory for this universe’s laws of physics. I also don’t know much about human anatomy with the exception of the brain. I couldn’t point out on my body where my kidneys are, and I can’t recall offhand what my liver does.2
Should I, so far as curiosity is concerned, be more intrigued by my ignorance of the ultimate laws of physics, than the fact that I don’t know much about what goes on inside my own body?
If I raised my hands and cast a light spell, you would be intrigued. Should you be any less intrigued by the very fact that I raised my hands? When you raise your arm and wave a hand around, this act of will is coordinated by (among other brain areas) your cerebellum. I bet you don’t know how the cerebellum works. I know a little—though only the gross details, not enough to perform calculations . . . but so what? What does that matter, if you don’t know? Why should there be a double standard of curiosity for sorcery and hand motions?
Look at yourself in the mirror. Do you know what you’re looking at? Do you know what looks out from behind your eyes? Do you know what you are? Some of that answer Science knows, and some of it Science does not. But why should that distinction matter to your curiosity, if you don’t know?
Do you know how your knees work? Do you know how your shoes were made? Do you know why your computer monitor glows? Do you know why water is wet?
The world around you is full of puzzles. Prioritize, if you must. But do not complain that cruel Science has emptied the world of mystery. With reasoning such as that, I could get you to overlook an elephant in your living room.
1 Physicists should ignore this paragraph and substitute a problem in evolutionary theory, where the substance of the theory is again in calculations that few people know how to perform.
2 I am not proud of this. Alas, with all the math I need to study, I’m not likely to learn anatomy anytime soon.