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The reason fiberoptic is better than a mirrored duct for data transfer is because you can pack say 32 or 64 fibers into a cable, that means 32 or 64 points of light that are either "on" or "off", creating a 32-bit or 64-bit word size and enabling data transfer. You can't do that with ducts.
There is an on and an off state. Either the light is on or the light is off. That's how it translates into binary. Literally that's what binary data is: a single data-point is either on or off. Put a bunch of them together to create words with 2^n^ possible combinations per word where n is the number of datapoints. For electrical data, that's the voltage level of one wire or bus lead. For fiberoptics, it's each individual fiber. It's either on or off, that's the whole point.
The mirrors don't have to be angled precisely. If you take a cylindrical tube, and make the inside a mirrored surface, then all light traveling down it will continue traveling downward as it bounces. The only time the angle matters is around turns, but that's easy enough to angle correctly.
It also doesn't need to be columnated, but the thing about the fish-eye dome is that with a flat lense on bottom, it does output columnated light from the wide-angled light it receives. That's how convex defraction works.
And dust wouldn't be an issue if your tubes are sealed.
Fiberoptics would technically work, but it's more material than you need because it would require running fiberoptic cables everywhere instead of just using hollow chromed tubes. Also, the quantity of light it can receive and transmit is limited to the thickness of the cable.
Fiberoptics are great for high-speed data transfer because of data-integrity and the fine-pointed nature of the fibers. But they aren't ideal for moving large amounts of light where precision isn't needed, e.g. enough natural daylight to brighten several rooms.
Not really. Yes, binary is on or off, but how the signal is read is it has a threshold for on/off. This is true for light, with fiber optics, and also electricity. The universe doesn't work on binary. We say "if the signal value is > X, do Y". Electrical engineering actually has to handle variability in the signal, while computer science just pretends it's actually binary.
I'm not just making up hypotheticals. If your idea were better it would be used. Fiber optics to transfer light is actually a thing that's done. Here is a company selling that product, and there are many others, but I've also seen things about large structures using a custom solution too. It literally does work and is actually done in reality.
I see your dornob and raise you one solatube
And yes, I know digital "on"/"off" isn't literally either 5V or 0V, it's really "high"/"low", but practically speaking that doesn't change anything about what I said and it's more cumbersome to use those terms in casual conversation because it assumes a knowledgeable audience. Either way, when the memory latches in the register, each bit is either on or it's off, and fiberoptics work the same as electrical in that sense. That level of complexity and precision is not needed for distributing daylight.
But that's my point. The data thing isn't relevant. It's just transmitting light. The fact it can transmit data doesn't means that's what it's for. It just transmits light of any intensity.
It's a lot easier to just run some cables than install specialty ducts though. It doesn't need as much space and you also don't need to worry about being in straight lines. You just run the cable wherever you want and the light ends up there. Fiber optic cables effectively are just tubes with mirrors, except they dynamically adjust to whatever shape they're in. If you've got a short path to the outside, sure, do the duct, although you might as well just do a window. If it's to the interior of a building, especially if it's already constructed, fiber optic cables are the only reasonable option.