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Why?
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I once went down the rabbit hole of thinking about how the targeting works on the TNG kind of transporter. Like they need to know to the molecule where your body ends and the rest of the universe begins. And you want it to identify clothing, because you don't want to end up nude on the other side. Plus it needs to identify what creepy crawlies are a part of you and which were just randomly wandering by. We don't want any of those pesky Fly problems now do we? This might sound easy, but is actually extremely hard. The human body is very complex and like a ship of Theseus what is part of the body is a bit nebulous and can change. All of the microbiome in our gut is essential for us to stay alive. And more importantly we don't want to leave behind a puddle of crap every time we transport. Plus what happens if we come out the other end, do our intestines just implode? Or does the transporter fill them with air, leaving you to fart uncontrollably until you die?
And how does it know what clothes are? If I'm wearing shoes, does it know where the shoes end and the floor starts? What if I'm wearing skies? What if I'm barefoot on a carpet? What if it's a leather carpet? What if I'm wearing shoes made by folding carpet around my feet?
The only thing that makes sense is a super powerful AI system that can real-time scan every molecule and figure out what's what. And it doesn't only need to be smart, it also needs a lot of real world knowledge. It needs to know what is "logical" to include in every situation. This means it has to be an AGI, has to be superintelligent (at a minimum speed wise) and would most likely be sentient. Them being used for this one and only purpose is really cruel.
This leads me to the conclusion TNG style transporters are basically slavery and put a whole different spin on the morality of the people in that universe. Thank you for coming to my TED talk.
It doesn't have to be AGI, though it'd certainly help. It could be a Machine Learning algorithm (the stuff we call AI in marketing today). It just needs a lot of data to train on to recognize what we want to bring and what we don't. It's actually a particularly good application for ML.
With that said, they do have the computer, which seems to be pretty complex and potentially an AGI. There's also Data in TNG that is certainly an AGI. I don't think it's an issue.
I mean that's a fun speech and all but they actually address it. Look into the Heisenberg uncertainty principle. Then do a quick search for the Heisenberg compensator.
A computer that can manage the TNG holodeck will have no problem handling all the complexities of a transporter.
It does do that. It's canon that transporters take care of removing any foreign organisms.
It understands all those scenarios and relays them to the operator, who decides what to lock on.
I don't think this impossible contraption sounds simple.
The AI part is a good answer. It used to take someone quite a long time to remove the background from a photograph pixel-by-pixel, but now it takes an AI a few seconds. Give it 400 years and AI will be mind-blowing.