An example of deadly non-general AI

Thing is: a narrow AI that doesn't model human minds and attempts to disrupt it's strategies isn't going to hide how it plans to do it.

So you build your narrow super-medicine-bot and ask it to plan out how it will achieve the goal you've given it and to provide a full walkthrough and description.

it's not a general AI, it doesn't have any programming for understanding lying or misleading anyone so it lays out the plan in full for the human operator. (why would it not?)

who promptly changes the criteria for success and tries again.

Greg Egan's story The Moral Virologist is a bit similar :-)

In general, yeah, narrow AIs specializing in stuff like biotech, nanotech or weapons research can be really dangerous.

Narrow AI can be dangerous too is an interesting idea, but I don't think this is very convincing. I think you've accidentally snuck in some things not inside its narrow domain. In this scenario the AI has to model the actual population, including the quantity of the population, which doesn't seem too relevant. Also, it seems unlikely that people would use reducing absolute number of deaths as the goal function as opposed to chance of death for those already alive.

I think there can be a specialized AI that predicts human behaviour using just statistical methods, without modelling individual minds at all.

First of all, i admire narrow AI more than AGI. I can't prove that it won't affect us but your logic fails because of the phrase "then causes sterility or death." You just assumed that the AI will cause death or sterility out of the blue and that's totally false. The beauty of narrow AI is that there will be a human in the middle that can control what the AI outputs than an AGI which is totally uncontrollable.

Regarding the "reducing mortality" example, in biostats, mortality is "death due to X, divided by population". So "reducing cardiovascular mortality" would be dangerous, because it might kill its patients with a nerve poison. Reducing general mortality, though, shouldn't cause it to kill people, as long as it agrees with your definition of "death." (Presumably you would also have it list all side effects, which SHOULD catch the nerve-poison &etc.)

Doesn't a concept such as "mortality" require some general intelligence to understand in the first place?

There's no XML tag that comes with living beings that says whether they are "alive" or "dead" at one moment or another. We think this is a simple binary thing to see whether something is alive or dead, mainly because our brains have modules (modules whose functioning we don't understand and can't yet replicate in computer code) for distinguishing "animate" objects from "inaminate" objects. But doctors know that the dividing line between "alive" and "dead" is a much murkier one than deciding whether a beam of laser light is closer to 500 nm or 450 nm in wavelength (which would be a task that a narrow-intelligence AI could probably figure out). Already the concept of "mortality" is a bit too advanced for any "narrow AI."

It's a bit like, if you wanted to design a narrow intelligence to tackle the problem of mercury pollution in freshwater streams, and you came up with the most simple way of phrasing the command, like: "Computer: reduce the number of mercury atoms in the following 3-dimensional GPS domain (the state of Ohio, from 100 feet below ground to 100 feet up in the air, for example), while leaving all other factors untouched.

The computer might respond with something to the effect of, "I cannot accomplish that because any method of reducing the number of mercury atoms in that domain will require re-arranging some other atoms upstream (such as the atoms comprising the coal power plant that is belching out tons of mercury pollution)."

So then you tell the narrow AI, "Okay, try to figure out how to reduce the number of mercury atoms in the domain, and you can modify SOME other atoms upstream, but nothing IMPORTANT." Well, then we are back to the problem of needing a general intelligence to interpret things like the word "important."

This is why we can't just build an Oracle AI and command it to, "Tell us a cure for X disease, leaving all other things in the world unchanged." And the computer might say, "I can't keep everything else in the world the same and change just that one thing. To make the medical devices that you will need to cure this disease, you are going to have to build a factory to make the medical devices, and you are going to have to employ workers to work in that factory, and you are going to have to produce the food to feed those workers, and you are going to have to transport that food, and you are going to have to divert some gasoline supplies to the transportation of that food, and that is going to change the worldwide price of gasoline by an average of 0.005 cents, which will produce a 0.000006% chance of a revolution in France...." and so on.

So you tell the computer, "Okay, just come up with a plan for curing X disease, and change as little as possible, and if you do need to change other things, try not to change things that are IMPORTANT, that WE HUMANS CARE ABOUT."

And we are right back to the problem of having to be sure that we have successfully encoded all of human morality and values into this Oracle AI.

Imagine a medicine designing super-AI with the goal of reducing human mortality in 50 years

Do you mean increasing human mortality?