200 year is an entirely arbitrary period of time. The idea is that there's no way to predict when it will be possible to develop AGI but, if it happens at all, it will happen at some point in the future distant enough that nobody alive today will be around to say "I told you so".
You can ask how I know this. Obviously, I don't because I can't see into the future. But I can see the state of the art in the present and it's been baby steps for the last 70 years or so - and our capabilities have remained entirely primitive, industry hype nonwithstanding.
>> More importantly, people actually working on the problem of AI safety say they are doing things that appear, at least to them, to be useful. What makes you so sure they're wrong?
There's all sorts of opinions about how AI performance is accelerating ("exponentially"). In truth however, what has actually accelerated and in fact, plateaued in recent years is the performance in very specific tasks -object and speech recognition- and not in the general intelligence of AI systems. In fact, if you want to be more precise, we can only talk about advances in the context of very specific benchmarks, which is to say, specific datasets (like ImageNet) and according to specific metrics (say, F-score).
The problem is that all those benchmarks are arbitrarily chosen (iish; see below) and research teams spend a great deal of time tuning their systems to beat them. Which means, good performance in a benchmark tells us nothing about the extrinsic quality of a system: how it does in the real world, outside the lab and when the central assumption of PAC learning, that training and unseen data can be expected to have the same distribution (so that a system's training performance on the former predicts that on the latter) is not guaranteed. And then, performance in one type of task (e.g. classification) tells us nothing about the general capabilities of the system (i.e. general intelligence).
Singularitarians, like the people at MIRI (which your previous comment linked to) have focused on the performance of AI systems on modern benchmarks and the increase in compute, but modern benchmarks were essentially invented to allow some progress in machine learning, when mathematical results showed that progress was impossible. These previous results include Gold's famous result about learning in the limit (from the literature on Inductive Inference). The relaxation of assumptions was suggested in Leslie Valiant's paper "A theory of the learnable", which introduced PAC learning, the paradigm under which modern machine learning operates.
And to clarify my point above- modern machine learning benchmarks are not exactly chosen arbitrarily, rather they are justified by PAC learning assumptions about the learnability of propositional functions (and those, only; in fact, modern machine learning systems are propositional in nature, which severely restricts the expressive power of their models, making it much harder to realise the promise of Turing-complete learning of many of them).
... that probably got a bit too technical. My point is that just because we see imrpovement in performance today, in the field of research that we call machine learning, that doesn't mean that there is actual progress in the understanding of what intelligence is, or our ability to reproduce it. In a way, we might have changed our metrics, but we haven't necessarily improved our performance.
>> (...) try to spread to other planets.
So we have a science fiction problem and we're looking for science fiction solutions to it? :)
>> Last point - considering just how big a problem AGI could be if they're right, just how many resources would you want to devote to it? Literally zero?
Well, again that depends on what we can do about the problem, which in turn depends on what we know about it. I guess, like you say, if we know nothing about the problem, we can try random things like spreading to other planets or genetically enhancing the whole human race's intelligence until we ourselves are superintelligent and our risk to be taken over by an artificial superintelligence is 0.
But, having 0 certainty about the nature of AGI, we have exactly the same chances to avert the danger from it by sitting on our hands, as we have by migrating to other planets. I believe Bostrom's superintelligence scenario involves a machine that eventually colonises Mars with secret minining robots? If you're prepared to entertain the possibility of truly-Super intelligence, there's probably nothing you can do about it anyway.