In that case, the magic wand has a high degree of optimization power. It is extremely good at converting things it touches into gold, in all possible environments. But it is perfectly plain that the wand is not intelligent. So that definition of intelligence is mistaken.

The wand isn't generally intelligent. Maybe by some stretch of the definition we could sorta say it's "intelligent" at the task of turning things to gold. But it can't do any tasks other than turning things into gold. The whole point of AGI is general intelligence. That's what the G stands for.

Humans are generally intelligent. We can apply our brains to widely different tasks, including many that we weren't evolved to be good at at all. From playing Go to designing rockets. Evolution is generally intelligent. It can find remarkably good designs for totally arbitrary objective functions.

I think general optimization ability is a perfectly fine definition of intelligence. It includes things like humans and evolution, and some kinds of simple but general AI, but excludes things like animals and domain specific AI. It defines intelligence only by results. If you can optimize an arbitrary goal you are intelligent. It doesn't try to specify what the internal mechanisms should be, just whether or not they work. And it's continuous - you can have a degree of very stupid optimizer like evolution, all the way to very good/intelligent ones like humans.

Intelligence is the ability to engage in abstract thought. You could characterize that as pattern recognition, except that it is the ability to recognize patterns in patterns in patterns, recursively.

This definition is really vague. You are just shoving the hard problem of defining intelligence into the hard problem of defining "abstract thought". I guess the second sentence kind of clarifies that you mean. But it's not clear at all that humans even meet that definition. Do humans recognize patterns in patterns? I don't think so. I don't think we are consciously aware of the vast majority of our pattern recognition ability.

The most intelligent AI we have, is not remotely close to that. It can only recognize very particular patterns in very particular sorts of data.

Not really. Deep neural networks are extraordinary general. The same networks that win at Go could be applied to language translation, driving cars, playing pacman, or recognizing objects in an image.

One example of that was the case of AlphaGo, where Eliezer called it "superintelligent with bugs,"

The exact quote is "superhuman with bugs". In the context, he was describing the fact that the AI plays far above human level. But still makes some mistakes a human might not make. And it's not even clear when it makes mistakes, because it is so far above human players and may see things we don't see, that makes those moves not mistakes.

The orthogonality thesis is a similar mistake of that kind; something that is limited to seeking a limited goal like "maximize paperclips" cannot possibly be intelligent, because it cannot recognize the abstract concept of a goal.

A paperclip maximizer can recognize the concept of a goal. It's not stupid, it just only cares about paperclips. In the same way humans are programmed by evolution to maximize sex, social status, and similarly arbitrary goals, there is no reason an AI couldn't be programmed to maximize paperclips. Again, perhaps humans are not intelligent by your definition.

Unless you believe there is some magical point where there is a sudden change from stupid to intelligent, we are still extremely far off from intelligent machines.

Yeah that seems quite obviously true. Just look at the chimpanzees. By some accounts the main difference in human brains is they are just scaled up primate brains - 3 times as large, with a bit more sophisticated language ability. And suddenly you go from creatures that can barely master simple tools and can't communicate ideas, to creatures capable of technological civilization. 500 million years of evolution refined the mammal brain to get chimps, but only about a million was needed to go from stupid animals to generally intelligent humans.

I don't see any reason to believe AI progress should be linear. In practice it is clearly not. Areas of AI often has sudden discontinuities or increasing rates of progress. I don't see any reason why there can't be a single breakthrough that causes enormous progress, or why even incremental progress must be slow. If evolution can make brains by a bunch of stupid random mutations, surely thousands of intelligent engineers can do so much better on a much shorter time scale.

as is evident in the behavior of children, which passes imperceptibly from stupid to intelligent.

This isn't a valid analogy at all. Baby humans still have human brains running the same algorithms as adult humans. Their brains are just slightly smaller and have had less time to learn and train. Individual AIs may increase in ability linearly as they grow and learn. But the AI algorithms themselves have no such constraint, someone could theoretically figure out the perfect AI algorithm tomorrow and code it up. There is certainly no law of nature that says AI progress must be slow.