The question of the bounds of automation is a really good one. I think there are two kinds of things that make a job hard to automate: things involving the brain, and things involving the body.
For things involving the brain, there are three major categories of task: tasks with a clear goal and a predictable environment (e.g. factory work), tasks with a clear goal and an unpredictable environment (e.g. driving a car or having a semi-structured conversation), and tasks where the goal itself isn’t clear (e.g. psychotherapy).
The first category is the easiest to automate, and there are basically no technical obstacles from the brain side. The second one is the one that we’re just beginning to be able to approach; things like smart assistants and self-driving cars represent a first stage of it. (I suspect that we’ll find that this category breaks into substages; for example, speech recognition works quite well now when there’s enough scope limitation, e.g. it can bias the recognizer based on things it expects you might be talking about. Completely freeform speech recognition, like taking dictation, remains significantly harder — for humans as well as computers, as it turns out.)
The third category is one where it’s hard to automate the task, because it’s hard to specify exactly what it is you want to automate. In these cases, automation is really a problem of defining what you want. Sometimes this works; for example, “medical diagnosis” is a very open-ended problem, but “reading an X-ray” or “spotting anomalies in an EKG” is much more closed-ended, so computers can help with that a lot. In other cases, weird approximations may turn out to work; for psychotherapy, it’s hard to forget that ELIZA was unreasonably effective compared to her ludicrous simplicity.
Tasks which are hard because of the body tend to fall into two categories as well: things that are hard because they happen in varied and unpredictable environments, like search-and-rescue, or things that are hard because there’s a high requirement of a physical human to interact with other humans, like child care. For the former, there’s a lot of work going on in robotics right now, but it’s still going to be a substantial amount of time until this works properly. For the latter, it’s not clear if there will ever be a good solution.
I suspect that the hardest job to automate would be child care. Child care is, after all, a lot more than just the mechanics of changing diapers; it involves the nonstop interaction by which children acquire language, an ability to read faces, and all sorts of other things. I have no idea what automated child care would even look like, even granted an arbitrary amount of Sufficiently Advanced Technology.
Compared to location dependence and independence, LI jobs tend to have no physical aspects (by nature), so are limited by brain factors. LD/plant jobs tend to involve a lot of predictable-environment fixed-goal work, a certain amount of troubleshooting, which is unpredictable-environment fixed-goal, and a certain amount of supervision, which is variable-goal. These three categories require decreasing numbers of people, and are decreasingly automatable, which is why I concluded that the overall number of LD/plant jobs will decrease to a very small fraction of total jobs, with the remaining jobs being fairly highly specialized. (The example of the transition from large numbers of stevedores to small numbers of robotic crane operators at docks is illustrative)
LD/people jobs tend to be body-limited and so harder to automate. Because they almost entirely involve direct human interaction, none of them are predictable-environment jobs. Many of them require response to highly varied physical environments, and so have body constraints from that side; and the remainder require such personal interaction that it’s really a human requirement.
(LD/plant and LD/people may be the wrong terms, I’m realizing; it’s really “LD because you need equipment which has to be in a fixed place,” and “LD because you need to be physically adjacent to your customers” — sort of “LD/means of production” and “LD/point of consumption.” Search and rescue, for example, is LD/c0nsumption; the term “LD/people” seems a bit off for it. But anyway.)
Of course, for some jobs, it’s hard to tell where they fall. I would have guessed that psychotherapy was as LD/people as it gets, except that ELIZA proved that there wasn’t an intrinsic need for a person; and today I know a lot of therapists who work in a very LI fashion, seeing people over the phone or VC.
Interesting question: Where does clergy fall on the spectrum?