I think if you measure productivity in terms of coconuts over man hours, productivity could rise indefinitely if it's at all possible to make robots that repair themselves and don't require any non-renewable resources.
Anyway, I think the first people to lose their jobs would be the ladder makers.
I think the best thing is to ask them to warm up with something basic like a scale, and let them work their way up as their comfort level increases. I knew some people who were particularly pleasant and easy going, so they were able to relax people suffering from performance anxiety.
There are interviewers who treat coding interviews as a high pressure, adversarial exercise, though. On the other hand, those sorts of people are rarely a joy to work with.
IIRC even the human brain has the 'adversarial' image flaw (these images will be unique to each person), but one simple workaround is to alter the input image via eye movement (which happens unconsciously).
Anyway, I think the first people to lose their jobs would be the ladder makers.