I agree with the premise that there will be fewer jobs but not that basic income is the solution. Not working can be very unhealthy for most people and I imagine people doing nothing instead of being "artists and scientists".
a) basic income, or
b) all the unemployed who can not get a job in the new economy are given a government job. The work in the job doesn't matter, as long as it provides a fig leaf to allow the government to give them the money they desperately need to live.
If its not entirely clear, I think that these non-jobs are are an unfair and incredibly expensive way of giving out benefits. The richer would be better off with a basic income (free money! smaller more efficient government meaning taxing the rich less!). The poor would be better off with a basic income (no social workers or benefit admins judging you! future is predictable so able to start investing for the future!). Its only annoying for those of us in the middle, those who will not benefit much from a basic income (because it won't be a huge amount of money, our taxes are unlikely to decrease) but will also not see much benefit from it (I probably already had a safety net in terms of friends and family, and the basic income will be too small to support the lifestyle I am used to anyway).
Basically, take all those cool programs that the left seems to like and make folks who claim to be unable to find a job be the ones to actually do the work.
Once robots take over, eliminating these basic jobs will be so cheap that no one will object. Until then, we shouldn't get ahead of ourselves.
And what if there simply isn't enough work, in the traditional sense, to go around? This is a very real issue as automation increases and this time around the newly jobless can't go work on Ford's assembly line or take stenography classes. The fact is there are going to be far more people without jobs than there are jobs available.
It's kind of ironic that in 2015 work is fetishized to a degree that would make Karl Marx blush. This is a worrying trend. As another contributor has already pointed out, if we don't update our, quite literally, outdated attitude towards work and employment we are potentially facing some very serious social unrest.
A basic income doesn't prevent you from working for a small amount of money. (And people might even elect to do that, if the job has other good sides.)