The NYT has a strange piece which treats the idea of a four day work week as a sort of alien concept that perhaps we will see in the 22nd century. It is bizarre because there has been a consistent shortening of the length of work years for well over a century. In Germany, France, and other northern European countries the average work year is between 1400 and 1500 hours. This is due to the fact that workers are now guaranteed 5 to 6 weeks a year of vacation, in addition to paid sick days and paid family leave. The United States has been to a large extent an outlier in that it has seen relatively little reduction in work time over the last four decades.
Presumably, this long trend towards shorter work years will continue. While it may not take the form of a four day work week, workers in many countries have already seen an equivalent reduction in work hours. It is also worth noting that if it really turns out that robots will eliminate many of the jobs that now exist (the productivity data point in the opposite direction) then shorter work years is an obvious way to keep people employed.