I think industrious culture became industrial culture when a couple of things happened:

1. Fewer and fewer of the workforce was engaged in agriculture, thanks to mechanization and industrial methods being applied on the farm;

2.  We (humans) learned how to systematically use past solar income--fossil fuels--to accomplish present work.

Industrial culture could be sustainable, if we can find a way to run it on current solar income.  Current solar income will probably support way fewer humans than we have now, if we want anything like our current (even our current world-average) standard of material well being.  

Industrial society is not sustainable. Unsustainable systems change--or disappear.