Social complexity does not derive directly from surplus energy. It would be more accurate to say that surplus energy allows increased specialization, which in turn allows more complex societies. Put another way: surplus energy increases the percentage of the population that can do something other than farming.
Take European society in the High Middle Ages. Before the Black Plague, the population in some areas of Europe was as large as it would be in the 1950’s. But the society was still very simple, because virtually everybody needed to be a farmer. Without oil, all of society’s energy came from the land. Furthermore, each farmer could produce just enough food to feed himself and his family, and to feed his farm animals. Almost all of the energy produced had to be re-invested into the process of farming, with very little surplus.
What surplus did exist, when pooled together, was barely enough to feed the king, his knights, the local lords, a few merchants and tradesmen, and a few other people. But 95% of the population had to be farmers. There was not enough spare food to support a “Food and Drug Administration,” or a “National Aeronautics and Space Administration,” or a “Microsoft Corporation.” The extra food simply didn’t exist.
Now we’ve discovered an enormous source of surplues energy: oil. This surplues energy allows us to work the land mechanically, allowing the population the freedom to occupy all of the different kinds of jobs that you see around you. If the oil running our machinery begins to run short, more and more of the population will have to go back to farming.
The snag, of course, is that human population has since exploded to numbers that are far, far beyond what can be fed without oil-driven agriculture. But that’s a problem for the next generation . . .