There are a huge number of people doing energy modeling. In my opinion, nearly all of them are going astray in their modeling because they don’t understand how the economy really operates.
The modeling that comes closest to being correct is that which underlies the 1972 book, The Limits to Growth by Donella Meadows and others. This modeling was based on physical quantities of resources, with no financial system whatsoever. The base model, shown here, indicates that limits would be reached a few years later than we actually seem to be reaching them. The dotted black line in Figure 1 indicates where I saw the world economy to be in January 2019, based on the limits we already seemed to be reaching at that time.
The authors of The Limits to Growth have said that their model cannot be expected to be correct after limits hit (which is about now), so even this model is less than perfect. Thus, this model cannot be relied upon to show that population will continue to rise until after 2050.
Many readers are familiar with Energy Return on Energy Invested (EROEI) calculations. These are favorites of many people following the Peak Oil problem. A high ratio of Energy Returned to Energy Invested is considered favorable, while a low ratio is considered unfavorable. Energy sources with similar EROEIs are supposedly equivalent. Even these similarities can be misleading. They make intermittent wind and solar appear far more helpful than they really are.
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