average one barrel of oil to find, extract, and process about 100 barrels of oil. The ratio, for discovery of fossil fuels in the United States, has declined steadily over the last century from about 1000:1 in 1919 to only 5:1 in the 2010s. Since the invention of agriculture, humans have increasingly used exogenous sources of energy to multiply human muscle-power. Some historians have attributed this largely to more easily exploited (i.e. higher EROI) energy sources, which is related to the concept of energy slaves. Thomas Homer-Dixon argues that a falling EROI in the Later Roman Empire was one of the reasons for the collapse of the Western Empire in the fifth century CE. In "The Upside of Down" he suggests that EROI analysis provides a basis for the analysis of the rise and fall of civilisations. Looking at the maximum extent of the Roman Empire, (60 million) and its technological base the agrarian base of Rome was about 1:12 per hectare for wheat and 1:27 for alfalfa (giving a 1:2.7 production for oxen). One can then use this to calculate the population of the Roman Empire required at its height, on the basis of about 2,500–3,000 calories per day per person. It comes out roughly equal to the area of food production at its height. But ecological damage (deforestation, soil fertility loss particularly in southern Spain, southern Italy, Sicily and especially north Africa) saw a collapse in the system beginning in the 2nd century, as EROI began to fall. It bottomed in 1084 when Rome's population, which had peaked under Trajan at 1.5 million, was only 15,000. Evidence also fits the cycle of Mayan and Cambodian collapse too. Joseph Tainter suggests that diminishing returns of the EROI is a chief cause of the collapse of complex societies, which has been suggested as caused by peak wood in early societies. Falling EROI due to depletion of high quality fossil fuel resources also poses a difficult challenge for industrial economies, and could potentially lead to declining economic output and challenge the concept (which is very recent when considered from a historical perspective) of perpetual economic growth. Criticism of EROI EROI is calculated by dividing the energy output by the energy input. Measuring total energy output is often easy, especially in the case for an electrical output where some appropriate electricity meter can be used. However, researchers disagree on how to determine