Excluding for the moment cornucopians & extreme optimist, most informed souls on the planet are of the opinion that humanities current level of impacts on our common finite world can not be indefinitely maintained into the future. Any hope of achieving a sustainable future, first requires us to honestly access our demands & impacts. For without a good knowledge of the size and scope of the impacts, one can not seriously attempt to bring humanities demands into balance with what the environment can comfortably provide over the long term.   I = PAT in the original version of this equation (Ehrlich and Holdren 1971; Ehrlich and Ehrlich 1991, 1992). "The impact (I) of any group or nation on the  environment can be viewed as the product of its population size (P) multiplied by per-capita affluence (A) as measured by consumption, in turn multiplied by a measure of the damage done by technologies (T) employed in  supplying each unit of that consumption" (Ehrlich and Ehrlich 1991~7). Without a single set of tightly codified units typical of equations in physics; mass in Kg, speed in metres per second, et cetera,   I=PAT (and for that matter all the other variation discussed on this page)  formulation  lacks the universality that users often would impose upon it.  Be that as it may the  I=PAT formulation is successfully utilized to make comparisons between various cases where common denominated variables can be isolated. Useful units to base comparisons on are  Tons of Greenhouse Gases for each variable, or alternatively Energy consumption encapsulated in each variable. But beware of an all too common temptation to express Affluence (A) as a countries GDP (Gross Domestic Product) thus distorting any results with all the vagaries of inflation rates & foreign exchange fluctuation between the countries being evaluated.  Unfortunately over the years the I=PAT formulation has been often re-defined, then used with subtly different meanings for the variables;- I=P*A*T where I is environmental impact, P is population, A is, per capita economic activity (referred to as affluence) and T is the impact per unit economic activity (referred to as technology). In typical applications, data are obtained on impact, population and affluence and the equation is solved for T T=I/(P*A). Noted in the 1994 paper "Rethinking the Environmental Impacts of Population, Affluence and Technology" by Thomas Dietz & Eugene A. Rosa. Fortunately the same paper does provide a   A Stochastic Reformulation;- The IPAT model can easily be reformulated in stochastic form: I=aPbAcTde where I, P, A and T remain environmental impact, population size per capita economic activity and impact per unit economic activity. Now a, b, c, and d are parameters and e a residual term. Data on I, P, A and T can be wed to estimate a, b, c, d and e using standard statistical methods such as regression analysis and its kin. This reformulation of the model requires multiple observations (over units, over time or both) on I, P, A and T. This is an important distinction from the accounting model where one term is derived from the values of the other three. The accounting model only requires data on any three of the four variables for one or a few observational units. But the advantage of this stochastic reformulation is that it converts the IPAT accounting model into what is certainly the most standard formulation for quantitative social research   In the mid-1990s it was realized that  I=PAT  formulations' simplicity tend to exaggerate or distort the importance of T (technology) in isolation.  Technology being commonly miss-construed as some-sort of self-perpetuating evil demon in the ecological drama.   This false view popularized the myth that all humanities problems could be solved by returning to a  more natural  low-tech lifestyle. Superficially the formula does  imply that a reduction in T (technology) will equate to a reduced Impact, but this not how life actually is. Take a sewage-treatment works as an example of technology, removing this piece of beneficial technology from a social situation will dramatically heighten the impact of that given society on there immediate environment. So the I=PAT expression (as is) can only function as an explanation of particular Impacts, rather than as an generalized formulation for use in the modelling and study of various impact scenarios.  In an attempt by various academics at the time to rectify these shortcomings of the original formulation,  T was replaced by X so as to allow explicit identification thence consideration for the main things that drive a societies impact on the environments, and should thus be considered in any rigorous assessing of impacts.  I = PAX  where X= [C,I,T,E] By replacing Technology by X  this equation was more flexible in dealing with the complex of  driving factors, beyond Population and Affluence. Unfortunately as X was segmented as  CITE = Culture, Institutions, Technology &  Effects.  While this is not a problem when the formulas are considered independently of each other, having two different meanings for I prohibits them being sensibly merged.  Another difficulty is that while I=PAT or I=PAX could be tenteratively treated as mathematical equations substituting hard numbers like census data for say the Population,  X=[C,I,T,E] is not a mathematical equation but rather a knowledge rule (or business rule). So in the interest of flexibility and clarity we suggest changing the term 'Institutions' to 'Structures' in all their forms;- Social Structures, Political Structures, Commercial Structures.  infraStructures.  This then gives us ;-.  I = PAX  where X= [C,S,T,E]   In this formualtion Technology is better contextualized as a attribute of the interplay between a region's broader social dynamics.  Recognizing that a given technology may prove benificial in one social context, while at the same time the same technology could be very destructive in another context.  Irrigation is a good example of a techology  that can be a blessing or curse dependant on where and how it is implemented. So in this formulation the varibales are understood as;- I = Impact of any country or region on the environment, P = country or region's Population size, A = per capita Affluence as measured by consumption of material &/or energy, or production of waste, X = C,S,T,E, the Culture affecting the Structures [Social, Political, Commercial etc.] affecting the usage of T echnology with associated  Effects [Efficiencies / inefficiencies] C the way Culture can act as a multiplier or inhibitor of Population typical numerical effect. S = Social, Political, Commercial Structures as an indicator of the interface between the Population and the geography, topography & climate. where it exist. Possible best measured by the requirement and consumption of energy & materials in the movements required of same.  Put simply the further and faster a population must travel. the larger the impact must be. T =material & energy required for the Technology. E =E ffectiness or benefit of the energy expended [Efficiencies / inefficiencies].   Taking care to remember that X=C&S&T&E {where "&" (or the comma "," shorthand) is a logical AND set-operator} expressed in this shorthand, can never be incorperated as-is into a mathematical equation. X=[C,I,T,E] formulation being a knowledge rule, likewise where-ever it maybe used will also be restricted to functioning as a knowledge statement not a mathematical equation. So by substitution of the Xs one can now express the whole Impacts question as a single expression of the knowledge content, thus....  I = PA[ C,S,T,E] As purpose of the knowledge expression is to encompass all of the factors impinging on a subject, thus the inherent style of knowledge rules often appear to be overly redundant, when considered from a mathematical tradition.  It is quite true that in different situation given some of the variables identified,  other unknown values would be readily calculable from those already ascertained. As an example in some cases knowing the Population,  Technology and Efficiency, then the Affluence of the society would be readily predicable. Sometimes once the Population & Affluence values are known  all the other variables summarised as X are effectively irrelevant. In many cases the Culture and socio-political Structure could be safely ignored as they entail no appreciable magnification of the consequence attributable to the raw Population numbers.  However while redundancy of values in specific cases may enable tailored mathematical formulation for calculation of verified cases,  that is not a sound argument for an awareness  ( which after all is what a knowledge rule codifies ) being restricted to a subset of all the factors impinging on the subject of determining humanities Impacts.      Comments to webmaster Copyright © Rupert Edwards 1998-2005 Last update: December 2005 Southern Summer This page is located at http://www.geocities.com/RainForest/Canopy/2265/