Breaking down the question
The operative phrase is changing equations. The examiner is not asking for a static comparison of sociology with economics, political science, history, psychology and anthropology — the familiar textbook drill of similarities and differences. The word changing demands a narrative of movement: how the relationship has evolved from the nineteenth century to the present.
Equations is the second cue. It implies a balance of give and take — borrowing, overlap, rivalry, division of labour — rather than a one-way influence. A strong answer therefore tracks the relationship across at least three phases: the early struggle of sociology to establish itself as a distinct discipline, the mid-twentieth-century settlement of jurisdictional boundaries, and the contemporary drift towards interdisciplinarity where the boundaries have grown porous.
The scope of the topic — Sociology — The Discipline — means the answer should ultimately illuminate what is distinctive about sociology itself. The changing equations are worth discussing precisely because they show sociology defining, defending and then relaxing its identity.
How to approach it
Open by locating sociology's birth in the same nineteenth-century ferment that produced the other social sciences, drawing on the account of modernity and the emergence of sociology. This establishes that the disciplines share a common parentage in the attempt to make sense of the modern industrial order.
Then structure the body around the three phases of the relationship rather than discipline by discipline. Within each phase, illustrate with concrete pairings: sociology and economics, sociology and political science, sociology and history, sociology and anthropology, sociology and psychology. Show borrowing running in both directions.
Close with a measured judgement: the boundaries have not dissolved but softened, and interdisciplinarity is now the dominant mode. Avoid a mere list of definitions; the examiner wants the dynamic.
Model answer
Sociology and its sister social sciences are children of the same intellectual revolution. The collapse of the old order under the twin pressures of the French and Industrial Revolutions created an urgent need to understand a society in transformation, and out of that need economics, political science, history, anthropology, psychology and sociology all took recognisable modern shape. Their subsequent relationship has passed through distinct phases, and it is this movement — not a fixed table of contrasts — that the question invites us to trace.
Phase one: differentiation and the staking of claims. The founders of sociology had first to justify a new discipline where established ones already existed. Comte placed sociology at the apex of the sciences as the study of society as a whole, integrating what the others treated in parts. Durkheim fought hardest for autonomy, insisting in The Rules of Sociological Method that social facts form a reality sui generis, irreducible to individual psychology or economic calculation. His demonstration in Suicide that even so private an act had social causes was a deliberate raid on the territory of psychology, asserting sociology's distinctive explanatory power. In this founding phase the equation was competitive: sociology defined itself by marking out what the others left unexplained — the social bond itself.
Phase two: consolidation and division of labour. By the mid-twentieth century a rough jurisdictional settlement had emerged. Economics took the production and exchange of wealth, assuming the rational self-interested actor; political science took power, the state and government; history took the past and the particular event; psychology took the individual mind; anthropology took small-scale, non-literate societies. Sociology claimed the study of social relationships, institutions and structures in modern society. The equation here was one of specialisation, each discipline cultivating its own garden. Yet even at its height the settlement leaked. Weber's work straddled every boundary — his Protestant Ethic fused economic, religious and historical analysis, and his account of authority is as much political science as sociology. Sociology, being the most general of the social sciences, could never fully seal itself off.
Phase three: convergence and interdisciplinarity. The late twentieth century saw the walls come down. The realisation that real social problems — poverty, development, gender, the environment, crime, health — respect no disciplinary boundary drove scholars to collaborate and to borrow freely. Fresh hybrid fields testify to this: economic sociology and behavioural economics blur the line with economics; political sociology sits between sociology and political science; social history and the Annales school brought sociological questions into history; social psychology bridges the individual and the collective; and sociology and anthropology have converged so far that their methods and theories are now largely shared, the anthropologist studying the modern city and the sociologist attentive to culture and meaning.
The traffic runs both ways. Sociology has taken statistical and modelling techniques from economics, network and systems ideas from elsewhere, and the concept of culture from anthropology. In return it has given the other sciences the indispensable insight that no human activity — economic, political or psychological — takes place in a social vacuum. Rational-choice economics has had to absorb the sociology of trust and institutions; political science leans on sociological accounts of class, community and social movements to explain voting and revolution.
Assessment. The changing equation, then, is a movement from rivalry through demarcation to partnership. Sociology's early insistence on autonomy was a necessary act of institutional self-assertion; its present openness reflects both intellectual maturity and the intractable, boundary-crossing nature of contemporary problems. The distinctiveness of sociology has not been lost in this convergence but relocated. It survives in what C. Wright Mills called the sociological imagination — the capacity to connect private troubles to public issues, individual biography to social structure and history. That synthesising vision, the grasp of society as an interconnected whole, remains sociology's particular gift to the family of social sciences even as the fences between them grow low.
Examiner's perspective
The commonest weakness on this question is to ignore the word changing and instead reproduce a memorised chart of how sociology differs from economics, history and the rest. Such an answer describes the equation but never shows it moving, and cannot reach the upper band.
Examiners reward a genuinely developmental account — differentiation, consolidation, convergence — supported by concrete examples of borrowing in both directions and by the hybrid sub-disciplines that prove the boundaries have softened. Naming founders precisely (Durkheim's raid on psychology in Suicide, Weber's boundary-crossing) lends authority.
The strongest scripts close by turning the discussion back on sociology itself, arguing that interdisciplinarity has relocated rather than erased its distinctiveness — its holistic, structure-and-meaning vision captured in the sociological imagination. A precise verdict of this kind lifts the answer above the generic comparison.