Mathematical Modelling

Exploring habit strength

Habit strength emerged as a central concept in early motivation psychology when Clark L. Hull (1943) proposed that behaviour could be mathematically modelled as a lawful function of learned habits and current drives, formalising human motivation through equations such as sEr = D × H, in which the excitatory potential of a response depended on both an organism’s internal need state and the strength of prior learning; this framework was refined by Kenneth W. Spence (1956), who extended Hull’s quantitative approach to include gradients of reinforcement and inhibition, helping to shape the broader drive theory tradition that influenced later cognitive-behavioural models, computational accounts of learning, and modern habit-formation science. By revealing that motivation is not mysterious but measurable, this work empowers individuals to build wellbeing through consistent, small behaviours that strengthen helpful habits over time, while offering society a blueprint for designing environments, including schools, workplaces, and public-health systems, that reliably support healthier, more equitable behavioural patterns. Mathematics provides us with a helpful analytical tool for modelling complex realities, but it can only ever map reality, and then only to a limited extent. The whole of existence represents an infinitely complex multi-factorial reality, fully known only by God. Although unable to fully comprehend that reality ourselves, through partnership with the Spirit of God we may work effectively with it and benefit from it.