Hossein Jorjani
First publication: 2026 – 07 – 18
Since the Scientific Revolution, observation and experiment have traditionally been regarded as the two principal sources of scientific knowledge. Observation acquires data from naturally occurring phenomena without deliberate intervention, whereas experiment generates data by systematically manipulating conditions to test specific hypotheses. These two modes formed the methodological foundation of modern empirical science and remain indispensable today.
During the twentieth century, however, two additional epistemic modes assumed increasing importance. The first is mathematical modelling, in which the consequences of theoretical assumptions are derived through formal mathematical analysis. Such models permit quantitative predictions even when direct observation or experimentation is impractical, impossible, or ethically impermissible. Astronomy, climate science, epidemiology, evolutionary biology, and theoretical physics all depend extensively upon this mode of inquiry.
The second is computational simulation (in silico experimentation), in which mathematical models are implemented computationally to explore their behaviour under a wide range of conditions. Simulations frequently generate synthetic datasets that can be compared with empirical observations or experimental results. They are particularly valuable for studying systems too complex for analytical solution or inaccessible to direct experimentation, such as galaxy formation, ecosystem dynamics, protein folding, or evolutionary processes.
These four epistemic modes should not be regarded as competing alternatives but as complementary components of scientific inquiry. Observation and experiment provide empirical constraints upon theory, while mathematical modelling and computational simulation extend the capacity of scientific reasoning beyond the limits of direct observation and laboratory experimentation. Modern science increasingly advances through the systematic integration of all four modes rather than through reliance upon any one of them alone.
Hossein Jorjani 