Part 13/16:
While Markov chains are remarkably versatile, they have limitations. Complex systems like climate change involve positive feedback loops—where effects reinforce each other—making future states hard to predict with simple models. Similarly, certain interconnected systems involve memory effects beyond the current state, requiring more sophisticated approaches.
Nonetheless, the fundamental memoryless property of Markov chains—allowing focus on the present rather than the entire history—remains a powerful tool. This simplicity enables scientists and engineers to model, analyze, and predict a wide array of phenomena, from the spread of diseases to the behavior of molecules and social dynamics.