Ray Dalio's 'Principles for Dealing with the Changing World Order' analyzes 500 years of history to reveal a 'big cycle' of empire rise and decline, driven by economic, financial, and geopolitical factors. He illustrates how events like currency devaluations, wealth gaps, and internal/external conflicts repeatedly lead to shifts in world power, using examples from the Dutch, British, and US empires. The video emphasizes that understanding these timeless cause-and-effect relationships and adhering to principles of earning more than spending and treating each other well are crucial for navigating future global changes.