Why modern economics fails to solve its own oldest paradoxes
In short: Standard economic models struggle with fundamental questions like how much debt to take on for an investment. The problem isn't a lack of data, but a flawed concept of randomness. By applying the mathematics of irreversible time from statistical physics, we can finally find formal solutions that align with human intuition.
For centuries, economics has relied on traditional concepts of randomness—essentially counting favorable outcomes within a set of hypothetical possibilities. However, Dr. Ole Peters argues that this approach is insufficient for complex systems. The shift began in the 1850s with the development of statistical mechanics, which recognized that whether a possibility exists is often less important than what actually materializes over time. This conceptual shift occurred during a silent revolution in the late 19th century. It moved away from simply listing potential outcomes toward observing actual materializations.
The core issue lies in ergodicity. In equilibrium systems, an average taken over time in a single system is identical to an average over a set of hypothetical possibilities (an ensemble average). This allows for simpler calculations. However, economic systems are typically non-equilibrium systems and are therefore non-ergodic. Because they are not ergodic, the old methods used since the 1650s fail to accurately describe them, leading to persistent issues in understanding market stability and wealth inequality. These non-ergodic dynamics are why modern techniques are specifically appropriate for economic analysis. The current reliance on outdated randomness has historically hindered the field's progress.
By incorporating Boltzmann's 1870s probability theory and 20th-century mathematics, economists can treat risk as a consequence of an uncertain future and irreversible time. This framework provides complete formal solutions to classic problems that current models cannot solve, such as the St Petersburg paradox and the leverage problem—the question of exactly how much wealth one should commit to a favorable investment based on defined notions of reward and risk. The leverage problem specifically asks how much of our total wealth should be committed to a single opportunity. These new mathematical tools provide solutions that finally match our intuitive sense of risk.
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Sources
- Summary by Intellect · source: Time for a Change: Introducing irreversible time in economics - Dr Ole Peters
- Also: Time for a Change: Introducing irreversible time in economics
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