Various experiments in optimization algorithms derived from probabilistic observer selection effects
Importance of observer selection effects in exponential reference classes
The measure problem in cosmology is one of the big unsolved questions in science, because it deals with the question "why are we here?". In an eternal inflating universe, the number of observers are growing exponentially, and the rate of doubling, a trillionth of a trillionth of a second, permits a staggering observer selection effect related to optimization. A world where observers see this effect is called an "exponential reference class".
For example, an observer might find itself living in the first civilization in the galaxy, because there are more civilizations at this stage in time at the overall scale of the universe. At the same time there is no direct observations of these other civilizations, because they exist beyond the observable horizon. The observer notices this fact as an anomaly from expected observations in a flat reference class, and concludes that observations are more likely to be made in an exponential reference class.
Other curious observations indicating an exponential reference class in our universe:
- The staggering complexity of the human brain
- The relative early formation of Earth compared to expected formed planets
- Fine tuning of physical parameters
If we could learn more about the exponential reference class, then we could make more accurate predictions about what observations to make in a such universe, and if they are confirmed it could lead to a new worldview.
Exploiting the exponential reference class for optimization
The exponential reference class can be mathematically modeled as a system distributed over states, where the states are related by some probability and a cost function of time. An observer can be modelled as a particle moving around randomly.
Given any conditional state of the system, the path that a particle takes between any two states follows Brownian motion of statistical mechanics in the flat reference class. In an exponential reference class, most particles, depending on the doubling rate, minimizes the time between the two states.
This means that the exponential reference class automatically optimizes for minimum time across all possible configurations. From this it follows that Brownian motion in a flat reference class is transformed into optimization in the exponential reference class. This mathematical transform depends on the specific optimization problem.