> almost all real numbers contain an infinite amount of information. Since a finite volume of space can't contain more than a finite amount of information [..]

> almost all real numbers contain an infinite amount of information. Since a finite volume of space can't contain more than a finite amount of information [..] The Kolmogorov complexity can't be higher than the state of the initial system, the dynamics, and a time parameter. Even if the system's current state involves real numbers, you would have a finite description of it as long as the time values, dynamics, and initial conditions are computable. I also think it's subtle to apply the Bekenstein bound here. Even if the numbers going in have infinite precision, that doesn't mean the relevant information quantity is infinite. For example, a qubit's density matrix has three real-number parameters and yet its von Neumann entropy is never more than 1 bit.