What is time? Since the function of the brain is closely tied in with that of time, investigating the origin of time in the brain can help shed light on this question. In this paper, we propose to use simulated evolution of artificial neural networks to investigate the relationship between time and brain function, and the evolution of time in the brain. A large number of neural network models are based on a feedforward topology (perceptrons, backpropagation networks, radial basis functions, support vector machines, etc.), thus lacking dynamics. In such networks, the order of input presentation is meaningless (i.e., it does not affect the behavior) since the behavior is largely reactive. That is, such neural networks can only operate in the present, having no access to the past or the future. However, biological neural networks are mostly constructed with a recurrent topology, and recurrent (artificial) neural network models are able to exhibit rich temporal dynamics, thus time becomes an essential factor in their operation. In this paper, we will investigate the emergence of recollection and prediction in evolving neural networks. First, we will show how reactive, feedforward networks can evolve a memory-like function (rec- Chung, Kwon, Mann, and Choe ollection) through utilizing external markers dropped and detected in the environment. Second, we will investigate how recurrent networks with more predictable internal state trajectory can emerge as an eventual winner in evolutionary struggle when competing networks with less predictable trajectory show the same level of behavioral performance. We expect our results to help us better understand the evolutionary origin of recollection and prediction in neuronal networks, and better appreciate the role of time in brain function.