Designing an agent that can grow cognitively from a child to an adult human level of intelligence is the key challenge on the roadmap to human-level artificial intelligence. To solve this challenge, it is important to understand general characteristics of the expected learning process at a level of mathematical models. The present work makes a step toward this goal with a simple abstract model of a long-term learning process. Results indicate that this process of learning is characterized by two distinct regimes: (1) limited learning and (2) global learning chain reaction. The transition is determined by the set of initially available learning skills and techniques. Therefore, the notion of a critical mass for a human-level learner makes sense and can be determined experimentally.