The Teaching Model

1. The grid consists of individuals possessing a continuous level of knowledge ranging from 0 (Completely Ignorant) to 1 (Fully Omniscient), visualized as a gradient from white to blue.

2. Every individual acts under a constant pressure of memory loss. At any moment, there is a probability that an individual will instantly die and be replaced with a new particle with no knowledge.

3. If an individual does not forget, they randomly select one of their immediate neighbors to engage in a two-way "teaching" session.

4. During an interaction, both neighbors learn from each other. The amount learned is proportional to how much the other person knows - you learn more from an expert than from a novice.

5. Learning is also scaled by how much the learner doesn't know. As an individual approaches full omniscience (1.0), their ability to learn new information slows down, preventing values from exceeding the maximum.

6. The simulation demonstrates a dynamic balance between the viral spread of knowledge through local interactions and the random decay of knowledge due to forgetting.