SEPP reframes the very nature of human understanding. The principle suggests that "to understand" a phenomenon is not to have a perfect, one-to-one mental copy of it, but rather to possess a simple formal model whose expressive power is sufficient to predict the aspects of the phenomenon we care about.

The Feeling of Insight

The "Aha!" moment—the feeling of suddenly understanding a complex problem—can be formalized through SEPP. It is the moment when we discover a new, much simpler formal system ($F_{new}$) that has the same or even greater expressive power than our previous, complicated, and messy collection of thoughts ($F_{old}$). That is, $K(F_{new}) \ll K(F_{old})$ while $\mathrm{Exp}(F_{new}) \ge \mathrm{Exp}(F_{old})$.

This is the essence of a scientific or mathematical breakthrough. Newton's laws of motion are a profound insight because they are an incredibly simple formal system that replaced a vast, disconnected set of empirical observations about planetary motion and terrestrial mechanics. The feeling of "understanding" is the feeling of this massive informational compression.

Explanation as a SEPP Trade-Off

This framework implies that there is no single "best" explanation for any complex phenomenon. An explanation is always a choice of a model on the SEPP spectrum, and the "best" explanation depends on the purpose of the explanation.

• Explaining to a Child: When explaining a complex topic (like gravity) to a child, we choose a model of maximal simplicity (e.g., "the Earth pulls things down"). This model has very low complexity and very low expressive power (it can't explain orbits), but it is sufficient for the child's needs.
• Explaining to an Engineer: To a rocket scientist, we use a much more complex model (Newtonian mechanics). The increase in axiomatic complexity "buys" the necessary expressive power to perform calculations and build a rocket.
• Explaining to a Physicist: To a physicist studying Mercury's orbit, we must use an even more complex model (General Relativity), as the expressive power of the Newtonian model is insufficient to account for the subtle, high-entropy relativistic effects.

The principle of Occam's Razor is not a metaphysical command to find the "simplest" theory, but a pragmatic rule for choosing a model on this spectrum: Choose the simplest possible formal system that has the required expressive power for your specific task. To choose a model that is more complex than necessary is inefficient. To choose one that is too simple is to have a tool with insufficient power to do the job.