Imagine an AI that not only understands code but can also explain it in different ways – like a helpful colleague summarizing key points or sketching a flowchart. This is the power of "equivalent representations," where AI generates alternative forms of code that preserve its original meaning. Researchers explored this fascinating concept by employing two large language models (LLMs) in a self-reflective process. One LLM generates an alternative representation (like a comment, pseudocode, or even a mathematical formula), while the second LLM tries to reconstruct the code based on this new representation. The accuracy of the reconstruction is used as feedback to refine the initial representation, creating a loop of continuous improvement. In the open setting, where LLMs are free to express code in any form, they displayed impressive diversity, generating dictionaries, tables, XML, and even SQL-like queries. This reveals a surprising depth of understanding – LLMs don't see code as mere text but as structured sequences with inherent grammar. This also hints at how LLMs might reason about API functionality from code text alone. In the constrained setting, focused on generating specific forms like comments or flowcharts, the AI demonstrated significant potential for real-world software tasks. By iteratively refining the equivalent representations, the self-reflection method substantially reduced AI "hallucinations" – those moments where AI generates plausible-sounding but incorrect information. This method generated comments that help developers quickly grasp the purpose of code and produced pseudocode and flowcharts that illustrate code flow, facilitating optimization. Looking ahead, this research could transform how we generate code. Imagine describing a software requirement in a way tailored to AI's understanding, perhaps using mathematical expressions instead of natural language for numerically intensive tasks. This new paradigm could open up exciting possibilities, allowing LLMs to generate more complex and accurate code from LLM-friendly requirement descriptions and supporting a wider range of software engineering tasks in the future.