#mental-model #mathematic #chemistry #nature #analogy Created at 030423 # [Anonymous feedback](https://www.admonymous.co/louis030195) # [[Epistemic status]] #shower-thought Last modified date: 030423 Commit: 0 # Related - [[Philosophy/Rationality/Mental model]] - [[Philosophy/Rationality/Leveraging LLMs with mental models]] - [[Philosophy/Humans/Internet meme as mental model]] - [[Mathematic/Mathematical structure]] - [[Philosophy/Rationality/Models/Soul in the game]] - [[Computing/Architecture]] # TODO > [!TODO] TODO # Isomorphism Imagine two kids have different sets of blocks, but the blocks are all the same size and shape. Even though the sets may look different on the surface, the underlying structure of the blocks is isomorphic. Just like the blocks can be arranged in different ways to create different structures, isomorphic structures in other areas can also be arranged differently to create different behaviors or functions. ![a stunning photograph of a macro butterfly, 8 k, natural lighting ](https://lexica-serve-encoded-images.sharif.workers.dev/md/18f88255-e86a-4cbe-b9ea-a26f8b160025) Even though two different species of butterflies may look different in color and pattern, they have identical wing structure, number of antennae, and body shape. This means they share the same underlying structure or essence, which is isomorphic. Similarly, in mathematics or computer science, isomorphic structures may look different on the surface but share the same underlying structure or properties. ![black bear alone against a white background, by Currier and Ives, coloring book page, black and white, pen & ink drawing](https://lexica-serve-encoded-images.sharif.workers.dev/md/046dd8ec-d51f-4909-84f7-2c3569d057bc) Isomorphism can be compared to the concept of convergent evolution in nature. Convergent evolution is when different species evolve similar traits independently due to similar environmental pressures. Similarly, in isomorphism, different systems can have similar structures or behavior, even though they have different underlying mechanisms or functions. Just as two unrelated species may have similar adaptations to survive in their environment, two unrelated systems may have similar structures or patterns to fulfill their respective functions. ![harmless leopard spotted marine tapir wildlife for Monster Hunter, concept art from different angles, incredibly detailed, D&D, finished concept art, digital art on Pixiv, trending on Artstation](https://lexica-serve-encoded-images.sharif.workers.dev/md/05b8f661-8296-4d5b-8745-b644d736d973) In chemistry, isomers are molecules that have the same chemical formula but different structures. Just like isomorphic structures have the same underlying structure but can appear different, isomers in chemistry have the same number and types of atoms, but the atoms are arranged differently. This can result in different chemical properties and reactions. Similarly, isomorphic structures in mathematics or computer science may have different surface-level behaviors or functions, but share the same underlying structure or properties. ![distorted dopamine molecule 3 d ](https://lexica-serve-encoded-images.sharif.workers.dev/md/055f843a-d210-483d-9b3f-710035ee59a4) Isomorphism can be used in daily life as a mental model to identify similar underlying structures or patterns in seemingly different areas. It can help us better understand and analyze complex systems, as well as find new solutions or ideas by applying insights from one area to another. By recognizing isomorphic structures, we can better appreciate the underlying unity and interconnectedness of different fields, and see the beauty in diversity and complexity.