information and structure
In order to unearth an underlying structure, you need to selectively forget some of the available information. This meta-principle is manifested in so many places that it would be pointless to make a list. (In some sense the notion of cognition is based on it. No wonder why it is so ubiquitous.)
Here is a quick mathematical example. In order to assign a singular chain complex to a topological space, we collate together face maps to create boundary operators. While doing so, we lose a lot of information. (The images of these operators are quite small.) Yet enough information is encoded to recover topological invariants such as the Euler characteristic.
Here is a quick mathematical example. In order to assign a singular chain complex to a topological space, we collate together face maps to create boundary operators. While doing so, we lose a lot of information. (The images of these operators are quite small.) Yet enough information is encoded to recover topological invariants such as the Euler characteristic.
