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Very interesting read. Nowhere on his desiderata does "uniqueness" come in. The rest of his examples show that it is indeed not a desirable quality, as the same
by hatmatrix 4y ago
Very interesting read. Nowhere on his desiderata does "uniqueness" come in. The rest of his examples show that it is indeed not a desirable quality, as the same abstract object benefits from different representations to make apparent its relation to other abstract concepts in each specific context. Or simply to reduce cognitive overhead.
- eternityforest 4y agoYeah I didn't get the point of that either. If you rearrange and solve for a different variable, for practical purposes outside of pure math(If you are thinking like a coder), you have a completely new equation that happens to be derivable. It's almost like compiling. But since mathematicians absolutely love finding common patterns in things, maybe there's some new innovation that a representation with uniqueness would enable?
- Twisol 4y ago"Normal forms" are definitely a thing, most clearly in linear algebra but certainly elsewhere as well. Being able to normalize any description of an object to a single unique canonical description is incredibly useful! But we don't always want to work with normal forms, for one reason or another, and there can be multiple kinds of normal form to choose from depending on your needs. For instance, if you do anything with something in a normal form, chances are it's no longer in a normal form! The lack of closure properties like this means you may only normalize at the very end of a series of manipulations, during which you're using a more suitable notation.