TB: Abstractions Can Be Useful

The right abstraction can make an intractable problem tractable by revealing structure invisible at the concrete level. Working in a more abstract domain often unlocks tools — continuity, differentiation, symmetry — that don't exist in the original domain.

The instinct to stay concrete is often counterproductive. The key question is: which abstraction adds the most useful machinery? Moving to the right level of abstraction is a craft — too abstract and you lose contact with the specific; too concrete and you can't see the pattern.

• Abstractions can be useful (source note): Proving things about polynomials is much easier than proving things about integers — polynomials have roots and can be differentiated. (From Fearless Symmetry)

• The Map is Not the Territory
• Commutation Acts Like Differentiation
• It Pays to Get the Design Right