index b637771..78fdf6d 100644
@@ -26,7 +26,7 @@ each level loses some detail and gains generality. at level 1, you know you're t
abstraction has a cost: the more abstract you go, the harder it is to connect back to concrete reality. this is why abstract math feels "useless" — the connection to specific applications is indirect.
-but the trade-off is worth it when the same structure appears in many different domains. [linear algebra](/wiki/structural/linear-algebra-as-thinking) works for physics, data science, economics, and natural language processing because the abstraction (vector spaces) captures structure shared by all these domains. if you'd stayed concrete — "column of numbers" — you'd never see the connections.
+but the trade-off is worth it when the same structure appears in many different domains. [[structural/linear-algebra-as-thinking|linear algebra]] works for physics, data science, economics, and natural language processing because the abstraction (vector spaces) captures structure shared by all these domains. if you'd stayed concrete — "column of numbers" — you'd never see the connections.
the skill is knowing when to abstract and when to stay concrete. abstract too early and you're doing math for math's sake, disconnected from reality. abstract too late and you're solving the same problem over and over without realizing it's the same problem.
@@ -52,12 +52,12 @@ this sounds absurdly abstract, and it is. but it's also powerful:
- it identifies universal patterns that recur across all branches of math (products, coproducts, limits, colimits)
- it provides a language for talking about mathematical structure itself
-in [computer science](/wiki/stem/computer-science), category theory has found practical applications: functional programming languages like Haskell use categorical concepts (monads, functors) as programming abstractions. a monad in Haskell is the same mathematical object as a monad in category theory — the abstraction crosses from pure math to software engineering.
+in [[stem/computer-science|computer science]], category theory has found practical applications: functional programming languages like Haskell use categorical concepts (monads, functors) as programming abstractions. a monad in Haskell is the same mathematical object as a monad in category theory — the abstraction crosses from pure math to software engineering.
## the deep point
abstraction is not escape from reality — it's compression of reality. a good abstraction captures the essential structure and discards the irrelevant details. the power of mathematics is that its abstractions are *remarkably good* at capturing the structures that matter.
-this is the core of the [organizational lens](/wiki/structural/the-organizational-lens): each branch of math provides an abstraction layer, a way of seeing structure. [sets](/wiki/structural/set-theory-as-thinking) abstract classification. [calculus](/wiki/structural/calculus-as-thinking) abstracts change. [linear algebra](/wiki/structural/linear-algebra-as-thinking) abstracts direction and transformation. [topology](/wiki/structural/topology-as-thinking) abstracts connectivity. [groups](/wiki/structural/symmetry-and-groups) abstract symmetry.
+this is the core of the [[structural/the-organizational-lens|organizational lens]]: each branch of math provides an abstraction layer, a way of seeing structure. [[structural/set-theory-as-thinking|sets]] abstract classification. [[structural/calculus-as-thinking|calculus]] abstracts change. [[structural/linear-algebra-as-thinking|linear algebra]] abstracts direction and transformation. [[structural/topology-as-thinking|topology]] abstracts connectivity. [[structural/symmetry-and-groups|groups]] abstract symmetry.
the question isn't "is this abstraction useful?" — it's "is this the right level of abstraction for the problem at hand?" too concrete and you're lost in details. too abstract and you're lost in generality. the sweet spot — where the abstraction reveals structure without obscuring specifics — is where mathematics does its best work.
\ No newline at end of file