index dc275da..0340cab 100644
@@ -10,7 +10,7 @@ the digital world is built on math. not approximately, not metaphorically — li
in 1937, claude shannon's master's thesis showed that boolean algebra (true/false, AND/OR/NOT) could be implemented with electrical switches. this single insight is the foundation of all digital computing. every transistor in your phone is computing a boolean function. a modern chip has billions of them, all doing math.
-the instruction your CPU is executing right now — reading a value from memory, comparing two numbers, jumping to a different part of the program — is a sequence of boolean operations on binary numbers. [arithmetic](/wiki/immediate/arithmetic-everywhere) at the hardware level.
+the instruction your CPU is executing right now — reading a value from memory, comparing two numbers, jumping to a different part of the program — is a sequence of boolean operations on binary numbers. [arithmetic](/wiki/immediate/arithmetic-everywhere) at the hardware level. and boolean algebra is really [[structural/set-theory-as-thinking|set theory]] in disguise — AND is intersection, OR is union, NOT is complement. the entire digital world rests on set operations.
## algorithms and complexity
@@ -48,6 +48,8 @@ modern AI is mostly [linear algebra](/wiki/structural/linear-algebra-as-thinking
the semantic space example from my essay is a direct application: word embeddings represent meanings as vectors, and the geometry of the vector space captures semantic relationships. "woman" + "king" - "man" ≈ "queen" works because the vector arithmetic in embedding space mirrors conceptual relationships.
+[[structural/topology-as-thinking|topological data analysis]] is an emerging tool — using persistent homology to find the "shape" of high-dimensional datasets that linear methods miss.
+
## the deep point
computer science demonstrates that math isn't just about numbers — it's about computation, information, and the fundamental limits of what can be known, computed, and communicated. some problems are provably unsolvable (the halting problem). some are solvable but take longer than the age of the universe. understanding these limits is itself a mathematical achievement.
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