# 12-240/Linear Algebra - Why We Care

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## Linear Algebra is the Small Scale Theory of Everything

• To study the large, start with the small.
• In small scales, every space is a vector space.
• Indeed if you walk a mile east, a mile north, a mile west and a mile south, you're back were you started, but if you fly a 1,000 miles east, a 1,000 miles north, a 1,000 miles west and a 1,000 miles south, you're not back were you started (where will you be?).
• In small scales, every function is a linear function.
 $\longrightarrow$ $z$ $\mapsto$ $z^2$ (code)
• The world doesn't come with coordinates.
• Hence whenever we can we work without a basis, and when we do study bases, we study all of them.

See also The Mathematica notebook QuiltPlot.