How subtraction makes the universe more robust | #SoME3

#some3 #algebra #vectors #logic

It's time for the yearly Summer of Math Exposition again. In this year's entry, we explore anti-symmetric operations such as subtraction and logical implication. We discover that anti-symmetry has many advantages. It makes things like determinants, wedge products, and velocity vectors more invariant under many types of transformations.

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0:00 A video about something simple
0:45 Anti-commutativity
1:56 Replacing subtraction with addition
3:23 Logic
5:26 Symbols should reflect properties
7:41 A new symbol for subtraction
9:45 The geometry of subtraction
12:53 Subtraction makes things robust
14:21 Examples of anti-commutativity
16:26 A new perspective

#some3