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What happens if you multiply things that aren’t numbers? And what happens if that multiplication is not associative?

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Multiplication of numbers is an associative property and we can make sense of “multiplication” between things that aren’t numbers but that’s not considered as associativity. And since we’re talking about associativity, you might wonder about that other property of real numbers: You know: when multiplying two numbers, swapping their order doesn’t change the answer. This property is called commutativity. But keep in mind: it’s a very special property to have! Not everything in life is commutative. For example, getting dressed in the morning... putting on your socks and then your shoes is NOT the same as first putting on your shoes and then your socks.

Link to Resources:

The Fundamental Group: ‘Loop concatenation’
http://www.math.uchicago.edu/~may/VIG...

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