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AlanCrowe comments on Book Club Update, Chapter 2 of Probability Theory - Less Wrong
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Communication? I think you mean commutation.
The two big algebraic properties are
associative: (x+y)+z = x+(y+z)
commutative: x+y = y+z
The prefix function notation used in Eq 2.13 uglifies the associative law so badly that ones eyes can barefly focus on it, but I still think Jaynes makes the right choice. Introducing a new infix operator here would feel like sleight of hand.
The associative law is usually seen as more basic than the commutative law. Matrix multiplication is associative but not commutative. Composition of maps is associative but not commutative. The theory of commutative groups is much simpler than the theory of groups in general; for example a subgroup of a commutative group is always normal.
Aha, that makes perfect sense, thank you :) I had a feeling there was something going on there to that effect, but I could not put my finger on it till your reply. thanks.