andrewducker: (Default)
andrewducker ([personal profile] andrewducker) wrote2017-08-22 12:00 pm
simont: A picture of me in 2016 (Default)

[personal profile] simont 2017-08-24 09:30 am (UTC)(link)
Mark Dominus is not a complete fool, so I'm sure he does know all of this, and indeed surely that is exactly the stuff he had in mind when he wrote 'commutativity and associativity of addition in disguise'.

Remember that he's playing this game with one of his children, so he's intentionally trying to see things from the point of view of someone less mathematically sophisticated than you (or me, or himself).

The 'disguise' he mentions is that subtraction looks like a separate mathematical operation, precisely because we use the shorthand ab rather than writing a+(−b) every time. So, to somebody who's still learning (or has only recently learned) the notation and the permitted transformations of expressions, there appears to be an extra operation and a whole extra set of laws to learn, until you reach the level of both practice and understanding that lets you effortlessly see through that notational convention of 'addition and subtraction operators' to the underlying reality of 'actually it's all just addition and negation'.