norm morphisms

Posted in Uncategorized by sarkology on November 24, 2012

How do we identify with the protagonists of a story? We do this via “norm morphisms” (the google results you see for this term have nothing to do with the intended meaning here).

A morphism is loosely speaking a structure-preserving map. If we have objects A, B, then a morphism f:A->B maps “stuff” from A to “stuff” of B while preserving some structure common to both A and B. An example is the map x |-> log x from the positive real numbers to the real numbers. In which case xy gets mapped to log xy = log x + log y. Hence the multiplicative structure in the positive real numbers is preserved in the additive structure in the real numbers.

So maps from a tiny object can reveal structure in a large object.

So for example, you might read about Batman fighting the Joker. Inspired by this vigilante exploit you call the cops on these hapless youths smoking weed by the river behind your house. Nevermind the morality of this in the eyes of others, you see this as essentially upholding a particular norm we can roughly state as: “the authorities fail to eradicate all the scoundrels there exist, so it is up to us to take up the slack”. Here we see a norm morphism from your informing on the marijuana smokers to Batman fighting the Joker. The relevant “structure” being preserved is one of vigilantism.

In videogames too there are norm morphisms. So for example in Batman: Arkham City, you get to play as Catwoman, who has this ability to leap around the city. Not in one bound though. In other to execute such large traversals of the environment you have to press a sequence of buttons at the right moments in order to execute a sequence of leaps to your chosen destination. Here there exist a norm morphism from the skill of your button presses to the skill of Catwoman’s aerial acrobatics. Now button pressing might not seem terribly impressive, but apparently it is enough to create the required sense of immersion. If you think about it, this is not so different from how we read novels. We compute norm morphisms from our pathetic lives to the epic exploits of our greatest fictional heroes. This all is enough to maintain a suspension of disbelief, but most importantly of all to inculcate the relevant norms within our conscience.


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