In Rabbinical Judaism, hermeneutics – deep reading and critical analysis – became the explicit substitute for the act of sacrifice. The connection, I take it, is that both are discriminatory. In Christianity, sacrifice continues, but in a more sublimated form: the rite of eucharist. In both cases, the tendancy is away from violence.
Pueblo religion transformed the bloody sacrificial traditions of greater Mesoamerica in a similarly ingeneous fashion. Prayers are animated, given shape, by carved and feathered prayer sticks fashioned by the petitioner himself, or in the case of a woman by her husband. They are, in fact, effigies of the petitioner. Their use is phenomenologically similar to the act of crossing oneself.
It is at this crossroads in the self that the most important sacrifice is enacted.