In recent years, a disagreement has erupted between two camps of philosophers about the rationality of bias toward the near and bias toward the future. According to the traditional hybrid view, near bias is rationally impermissible, while future bias is either rationally permissible or obligatory. Time neutralists, meanwhile, argue that the hybrid view is untenable. They claim that those who reject near bias should reject both biases and embrace time neutrality. To date, experimental work has focused on future-directed near bias. The primary aim of this paper is to shed light on the debate by investigating past-directed near bias. If people treat the past and future differently with respect to near bias, by being future-directed but not past-directed near biased, then this supports a particular version of the hybrid view: temporal metaphysic hybridism. If people treat the past and future the same with respect to near bias, then this supports a simple version of time neutralism, which explains both future bias and near bias in terms of the functioning of a single mechanism: the anticipatory/retrospectory mechanism. Our results undermine the claim that people are future-directed, but not past-directed, near biased, and hence do not support temporal metaphysic hybridism. They also fail to support simple time-neutralism; instead, they suggest that there are multiple mechanisms that differently shape future- and past-directed preferences.