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This paper develops a climate-economy model with uncertainty, irreversibility, and active learning. Whereas previous papers assume learning from one observation per period, or experiment with control variables to gain additional information, this paper considers active learning from investment in monitoring, specifically in improved observations of the global mean temperature. We find that the decision maker invests a significant amount of money in climate research, far more than the current level, in order to increase the rate of learning about climate change. This helps the decision maker make improved decisions. The level of uncertainty decreases more rapidly in the active learning model than in the passive learning model with only temperature observations. As the uncertainty about climate change is smaller, active learning reduces the optimal carbon tax. The greater the risk, the larger is the effect of learning. The method proposed here is applicable to any dynamic control problem where the quality of monitoring is a choice variable, for instance, the precision at which we observe GDP, unemployment, or the quality of education.