The prospect of learning about various uncertainties relevant to analyses of the climate change issue is important because it can affect estimates of the costs of both damages and mitigation, and it can influence the optimal timing of emissions reductions. Baseline scenarios representing future emissions in the absence of mitigation are one of the major sources of uncertainty. Here we investigate how fast we might realistically expect to learn about the outlook for long-term population growth, as one determinant of future baseline emissions. That is, we estimate how long it might take to substantially revise current estimates of the likelihood of various population size outcomes over the twenty-first century. We draw on recent work showing that, because population growth is path dependent, we can learn about the long term outlook by waiting to observe how population changes in the short term. We then explore the implications of uncertainty and of this learning potential for mitigation costs and for optimal emissions. Using a simple model, we show that uncertainty in population growth translates into an uncertainty in the optimal tax rate of about $200/tC by 2050 for a range of stabilization levels. When learning is taken into account, it allows for mitigation strategies to change in response to new information, leading to a slight reduction in the expected value of mitigation costs, and a substantial reduction in the likelihood of high cost outcomes. We also find that while learning can lead to large revisions over the next few decades in anticipated population growth, this potential does not imply large changes in near-term optimal emissions reductions. Results suggest that further work on the potential for learning about other determinants of emissions could have larger effects on expected mitigation costs.