For the last century, economists have assumed that agents have ‘deep’ time preferences — in other words, agents value pleasures and pains in t years more than pleasures and pains in t+1 years. By contrast, philosophers have argued that discounting future rewards results from `’myopia,’’ i.e. imperfect foresight. We develop this alternative hypothesis. Specifically, we show that time discounting arises naturally when a perfectly patient Bayesian decision-maker receives noisy signals about the future (instead of being able to make noiseless forecasts). The resulting signal-noise extraction problem leads the Bayesian agent to effectively down-weight delayed utils. Our benchmark model of imperfect forecasting implies that agents act ‘as if’ they have hyperbolic time preferences, including exhibiting systematic preference reversals. However, our model implies that agents do not choose commitment — their deep time preferences are dynamically consistent. Our model also implies that agents with more experience/intelligence will behavior more patiently.