I study altruistic choices through the lens of a cognitively noisy decision-maker. I introduce a theoretical framework that demonstrates how increased cognitive noise can directionally affect altruistic decisions and put its implications to the test: In a laboratory experiment, participants make a series of binary choices between taking and giving monetary payments. In the treatment, to-be-calculated math sums replace straightforward monetary payments, increasing the cognitive difficulty of choosing. The Treatment group exhibits a lower sensitivity towards changes in payments and decides significantly more often in favor of the other person, i.e., is more altruistic. I explore the origins of this effect with Bayesian hierarchical models and a number-comparison task, mirroring the "mechanics" of the altruism choices absent any altruistic preference. The treatment effect is similar in this task, suggesting that the perception of numerical magnitudes drives treatment differences. The probabilistic model supports this interpretation. A series of additional results show a negative correlation between cognitive reflection and individual measures of cognitive noise, as well as associations between altruistic choice and number comparison. Overall, these results suggest that the expression of altruistic preferences -- and potentially social preferences more generally -- is affected by the cognitive difficulty of their implementation.