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The question of whether pre-training on geometric tasks is viable for downstream transfer to semantic tasks is important for two reasons, one practical and the other scientific. If the answer is positive, we may be able to reduce pre-training cost and bias from human annotators significantly. If the answer is negative, it may shed light on the role of embodiment in the emergence of language and other cognitive functions in evolutionary history. To frame the question in a way that is testable with current means, we pre-train a model on a geometric task, and test whether that can be used to prime a notion of 'object' that enables inference of semantics as soon as symbols (labels) are assigned. We choose monocular depth prediction as the geometric task, and semantic segmentation as the downstream semantic task, and design a collection of empirical tests by exploring different forms of supervision, training pipelines, and data sources for both depth pre-training and semantic fine-tuning. We find that monocular depth is a viable form of pre-training for semantic segmentation, validated by improvements over common baselines. Based on the findings, we propose several possible mechanisms behind the improvements, including their relation to dataset size, resolution, architecture, in/out-of-domain source data, and validate them through a wide range of ablation studies. We also find that optical flow, which at first glance may seem as good as depth prediction since it optimizes the same photometric reprojection error, is considerably less effective, as it does not explicitly aim to infer the latent structure of the scene, but rather the raw phenomenology of temporally adjacent images.