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Local and global patterns of an object are closely related. Although each part of an object is incomplete, the underlying attributes about the object are shared among all parts, which makes reasoning the whole object from a single part possible. We hypothesize that a powerful representation of a 3D object should model the attributes that are shared between parts and the whole object, and distinguishable from other objects. Based on this hypothesis, we propose to learn point cloud representation by bidirectional reasoning between the local structures at different abstraction hierarchies and the global shape without human supervision. Experimental results on various benchmark datasets demonstrate the unsupervisedly learned representation is even better than supervised representation in discriminative power, generalization ability, and robustness. We show that unsupervisedly trained point cloud models can outperform their supervised counterparts on downstream classification tasks. Most notably, by simply increasing the channel width of an SSG PointNet++, our unsupervised model surpasses the state-of-the-art supervised methods on both synthetic and real-world 3D object classification datasets. We expect our observations to offer a new perspective on learning better representation from data structures instead of human annotations for point cloud understanding.