It is a truism among ethologists that one must not forget that animals perceive and represent the world differently from humans. Sometimes this caution is phrased in terms of von Uexküll's Umwelt concept. Yet it seems possible (perhaps even unavoidable) to adopt a common ontological framework when comparing different species of mind. For some purposes it seems sufficient to anchor comparative cognition in common-sense categories; bats echolocate insects (or a subset of them) after all. But for other purposes it seems necessary to find out more about how organisms organize their perceptions into biologically significant and perhaps cognitively meaningful states. Complex animals have high bandwidth sensory channels that feed into large nerve networks with very complex dynamics. Even for relatively simple animals belonging to species believed to have a small, fixed number of neurons, the odds are very much against any two animals of the same species, let alone different species, having exactly the same couplings to the environment, the same dimensionality in their nervous systems, or the same dynamics. Given such diversity (which von Uexküll himself recognized), how should we think about shared representation, shared meaning, and cognitive similarity between individuals and species?