We argue that attempting to quantify open-endedness misses the point: The nature of open-endedness is such that an open-ended system will eventually move outside its current model of behavior, and hence outside any measure based on that model. This presents a challenge for analyzing Artificial Life systems, leading us to conclude that the focus should be on understanding the mechanisms underlying open-endedness, not simply on attempting to quantify it. To demonstrate this, we apply several measures to eight long experimental runs of the spatial version of the Stringmol automata chemistry. These experiments were originally designed to examine the hypothesis that spatial structure provides a defense against parasites. The runs successfully show this defense, but also show a range of innovative, and possibly open-ended, behaviors involved in countering a parasitic arms race. Commencing with system-generic measures, we develop and use a variety of measures dedicated to analyzing some of these innovations. We argue that a process of analysis, starting with system-generic measures but going on to system-specific measures, will be needed wherever the phenomenon of open-endedness is involved.

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