2023-04-09

coordinate-free reading?

The world is O(3) equivariant. Meaning: The laws of physics don't depend on the orientations of things, nor do they depend on the orientation of your coordinate system. But handwriting—and printed words—are not equivariant: Writing systems have a definite orientation and parity. Indeed, it can be hard to read things when they are reversed in a mirror or at an odd angle. Pick up a paper from your desk and read it. Before you start, you have to orient it. How do you do that?

My answer is: Context. I think you try different orientations until one seems to work for the reading. You can't always tell from a single letter (like an M or a W or an O), but you can tell once a string of a few letters or numbers are visible. Inspired by all this, Villar and I are making this data set (among others) for learning and reasoning tasks:

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