Punoxysm comments on Summary of the first SoCal FAI Workshop - Less Wrong Discussion
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This modified simplex, where some coordinates are constrained to be equal, shouldn't be impossible to project on, but it does seem like you have larger problems. Ah well.
But I figure there should be some approach that works spiritually with whatever you're trying to do (which is not 100% clear to me) just because there are so many ways to project vectors, or sampled versions of those vectors.
What specifically do you hope to gain from your probability distribution over 1/2 probability on all sentences?