highSyzygy(M, Optimism => 1)
If highSyzygy(M) chooses the p-th syzygy, then highSyzygy(M,Optimism=>r) chooses the (p-r)-th syzygy. (Positive Optimism chooses a lower "high" syzygy, negative Optimism a higher "high" syzygy.
Are there cases when positive Optimism is justified?