We don't even know a tighter lower bound for matrix multiplies than O(n²). Naive is O(n³), strassen is O(n^2.8). And those are simple, low-level kernels. At the

We don't even know a tighter lower bound for matrix multiplies than O(n²). Naive is O(n³), strassen is O(n^2.8). And those are simple, low-level kernels. At the higher level we also do not know tight lower bounds. But we do know some loose bounds from nature, e.g. how much data and energy a human consumes over its lifetime.