The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies numerical ill-condition. The papers also quantify this tradeoff. The main method for proving these results is via a potential function called quasi-entropy, reminiscent of Shannon entropy. The quasi-entropy method opens new doors to understanding the computational complexity of the im…