alt Hacker NewsIt fascinates me that there's something like this in something as solid and rigid like matrix multiplication. What causes something so rigid to break apart and "leak" at very large scale? Why does the "optimization" appear to be very, very small? Why does galactic algorithm exists? I can't imagine long division suddenly breaking apart after a billion digit, the structure seems very stable? I have heard before that matrix multiplication is apparently optimize-able at very, very large scale.
Does anyone have an intuition to what causes it? What happens at these large scale (or very small)?
One way to think about it is that the classical algorithms are the ones that are fast for small numbers. Galactic algorithms often work for small inputs, it's just that to be faster you need big inputs. A common case of this is a requirement that log(n)<<klog(log(n)). If k=100 then this algorithm will take huge sizes to win