Comment by burpingtree

The argument in the article isn’t about whether big O notation is useful it’s about whether the n in any particular big O is relevant. In this case the algorithm’s claim is that you can multiply arbitrarily large numbers faster than n log n where n is the size of the numbers being multiplied. But that result holds only if you don’t include the cost to multiple arbitrarily large complex numbers in that n, which are assumed to be able to multiply in constant time.