My gut, reading the HN title, was "half the time". I had to read the article, to see how many words piled up before he said that.
Of course, considering finite fields of prime power order, one might leap to the conclusion "a quarter of the time". One can adjoin "i" for prime powers p^n for half the primes and odd n.
Why is that? My guess would be that you could adjoin an i all the time to the p^n field and get the p^2n field, as long as you had p = 4k + 3. But that's admittedly based on approximately zero thinking.
My gut, reading the HN title, was "half the time". I had to read the article, to see how many words piled up before he said that.
Of course, considering finite fields of prime power order, one might leap to the conclusion "a quarter of the time". One can adjoin "i" for prime powers p^n for half the primes and odd n.
Alas, this be wrong, for an amusing reason.
Why is that? My guess would be that you could adjoin an i all the time to the p^n field and get the p^2n field, as long as you had p = 4k + 3. But that's admittedly based on approximately zero thinking.