I think his argument goes as follows. If you have N numbers in memory, then you have to use pointers of size log N bits. Because pointers use the same number of

I think his argument goes as follows. If you have N numbers in memory, then you have to use pointers of size log N bits. Because pointers use the same number of bits as numbers, this means that the numbers have to be log N bits. Because radix sort does one O(N) pass per bit, this means that total time will be O(NlogN). If we sort numbers of a fixed, known, size w', that is independent of machine word size w, then the argument breaks.