I thought 56K was the fastest speed possible with conventional
> telephone cable. How can DSL be so much faster with the same old > cable?
The 56K is the limit of a voice channel on a phone switch, not of a copper cable. Rather than going through the phone switch, the DSL signal is split out at the central office and feeds into a device called a DSLAM which is sort of a super duper high speed modem that can run several megabits/sec over a good enough copper pair.