another complicated GM design
apparently the engineers were concerned that people would turn the knob backwards and damage the timer. All the 1963 forward dishwasher timer dials had an internal clutch set-up (the white piece in the center) so the outer dial would just spin if turned counter-clockwise. However, the 1960 - 62 models did have a dial that seperated (unscrewed like Bob said) if turned counter-clockwise. They did away with that by the 63 model year. Apparently kids were unscrewing the knob and "lost" it, leaving mom with a non-working dishwasher.
This was actually noted in the 63 literature as a sales point.
And talk about crazy, in 1965 for some insane reason, Frigidaire had a dishwasher timer with a smaller sized shaft that would only take one specific knob. Even though it shared graphics with the other models, it never fit anything else.