I\'d like to fix the cursor to the centre line of the screen, so that when I press Ctrl-N or Ctrl-P, the page itself moves up or down, and the cursor stays still.
Ha
M-x scroll-lock-mode, which could be used to put the Scroll Lock key to good use too:
M-x scroll-lock-mode
(global-set-key (kbd "") 'scroll-lock-mode)