It might be consolation to Rincewind to know that there is a dimension where there is something better than magic, if only he knew what it was. Dr Rjinswand knows what it is: he calls it Nuclear Physics.
It would appear that in order to meet his fervent desire to cheat Death while plummeting through a suddenly non-existent noble dragon, Rincewind was temporarily transported to the nearest available dimension within the Multiverse where this could be arranged: this turned out to be Roundworld.
From the tale related in The Colour of Magic, it can be inferred that the energies of Rincewind and Rjinswand temporarily fused. As it was his dimension and home planet, the law of conservation of energy dictated that Dr Rjinswand was the dominant personality, and after a few moments of confusion, all memories of having been Rincewind were forgotten.(To illustrate this point, think of what happens when a witch goes Borrowing and lingers in another mind for too long.) No doubt had Jack Zweiblumen also awoken, he would have had brief confused memories of being somebody called Twoflower.
Inertia may have preserved this situation, were it not for the sudden arrival of The Luggage - the sudden fright precipitated separation of the personalities, and their downward plummet towards the Rim Ocean was suddenly resumed without benefit of intervening airliner, but from a survivable height.
Given that Rincewind was the (largely unwilling) explorer of Roundworld in The Science of Discworld, an interesting question arises here. Were he to be sent into Roundworld during the brief period of time where Dr Rijnswand is alive and practicing medicine to stricken nuclear reactors, would the two personalities fuse again? And let's say Rijnswand was working on stabilising a malfunctioning reactor core, (perhaps one exhibiting signs of breakaway oxidisation phenomena*) say at Three Mile Island or Chernobyl, at exactly the time when the Faculty sends Rincewind into Roundworld. All of a sudden, the person dealing with a rogue nuclear reactor is no longer Rijnswand, but - for just long enough - a panic-stricken Wizzard from a different dimension... this may explain much...
- Breakaway oxidisation phenomena - a less alarming way of saying It's uncontrollably on fire