Fantasy readers tend to read fantasy novels to escape reality and enter a world of magic, swords, and sorcery. We want a vacation from the humdrum of the everyday grind. And you know what? Rincewind's the same way. He lives in a world with swords and sorcery in abundance, but all he wants is a vacation from that magical malarkey. He, too, is ready for something completely different.
Try, Try, Try to Understand
Rincewind's problem with magic is that it doesn't actually solve any of life's major problems, and on the rare occasion it does solve one, it has an awful tendency to cause more. As he tells the camera imp:
"no spells are much good. It takes three months to commit even a simple one to memory and then once you've used it, poof! it's gone. That's what's so stupid about the whole magic thing, you know. You spend twenty years learning the spell that makes nude virgins appear in your bedroom, and then you're so poisoned by quicksilver fumes and half blind from reading old grimoires that you can't remember what happens next." (1.14.41)
As this example shows us, the magic of the Discworld isn't the something-for-nothing system of a Harry Potter novel. It takes time, energy, and effort to get what you want.
The novel calls this the "Law of Conservation of Reality" (2.1.7), and it's an every action has an opposite and equal reaction type of law. If you want to build a house, you'll probably spend as much time learning and then building the house as you would learning and then performing the spell to build the same house. If you want to coax nude virgins (yep, plural) to join your evening frivolities, you'll spend as much time mastering the subtle art of the pick-up line as you would learning the spell of materialization.
Simply put: Spells are pretty weaksacue and, for the most part, totally impractical.
This has lead Rincewind to spend a good portion of his life looking for a source other than magic with which to accomplish tasks. He thinks Twoflower's notion of "reflected-sound-of-underground-spirits" (1.15.45) might prove a suitable replacement until he discovers that it is as impractical as, if not just another form of, magic.
So instead, Rincewind decides that what he really wants is a "universe [ruled] by logic and the harmony of numbers" (2.1.15). A universe that sounds suspiciously like our own.
I'm a Magic Man
The symbol behind magic and its non-magic magic counterparts seems to be the tools people create to survive in their particular universe.
On the Discworld, magic is an actual thing, and it allows people to do things they couldn't do naturally. They can create dragons, teleport great distances instantaneously, and create fire without the tedium of having to invent a lighter or go it the old-fashioned way. The drawbacks to all of this are as mentioned above—it's not easy and the effort often doesn't make it worthwhile.
On our Roundworld, science and technology are our magic. They allow us to do things that nature didn't intend for us, such as fly, communicate over long distances, and observe events from the past and hundreds of miles away. The drawbacks are that sometimes technology fails, sometimes we can't comprehend the implications of a scientific discovery, and of course, the creation of tech support.
Sometimes the drawbacks and advantages can be eerily similar. For example, the Internet allows us to incorporate society into our lives with a greater ease than ever before, but on the downside, the Internet also allows us to incorporate society into our lives with a greater ease than ever before. Sometimes you just want to get away, you know? It's a lot harder to do these days than it was pre-Internet age.
In both cases, the end result is the same: tools. Magic and science are tools. Both can make life easier, but neither is going to solve all the problems. Life is life, and it's going to stay that way because it's been doing pretty well for itself, so why mess with a formula that works? Fantasizing about a new set of tools—whether it's magic or science, depending on your reality—won't change the fact. If Rincewind could pop over to our universe, he'd understand this, just as we see it by reading about his misadventures.