Is the astronomical structure of the Discworld widely known by its inhabitants?

Question

Until recently, I'd assumed that the astronomy of the Discworld - its flat shape and the fact that it rested on four elephants riding on the back of Great A'Tuin - was common knowledge within the Discworld itself. Everyone there seems to know, at least, that the world is flat. But then I found the following quote in Equal Rites, an exchange between Smith and Granny Weatherwax:

"They're both magic. If you can't learn to ride an elephant, you can at least learn to ride a horse."

"What's an elephant?"

"A kind of badger," said Granny. She hadn't maintained forest-credibility for forty years by ever admitting ignorance.

So apparently not only the simple Smith but also the somewhat wiser Granny are unaware of the nature of the creatures on whose backs their world is riding. Which begs the following question.

How aware are Discworlders, in general, of the fact that their world is a disc riding on the backs of elephants and a giant space turtle?

Answer 1

Out of Universe

In his The Folklore of Discworld, Terry Pratchett confirms that knowledge that the astronomical composition of the Discworld (e.g. disc/elephants/turtle) is known by everyone on the disc, albeit with some small exceptions.

The absolutely central, incontrovertible fact about the Discworld is that it is a disc. At least, it’s incontrovertible unless you adhere to the Omnian religion, in which case you must controvert it like billy-o
...
Clearly, fragments of information have drifted through the multiverse and taken root here and there. But the full and glorious Truth is known only on the Discworld. The Turtle Moves!

In Universe

We also have multiple pieces of in-universe evidence from the Discworld novels that show that this knowledge is very widely held.

It has been proven by direct observation.

The Great Turtle was a mere hypothesis until the day the small and secretive kingdom of Krull, whose rim-most mountains project out over the Rimfall, built a gantry and pulley arrangement at the tip of the most precipitous crag and lowered several observers over the Edge in a quartz-windowed brass vessel to peer through the mist veils.

The early astrozoologists, hauled back from their long dangle by enormous teams of slaves, were able to bring back much information about the shape and nature of A’Tuin and the elephants but this did not resolve fundamental questions about the nature and purpose of the universe.

The Colour of Magic

Ephebian scholars have known it for centuries and have written works that are widely available.

Vorbis shrugged. “The writer claims that the world…travels through the void on the back of four huge elephants,” he said.

...

“Most curiosity is,” said Vorbis. “It leads the mind into speculative ways. Yet the man who wrote this walks around free, in Ephebe, now.”
Drunah glanced at the scroll.
“He says here he went on a ship that sailed to an island on the edge and he looked over and—”

Small Gods

This knowledge is widespread throughout the 'civilised' world.

That wasn’t poetic imagery but plain fact, since the world was quite definitely flat and was, furthermore, known to be carried through space on the backs of four elephants that in turn stood on the shell of Great A’Tuin, the Great Sky Turtle.

Equal Rites

The Wizards know (obviously). They can also directly observe the Discworld through magical means.

The shape around Simon’s head was the world.
That was quite clear, although the glitter and rush of the little lights blurred some of the detail. But there was Great A’Tuin the sky turtle, with the four Elephants on its back, and on them the Disc itself. There was the sparkle of the great waterfall around the edge of the world, and there at the very hub a tiny needle of rock that was the great mountain Cori Celesti, where the gods lived.

Equal Rites

Basic schooling on the Sto Plains evidently includes instruction on the nature of the world.

“About the universe is what I meant,” said Albert hurriedly. “I mean, have you ever thought about it?”
“I know the Disc is carried through space on the backs of four elephants that stand on the shell of Great A’Tuin,” said Mort.

Mort

The Dwarves are well aware (and have been for some very considerable time).

They say that the fifth elephant came screaming and trumpeting through the atmosphere of the young world all those years ago and landed hard enough to split continents and raise mountains.

...

As for the dwarfs, whose legend it is, and who mine a lot deeper than other people, they say that there is a grain of truth in it.

The Fifth Elephant

Vetinari, Slant and the majority of Ankh-Morpork's gentry all know.

"Really? Well, we can do without magic for a couple of years, can't we?" said Mr Slant, managing to suggest that this would be a jolly good thing, too.
"With respect," said Ponder, without respect, "we cannot. The seas will run dry. The sun will burn out and crash. The elephants and the turtle may cease to exist altogether."
"That'll happen in just two years?"
"Oh, no. That'll happen within a few minutes, sir. You see, magic isn't just coloured lights and balls. Magic holds the world together."
In the sudden silence, Lord Vetinari's voice sounded crisp and clear.

The Last Hero

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Further evidence of the flatness of the world can be seen when people refer to the four cardinal directions.

"It's Rimwards" - The Last Continent

“The dragons headed hubward,” - The Colour of Magic

"You know that tower widdershins of Lancre" - Going Postal

“Oh, a sub-sect of the Turnwise Klatch philosophical system of Sumtin" - Wyrd Sisters

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As to the very specific question of why Granny Weatherwax doesn't know what an elephant is, the reality is that she lives in a very small village and hasn't traveled extensively (yet).

Her knowledge of the world comes from elementary schooling, supplemented by occasional visits from peripatetic teachers, missionaries and the reading of a single journal, the excellent 'Goatberger's Almanack And Booke Of Dayes' which presumably contains the occasional crude woodcut but is highly unlikely to offer much by way of detailed description of elephants.

It's hardly surprising that she's unaware of precisely what an elephant actually is, other than that it's a large weird-looking animal.

Answer 2

A few things go into this answer… The Omnians believe it is a globe and are considered odd, as we are told, by most inhabitants.

This seems a bit like misconception of people believing the Earth is Flat is a wide spread thing at any time in human history. To just about everyone it is rather obvious that the world is not flat and to the Discworlders that it is. This is because of the physics/magics involved and how, for example, the sun travels through the sky during the year. Pratchett was fond of making Discworld very similar but slightly off to the real world and in this way it becomes likely that he envisioned the same thing that happened on Earth would happen on Discworld and that is, the modern era is probably the era with the most amount of people believing that the opposite of the reality they live in is true. It is likely that there is plenty of conspiracies within that group too, but in the overall population it is likely a low percentage of the total that believes that the Discworld is round.

In one of the books where we are told one continent is pretty much cut off from the others and everything beyond a certain distance is all just a mystery. I forget the name of the book, but it had Rincewind, the Barbarians, Two-Flower, and it was a parody of asian countries.

And lastly… there is a problem with your thinking from how you take those lines. Smith and Granny don't know what an Elephant is. This does not mean they do not know that the Discworld rests on the backs of 4 Elephants on the back of A'tuin.

Another thing to keep in mind is that up until recently in Discworld history the Elephants and A'tuin are outside of most of the population's ability to view them and ability to "scientifically verify". Remember in The Color of Magic it's a big deal and people think it's a bit nuts to be going over the edge of the Disc to observe some information? If that information is only gotten in that "insane" of a way, then certainly there have only been a few adventurers if any before Rincewind and Two-Flower that got to directly see A'tuin, let alone the Elephants who would have to be much more hidden than A'tuin to the world in general.

So they're in a state of knowledge about where we were before Magellan made his voyage to just after we were able launch to rockets into space and physically observe the reality. They know, but it's all loosely verified.

Answer 3

One thing not noted so far in answers is the motion of the sun during the seasons.

It's made clear through several books that summer happens when the sun rises and sets near the rim-hub line. Winter happens when it rises/sets perpendicular to that line.

This means that one summer the sun moves across the sky in one direction, and the next summer (summer II or summer segundus) it move the opposite direction! It takes 800 discworld days for the sunrise to return to the same location. But there's only 400 days between midwinters.

This means it's pretty obvious to everyone the world is a disc.

But, as to how widespread is knowledge of whether the disc is on the back of 4 elephants standing on a giant turtle, that is a much harder answer.

Depending on which time period and which part of the disc you want your answer to come from, we get - very limited to fairly well spread.

The Omnian view is odd because of their stance on globe versus disc, not because of space turtle. The knowledge of the space turtle seems to be limited to people like Didactylos or the Omnian captain who have had the opportunity to see over the Rim.

But Small Gods is set many hundreds of years before most Discworld novels. By the time of Rincewind, we see evidence that the knowledge of the existence of the turtle is more widespread. But, again, this knowledge can still be limited - particularly in more "traditional" parts, like Lancre (home of Granny Weatherwax). It's like people here knowing the earth is round and moves around the sun, but not understanding space-time curvature.