In Springfield: Homer goes through all the stages of evolution, and that annoying Agnes Skinner even finds a way to bother him in prehistoric times. (At least Seymour is safe.)
IRL: Homer starts off as a lungfish (the immediate ancestors of land-living vertebrates), according to Steve Brusatte, paleontologist at University of Edinburgh.
Next, Homer transforms into a "fishopod," which were mostly aquatic but evolved fingers, toes, and other features, he said. This is around 390 million years ago.
Finally, Homer transforms into Dimetroden. "Dimetrodon looks like a dinosaur — a big, bulky, reptilian beast from long ago. But it's not a dinosaur. It's actually more closely related to mammals than it is to dinosaurs," said Brusatte.
Here's the thing: Dimetroden lived tens of millions of years before dinosaurs even existed. Homer — as Dimetroden — wouldn't be able to observe dinosaurs on the cliff. Pterosaurs didn't exist at the same time either, so Agnes Skinner wouldn't be flying overhead. Unless time and space bend to allow all these creatures to exist at the same time.