Whenever divine or monstrous elements mix with the mortal world, they generate Mist, which obscures the vision of humans. You will see things just as they are, being a half-blood, but humans will interpret things quite differently. Remarkable, really, the lengths to which humans will go to fit things into...
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their version of reality.
This mist helps the immortal world stay hidden. Different versions of reality is a big theme in the book, as we see examples of how mortal humans interpret situations differently in order to conform to their version of reality. For example, while humans might grumble about the mechanical failure on a bus causing an explosion, immortals would understand it is due to a bolt of Zeus's lightning:
During third grade, a man in a black trench coat had stalked me on the playground. When the teachers threatened to call the police, he went away growling, but no one believed me when I told them that under his broad-brimmed hat, the man only had one eye, right in the middle of his head.
Before that—a really early memory. I was in preschool, and a teacher accidentally put me down for a nap in a cot that a snake had slithered into. My mom screamed when she came to pick me up and found me playing with a limp, scaly rope I'd somehow managed to strangle to death with my meaty toddler hands.
As a half-blood, Percy has caught on to the immortal elements around him. But since he is surrounded by humans, he has been taught to believe they are hallucinations, or his imagination running wild:
"His imagination," Mr. Brunner insisted. "The Mist over the students and staff will be enough to convince him of that."
Mr. Brunner and Grover try to protect Percy by using the mortal's perception of reality to convince Percy the supernatural things he sees are hallucinations. Mr. Brunner and Grover also show us how the immortal world stays hidden from the mortal world through their disguises.
Grover is a satyr (half human, half goat). He is Percy's keeper, but when they meet, Percy is still unaware of the truths of the immortal world. At school, Grover hides his goat legs and the humans believe he has some sort of muscular disease in his legs.
Similarly, Mr. Brunner moves around the mortal world in a motorized wheelchair. But at Camp Half-Blood, Percy learns that his favorite teacher's real name is Chiron and that he is a centaur with the body of a horse.