The symbol is not an actual infinity. The abstract concept we access with our minds is an actual infinity. That's the point. The abstract principle cannot it

The symbol is not an actual infinity. The abstract concept we access with our minds is an actual infinity. That's the point. The abstract principle cannot itself be embedded in a program or symbol. All we can do is describe it with rules we infer from observing it. Like a painting of a tree will never be the tree itself, and we will not be able to infer everything about the tree just by looking at the painting.