I don't want to be a nitpicker, but with sufficient patience ignorance can be cured. Therefore, in the vast scheme of things, it is bound and finite and may actually decrease with time as "right thinking" prevails. As a young child is "ignorant" and must be taught, or my father-in-law is rock hard stupid and nothing will change that, ever. Stupidity knows no bounds and is therefore infinite. The case is still out on hydrogen.
Regards,
GtG
It totally violates the laws of entropy.