Families of ‘gigantic finite number’ functions found thus far
Giant finite number functions that could be represented with ludicrous brain-size/resources
These strike me as basically the same thing relative to my imagination. The biggest numbers mathematicians can describe using the fast-growing hierarchy for the largest computable ordinals are already too gigantic to… well… they’re already too gigantic. Taking the Ackermann function as primitive, I still can’t visualize the Goodstein sequence of 16, never mind 17, and I think that’s somewhere around w^(w^2) in the fast-growing hierarchy.
The jump to uncomputable numbers / numbers that are unique models of second-order axioms would still be a large further jump, though.
These strike me as basically the same thing relative to my imagination. The biggest numbers mathematicians can describe using the fast-growing hierarchy for the largest computable ordinals are already too gigantic to… well… they’re already too gigantic. Taking the Ackermann function as primitive, I still can’t visualize the Goodstein sequence of 16, never mind 17, and I think that’s somewhere around w^(w^2) in the fast-growing hierarchy.
The jump to uncomputable numbers / numbers that are unique models of second-order axioms would still be a large further jump, though.