User blog comment:Alemagno12/Unthinkable numbers/@comment-31663462-20170417232155/@comment-30754445-20170418001743

"All numbers are thinkable" - actually that's not true.

The human brain has finite processing power, so the number of possible human "thoughts" is finite. Ergo, there are numbers which cannot be grasped in any way or form by the human brain.

And they don't even have to be that large, either. Any number that has (say) a googol random digits will be "unthinkable" (not only to humans, but to any other physical being smallert than the observable universe). When it comes to numbers bigger than a googolplex (which is tiny by googological standards) only a tiny fraction of them are accessible to mere mortals like us.

Of-course, there has to be some gray areas as to what "thinkable" means exactly, otherwise we'll reach a variant of Barry's Paradox with the phrase "the smallest unthinkable number".