Indescribable things cannot be described in a finite number of words. That’s because each one contains an infinite quantity of information.
I would disagree with that. Suppose you take a plank scale recording of the entire quantum wave function (within Hubble volume), along with some kind of look at this bit pointer. (A few web pages about the colour red should do it.) This contains all the information about the colour red. The whole universe is there to tell you the clustered structure of thingspace, the extra article is so you can pick out the “red” cluster as opposed to the “turtles” cluster. Whether or not there is any way to get this info into the brain of a blind human is anther question, but the info is there. A complete description of “the sensation of red” is finite. Much of the info could be got into the brain of a blind human, say with a series of talks on optics, vision ect. However the brain is incapable of doing arbitrary format conversions.
Whether or not uncomputable numbers require infinite info is getting into weird subtleties of logic, model theory ect.
I would disagree with that. Suppose you take a plank scale recording of the entire quantum wave function (within Hubble volume), along with some kind of look at this bit pointer. (A few web pages about the colour red should do it.) This contains all the information about the colour red. The whole universe is there to tell you the clustered structure of thingspace, the extra article is so you can pick out the “red” cluster as opposed to the “turtles” cluster. Whether or not there is any way to get this info into the brain of a blind human is anther question, but the info is there. A complete description of “the sensation of red” is finite. Much of the info could be got into the brain of a blind human, say with a series of talks on optics, vision ect. However the brain is incapable of doing arbitrary format conversions.
Whether or not uncomputable numbers require infinite info is getting into weird subtleties of logic, model theory ect.