Gödel, Escher, Bach: an Eternal Golden Braid

Okay, this next one, Ringo Lebowski, awesome name by the way, says, "Please do a panel," five stars.

"Please bring some of these guests together for a roundtable-style dialogue, maybe as a live event." And then goes on to say that mo- "Both seasons of the show make for an excellent primer on artificial intelligence and the philosophy of the mind." And then goes on to, to recommend some other things, which is really cool and which I'm excited about, um, is asking us to look into the analytic philosophy books by Gödel, Escher, Bach, and Darwin's Dangerous Idea.

Uh, we will do just that.

It says, "Discuss them on the show." We will do all these things.

But if all math is is proof, and if all a proof does is build upon indisputable axioms in a purely logical way, and if every proof is a question with only two answers, yes or no, true or false, then how can any question be ambiguous or difficult to understand? All you need to do is remember the correct axioms or proofs and apply them in the right way at the right time.

The cognitive and computer scientist Douglas Hofstadter, best known for his concept of strange loops as explored in his tome Girdle Escher Bach, An Eternal Golden Braid, gave one answer to this question in a 2012 essay, which went lightly viral over the past year.

In response to a question from a reader of the journal Mathematics in School about the experience of being a distinguished mathematician, he first demurred, protesting his mathematical bona fides.

And then he went further, writing of the traumatic experience of waking up to his own mathematical inadequacy and limitation.

If there is one, it will not stay inside computers.

Gradual progress can get you to a destination, hopefully we have all read our Godel Escher Bach, and at some point in this gradual, but accelerating, progress any particular dangerous capability often shows up rapidly, in that it suddenly will feel different in kind.

A lot of tasks have O-ring elements where solving the previously weakest link or getting a threshold of reliability snaps them into place or allows you to start hill climbing.

Via Tyler Cowen, Catherine Bindley at Wall Street Journal makes a similar point this week.

I'm, I'm quite a bit older than you, so I think [chuckles] it came out when I was in grad school or something.

The book that played a similar role for me was Gödel, Escher, Bach when I was in high school.

And but I'm curious, just a quick question, like, do you feel like Penrose's thesis in that book is actually correct, or is it just something that sparked your interest in-

The one that [clears throat] human minds can do non-computational things?