Loops, pain and Gödel

A recent Radiolab episode brought some interesting things together by exploring loops, repetitions, and self-referencing phenomena.

Among other things, they told the story of Melanie Thernstrom (The Pain Chronicles) who, in trying to manage her pain, investigated the self-inflicted pain of religious rites. She later did some work with neuroscientist Sean Mackey.  Mackey had seen how pain can be affected by changes in ones state of mind and he considered that if an individual could somehow watch the pain signaling activity, perhaps they could control it.  “All of our pain is in our head,” he says definitively. Pain is a conversation between the brain and the body.

Mackey set Melanie up in an MRI and gave her access to a view of her brain.  The part of the brain she watched is known to be involved with pain perception, and with “turning pain up and down.”  To make what she was seeing comprehensible, the brain activity was illustrated with a visual metaphor, a fire. Melanie describes her effort, her failed attempts, and how she was finally able to do it.  But she can’t quite do it without the visual feedback that she was getting from her work with Mackey.  It seems that something significant is gained by being able to look at what the brain (or the body) is doing, and for this to be something we can understand.

It was the visual component of this loop that I found most intriguing – the fact that one of the ways we can gain access to an unconsious internal mechanism is by representing it.  This is the way I think about mathematics – as the represention of internal mechanisms that allows our conscious participation in how the body can know, anything.

Steve Strogatz adds a specifically mathematical experience to this episode with some talk about Gödel’s Incompleteness Theorem. He described how mathematicians and philosophers struggled with what has come to be called the barber paradox, or the statement that in a particular town, the barber shaves everyone who doesn’t shave himself.  Can the barber shave himself?  Who shaves him?  Russell teased this kind of problem out of set theory (as if it was an unfortunate tangle) but later Gödel was lured more deeply into these paradoxical loops.  He probed mind boggling claims like: “This statement is a lie.”  If it’s true then it’s false and if it’s false then it’s true.  A careful analysis of the problem led him to his famous Incompleteness Theorem, definitively establishing that certain things in mathematics are simply undecidable. And so there may be something that is true but cannot actually be proven.

It was suggested that Gödel found this liberating because, as Strogatz states it, “There was profound mystery forever.”  All wasn’t mechanical.

Janna Levin,who recently wrote a  book about Gödel, also spoke on the program. I found an interview with her online where she says some interesting things.  Like this for example:

We mine our own mind, and that’s how we uncover these seemingly external truths. Gödel only believed in the mind part. He wasn’t so sure about the external reality part, and he often said things like — I think I even saw it on the Simply Gödel website – that “I don’t believe in natural science.” And I think what he meant by that is he just wasn’t sure about external reality. He was really doubtful of it, which is so strange. But he really believed that mathematical concepts existed, they were real, and that the mind migrated to this pure, platonic reality, and migrated over reincarnations. He really believed in transmigration of the soul. So he was pretty out there.

When she talks about the choices she made for how to write her story of Gödel and his insight she says:

I could do more to create an impact of that idea, on the sense of the feeling that hits you in your solar plexus, of what it means to know something’s true, but can’t prove it to be true. And to only be able to approach truth, and yet for it to be your obsession.

 

We mine our own mind, and that’s how we uncover these seemingly external truths. Gödel only believed in the mind part. He wasn’t so sure about the external reality part……………It’s probably all the same thing…