Tuesday, September 23, 2003

Teacher, My Brain Has Halted

Are we smart enough to understand the universe? (This is another thought inspired by Evelyn Fox Keller's book Making Sense of Life.) This will sound obvious, but our brains are part of the universe, so it's an open question of whether we can reflectively understand it. It's almost an article of faith among scientists that any phenomenon can be explained, given enough research, but there's no reason to necessarily believe that. There very well may be phenomena more complicated than our brains can comprehend. Why not?

In fact, if we turn to Turing Machines, we know that there is an infinity of functions that TMs cannot compute. The most famous, the Halting problem, is precisely a reflective problem of understanding oneself, of predicting what a Turing Machine will do when confronted with a question about a Turing Machine. Unknowable. Could it be that the problem of consciousness is our Halting Problem? We all seem to assume, albeit in a completely unspoken way, that we will eventually crack the code of consciousness; sure, it's a tough problem, but as technology improves, we'll get it sooner or later.

But maybe not. Maybe the human brain -- the human mind -- is structurally incapable of answering questions about itself. There's certainly strong reason to believe that in general computational models have limited reflective ability, and certainly if you believe that human brains are Turing Machines (you chump!), you must acknowledge uncomputable functions. The universe is a big place, and it might just be bigger than our minds will ever get.