A lot of my reading for the past week or so seems to have been nudging my thoughts in a particular direction, the result of which is, hopefully, enough clarity in my own thinking to be able to elucidate and distill these varied sources into a coherent post. Each of these bits of reading, despite the varied sources, have all touched on the same theme- the limits of human knowledge.
I've been working my way, for a few weeks now, through James Gleick's The Information, which is on the history of, well, information, but more specifically how our understanding of information, how it is quantified and how it is transmitted, has changed through the centuries. But as he moves into the previous century, he touches on, and reminded me of, the work of a pair of thinkers, Godel and Turing, who demonstrated, definitively, that there are indeed upper limits to what we can possibly know, at least in the realms of mathematics and algorithms (and if there are limits there, what, indeed, could be free of limits?)
Then, I ran across an article in this month's Harper's by Alan Lightman, physicist at MIT, writing about the fundamental shift taking place in theoretical physics, from expecting, as they did a few decades ago, to ultimately be able to distill the physical laws of the universe to a single theory, to recognizing, as they do now, that the most fundamental laws of the universe, or rather, the multiverse (which is half the problem), may be irretrievably beyond our reach.
These extended readings, plus a splash of thought here and there, an article or two in Scientific American, a friend's blog post, a late night "discussion" (okay, argument) with an acquaintance, have all been stirring my mind on this topic. And, for whatever reason, it seemed the best way for me to explain my thinking was with a parable. I've never tried my hand at parable writing before, so bear with me...
A young woman lived in a village at the foot of a tall, tall mountain. So far as she knew, despite many attempts by villagers and outsiders, no one had ever reached the summit. One day, she decided she would try. Before she set out, she sought the advice of one of the elders of the village, one who had been witness to many attempts to scale the mountain. She asked the man, "Why has no one been able to scale the mountain?" He replied, "Because a pack of ferocious werewolves inhabit the caves just where the mountain grows steep, and they have torn to shreds anyone who has attempted the climb. You will never reach the peak."
Since she had never seen a werewolf in all her life, she set out anyway, despite the dire warning. She climbed and she climbed, until she reached the place where the mountain grows steep, yet she saw no werewolves, despite seeing a number of caves. However, before long, the climb became impossible, because an incredibly slick ice covered the trail. So she turned around and walked back to the village.
She went directly to the trading post and bought a pair of crampons. When the trader asked what she needed them for, she told him she intended to climb the mountain. Shocked, he said, "But you'll never make it! Just above the tree line live terrible mountain trolls who will eat your flesh. You will never reach the peak."
Since she had never seen a mountain troll in all her life, she set out anyway, despite the dire warning. She passed the slick ice which had stopped her before, and continued her climb. She reached the tree line, but saw no mountain trolls. However, she realized that without trees to grab onto, even the crampons were not enough. So she turned around and walked back to the village.
She went directly to her uncle's house and asked to borrow the ice pick she knew he had in his shed. When her uncle asked what she needed it for, she told him she intended to climb the mountain. Astonished, he said, "But you'll never make it! Where the glacier begins live frost giants who will pulverize you with their fists. You will never reach the peak"
Since she had never seen a frost giant in all her life, she set out anyway, despite the dire warning. She passed the slick ice and then the tree line and came to the foot of the glacier, but saw no frost giants. However, she realized that even with the ice pick and crampons, the glacier was too slick to climb, for one slip would be certain death. So she turned around and walked back to the village.
She went directly to a friend who kept horses and asked to borrow a length of rope. When her friend asked what she needed it for, she told her that she intended to climb the mountain. Terrified, her friend said, "But you'll never make it! The sky god forbids anyone from climbing to the peak, for that is his realm. He will strike you down with lighting for climbing so high. You will never reach the peak."
Since she had never seen a god in all her life, she set out anyway, despite the dire warning. She climbed past every point which she had been told she would never pass, and began to climb the glacier. With the help of the crampons, ice pick and rope, she climbed very far, and climbed for a very long time, but she never saw a sky god, heard no thunder, nor saw any lightning. However, she eventually reached a wall of ice many hundreds of feet high, much farther than her rope was long, and certainly farther than she could ever hope to toss one anyway.
Saddened by her realization that she would never reach the peak, she began the long climb down. Turning, she looked out across the vast landscape beneath her, and up into the stars above, and realized that very few had seen the world from this vantage. She let the sight take her breath for a moment, and then retraced her steps to the village.
Since she had been gone much longer than any of her previous excursions, some of the villagers had set out in search of her, though they did not have to go far because she met them just outside the gates of the village. Among them were the elder, the trader, her uncle and her friend. When they asked her, "Did you reach the peak?" she quietly shook her head.
"See?" they said. "We told you you'd never reach the peak. We were right all along."
There are fundamental limits to human knowledge. Kurt Godel showed that any mathematics which is sufficiently complex to include arithmetic is fundamentally inconsistent or incomplete. Alan Turing showed that the same was true of algorithms, i.e. computers. Werner Heisenberg showed that we cannot know both a particles position and momentum simultaneously. Modern physics is learning that we may very well live in one universe among an infinity of universes, and the laws governing that multiverse will forever remain unknowable to us.
But does this mean that anything goes? Can we thus be intellectually and morally sound if we populate our mountain with monsters and deities? Just because there are things that we can't know, does that mean we know nothing?
There is nothing more important to a seeker of knowledge than the wisdom and humility to say, when necessary, "I don't know." This is what set Socrates and Siddhartha Gautama leagues ahead of their contemporaries, and worlds ahead of religious demagogues, prophets and other liars. But pretending that the limit of our knowledge is just beyond the point from which we begin is foolishness and cowardice.
Perhaps one more example will make this clearer. The number pi, 3.1415926535897932384626 4338327950288... which is the ratio of a circle's circumference to its diameter, is an infinite string of random digits. Despite having been calculated to tens of trillions of decimal places, no repetition, recurring sequence or end is in sight.
So if someone asked you, "What do you think the trillionth trillionth trillionth digit of pi is?" you could go with "7" or "4" or "0." But, since no one actually knows what that digit is, since no one could possibly know what that digit would be, would you be remiss to say "tangerine"?
I think you would be. Just because we don't know the exact answer to many, many questions, and we never will know the answer to some of them, does not mean that we can't eliminate some, often many, possibilities.
Many people wish to reserve the right to say "tangerine," or "God" or "magic" or "miracle" or "fairies" or "mystical energies" whenever they are faced with a question they don't know the answer to or, more often these days, don't wish to know the answer to. Ironically, I think this stems primarily from our arrogant assumption that we have a right to know everything there is to know. It is in our nature to be terrified of doubt and skepticism, because they represent the unknown, the shadowy stalker just outside the firelight that kept our ancestors awake at night. Answers are comforting. They make us feel powerful and special. (Especially when those answers tell us we are special.)
But we are fooling ourselves. There is much we don't know, and never will. Still though, there is a lot more wisdom, when faced with a devilish mathematician, to say, "I don't know what the umpteenth digit of pi is, but I bet it is somewhere between zero and nine," than settling, smugly, on "Tangerine."