By N.S. Palmer
“Metaphysics is the finding of bad reasons for what we believe on instinct.”
It’s not poetic, nor even grammatically correct, but it’s a question that everyone eventually asks: “Why are we all so messed up?”
I can’t presume to offer the complete answer, but I do have a little piece of it to share. It has to do with epistemology.
Epistemology. That’s the study of how we acquire and test our knowledge, as well as how our knowledge is structured and what it means “to know something.”
For example, suppose I say that “I know there is an elephant in the closet.” What exactly am I saying? Common sense gives a threefold answer:
- I have adequate evidence to believe that there is an elephant in the closet. In other words, my belief is justified.
- There is, in fact, an elephant in the closet. In other words, my belief is true.
- I believe that there is an elephant in the closet. In other words, I really do believe what I claim.
Those three criteria are embodied in the usual definition of knowledge as “justified true belief.”
However, most situations are far more complicated than just having an elephant in your closet — however troublesome that might be. If you suspect that you have an elephant in your closet, it’s easy to find out. Just open the door and look. Then you know.
Harder than having an elephant in your closet
But consider a different kind of situation. This is a puzzle given by New York Times columnist John Tierney:
My mother presented me with that puzzle after our weekly family dinner last Sunday night. Such are dinners at Mom and Dad’s house: It’s like being on a quiz show, except that you get a home-cooked meal and there are no cash prizes. Sitting at the dinner table are three medical doctors, an art historian, an entomologist-biochemist who looks like movie actress Anne Hathaway, a computer expert, a golf pro, a four-year-old prodigy, and me. Every one of us secretly believes that he or she is the smartest, and is determined to prove it. Over chicken and pasta, the conversation leaps from obscure diseases to medieval manuscripts, the life cycles of bugs, computer software, and the latest doings of Tiger Woods. Over dessert, an impromptu lesson in Spanish, German, or Hebrew for the boy. But I digress.
(Note: If you want to have a go at Tierney’s puzzle on your own, stop reading here. I’m going to start talking about the solution.)
My mother wanted to know the solution to the puzzle, which The New York Times columnist avowed had stumped him. She gave the puzzle to me because I’m the mathematics geek of the clan, am single, and therefore have the most free time. The figures looked at first glance like ancient numerals, perhaps from the Babylonian, Chinese, or Indian number systems. I wasn’t sure which. When I got home and looked them up, I found that they weren’t ancient numerals.
Then I latched onto the last word of the hint in the puzzle description: “knots.” An area of mathematics called “knot theory” investigates, among other things, what happens when you manipulate knot-like geometrical figures in certain ways. I didn’t know much about knot theory, and it wasn’t a perfect match anyway, but it was close enough for me to theorize that:
- The second and third figures on row 1 were rotations and twists of the first figure.
- The fifth figure on row 1 was a rotation of the fourth figure.
I concluded that there were two series of three figures each. For the answer, I needed a figure on row 2 that was a rotation or twist of the fourth and fifth figures on row 1:
- The fourth figure was a triangle pointing downward.
- The fifth figure was a horizontal line, as if the triangle had been rotated toward us in 3-D space and we were seeing it from the side.
Rotating the figure one more time, toward us in 3-D space, gives us a triangle pointing upward. That’s answer (c), which I triumphantly emailed to my mother and the other family members who had been present at dinner.
The Web to the rescue
I decided to check the Web to see if Tierney had posted an answer. However, the Web version of his puzzle included some vital information that wasn’t in the printed clipping:
The most important new information was that row 1 consisted not of five figures, but of four figures and a blank. And the horizontal line in fifth place, which didn’t look too different on the newspaper clipping, was clearly a different color on the Web page.
I took another look at the hint. It says something about mirroring, also part of knot theory. The next solution was easy. The first figure on row 1 is the numeral 1 paired with its mirror image. The second is the numeral 3 paired with its mirror image, the third is 5, and the fourth is 7. So the series is 1-3-5-7, consecutive odd numbers. The next figure should be the numeral 9 paired with its mirror image. And that makes the answer either (a) or (d), assuming that Tierney drew the nines in an eccentric way.
Well, duh. That wasn’t hard.
One of my brothers was unimpressed both with the puzzle and with my two solutions. He emailed three more puzzles that he thought might be more challenging:
And a second puzzle:
And a third puzzle:
Yes, Virginia, there really is a point to all this.
The point of the discussion is this. Tierney’s puzzle deals with a very limited set of simple geometrical facts. It asks the reader to explain those facts and to predict another very simple geometrical fact. But even in that simple situation, different answers are possible. The answer you get depends not merely on the evidence, but on your background and interests. It also depends crucially on which pieces of evidence catch your attention.
The same applies to my brother Steve’s puzzles. For most people, the answer to puzzle 1 is obviously “B” because it would complete a series of progressively larger squares. Likewise in puzzle 2, the spatula is the only item that isn’t an animal, while in puzzle 3, the television character of “Barney” is the only item that isn’t a dictator.
However, other interpretations are possible. In puzzle 3, for example, the Soviet dictator Josef Stalin “does not belong” because he’s the only person not waving at least one hand. The fact that different solutions are possible makes it hard to design such puzzles for standardized tests, such as college aptitude tests. What such puzzles really measure is test-takers’ ability to find the solution that the test-designers expect. Truly creative people sometimes score badly on such tests because their solutions, though logical, are unexpected* and therefore “wrong.”
And all those puzzles represent very simple situations with very limited data sets that you evaluate to get a solution. Real-life situations involve hundreds or thousands of pieces of information that are connected, or not, in ways that are often unclear.
Real-life situations are even more prone to have multiple, equally-logical explanations. Which explanation you choose depends on your prior assumptions about the situation, about people, and about how the world works. It depends crucially on which pieces of evidence you spotlight, which pieces you ignore, and which pieces you outright reject. For example:
- Conservative economists who look in good faith at official economic data think it shows clearly that we must give more tax cuts to the rich and get rid of regulations that inconvenience giant corporations.
- Liberal economists who look in good faith at official economic data think it shows clearly that we must increase taxes on the rich and more aggressively regulate corporate misbehaviour.
- In the Middle Ages, doctors liked to treat illnesses with leeches. They noted that people treated with leeches often got better. But so did people not treated with leeches, a fact which the doctors’ theory caused them to discount in evaluating the merits of leech therapy.
- Scientists who contemplate the symmetry and elegance of the physical universe often get a feeling of transcendence. They conclude that it’s because the physical universe is all that exists and is just wonderful.
- Christians who contemplate the works of God and read the New Testament get a feeling of transcendence. They conclude that it’s because God is infinitely good, Jesus is right there with him, and that only Christians can go to Heaven.
- Muslims who contemplate the works of God and read the Qu’ran get a feeling of transcendence. They conclude that it’s because Allah is running things, Mohammed was right, and that only Muslims can go to Heaven.
A little intellectual humility
What it really comes down to is this: Most of what we consider our “knowledge” either consists of, or is based on, WAGs (wild-a**ed guesses) that we simply follow until something better comes along.
It’s relatively harmless until our WAGs combine with our arrogance to make us demonize and try to destroy people who disagree with us. What we need is a touch of humility: The awareness that however sure we are that we’re right, we still might be wrong. We should accordingly proceed with caution, giving due respect to the viewpoints, rights, lives — and the feelings — of others.
Of course, I might be wrong about that. But I’m sticking with it until something better comes along.
*There is a relevant story about Nobel laureate physicist Niels Bohr, a pioneer of 20th-century atomic theory. When Bohr was a student, a professor supposedly gave the following problem on a test: “Use a barometer to determine the height of a tall building.” Obviously, the professor was expecting students to solve the problem by measuring the atmospheric pressure at the bottom and top of the building, but Bohr had a different solution. “Go to the top of the building. Tie a long piece of string to the barometer. Lower it to the ground. Measure the amount of string that you lowered over the side of the building, then add its length to the height of the barometer. The sum is the height of the building.” It’s not the expected answer, but it’s a correct answer.
Copyright 2009 by N.S. Palmer. May be reproduced as long as byline, copyright notice, and URL (http://www.ashesblog.com) are included.