Saturday, November 14, 2015

Think About It

     A bat and a ball together cost $1.10. The bat costs a dollar more than the ball. How much does the ball cost?

     Do you have an answer? Most people come up with ten cents. It seems obvious, doesn't it? You don't have to do a lot of math.

     This problem is offered by Philip Tetlock in his book Superforecasting: The Art and Science of Prediction. He offers this simple problem to illustrate one of his central tenets, that we all have two kinds of thinking. System 1 is automatic -- rapid-fire processes that we use all day long to read a book, walk down the street, decide to duck into a coffee shop. System 2 is the realm of conscious thought, when we stop and focus and try to figure something out.

     System 1 always comes first. It is fast and ready with an answer. System 2 is the critic. It looks at the evidence, breaks things down, analyzes what's really going on.

     So now that you know about System 2, is the answer ten cents correct? Ten cents feels right. But it is wrong.

     Here's another problem that Tetlock poses. How many piano tuners are there in Chicago?

     Does the problem seem ridiculous? How would anyone know? Well, start using System 2. Here's a hint: There are about 2.7 million people living in Chicago.

     So how many pianos do you think are in Chicago? A piano is pretty expensive; and a piano wouldn't fit in most city apartments. Maybe one out of a hundred people? But then you have to add in pianos at schools and bars and concert halls. So, maybe two pianos per hundred people? That would give us 54,000 pianos in Chicago.

     How often are pianos tuned? Probably once a year on average. How many pianos can a piano tuner tune in a day? Maybe three or four? We don't know. That's a guess. The average person works about 225 days a year. So a piano tuner can tune somewhere between 675 and 900 pianos a year -- for an average of, let's say 800 pianos. If you have 54,000 tunings, and each tuner does 800, you simply divide 54,000 by 800, and you get 67 piano tuners.

     So how many piano tuners are actually in Chicago? About 70. (The exact number is elusive because of the inaccuracies of listings). So . . . not a bad guess.

     What's the point of all this? We make forecasts, based on incomplete information, pretty much all the time. When should we start our Social Security benefits? To answer that, we have to assess our current situation, estimate what our expenses are going to be, figure out the tax consequences, forecast how long we're going to live.

     If you're going to invest some of your IRA in a mutual fund, you need to forecast what will happen to the American economy over the next several years. If you're faced with a decision about going to college, or taking a new job, or moving to a new neighborhood, how do you decide if it's a good move without considering what the effects are going to be, without forecasting the future?

     Or if a politician is trying to sell you a program, whether it's constructing a wall or offering free college tuition, you need to make a judgement about whether it's credible or not. You can't do that with any accuracy by just making a snap judgment based on System 1. You have to engage System 2. Keep an open mind, consider the evidence, look at the arguments against the question at hand, and be ready to change your mind if your System 1 answer does not hold up to scrutiny. Changing your mind is not a sign of weakness; it's a sign of intelligence.

     Or as Tetlock puts it, if you want to live in the real world, your beliefs are "hypotheses to be tested, not treasures to be protected."

     Finally, the answer? Five cents. Right?

9 comments:

Cindi said...

If one is a builder, who has been building near impossible construction sites for decades,successfully, then if that person said he could build a wall, I would believe him.
If the other person, who has been a habitual liar her entire lifetime (tells her daughter the Benghazi attack was due to terrorists, then tells the public and the survivors of the people who got killed it was due to a fictitious video)then if she told me she was going to give everyone free college, I'd know she was again blowing smoke up my ass.

Simple deduction.

Thanks for sharing, Tom.

Wisewebwoman said...

Much food for thought. We need brain exercises and critical thinking skills more as we age.

Thank you Tom.

XO
WWW

Linda Myers said...

You're right. Good post for me to read on a Saturday morning.

Olga Hebert said...

Well, I knew ten cents wasn't the right answer (any points for that much?) but I had trouble thinking through how to get the correct answer so I guess my system 2 needs some work.

DJan said...

I'm afraid I don't even seem to HAVE a System 2. I don't see why the correct answer isn't ten cents. I'll wait for my mathematician husband to explain it to me. :-)

Meryl Baer said...

The problem often is reading too quickly and jumping to a conclusion based on System 1 thinking.

Tom Sightings said...

If the ball cost 10 cents, then the bat would cost $1.10, and together they would cost $1.20. But if the ball cast 5 cents, then the bat would cost $1.05, and together they would cost $1.10. It's a tenth-grade algebra problem ... one that I got wrong at first as well, which is why I found it so interesting.

rosaria williams said...

Now, this is the kind of thinking we should all engage in, at any age. Great example, btw.

Darkseas said...

Actually, Tom, System 1 and System 2 are only Tetlock's "central tenants" in that they're central to his argument. He has taken this understanding from Daniel Kahneman's book, Thinking Fast and Slow which is a fine summary of a large body of work, a lot of which is Kahneman's own. Kahneman attributes the terms System 1 and Syetem 2 to psychologists Keith Stanovich and Richard West.

Basically, Tetlock's work is related to Systems 1 and 2 mostly in terms of how he uses them for predictions. Besides his current book, he's also known for this work in his 2005 book Expert Political Predictions.

Let's just say you've been very generous with the credit you've given to him.

As for the Algebra I problem:

Let X be the cost of the ball, so
X + $1.00 is the cost of the bat.

Together, both cost $1.10, so

$1.10 = X + (x + $1.00)

The equation reduces down to

$1.10 = 2X + $1.00, so
$.10 = 2X, so
$.05 = X