An Accurate Guess Is Still Just A Guess
“Will you teach me something that is college-level?” my ambitious and competetive soon-to-be third grader requested.
I was reading the Sunday paper so I tried to do a little dodging. “You have to learn all the elementary stuff before you learn the college stuff. That’s why we go to elementary school first.” Then I added a classic line, “Go read a book. Reading anything will help you prepare for college.”
Yes, I was dropping the ball.
Blake contined to prod me for some type of brain-food activity. I noticed a funky multi-colored bouncy ball on the table. It reminded me of a movie Israel and I just watched, Match Point. I only need to tell you that Woody Allen directed it to give you an idea of what type of movie it was.
The story revolves around the luck factor. In tennis, there are times when your ball hits the net and bounces straight up. Where it goes from there has nothing to do with your skill, but pure luck. Chance.
As much as we like to factor our skill and talent into our successes, we often fail to note the innumerable avenues on which luck travels around us.
The bouncy ball on our table provided me an idea for an activity to occupy Blake. I told him to get a piece of paper and a pen. He dashed around the room in exhilerated bliss. He came back with the items. I handed him the ball and told him to let it drop straight down onto a line in the floor that he chooses. He was then to record the direction the ball headed after the first bounce. He would do this ten times. Here are the results:
1. Right
2. Under the line.
3. Right.
4. Under.
5. Under.
6. Right.
7. Under.
8. Over the line.
9. Over.
10. Over.
I asked Blake if he saw any kind of pattern in the direction the ball went. He said, “Not completey. But it is starting to go over the line all of a sudden!”
He was excited, as if he was onto something.
“Do you think there is something causing the ball to go in a certain direction? Maybe the way your hand drops it, or a crease where it hits the floor?” I asked.
Those possibilities didn’t interest him. He felt there was something within him that was predicting the direction of the ball, but he didn’t have his finger on it yet. This is a topic I’ve been wanting to experiment with Blake on because he thinks he can make accurate predictions based on his feelings.
He’s often asked me questions like, “Mom, what do you think the percentage is of people who go to college?”
My reply is something like, “Well, I don’t know. I’ve never paid attention to that statistic so I’d have to look it up.”
And he comes back with “I think it is . . . 60 percent. No, 63! That’s it! It’s 63 percent.”
“Interesting,” I answer back. “And what information do you base your answer on?”
“It just feels like that’s what it is.”
“Is that an accurate predictor? Your feelings of what it is?”
“Yes.”
No matter how many times I’ve explained to Blake that his feelings can’t give him an accurate answer at that type of question, he doesn’t get it yet. I realized this is something I’m going to have to show him.
So I changed the direction of our experiment with the ball. I turned the paper over to the other side. He was now going to predict which direction the ball would bounce, then drop the ball, and I would record whether his guesses were right or wrong.
Here are the results:
1. Wrong
2. Right
3. Wrong
4. Wrong
5. Right
6. Right
7. Wrong
8. Right
10. Wrong
Before showing him the results on paper, I asked him if he thought he had been right most of the time or wrong. He said, “I think I was mostly right.” This surprised me because we spent a lot of time in the middle of the experiment talking about the third and fourth tries being wrong. And the last try was also wrong. Still, this didn’t give him the lasting impression of having mostly guessed wrong. At least he has confidence in his abilities!
I showed him the paper and added them up. Six wrong guesses and four right guesses.
I then asked him, “How many possibilities were there?” His answer was four: Over the line, under the line, right or left.
My next question was, “What if this activity had 100 possibilities? Would that have made it harder or easier to make a correct guess?”
He answered, “Harder.”
“This activity only had four possibilities, making it easier to guess correctly just by chance. Still, you guessed wrong more than you guessed right. Do you think there is a pattern here for where the ball goes, or do you think it is all random chance, both where the ball goes and whether your guess is right or not?”
It was interesting because he made the connection, and yet he still wanted to hold onto the idea that he had some ability to predict the direction of the ball.
In Michael Shermer’s book, How We Believe, Shermer shared his hypothesis of a human Belief Engine. “Humans evolved to be skilled pattern-seeking creatures. Those who were best at finding patterns (standing upwind of game animals is bad for the hunt, cow manure is good for the crops) left behind the most offspring. We are their descendants. The problem in seeking and finding patterns is knowing which ones are meaningful and which ones are not.”
Blake made four “hits,” as Shermer calls them, or in other words, Blake made four accurate guesses when he was making his predictions about the balls. Sometimes it only takes one accidental hit for someone to think they are onto something. I explained to Blake that this is why some fortune-tellers, astrologists, self-proclaimed prophets and the like, think they have the power to predict. They got a hit. A lucky guess. Sometimes they get many hits. But how many misses do they also get in the process?
This activity with Blake was just a seed. I think it will take a few similar experiences such as this before he gets it. Shermer stated the following about the tendency to think the way Blake does:
It is normal. It is in all of us. Stuart Vyse shows, for example, that superstition is not a form of psychopathology or abnormal behavior; it is not limited to traditional cultures; it is not restricted to race, religion, or nationality; nor is it only a product of people of low intelligence or lacking in education. There is variance in magical thinking among individuals, or course, but all humans posses it because it is part of our nature, built into our neuronal mainframe. We do not live in a Pleistocene environment, but our minds were built there and often function as if we do.
The good news is that the more answers we have to life’s mysteries, the less we rely on superstition and errors in our pattern-seeking. For this reason, my focus in raising my children has less to do with telliing them there is no god and more to do with teaching them accurate ways of finding answers.
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July 24th, 2006 @ 5:30 pm
I LOVE Shermer. And I think the experiment you and Blake conducted (and the resulting discussion) is exactly how I’d like to present such analytical thought processes to our girls.
Also, excellent illustration of hits and misses as it relates to psychics. No matter how I try to explain that to friends who want to believe, they still persist in wanting to believe. Which is what the psychics count on, of course.
July 24th, 2006 @ 11:06 pm
Awesome Post, Noelle.
I love Shermer too.
Since leaving the mormom church, I’ve become much more logically-based, relying less and less on feelings being the basis for how I solve my problems or look at the world. It’s better way to live as I am happier, calmer, and better at living than I was before.
July 25th, 2006 @ 7:42 am
An aspect of superstitious thinking that relates to this is how people who feel their prayers or feelings or thoughts alter the world around them crash harder when they ‘fail’ at it than people who realize the limitations of their influence.
My friend has needed a car badly for a while now – just two days after he put a down payment on one, another car was offered to him for free. Since the deposit is non-refundable (and he’s nearly broke), he’s beat himself up over it – feeling he ‘should have known’, even citing that his sister-in-law had a dream that predicted the second car.
Frustrating – yes. Against reasonable odds – thus ‘unlucky’ – yes. But a product of personal failure? NO!
How wonderful that you managed to introduce the subject to Blake, especially after noticing a tendency to feel he can control things outside of his control.
Positive attitude and confidence does indeed tend to bend things our way – because that behavior is appealing to others and holds back our own discouragement. There is no loss in the world at this realization. You gain unpolluted expectations – and save yourself suffering when things don’t go your way.
Another friend of mine is dying in the hospital – she is 55, and it came as a surprise to everyone who knows her. There is little that can be done, we are informed by her family, except they are asking for prayer. The people who are praying for her have described their feelings about it – saying how unfair it is that my friend should die. One has told me how much this has ‘shaken her faith’ because our friend is such a good person. When reality encroaches on people with a supernatural worldview – they suffer more greatly because they feel betrayed by their magic.
How much less suffering would be in the world if people were less likely to attribute supernatural causes, and spent their time learning how things really work?
July 25th, 2006 @ 8:08 am
Interesting. If you don’t mind my siding with your son briefly, I find it quite interesting that he was right 40% of the time (and you seemed to have left off result number 9–I assume it was “wrong” as well?)
Given that there were 4 possible outcomes, and you measured in a binomial fashion (“right” or “wrong”) one would expect, in the long term, that his correctness would be 25%. That is, there is a 1 in 4 chance of getting it “right” and a 3 in 4 chance of being wrong.
Your son, at least in the small sampling “Beat the odds.” Good on him!
Steve
July 25th, 2006 @ 10:25 am
Like mothergoosemouse said, psychics are a good illustration of this kind of thing.
Cold reading: He also knows that for every several claims he makes about you that you reject as being inaccurate, he will make one that meets with your approval; and he knows that you are likely to remember the hits he makes and forget the misses.
…
Shermer’s books are really interesting. I especially liked his book Why People Believe Weird Things.
July 28th, 2006 @ 8:48 am
More in depth on the experiment itself:
The four possible outcomes are not known to be equally likely outcomes. The ball may well have bounced some ways more often than others due to the layout of the floor, the angle of the drop, increasing fatigue of the dropper, inferring patterns from previous drops (legitimate, as it is a fallible human hand doing the dropping)- – and the affect of announcing the prediction rather than writing it down or otherwise keeping unknown to the dropper until the ball has dropped. As well as other variables – lighting, the ball behaving differently with use/warmth, other activity in the area, distraction, etc.
That Blake was right 40% of the time rather than 25%, is inconsequential. Played out, he could have spans that he was right 100% of the time, but over the course of a thousand tries (rather than 10) he would most likely be on the 25% mark.
Beating the odds by 15%, on a test of 10 trials, does little to establish a base line – it showed that he wasn’t right ‘most of the time’ as he had believed. He could have been 100% accurate on one trial, and it wouldn’t have been a significant predictor of ‘ability’ or future success.
That any of us exist means a single sperm had to beat odds of one in several million. As Bill Bryson said in A Short History Of Nearly Everything – ‘we are all lottery winners’.
July 30th, 2006 @ 9:34 pm
Ron:
Good points. It’s why you see I wrote things like “at least in the small sampling” and “one would expect, in the long term.”
My point was simply that one shouldn’t attempt to teach a valuable life lesson with only 10 samples, and not use “most of the time” as a measure of success when in the long run one could only expect 1 in 4 guesses to be correct.
I was actually quite interested, however, in the fact that in the first set of data presented the ball never went “left.” Yes, there are tons of explanations for that, from the spin of the hand to the slope of the floor. It just seems to be a far more interesting question “why did it not go left?” And actually, if we move the odds to 1 in 3 of guessing it correctly, we find a much closer match (33 1/3 % compared to 40%)
Hey, this is a blog, not a peer reviewed statistical journal.
August 4th, 2006 @ 7:11 am
[...] She has another post I just read that I found really good, called “An Accurate Guess is Still Just a Guess” where she describes a lesson for her son in reasoning, the effect of chance on our understanding of the world, and the ingrained desire we humans have to find patterns in our reality where patterns may not exist. Her blog is deffinitely going in my links! [...]
August 5th, 2006 @ 4:36 pm
Cool thing to do with your kid, but remember that some lessons just won’t “take” until your kid has the cognitive skills needed to deal with it. Just be patient….
As far as the ball not bouncing left… That might have just been the way he happened to be gripping and releasing the ball.