Absurdly Driven looks at the world of business with a skeptical eye and a firmly rooted tongue in cheek. I have a friend who's a world-
Absurdly Driven looks at the world of business with a skeptical eye and a firmly rooted tongue in cheek.
I have a friend who’s a world-renowned mathematician.
He doesn’t think like me. Or you. Or, indeed, anyone else I know.
This is a good thing — certainly for him. Especially as mathematicians of one sort or another seem to be currently dominating the world.
But brilliance can have its occasional drawbacks.
I was moved to involuntary giggles, therefore, on reading a new piece of research emerging from the the University of Geneva in Switzerland and the University of Bourgogne Franche-Comté in France.
On the one hand, they had real normal adults with a standard university qualification. On the other were the brilliant mathematicians who likely had so many qualifications they couldn’t count them all.
The idea was to see if each group’s knowledge about the world would lead them to solve problems in their own ways.
Math problems. Math problems normally given to fifth-graders.
You might think the mathematicians would find these things insultingly easy.
Here’s one of the problems:
Sarah has 14 animals: cats and dogs. Mehdi has two cats fewer than Sarah, and as many dogs. How many animals does Mehdi have?
When Lazy Smurf climbs onto a table, he attains 14 cm. Grumpy Smurf is 2 cm shorter than Lazy Smurf, and he climbs onto the same table. What height does Grumpy Smurf attain?
The former is an example of numbers that can be seen as sets. In the latter case, these numbers can be seen on a horizontal or vertical axis.
These researchers wanted to make things fair. Very fair.
The gave both groups 12 such problems. They also gave them the answers.
All the researchees had to do was decide whether the answer was correct. Or whether the problem simply had no solution.
Now for the results.
I cannot possibly replicate the obvious excitement of one of the researchers, Hippolyte Gros. Here are (some of) his words:
One out of four times, the experts thought there was no solution to the problem even though it was of primary school level!
It’s reassuring that a scientist can exclaim with such glee.
Here were the bald figures. The normal adults got 82 percent of the axis-type questions right. Their performance dipped painfully with the sets-type questions. A piffling 47 percent of them got these right.
The math geniuses did quite well on the axis-type questions. A fulsome 95 percent saw the correct answers.
Oh, but when it came to questions such as Sarah and Mehdi’s cats and dogs, 24 percent of them thought this was an impossible problem.
Yes, subtracting 2 from 14 is, apparently, impossible.
Why was this? Other than the mathematicians were likely insulted on being forced to consider cats and dogs.
Another of the researchers, Jean-Pierre Thibaut, said that the Smurf-type questions inspire instinctive answers. It’s a straight subtraction.
However, he explained:
We need to change perspective for the problems describing sets, where we automatically try and work out the individual value of each mentioned subset, which is impossible to do. For instance, in the problem with animals, we look to calculate the number of dogs that Sarah has, which is impossible, whereas the calculation 14 – 2 = 12 provides the solution directly.
Clearly, though, one should feel uplifted that the math geniuses did appreciably better than the human proletariat. But come on, you’re a math genius. This is like asking a soccer player to kick a ball in the air.
Sometimes, though, we’re all blinded by the light. The light that shines inside our heads and tells us how clever we are and that the way we see the world is correct.
It’s worth occasionally dimming that light and trying to see what’s really there, what’s truly relevant and what’s actually being asked.
Oh, and if you want your kids to be good at math, make them study music.
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