## Resisting intuition

28 Dec, 2012 at 13:40 | Posted in Varia | 6 Comments

One of the main functions of System 2 is to monitor and control thoughts and actions “suggested” by System 1 … For an example, here is a simple puzzle. Do not try to solve it but listen to your intuition:

A bat and ball cost \$1.10.

The bat costs one dollar more than the ball.

How much does the ball cost? A number came to your mind. The number, of course, is 10: 10 cents. The distinctive mark of this easy puzzle is that it evokes an answer that is intuitive, appealing, and wrong … The right answer is 5 cents.

1. If the bat and the ball cost \$1.10 my intuition tells me this must be a very old problem. 🙂

2. This is similar to the thinking that keeps people from understanding closed-system arithmetic…and the money system…there is a feedback loop that affects the solution. The example provided here is one of the simplest examples. Because the total is known, the solution is always a matter of distribution.

It also demonstrates why students in algebra tend to not like word problems. The solution requires solving two equations with two unknowns (or trial and error).

x+y=1.1; x=cost of the bat, y=cost of the ball.
y=x+1; substituting for y…
x+(x+1)=1.1;
2x=0.1;
x=0.05; the cost of the ball
y=1.05; the cost of the bat

I apologize in advance if I am pointing out the obvious.

• Obvious maybe, but requires “rigorous” thinking. Kahneman showed about we typically use two modes of thinking, snap using intuition and sharp using calculation. We save time using snap judgment and only resort to rigorous thinking when it seems called for. However, it turns out that most people are not so good at making this distinction correctly and err by rushing to judgment. On the other hand, we probably all know a few people that waste a lot of time on rigor they don’t really need given the circumstances.

• “[W]e probably all know a few people that waste a lot of time on rigor they don’t really need given the circumstances” – we certainly do, and that’s something not only Kahneman has emphasized, but also e.g. Gerd Gigerenzer (https://larspsyll.wordpress.com/2012/04/16/what-can-economists-know/)

3. hmm.. personally I think intuition is underrated, I mean is this the norm or an edge case.

4. if you want feedback try the Parrondo paradox!