Here’s a simple arithmetic question: A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost
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When I read the opening problem I carefully didn't scroll down, first thought ten cents then did the "reverse calculation" and saw that wasn't right, so I grabbed a pad and wrote it out algebraically. I used B for Bat and L for Ball. B=L+100 and B+L=110. So L+100+L=110. So 2L=110-100, 2L=10, and L=5.
Then after reading the rest of it, I'm afraid I revealed myself to be, in fact, unintelligent, as I was apparently too stupid to accept my first but obviously wrong thought. Now my brain really hurts.
And I'd heard the pond question way back in elementary school. Got it right then too, after some thought.
It is that the Professor is describing what can be best expressed through math, but we take shortcuts by constructing narratives (stories) out of it. Check this out:
Had a conversation about this just this evening actually, about the usefulness of studies of the brain and/or psychology--the smart person who studies these fields should learn to recognise the common pitfalls and biases in their own thinking, not just in others. I find whenever I read a book about brain workings ("The Neurotourist" being the latest one, and much recommended) I check myself and become hyper aware all the bloody time. Dunno whether it makes me more accurate arriving at "correct" answers, but it definitely takes me longer.
I had no problems with the arithmetic questions, BTW ;)
Bat = $1.10 + ($1.00 - Bat) Bat = $2.10 - Bat 2 x Bat = $2.10 Bat = $2.10/2 Bat = $1.05 Ball = Bat - $1.00 Ball = $1.05 - $1.00 Ball = $0.05
Sounds about right. Or to put it into words, you have to evenly split the difference between the bat and the ball for the difference to come out as $1.
Comments 4
When I read the opening problem I carefully didn't scroll down, first thought ten cents then did the "reverse calculation" and saw that wasn't right, so I grabbed a pad and wrote it out algebraically. I used B for Bat and L for Ball. B=L+100 and B+L=110. So L+100+L=110. So 2L=110-100, 2L=10, and L=5.
Then after reading the rest of it, I'm afraid I revealed myself to be, in fact, unintelligent, as I was apparently too stupid to accept my first but obviously wrong thought. Now my brain really hurts.
And I'd heard the pond question way back in elementary school. Got it right then too, after some thought.
But an interesting read anyway. ;-)
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It is that the Professor is describing what can be best expressed through math, but we take shortcuts by constructing narratives (stories) out of it. Check this out:
http://www.quora.com/Mathematics/What-is-it-like-to-have-an-understanding-of-very-advanced-mathematics/answers/873950
Turns out, there is only a very tiny number of problems that can be expressed well with mathematics, let alone be solvable.
-Qaexl
Reply
I had no problems with the arithmetic questions, BTW ;)
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Bat + Ball = $1.10
Bat - Ball = $1.00
---
Bat = $1.10 - Ball
-Ball = $1.00 - Bat
So:
Bat = $1.10 + ($1.00 - Bat)
Bat = $2.10 - Bat
2 x Bat = $2.10
Bat = $2.10/2
Bat = $1.05
Ball = Bat - $1.00
Ball = $1.05 - $1.00
Ball = $0.05
Sounds about right. Or to put it into words, you have to evenly split the difference between the bat and the ball for the difference to come out as $1.
-Qaexl
Reply
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