Note: these posts are copied over from the ‘mathbucket’ section of my old tumblr blog and I haven’t put much effort into this, so there is likely to be context or formatting missing.
The Cognitive Reflection Test came up in the SSC Superforecasters review. I’ve seen it a couple of times before, and it always interests me:
- A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
I always have the same reaction, and I don’t know if it’s common or I’m just the lone idiot with this problem. The ‘obvious wrong answers’ for 2. and 3. are completely unappealing to me (I had to look up 3. to check what the obvious answer was supposed to be). Obviously the machine-widget ratio hasn’t changed, and obviously exponential growth works like exponential growth.
When I see 1., however, I always think ‘oh it’s that bastard bat and ball question again, I know the correct answer but cannot see it’. And I have to stare at it for a minute or so to work it out, slowed down dramatically by the fact that Obvious Wrong Answer is jumping up and down trying to distract me.
I did a maths degree. I have a physics phd. This is not a hard question. Why does this happen?
I know I have a very intuition-heavy style of learning and doing maths. For the second two I have very strong cached intuitions that they map to, whereas I’m really lacking that for the first one for some reason. I mean, I can visualise a line 110 units long, and move another 100-unit line along it until there’s equal space at each end, but it’s not some natural thought for me.
The CRT was designed to assess a specific cognitive ability. It assesses individuals’ ability to suppress an intuitive and spontaneous (“system 1”) wrong answer in favor of a reflective and deliberative (“system 2”) right answer.
Yeah so that definitely isn’t getting tested for me. My System 2 hates maths and has no intention of putting in any effort on this test, but luckily System 1 has internalised the ‘intuitive and spontaneous’ answer for two of the questions for me. I will fail the first question unless my equally strong ‘the answer can’t be that obvious’ intuition fires, but that one makes me seriously worried about my answer to 3. as well.
My inability to internalise the bat and ball thing might be a quirk of my brain, but I’m sceptical of this test in general. It’s extremely vulnerable to having the right cached ideas.