Check Your Reflection

Opening Statements

June 2008 Issue
By G.M. Filisko

Want to compare yourself to the judges? Take the cognitive reflection test and see how well you score. If you get these right, you’re cognitive; get them wrong and you’re intuitive; cheat by looking at the answers under the sidebar heading and you’re human.

A bat and a ball cost $1.10 total. The bat costs $1.00 more than the ball. How much does the ball cost?
If it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?
In a lake, there’s 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?

Sidebar

Answers: 1. The answer is 5 cents, not 10 cents. 2. The answer is five minutes, not 100 minutes. 3. The correct answer is 47 days, not 24 days.

Comments

Report Abuse

Posted by math person - Jun 13, 2008 11:41 am CST

Does anyone have an explanation for #2? I think that 1 and 3 are straightforward and 3 is a matter of sequence algebra, but what about 2?
Posted by JB - Jun 13, 2008 12:11 pm CST

While I find this test and related article very interesting, I don’t necessarily agree entirely with the general findings. I don’t feel this is really a fair or accurate representation of the way judges may or may not make a decision from the bench. And no, I am not a judge nor did I totally bomb the test. However, I am quite familiar with cognitive testing and function from both professional and personal experience.
These are, however, great questions that can offer some insight to cognitive vs intuitive thinking on the fly, but for things that are inconsequential. The answers to these questions have no actual long term impact. For instance, the reactions of the individuals or judges who were asked these questions might have been different if they were focused on a child in a custody or guardianship hearing. Or a decision that could effect the livelihood of an individual/family or multiple people in perhaps a corporate case.
I know from my own experience that when I sat with a medical ethics review board, where the issue at hand was often whether the doctor was justified in discontinuing or continuing treatment (in a state with an imminent death law) I thought very long and hard about the impact my decision might have - on not only the patient, family and close friends but the physician and staff involved as well. That may seem radical to some people but if we were dealing with a young physician who wanted to continue treatment on a patient who never gave any verbal indication of what their wishes were and now was unable to speak for them self, had no living will or DNR with family members that wanted to discontinue treatment (but were not necessarily unified), making a decision or recommendation was quite difficult. If there was behavior that an average reasonable person would perceive as irrational or out of control being exhibited by various family members involved (as there often is/was of family under such stressful conditions) any sort of “spontaneous, effortless, and fast decisions” were not only impossible but would have been totally inappropriate. Yet, when I looked at the questions above, I answered them without giving them much thought at all - what is considered being one of the “intuitive, rather than cognitive, decision-makers”.
Now, compare that to domestic/family law or juvenile cases. Or what about a corporate case where the litigants (aka former employees) stand to lose every cent of their retirement funds? And what if the majority of those litigants are in their mid to late fifties? How stressed out are the litigants? Are there possibly any underlying personality disorders? I’ve seen the worst of side of people, as I’m sure many a judge and lawyer have, come out in court. Litigants and lawyers alike. Sometimes people who are predisposed to or have underlying personality disorders are pushed to their absolute limits and exhibit their most notorious and worst behavior under conditions such as these. I would think - I certainly hope that judges actually concentrate and/or deliberate to reach their decisions. I honestly believe that in dealing with cases/scenarios such as these that the vast majority are cognitive decision-makers.

From a different view, I answered questions quite similar to these much differently under a very different set of circumstances. The short version, a virus attacked my brain. My answers to questions like these and many other ones, no matter how silly they might have seemed to most people at first glance, would have a long term impact on me. Potentially, the results had a direct effect on my treatment. Some years back, when I was involved with a neurology dept. presenting cases at a weekly brain tumor conference, I recall observing the same sort of reaction or response from our patients. They would often say that prior to brain tumor diagnosis, they most likely would have just blurted out the first answer that came to mind. However, once they were facing brain surgery, they gave far more thought to the questions.

I know, this isn’t brain surgery or even rocket science, and yes, judges can certainly make mistakes. Many do because, after all they are still human. But I think judges deserve more credit.
Posted by federal clerk - Jun 13, 2008 12:30 pm CST

@ math person

“It takes five machines five minutes to make five widgets.” Each machine makes one widget in five minutes. Put another way, it takes one machine five minutes to make one widget. The number of machines is equal to the number of widgets that can be made in five minutes. It takes one hundred machines five minutes to make one hundred widgets.
Posted by waterlogged - Jun 13, 2008 12:44 pm CST

#2 can be explained by calculating the minutes per piece per machine from the example then extrapolating to the answer. 5 machines/ 5 minutes / 5 parts means 5 minutes per machine per part. 100 machines at 5 minuters per machine per part means 100 parts in 5 minutes.
Posted by RES - Jun 13, 2008 07:59 pm CST

More importantly math person, how is question 3 a matter of sequence algebra, rather than basic logic? (Or IS sequence algebra basic logic???) The lily pad patch doubles in size ever day and covers the whole lake in 48 days. Therefore, the day before, day 47, the patch was half the size of the whole lake, or half the lake. Though I suppose this might be expressed in an algebraic equation, going through that exercise would certainly be more difficult and time-consuming, and unnecessary to boot.
Posted by RHG - Jun 15, 2008 11:49 pm CST

To RES [and math person]

#3 is a great question because it is impossible but appears simple: Even if the original lily patch was on one square millimeter, the entire surface of the earth would be covered on day 48. Since the human mind cannot grasp the significance of large geometric progressions, anybody who looks at the problem is forced to look only at the end or write the problem down. This is a great idea, but there are 2 obvious answers (47 and 24) starting at the end [47 and 24]. If you get it wrong, there is no easy way to check your work from the beginning because the numbers are ridiculously huge.

As an aside, I think it is more a matter of Analysis than Algebra [we’re dealing with the limits of a sequence]. The real issue is that this kind of question balances on the border between math and logic. All math rests on postulates that cannot be proven but can be derived through logic or observation (e.g., one cannot prove that 2+2=4). Here, logic allows one to solve the problem a priori, but one cannot check the problem by running through the entire sequence in one’s head.