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Are you an "intuitive" or a "reflective"? Quiz sorts us out

  1. May 6, 2017 #1
    I've mentioned in another thread that I'm slowly reading through a bunch of books this summer on the general topic of "knowledge and expertise vs. ignorance and opposition to expertise." One of these books is The Knowledge Illusion: Why We Never Think Alone, by cognitive scientists Steven Sloman and Philip Fernbach. The premise of the book is that collectively, humans know lots of stuff; but individually, we typically know far less than we think.

    I have some stuff to say about why I think this book is relevant to science education & science literacy in the U.S.; but so as not to put anyone to sleep, let me just quickly offer up the 3-question quiz I found in the book that has tickled me. I'm fairly certain that 200% - no, 300% at least! of PF members will pass the quiz, getting all three questions correct. But it's what the quiz purports to say about persons who don't pass it - who get the answers wrong - that is most interesting. More after the quiz; here it is:

    1) A bat and a ball cost $ 1.10. The bat costs one dollar more than the ball. How much does the ball cost?

    2) 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?

    3) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

    1) Ball costs 5 cents. 2) 47 days. 3) 5 minutes.

    Now . . . what is this quiz really for? Well, one of the key points in the book is that when human beings get together in groups, we know a HUGE amount of stuff. In fact we wouldn't have industry, science, farming, or pretty much any expert field without human beings becoming specialists and then the specialists sharing what they know with each other & with the rest of us. Whereas as individuals, we don't know squat about nearly anything of a technical nature that is outside our own particular field - but we think we do! This is why the book is titled The Knowledge Illusion - it's concerned with precisely this tension between group knowledge and the individual's belief that gosh darn it, we really do know all that stuff personally. Which leads us to argue with each other about complex issues we don't know anything about; make bad decisions about our personal finance, our healthcare, what the correct policy should be for foreign and domestic policy (which controls the candidates we then decide to vote for); etc., etc.

    Toward that point, here are some excerpts from The Knowledge Illusion about how people typically do on the quiz, and what Sloman and Fernbach think this shows:

    . . . Less than 20 percent of the U.S. population gets the three problems of the CRT right. Mathematicians and engineers do better than poets and painters, but not that much better. About 48 percent of students at the Massachusetts Institute of Technology got all three correct when Frederick tested them; only 26 percent of Princeton students did.

    The CRT distinguishes people who like to reflect before they answer from those who just answer with the first thing that comes to mind. People who are more reflective depend more on their deliberative powers of thought and expression; those who are less reflective depend more on their intuitions. These people differ in a number of ways. People who are more reflective tend to be more careful when given problems that involve reasoning. They make fewer errors and are less likely to fall for tricks than less reflective people fall for. For instance, they are better at detecting when a statement was intended to be profound or whether it’s essentially a random collection of words (like “Hidden meaning transforms unparalleled abstract beauty”).

    What’s more relevant to our discussion is that more reflective people— people who score better on the CRT— show less of an illusion of explanatory depth than less reflective people.​

    I think this distinction is pretty cool - and maybe something to keep in mind when I (a reflective) find myself trying to educate my wife or many of my friends about science or policy. If I slow down, I may realize that I'm dealing with someone who is an "intuitive"; I can then think about alternative ways of making my argument that will be more persuasive to someone of that sort. On the majority of complex issues that come up, my argument is typically "Let's admit it, you and I don't really know very much at all about X," X being whatever the issue is. But most people don't like hearing that they are ignorant about an issue and so are prone to denying it. The book makes a neat point here as well: If you are dealing with a well-meaning but misguided intuitive, first ask them to explain how X actually works; when they find they can't do so even to their own satisfaction, they are more likely to admit that indeed, they don't know as much as they thought. I can describe this strategy further if anyone is interested.

    P.S. Here is a link to a PDF of the study which originated the quiz and used it to gather scores from various student populations; a table with the scores is on p. 6 of the PDF: https://law.yale.edu/system/files/a...rick_CognitiveReflectionandDecisionMaking.pdf
    Last edited: May 6, 2017
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  3. May 6, 2017 #2


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    There is something to be said in support of intuitive thinking vs. reflective thinking. When I drive out of a parking lot making a left turn into traffic, I am able to do so without causing an accident or road rage. I do so alone without input from anyone, in fact I would be annoyed if a back-seat driver prompted me to "go now". Reflective thinking is addressing this problem as we speak in the design of self-driving cars by writing algorithms that will (hopefully) include all the factors that weigh in our intuitive decision to "go now" or not. I remember reading somewhere that intuitive thinking relies on the "reptilian brain", that had millions of years to evolve as a computer whereas reflective thinking relies on the prefrontal cortex, a relative newcomer as a computer that has not been fully debugged. Despite its limitations, the reptilian brain has served us well through our evolution.

    I think physics is considered "hard" because it requires one to set aside one's intuitive thinking and start thinking reflectively without prejudice or preconceptions. Not an easy task for 18-year olds who have not experienced this kind of thinking before. That is why I have been exhorting my students to leave their intuitive thinking at the door and retrieve it on their way out at the end of the lecture.
  4. May 6, 2017 #3


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    This was a nice read. However, I am still wondering what it means to be "intuitive".

    "Intuition", in my opinion, can still be right if it is a trained intuition. For example, I was able to solve all three examples above correctly, simply because I was trained to do, most likely like the 48% of the students in MIT did. I have received formal education in chemistry, which gave me a good intuition in chemistry at least in the specific area I research. That, however, does not mean I have good intuition in physics. Especially when all two of my quantum mechanics teacher back in undergraduate almost completely neglected teaching anything, I still have very bad intuition in QM even though I self-teach myself the best I can. I know this for a fact if I look back in time of when I was before entering college. I believe, that if I have taken formal education in physics, it might have been different.

    I think most people would first use their trained intuition to come up with new projects, and then contemplate on that idea in the "reflective mode" to make sure it is scientifically sound. In my experience, those who are successful have both good intuition and good reflection. Those who lack good intuition fails to come up with anything good in the first place. Those who lack good reflection fails in scientific integrity. Those who lack both probably should not pursue an academic career. So I do not think the "intuition" and "reflection" is on the same scale.

    This is exactly why I find the following:
    extremely important.
  5. May 7, 2017 #4


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    I agree with @HAYAO in that I think intuition can be learned for particular purposes.

    A non-scientific example might be chasing down fly balls (baseball) in the out field. when you first do this, it is probably not clear where the ball is going, so its not clear where you should run to, which makes you not so good an outfielder. However, after several reps (practice), you learn how to better judge where the ball will be going and you can immediately head in the right direction to catch it. this is when the process becomes intuitive.

    Mental tasks can be similar. However, knowing when it is appropriate to follow your intuitive instincts, or hold back to a moment of further reflection on situation you are confronted with would be where I think the important difference is between the intuitive or reflective people. I would think that even this decision of whether or not to reflect could become intuitive as one becomes more familiar with the situations that one is truly knowledgeable about and those that one is not.
  6. May 8, 2017 #5


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    I'd suggest, at least this is my first reaction, that these wrong answers are nothing intuitive at all. I'd say that what they call intuitive here is not intuitive at all, what they are is verbal thinking. Words are useful things, they can aid the thinking, and as we get very proficient with them they can replace the thinking they can do the thinking for us. And a lot of the time this is quite successful and an economy – it saves thetime and effort of having to translate back-and-forth between the image or the thing and the words for it. But the words working by themselves can be misleading in the ways exemplified.

    I think we come across this with some student answers in homework sections here using words that sound like the right kind of words. We come across it in political discussions – I often think "you can't actually think or believe what you're saying, but you know how to string the words together". You could say they string themselves together. (in fact the most indispensable skill of a politician is to be able to keep talking – however he's caught out, say in a TV interview he has to keep talking, it doesn't matter if anyone believes him or if he believes himself he just has to keep talking for that five or 10 minutes, if he stops he's lost.)
    Last edited: May 10, 2017
  7. May 9, 2017 #6
    I think the immediate lesson from this test is to learn some algebra. Show students how easy some confusing problems are if you know a little algebra.

    Problem 1 could be useful to teach about how to visualize an algebra problem using a marked line. For example, a mark is made to represent a distance "bat" along the line, then add an additional length for "ball" and mark the result 110, then subtract the distance "ball" from "bat" which gives 100. If you mark a line this way, you instantly see that "bat" is located at 105 and the length of "ball" is 5.

    In the paper they define "intuitive" as "executed quickly without any conscious deliberation" and "reflective" as "slower and more reflective." I think it's a useful distinction. However, if you know enough algebra, you can solve many problems almost automatically, just by writing down the formulas and doing the symbolic manipulations. As some have said, it's almost like the symbols have a mind of their own. Some would say our goal is to turn problems which require lots of thinking into problems which require little thinking. Maybe this kind of process needs a third label. We are solving hard problems without thinking much about them, because we know the technique.

    Have any of you ever had the following experience? You are taking a final exam. You studied hard during the course. When you are taking the exam, you seem to be working on automatic pilot. You are solving all the questions correctly, even the hard ones, without much conscious effort. But later you can't even remember the questions or how you solved them. What kind of process would that be?
  8. May 10, 2017 #7
    I both agree and disagree. Agree, because in my case, I've always thought of myself as "bad at math" even though I got fair grades in high school; and like so many students, I "hated word problems." So up until very recently, I probably would have flunked problem 1 on the quiz for lack of how to think about it - i.e the lack of algebraic skills you point to. However as of January I began reviewing my high school math, part of a campaign of self-study; and right before I read about the quiz I had been reviewing "systems of equations"; so I was delighted that I could use my new skills!

    Disagree, however, because I think even the inclination to study math on my own says something about my interests & inclinations - e.g. I have always been interested in science, both "soft" sciences such as behavioral psychology and "hard" sciences such as physics; I have always done a lot of research on issues and am definitely a "reflective" type by nature - which is not always a good thing, as I tend to be a slow thinker rather than a fast thinker, and fast thinking is often more effective provided you have the background necessary to make a decision.

    So maybe the definition given in the paper that you cite is only a partial definition? More important to me even than the skills is the aptitude and the inclination for reflective thinking. I would also include the willingness to doubt one's own conclusions; to at least attempt to view our actions and beliefs objectively (even though this is difficult to impossible); the willingness to at least sometimes seek out information that is contrary to our views (e.g. to go against "confirmation bias"); etc. Both modes of operating (instinctive vs. reflective) are valuable for survival; and both have their problematic sides - a reflective person can become indecisive, obsessed with gathering information rather than acting; an intuitive person may be prone to arrogance or bad decisions.
    Last edited: May 10, 2017
  9. May 10, 2017 #8
    This is a phenomenon that many cognitive scientists describe. Once we learn skills well enough, and acquire enough relevant experience, we can operate in what seems almost an unconscious or "intuitive" manner and do amazing things. I don't have all my books on cognitive science with me, otherwise I could give some relevant cites. I do remember the titles of a couple of good books, though somewhat dated by now, about how the unconscious does far more than most of us realize:

    The New Unconscious - edited volume, editors Ran R. Hassin, James S. Uleman, and John A. Bargh, 2006, Oxford University Press

    Strangers To Ourselves: Discovering the Adaptive Unconscious - by Timothy Wilson, 2004, Belknap Press.

    Also, Barbara Oakley touches upon this phenomenon in her book A Mind For Numbers; she calls the behavior you're speaking of "focused mode", versus "defused mode" in which we're not actively using skills but almost daydreaming. I can't find an excerpt on the web just now, but here's a book review of that book which mentions both these modes: http://www.motherjones.com/environment/2014/08/inquiring-minds-barbara-oakley-learning-neuroscience
  10. May 10, 2017 #9
    I think you're onto something, but you haven't quite reached it yet.

    Here's my take:

    Each of the three questions is phrased such that you are tempted to suppose the answer lies in completing a certain obvious pattern. Strictly speaking, that is true, but the phrasing leads you astray into the illusion that it's one clear pattern when it is actually a different pattern.

    This is best demonstrated by the last question. The pattern that jumps out to lead you astray is: 5 is to 5 is to 5, or: n is to n is to n. So, the knee-jerk temptation is to say it takes 100 minutes for 100 machines to make 100 widgets.

    The first question is more pernicious because the wrong pattern that first suggests itself is not even contained in the question. It is out there in commerce all around us: if thing A costs, say, $2.35 and thing B costs $3.35, it is easy to see that thing B costs "a dollar more than" thing A. We are primed, therefore, to react to the words "a dollar more than," by simply adding a whole dollar to the dollar column (or by subtracting a whole dollar from the dollar column when we want to find what is "a dollar less than" something). The question is designed to take advantage of that priming and stick it to you where it breaks down.

    The second question tempts you to apply a distance over time pattern to a problem that is not distance over time at all, for example: if it takes Joe 10 minutes to walk some distance d, how long does it take him to walk half that distance? You are tempted to forget the lily pads DOUBLE in area every day as opposed to adding some fixed amount to the total area every day. Your mind falls into the rut: " half the distance means half the time, therefore: half the area means half the time." Truth be told, this particular question does nothing deliberate to conflate the two different kinds of problems, it simply takes advantage of the fact people's knee-jerk reaction is to chose the simpler, more familiar, train of logic over the more complex and less familiar when they aren't paying full attention.

    In each case you are tempted to fall into a familiar and easy rut when the actual solution lies outside the rut. So, I don't find these questions to actually say anything about intuition vs reflection. They actually say much more about misdirection and inattention.
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