Thursday, September 22, 2011

Is that God speaking or last night's pizza?

Many of us have had a "gut instinct" about something. Somehow we "knew" what decision we needed to make. Or perhaps we "just knew" that we were going to get that job. Other times we can "just tell" something is wrong.

I remember a time as a young teenager when, walking home with a friend, I saw an ambulance turn off my road and head down the highway. The ambulance did not have any sirens going and there were no lights on. It looked like an ambulance on its way back from a call or even from the garage after a regular scheduled maintanance. It was clearly not in a hurry and there was no sign of an emergency.

But somehow I knew something was wrong at home. I told my friend I needed to go because that ambulance had come from my house. He laughed at me and pointed out that I could not even see my house, how could I possibly "know." But I did and when we walked in the door my mother was on the phone with my grandmother. She was telling her how my father had been electrocuted while working in a tree. He was ok and had asked the ambulance to stop at the house to tell my mother and let her know he was fine. To this day I can't explain how I "knew,"I just did.

If you have "instinct" or "gut feelings" about stuff, then you are also more likely to believe in God and go to church. At least that is what a recent study has discovered. Live Science has posted an article explaining the results. Here is some of what they say.

For many people, believing in God comes down to a gut feeling that a benevolent deity is out there. A study now finds that gut feelings may be very important in determining who goes to church every Sunday and who avoids the pews.

People who are generally more intuitive in the way they think and make decisions are more likely to believe in God than those who ruminate over their choices, the researchers found. The findings suggest that basic differences in thinking style can influence religious belief.

"Some say we believe in God because our intuitions about how and why things happen lead us to see a divine purpose behind ordinary events that don't have obvious human causes," study researcher Amitai Shenhav of Harvard University said in a statement. "This led us to ask whether the strength of an individual's beliefs is influenced by how much they trust their natural intuitions versus stopping to reflect on those first instincts."

I am not sure what to make of this since while I have had "gut feelings" I also tend to ruminate over some decisions, sometimes to the point that I make myself sick. But I am also not sure about the methods used for the test. Apparently researchers asked two questions. One was a math question, the other to write a paragraph about either their experience with intuition or reasoning. Those who answered the math question via their "first instincts" or wrote about intuition were more likely to believe in God.

I guess I must be a "gut level" person because according to the article that is how I would answer the math question. Here is the question.

The participants took a three-question math test with questions such as, "A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?" The intuitive answer to that question is 10 cents, since most people's first impulse is to knock $1 off the total. But people who use "reflective" reasoning to question their first impulse are more likely to get the correct answer: 5 cents.

I admit, I went with 10 cents. But I will also admit that I have yet to figure out how 5 cents is the right answer. I guess that is why my wife has the business degree with accounting.

Can anyone explain to me how the answer is 5 cents?


  1. Problem gives you a couple different equations to work from:

    bat + ball = 1.10
    bat = ball + 1.00

    If you combine those, you get

    ball + 1.00 + ball = 1.10


    2 * ball = 0.10

    Solve for ball ..

    ball = 0.05

    PS. I also have intuitive experiences, but when you get trained to solve algebra problems you usually exclude them from your "intuitive" methodology. That said, I had problems in advanced physics that I used intuition to solve correctly (but also using a more reductionist type of thinking in addition to intuitive).

  2. I in computer science research, so I have had some training. I also did ball = 1.1 - 1 = 0.1, but I am trained to check that the result is consistent with the preconditions: the difference bewteen bat and ball is then 1 - 0.1 = 0.9, which is not 1. So I had to find another answer... which happened to be 1.05 and 0.05. Which I also used intuition to compute, no explicit equations.

  3. Well Arcaedeme and Tomas, you clearly have better math skills than me. I haven't touched algebra since high school, except for a few months as I prepared for the GRE. I won't lie and say I understand the answer. I guess I will ask my wife! :)

  4. (x - y) ÷ 2 = z where x = combined cost of bat and ball; and y = required cost differential between bat and ball; and z is the answer required

    Thus: 1.10 - 1.00 ÷ 2 = z
    = 0.10 ÷ 2 = z
    = 0.05 = z

    I believe this works for all calculations of this kind?

  5. Hmm, apparently there are more mathematicians reading my blog than I realized!

  6. I was always good with math equations when symbols were used instead of words. So the question stumped me as well until I saw it translated into symbolic form then I understood it.
    So I think the math question given, only proves that a person has some training in math equations; I don't see how this has anything to do with intuition.
    I remember having an intuition moment at college when one Monday morning a student was not in that day. Briefly after I realized he was dead the teacher announced that he had died in a motorcycle accident. Why did I not think he was just sick? Intuition!

  7. I think John is looking for the opposite, for this to be explained in words and not formulas.

    A dollar is not a dollar more than ten cents - it is 90 cents more than 10 cents. $1.05 is $1.00 more than $.05.

    Does that help?

  8. James, yes, I think so, but let me show my ignorance. The problem says $1.10, so I am not sure how we got to $1.05? Does someone owe me 5 cents.

    I guess you all now know where my lowest score was on the GRE.

  9. James is getting close. The intuitive answer is more like this.

    You have to add the price of the ball plus the price of the bat, right?

    If the ball is 10 cents then add a dollar and that makes the bat 1.10, adding together makes the total 1.20, too much.

    So if the ball is 5 cents, that makes the bat 1.05, so the total is 1.10. See?

    The key for someone who thinks like you do is to make sure you take your conclusion and see if it really works in the problem. A better way to say that is that you have to guess at the answer and then see if it works. Just guessing is not right.

    In differential equations there is a method for solving that is called the method of judicious guessing. I think this should be taught to everyone who is not going to have to use math in their work. Basically you understand the concept of the way numbers work, and you take a stab at the answer, that is what you did. But you need to see if it is right. If you had done that you would have realized that it produces to high of an outcome and would have thought about it a bit differently knowing that the right answer had to be lower.

    So try the problem again, use your method and guess 10 cents and use the concept I just discussed and honestly see where it takes you

    (this is either going to result in me being called a genius or arrogant...)

  10. I want to clarify a bit too. What you are looking for is why your answer is not correct. Many people think that way, but that is not the way people trained in science, engineering and math typically think. They get stuck in the opposite paradigm, that is, trying to think why their answer has to make sense. In the business world many analytical types have a difficult time because many of the decisions are not a question of determining a precise answer, but in determining a good enough answer. Analyticals definitely check the answer because that is the proof. In other words, they typically don't ask the question as to why their guess was not right, they assume their guess is wrong and determine how wrong it is so that they can guess better.

  11. Brilliant answers James and DRT. I really appreciated the explanation of an intuitive approach. As far as business I concur, I do not use as much analytic skill there as intuition.

  12. DRT,

    You are a genius! Not arrogant at all. THANK YOU. Now I get it. I had got to the point where I was going to start counting out change to figure it out.

    But it does help explain the way intuition works. I think the editors of Live Science could have explained it better.