Sunday, May 15, 2011

Critical Thinking Quiz & The Three Doors


The other day, I wrote a blog post criticizing many in the adult population today because of their inability to read critically and exercise basic analytical reasoning. 
The title of that blog was Critical and Analytical Thinking are Lost Arts Amongst Many of Today's Adult Population. I wrote:

Most unfortunately, I'm getting the impression that, judging from the comments I often hear and from reading comments on Social Media websites, at least 85% of the adult population are incapable of well-executed critical analysis and reading. We live in a society today whereby far too many people have lost the ability to perform even the most basic levels of critical/analytical thinking when it comes to what they see or hear on TV or what they read in print. This is a very sad situation. People are not able to extract facts from conjecture. They seem to be incapable of deeply considering the motivations of the people they see/hear or read on the mass media.
Proper critical analysis will always examine a person's possible motivations for what they say or write. Too few adults today seem able to exercise this most basic ability.  

I then went on in that post to give several examples of how this works (or doesn't work) in real-life situations. I especially thought it was important because of the recent Fukushima disaster and how many people panicked and fled Japan without thinking carefully through the problem before making any decisions on what to do. It had much to do with how people filter the information that we receive daily from the mass media and how people today seem to be unable to rectify numbers and their relation to what they mean to our lives.

Of course, again, I got many comments criticizing me and even some people wrote nonsense and humorous comments like, "I give your reasoning an 'F' for failure." Most of those comments were deleted because they were so poorly written or were just outside of commenting guidelines. Those sorts of comments are, I believe, mostly from the people who are believers of AGW or think that dolphin slaughter in Japan is a crime... These are people who are definitely blinded by dogma and cannot fairly see the forest for the trees. (I will write separately on that too later).

I did get some mail (to my private mail account too) that were supportive. Thanks.

Now, I'd like to do a very simple logic experiment with you, dear reader. The fact of the matter is that critical reading skills and analytical reasoning are all based on mathematics (thinking with the left-side hemisphere of the brain is for logic, reasoning and math). These mathematics are not difficult. They are, though, in many cases counter-intuitive.

Let's take this short one question quiz and see how you do.

You are a contestant at a game show. There are three doors in front of you. The doors are marked doors, "A", "B" and "C". Behind one of these doors is $1 million USD in cash. Behind the other two doors are ham sandwiches.

You are asked to pick one door. For the sake of this quiz, let's say that you choose door "A". The game show hosts then shows you that behind door "B" is a ham sandwich. He then asks you if you want to keep door "A" or switch to door "C".

Question: What should you do? Should you stick with door "A" or switch to door "C"? 

(scroll down for answer)
Answer: You should now switch to door "C" as door "C" now has a 2/3 chance of winning. Staying on door "A" is a bad choice because door "A" only has a 1/3 chance of winning.

Just because the host has shown you that behind door "B" is a ham sandwich, that doesn't make your original choice of door "A" a 50/50 chance of winning. 

It is unmistakable that switching will increase your odds of winning from 1/3 to 2/3.

Now, I expect that many will comment (I hope you do) so that I can help you to see that switching is the correct answer and guarantees a 2/3 chance of winning.... Think about it, in old movies guys would do the peanut under the cup gambling with suckers? How do you think they always won? They don't have to cheat.


Here's a typical example of how the recent Fukushima nuclear disaster is used to spread fear by use of illogical reasoning. If anyone is bothered to investigate or think about it, they'd see that the chart below says many things:

Unfortunately, most people who view this chart and see the numbers and think, "Oh my God. Even Tokyo is under heavy radioactive fallout." The way this chart is drawn makes it look like all of Japan is under the area of dangerous radioactivity.

Look at Tokyo. It says, "0.064" microsieverts per hour. That sounds terrible, doesn't it? But what does that mean? Most people won't bother to think about it and will fear.

Let me give you an example of what this means.

Tokyo is experiencing 0.064 microsieverts per hour radiation. The typical one-way flight from Narita airport to New York is 190 microsieverts. If we must fully understand and gauge and compare our risk in Tokyo, then we must understand these terms and their relation.

So let's calculate the risk. The typical one-way flight from Narita airport to New York is 190 microsieverts. 

Now Tokyo is experiencing 0.064 microsieverts per hour radiation. Let's equalize that with our flight. What is our risk?

To calculate this very simple problem we divide 190 by 0.064. This equals 2,968.75 microsieverts. Divide that by 24 hours in a day equals 123 days. That means that the dose of radiation you get from living in Tokyo for 123 days is equal to the dose of radiation you get from one one-way flight from Tokyo to New York. 

- Thanks to Marilyn Vos Savant for the Monty Hall Dilemma in "The Power of Logical Thinking"

NOTE: I want to be the first one to admit that I had something wrong, or make a mistake. When I first posted this, I had miscalculated the radiation on the flight to New York. The flight to New York is 190 microsieverts per hour. It takes 10 ~ 11 hours to fly to New York. I had it calculated at 190 microsieverts total. So the amounts above are recalculated to show this error on my part. Sorry for the trouble. 


James said...

Actually, you didn't specify what the current going price for a ham sadwich is or how hungry I am, so it's not clear which prize I should be aiming for. ;)

I remember hearing this puzzle a long time ago and it got me the first time, but I eventually worked it out.

mikeintokyorogers said...

Ha! Ha! Ha! OK. You got me there James. It's a killer ham sandwich and you are starving!

boo said...

This is very disingenuous. First, you left out an important condition, that the host knows what is behind the doors and must open a ham sandwich door.
The 2/3 chance on switch only works with the above condition, which you didn't mention.

If the host opens doors at random (possibly revealing the money), which is the way you wrote it, then switching wins half the time.

So assuming you just left out that important condition by accident, I'm still not sure how this point relates to the topic of this post. This is one of the world's most famously difficult logical problems, and many of the world's top mathematicians got it wrong at first. If you're going to test people's critical thinking skills, may I suggest that it may be be better not to choose a problem that has stumped Nobel-Prize winners and the world's best mathematicians?

mikeintokyorogers said...

Thanks Boo... From a TV background, I think it is obvious that the host of the show would know what's behind the doors (otherwise this show would be very anti-climatic and get cancelled very soon!) Of course it goes without saying that the host of the show knows what's behind each door. It's his show.

But, I checked, and even though Marilyn Vos Savant agrees with me, that it is obvious that the host knows what's behind the doors (as in her peanut under the cups example), I checked and did find out that you are right:. Here is the exact text as the question was originally stated in "Ask Marilyn" in Parade Magazine:
"Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, which knows what's behind each door, opens another door, say 3, which has a goat. He says to you, "Do you want to pick door number "? Is it to your advantage to switch doors?

As far as what this has o do with critical reading and analytical thinking, let me quote from Amazon's page on Von Savant's book: "This book is for those of us whose brains stalled when faced with the threat of "word problems" in math class. Vos Savant shows us how even the most well educated can be semiliterate in the arts of reasoning and problem solving. She illustrates how easily we are duped by "counter-intuitive" problems whose solutions run against the grain of instinct. In part 1, vos Savant analyzes examples of these problems, including the famous "Monty Hall Dilemma" that initiated a deluge of mail from irate mathematicians after she posed it in her Sunday column. Part 2 unveils how easy it is to misunderstand mean-spirited statistics. This section also contains fascinatingly thorough descriptions of every conceivable verbal fallacy--a tour de force to delight the number-impaired. Part 3 is an eye-opening analysis of the ways politicians use statistics, "selective logic," and faulty reasoning to sway our votes. Vos Savant's clear, logical approach to convoluted problems is a tonic for anyone who feels queasy around economics, statistics, word problems, or politicians."

I see now that it might have been better had I written this article as a book review... Though, if I did that, I doubt that many would see the relationship from, say, stated radiation levels concerning nuclear accidents with panic, and rational thought.