Friday, November 16, 2012

Logically Speaking

Economists Should Be Logical
Driving home from New Jersey last night, I listened to podcasts of NPR's This American Life. I love the show. It's well done, it's informative and it's entertaining. There's just one thing about the show that from time-to-time causes me to say, "Hey, wait a minute. That's not even wrong!"

The thing that gets me going is how the narrators, interviewers and interviewees use logic, or more accurately, how they misuse (and in some cases abuse) logic. Sometimes the anti-logic leads to the same place one might get to through logical means; sometimes it wormholes to completely unfounded conclusions. I'm usually fine with the unfounded conclusions, unless one of them becomes the premise for the rest of the segment or show. In the latter case, I just skip ahead to the next segment or show.

Last night was particularly interesting to me because some of the logical gaffs were made by a Nobel prize winning economist who's focused on improving people's lots in life through education. I've always thought of economists as math-types, people who are sticklers for aptly applied logic, so his misuse of logic got my attention.

Teach Them to Fish
Over the last decade or two, the nature of human development initiatives has shifted from providing economic support to underdeveloped nations to improving the capabilities of the people in those nations; basically the thought has shifted from "give them a fish" to "teach them to fish". Most consider education to be a critical components of any plan to improve capability, so economists are trying to figure out how to make education more effective.

A considerable challenge is the fact that some people do well in traditional educational systems and others don't. The question last night was, "Why?" Why do some people acquire so-called "cognitive skills" more quickly and easily than others? The qualification of skills with the word "cognitive" led to a discussion of other types of skills or "non-cognitive" skills.

At that point everything got a little mushy. Since "non-cognitive" had a negative tone to it, the interviewer and interviewee searched for other phrases to substitute for it. They began by defining "cognitive skills" to mean the types of skills that are taught in school, e.g., math, reading, writing, and science. Non-cognitive skills were therefore the skills not taught in school, e.g., social interaction, leadership, resourcefulness.

Immutable IQ
Following a less than satisfying search for the right word, the Nobel-laureate said, "The thing about non-cognitive skills is that they can be taught. The problem with cognitive skills is that you're pretty much stuck with what you're born with. If you're in the top ten-percent of the IQ pool at eight years old, then you'll still be there at thirty-years old."

OK, this is where the rest of the show went down the drain. There's a commonly held belief that you can't change a person's IQ; it's innate and immutable. There are even some statistics that support this notion (but only if you're lousy at logic). Statistically, the performance of people on IQ tests doesn't change much over time. You score a 107 at five, 99.999% of the time you'll score pretty close to that at fifty.

The problem is that the statistic only shows a correlation; it doesn't show a causal-relationship. No one has answered the question: "why is that?" People have stated answers, (e.g., it's genetic or it's because the brain stops growing at a certain point), but no one has actually demonstrated a causal relationship. They know that the scores seem not to change. There are thousands of potential reasons why. For example, the answer could be, "Because no one believes she can change her IQ", or, "Because no one knows how to teach IQ."

Nonetheless, based on the fallacy that you absolutely cannot improve the level of someone's cognitive skills, an army of economists and educators are marching down the path to improving other skills. It's not a bad thing; learning other skills is quite useful. However, it's just silly to think that you can't help someone who "can't do math" to learn how to do math. The fallacy that became the premise of this episode nagged at me all the more because, no matter how math-challenged, I've never encountered someone whom I couldn't teach to do arithmetic, algebra, trig or calculus.

The confusion of correlation and causality is perhaps the most pervasively employed misuse of logic; it's nearly ubiquitous. All you have to do is watch a couple of television ads or listen to a political
pundit and you'll see it used several times. It's easy to assume that, because something's always gone a certain way, it always will go that way.

Sure, there are cases where it's a good assumption. However, to determine whether or not correlation can be trusted, one has to answer the question of causality. You see a correlation, you ask, "Why?"  Until the "Why?" is satisfactorily answered, you can't assume a causal relationship.

And, Or, Not
OK, enough of the confusion of coincidence and causality. Here's another little logical slight of hand that you can use to amaze your friends. Logic depends heavily on three words: and, or, and not. Undetected, one can completely change the meaning of a statement by substituting one word for another.

For example, take the statement:
You're not really busy if you're getting eight hours of sleep per night.
Seems pretty straight forward, right. If you sleep eight hours per night, you're not busy. Now let's add another statement.
You're not really busy if you have time to read the paper.
Another clear statement. If you have time to read the paper, you're not busy.

What if you don't have time to read the paper, but you are getting eight hours of sleep, or, if you've got time to read the paper, but are not getting eight hours of sleep? Are you busy?

That depends on how you connect the two statements. If you connect them with the word, "and", then you're busy. If you connect them with the word, "or", then you're not busy. If you simply provide the two statements on a checklist without any connecting words, then you're not busy.

Here's how it works. If you use the word "and" (e.g., If you're getting eight hours of sleep per night and you have time to read the paper, then you're not busy), then both side of the "and" must be satisfied to support the conclusion. However, if you connect the statements with "or" (e.g. If you're getting eight hours of sleep per night or you have time to read the paper, then you're not busy), then if either one is satisfied, the conclusion is supported.

Changing Polarity
What if you want to put the statement into the affirmative, e.g., "You're busy when..."?
This is where the slight of hand comes into play.  When you add or remove the word "not", everything flips: or becomes andand becomes or, not becomes not-not, not-not becomes not.

The affirmatively stated version of:
You're not busy if you're getting eight hours of sleep per night and you have time to read the paper.
You are busy if you're not sleeping eight hours per night or you do not have time to read the paper.
Note, the above translation is only works if you include all the factors that indicate busy-ness. If you have an incomplete list of things that qualify you as not busy, then you can't actually create a statement that would qualify you as busy.

Similarly, the affirmatively stated version of:
You're not busy if you're getting eight hours of sleep per night or you have time to read the paper.
You are busy if you're not sleeping eight hours per night and you do not have time to read the paper.
The rules are straightforward, but not always easy to apply. 

If you want to change the polarity of a conclusion (e.g., go from not busy to busy), then you must:
a) change the polarity of the contributing factors (e.g., go from sleeping to not sleeping) and,
b) exchange the words connecting the contributing factors (e.g., go from and to or, and go from or to and).

Finally, you can't transform a list that negates a conclusion into one that affirms a conclusion unless the negation list is exhaustive.

Leave out one "not" or leave in one "and", and you completely alter the meaning of the statement. 

This slight of hand is used frequently, oftentimes intentionally by political writers and pundits,  and inadvertently by people trying transform a negative statement into a positive one.

Try It at Home
How about teaching your kids about the fallacy of confusing coincidence and causal relationship and about the logical application of not, or and and, and then asking them to point out every time someone pulls a slight of hand.

It'd be fun, right?

Happy Friday,

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