Seeing the cards

Only a very few people see the answer to Wason's card selection problem immediately and easily.  Many seem never to see it, even when explained from a variety of viewpoints.  Most who eventually see its principle concept, logical (Boolean) implication, did not see it at first.

A non-"seer"

In the late 80's, I discussed the puzzle with a researcher who had published several papers on it's peculiar difficulties.  His explanation of the difficulties was this:  People don't encounter implication unless they take something like a college logic course: it can't be encountered in day-to-day activities because it's only a construct in academic minds.  Ordinary people have had no opportunity to learn implication, so they can't come up with the puzzle's solution. "They can't learn it," he said.

He gave me some of his publications.  I found them obscure, full of Boolean expressions, but weirdly used, in ways I couldn't follow.  Until I came across a description of equivalence as  "a  type of implication."  He apparently considered that implication means "not explicitly stated; something implied."  That's a colloquial definition of the word, but it's not the technical definition that goes with those Boolean equations.  His use of the word was reminiscent of the colloquial use of "energy" which is very unlike its scientific use, but gets widely used without awareness that there is a difference.

That discovery began to shed light on why, in our discussions in his office, he seemed not to accept my objections to defining energy with "Energy is the capacity to do work."  And why he saw no connection between that much debated definition and Wason's card puzzle.  I had wondered if, perhaps, authors who use that faulty definition just possibly might be confusing equivalence and implication.  Anyone who calls equivalence "a kind of implication" apparently really isn't "seeing" the distinction. 

I now believe he was unaware that both "implication" and "energy" have technical definitions that are very different from their more common usages.  The technical meanings have great conceptual power.  They are useful, but there's a barrier between merely learning them and actually using them.

The learning is ritual and rote.  Using requires understanding; "seeing" in the real world. 

Did that researcher seem a bit "dull" to me?  Was he someone I might expect would be a "C-student," or worse?  Quite the opposite!  He was quick, articulate, charming, and, I'm sure, would score very high on any IQ test.

Did I suspect he was seeing something a little beyond the edge of easy human comprehension that I was having difficulty seeing?  Absolutely not!  Not here anyway.  That can't be an issue when the question is merely the distinction that differentiates implication from equivalence.  That distinction is much like the distinction between green and orange: if you see it you wonder how anyone could not; if you don't see it, you are probably colorblind to the distinction.  You simply can't visualize that kind of distinction. 

Implication and equivalence are just as distinct as are green and orange.

When someone actually does "see" something you don't, you often get a powerful clue: the "seer" comes up with solutions which work with what to you are the most puzzling of questions.  Richard Feynman did that repeatedly.  We who watched him doing it were awed and couldn't see where his "miracles" came from.  He frequently said he didn't know how he did it.  But his suggestions were testable.  And very often right!  (And he immediately abandoned them when they were wrong.)

Next, a seer . . .


Implication: an alternative look.

Links to

Keys to understanding science lie in "seeing" various kinds of patterns, samenesses among differences.  The sameness that science sees almost always go unnoticed . . . until the seer stretches his mind.  (...or her mind.)
The logical relationship of implication is common to Wason's card puzzle and to the error of "Energy is the capacity to do work."  But this Boolean implication is abstract, at what Keith Devlin calls the "fourth level" of abstraction.  SEE

"Seeing" this level of abstraction requires some extra effort, and  effort of a possibly unfamiliar kind.  It involves looking in dimensions we never suspected exist.

The incidents described on this—and the next—page demonstrate how Devlin's suggestions of how of mathematics may have evolved can help us see some of the patterns in the mysteries of the human mind.  SEE


Feynman "emanated an aura" of brilliance.