Wason's card selection problem

Because so many logical errors that seem to be perniciously pervasive and persistent involve incorrect notions of implication relationships--that is, the concept of "if___then___"--we want to understand as much as we can about this much studied oddity from the cognitive sciences.

The intense interest in the puzzle was kicked off by a book published in the early 1970's by Percy C Wason (Cambridge University).  It was the subject of many popular publications, and Martin Gardner put a related, five-card,  puzzle with a diabolical twist in his "Mathematical Games" column in Scientific American.  Some of the published research was reminiscent of Richard Feynman's observation of the lack of understanding of virtually all of the authors of published K-12 science textbooks:  "...written by people who don;t know what the hell they are talking about."  The authors of the research and textbooks are very bright people, but neverthless sometimes eminate an aura of blindness to this important dimension of perception of patterns at the edges of human comprehension--patterns of patterns of...that constitute the more abstract mathematical patterns.

The relationship to the error of "Energy is the capacity to do work" is particularly noteworthy.  The widespread confusion of the energy of science with the energy of common use (Aristotle's concept) is one of the most important of common oversimplifications to be overcome before we can understand the simple (but subtle) basis of today's science.  It's worth a lot of effort to anyone who wants to get a leg up on seeing science.

One crucially important observation about misperceptions of "if___then___", is that people who are extremely intelligent by conventional notions of "intelligence" ("IQ or "g-factor," etc) might still be "logic blind" to that pattern of pattern (of pattern of...) which is implication -- blind to that Boolean thing which logicians represent with their Boolean equation.


Ratios -- proportions -- math
Assuming that the costs are proportioned out equally among the people paying, which of the following would cost you the most, which the least: Your state of three million people funds a new freeway costing six billion dollars; your city of a hundred thousand funds a new soccer stadium costing four million; your country of 250 million funds a new Coast Guard rescue vessle costing 600 million?
Your state:  Six billion dollars among three million people:  $2000 per person.
Your city:  Four million dollars among 100,000 million people:  $400 per person.
Your country:  600 million dollars among 250 million people:  $2.40 per person.
Euros in a dollar?
Pottles in a firkin?
.In mid summer, 2003 a Euro is worth about $.88.
A firkin  is 18 pottles, 
and calculating such unfamiliar conversions will be easy once ratios are understood.

...and look at the alternative test for climbing the five steps:

The tallest of the people in the sunlight is about six feet tall.  They are about 60% of the distance from the camera to the base of the vertical wall.  Estimate the height of the wall from the given information.

In the picture, measure the ratio of wall height to the height of the tallest person.
The height of the wall is this ratio times 6 feet--divided by 0.60.

Much of physics is done with simple proportions.  One of the simplest is Newton's Second Law of Motion: F = ma.

Two of the symbols are put in bold-face: this indicate that they are vectors.
Newton's second law is one of the most important laws of physics
A surprisingly small percentage of those of those who learn it can use it.
They don't understand it as the mathematical entity it is.
Acceleration, a, is a vector, and it is a limit of a ratio.

Some details of the difficulties are at the bottom of this page.


Elementary logic
"A Corvallis resident won the state lottery last year; although I wasn't a Corvallis resident last year I became one this year; therefore I will win the state lottery this year."  Explain why this reasoning isn't correct.
.Who finds this "logic" absurd?
Who can point out specific errors?
What percentage of people use such reasoning?

Pseudoscientific beliefs are based on similar lines of reasoning.
Advertisers and propagandists rely on similar lines of reasoning.
"Saddam is evil; 9/11 was an evil act; therefore, Saddam was behind 9/11."
More than half of Americans accepted something like that argument.

A course in elementary logic, in Boolean relationships, addresses such errors.

The above is a cousin of the Wason card problem.  Why?
Wason's study was based on Boolean implication because that is an unseen
logical pattern which shows up in very many errors of logc.

The errors in the above make simple associations--Corvallis resident - lottery winner,
for example--where the actual relationships are much subtler and more involved.
Oversimplification is the name of this game



Comparatives -- Superlatives