ON 1 SEPTEMBER 1983, Korean Airlines flight 007鈥攂ound for
Seoul鈥攕trayed inadvertently into Soviet airspace. The reaction from the
Soviet authorities was swift. Two fighter planes were scrambled to intercept it
and one fired an air-to-air missile that ripped through the airliner鈥檚 fuselage
and sent it plummeting into the Sea of Okhotsk. Two hundred and sixty-nine
people were killed.
Despite the international outcry, the Soviets remained unrepentant. An
unidentified plane had strayed into their airspace at night. They believed they
had every right to 鈥渟top the flight鈥�. But in spite of the decades of inquests
and analysis, nobody has been able to resolve why the airliner strayed so far
from its designated course. Why didn鈥檛 the pilots notice their error and correct
it?
The flight plan told the pilots what to expect. They knew that, if the plane
is on course, then the radar would show only water. For at least 25 minutes the
pilots could see that the radar was showing the land mass of the Kamchatka
Peninsula. But the crew did not draw what appears to be the obvious conclusion.
They maintained their heading and, minutes later, the Soviet fighter plane
struck.
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It seems an extraordinary error. But the same breakdown of logic might also
have been behind the meltdown at Chernobyl. Research published earlier this year
claims that these failures in reasoning are a common occurrence, arising
whenever we are faced with scenarios that include 鈥渇alsity鈥濃�攖hings that
may not be true. For flight 007, the results were catastrophic. But according to
Philip Johnson-Laird, a psychology professor at Princeton University, we also
encounter the same logical meltdown in events both serious and trivial
throughout our lives.
You might have experienced this logical breakdown while hiking or driving
with the aid of a map. If you are on course, then the landscape you see
corresponds to the features the map tells you to expect. But if you find
yourself off-course, working out your location鈥攁nd the way back to the
right road鈥攇ets much more difficult. You have to deal with false
situations: if you had been on the right track you would have seen a gate
leading into a wood, for example. But you didn鈥檛, and attempting to compare what
you didn鈥檛 see with what you should have seen leads you easily into confusion.
Eventually, you give up on the logical solution to your problem and head
onwards. When you do see something that relates to the map working out your
whereabouts becomes trivial. That鈥檚 because it鈥檚 easier to deal with a true
scenario than a false one.
For more than a decade, Johnson-Laird has been fighting against the received
wisdom among researchers who investigate human powers of reasoning. The widely
accepted model for the way we reason is known as 鈥渇ormal rules鈥�. According to
this hypothesis we use rational, logical rules when we think things through.
Johnson-Laird concedes that we are certainly capable of this kind of thought:
with care, we can slavishly follow logical rules of deduction. However, he
believes we don鈥檛 usually think that way. Yes, we can be rational if we really
put our minds to it, but we usually employ shortcuts that save us a lot of time
and effort. These shortcuts, he says, are our everyday mode of thinking.
Unfortunately, he adds, they can also lead us into making foolish mistakes.
Instead of pursuing a set of rules and following through every piece of
information to its logical conclusion, Johnson-Laird believes we construct
鈥渕ental models鈥濃�攊maginary sketches of the possibilities of a
situation鈥攁nd work from these. To test his hypothesis, Johnson-Laird
constructs deceptively innocent logic puzzles like the one below.
Only one of the following statements about a particular hand of cards is
true:
There is a king in the hand, or an ace, or both.
There is a queen in the hand, or an ace, or both.
There is a jack in the hand, or a ten, or both.
Is it possible that there is an ace in the hand?
On first examination the answer seems obvious: yes. But ask a formally
programmed computer the same question and it will tell you the opposite. If
there is an ace, then the first two statements are true. But the puzzle
explicitly states that only one statement is true. So an ace is not
possible.
Johnson-Laird tested Princeton University students with this problem, and 99
per cent of them got it wrong. The reason for that extraordinary degree of
error, he says, is that there is limited space in what researchers call 鈥渨orking
memory鈥�: the low-capacity, short-term memory that supports language, arithmetic
and reasoning. When we draw our mental models of a situation our working memory
runs out of space very quickly. So, to save time, space and effort, we leave
vital information off the 鈥渄rawings鈥�. The pictures are all there, but the
labels鈥攍ike 鈥渢his picture is only true if the other picture is
false鈥濃�攃an go missing.
The first casualty of a full memory is anything that鈥檚 not true, says
Johnson-Laird. People can cope with the potential falsity of single-clause
sentences, such as 鈥淧at loves Val鈥�. If someone says that鈥檚 untrue, it鈥檚 clear
what they mean. 鈥淏ut they are not so hot with the potential falsity of `John is
tall and Mary is short鈥�,鈥� he says. If we are told that this statement is false
there are suddenly a lot of options to consider. Does it mean that John is
short, or that Mary is tall, or that neither is tall or short, or that we can鈥檛
draw any conclusion about their heights? When anything but the simplest
situation involves falsity the number of possible scenarios quickly becomes too
great to hold in working memory. So, Johnson-Laird claims, we ditch the falsity
and hope for the best.
Take the playing card puzzle above. In that case, the mental model will
be:
king 鈥� ace 鈥� king and ace
queen 鈥� ace 鈥� queen and ace
jack 鈥� ten 鈥� jack and ten
Using this model, we assume that it is definitely possible to have
an ace: there it is, looming large in two of the lines. But what doesn鈥檛 make it
into the mental model is the fact that one鈥攁nd only one鈥攐f the lines
is true, so the other two are false. 鈥淲hen people think aloud about this
problem, they clearly realise that one assertion is true and the others are
false,鈥� says Johnson-Laird. But that doesn鈥檛 make it into their mental model
because it involves setting up a whole new set of models. When you consider the
case in which it is true that there is a king or an ace or both, you must also
work out what follows from the falsity of the other assertions. All these
possibilities have to be modelled, and suddenly there鈥檚 just too much
information to handle. So, instead, we stick with our 鈥渋nstinctive鈥�
answer鈥攚hich is wrong. Here the consequences are not particularly grave.
But when the Korean pilots took the same shortcut, it cost 269 lives.
Not persuaded? Then look at the puzzles Johnson-Laird devised to demonstrate
the power of the illusions the mind can create. The question in each test is,
can both statements be true at the same time?
Test 1
There is a pin and/or a bolt on the table, or else there is a bolt and a nail
on the table.
There is a bolt and a nail on the table
Test 2
There is a pin and/or a bolt on the table, or else there is a bolt and a nail
on the table.
There is a pin and a bolt on the table
Test 3
There is a pin and/or a bolt on the table, or else there is a bolt and a nail
on the table.
There is a nail but no bolt on the table
Test 4
There is a pin and/or a bolt on the table, or else there is a bolt and a nail
on the table.
There is no pin and no bolt on the table
In these four tests there is an inconsistent pair of statements, an illusion
of consistency, an illusion of inconsistency and a consistent pair. They are not
laid out in that order, however, and鈥攗nless you can think like a
computer鈥攊t is not at all obvious which is which.
In April this year, Johnson-Laird reported his results from performing these
tests on more than 500 students (Science,vol 288, p 531). Johnson-Laird
found that all but one of them were fooled by the illusions in precisely the way
the mental model theory predicted they would be.
Test 1 is an illusion of consistency. When you work this problem out,
Johnson-Laird believes, you make a 鈥渕ental model鈥� of the four possibilities from
the first statement:
pin
bolt
pin bolt
bolt nail
Here you have four possibilities, and the fourth is consistent with the
second statement that there is a bolt and a nail on the table. So it looks as
though the statements are consistent. The illusion lies in a couple of little
words that don鈥檛 make it onto the mental model: 鈥渙r else鈥�. If the first half of
the statement is true, then the 鈥渙r else鈥� means the second half is false, and
vice-versa. But we discard this complicated falsity, and process the problem
without it. We assume everything on the model is possible and fall for the
illusion.
Picture it like this. If we took the 鈥渙r else鈥� into account, this would give
the following mental model:
pin
bolt
pin bolt
bolt nail
where everything in plain type is only true if everything in bold is false, and
vice-versa.
If the first half of the statement (everything in plain type) is true, then the
鈥渙r else鈥� means the second half is false and there cannot be a bolt and a nail
on the table. So the second statement (鈥渢here is a bolt and a nail on the
table鈥�) is then inconsistent with the first. And if everything in the first half
is false, there is neither a pin nor a bolt on the table. Therefore there can鈥檛
be a bolt and a nail.
Test 2 replaces the second statement with 鈥渢here is a pin and a bolt鈥�. Now
the two statements become consistent. You鈥檒l find you get that right easily,
because the 鈥渙r else鈥� doesn鈥檛 need to be processed.
Test 3 is an illusion of inconsistency. If the second half (in bold in the
mental model above) is false, there can be a nail without a bolt. That fits
perfectly well with a true first half too. So there鈥檚 no inconsistency between
the two statements.
Test 4, by the way, is the inconsistent pair of statements: whichever half of
the first part is true, there is always either a pin or a bolt on the table.
How does Johnson-Laird know that his subjects made their mistakes because
they failed to grapple with the notion of falsity? What if their working memory
were simply filling up randomly? Johnson-Laird鈥檚 confidence comes from the
predictable nature of the errors people make. By invoking the problem with
falsity, he was able to anticipate exactly what mistakes the students would make
on each of the tests. 鈥淚f human beings were intrinsically rational, they should
make only sporadic errors similar to slips of the tongue,鈥� he says.
So maybe people are using invalid logical rules? No, he says, because that
would make people intrinsically irrational鈥攁nd we鈥檙e not: we understand
our mistakes when they are explained. The only answer, Johnson-Laird says, is
that we lose the 鈥渙r else鈥�. That gets rid of the complex falsity and makes our
lives easier.
We may have evolved to discard the falsity, since it saves a lot of mental
effort. Often we only need to think about those situations that are happening in
reality, and are therefore true. But when falsity does matter鈥攁s it did
for the Korean pilots鈥攖hat evolutionary adaptation can turn on us
spectacularly.
Johnson-Laird believes the pilots鈥� mental models of the situation with the
radar were lacking vital information. They probably looked something like
this:
On course 鈥� Water
Land
There is nothing in this model to depict the possibility that 鈥渢he plane is
on course鈥� is false. According to the report of the International Civil Aviation
Organization, the pilots on the Korean airliner may have been suffering from
fatigue, a situation in which they would be conserving every ounce of mental
energy. With a conditional 鈥渋f鈥hen鈥� statement, we are perfectly aware that
the clause following 鈥渋f鈥� could be untrue. But we don鈥檛 always make the effort
to flesh that possibility out. Johnson-Laird believes we often leave it as an
unexplored path in the back of our minds.
So when the land contradicted the possibility of the plane being on course,
the pilots had nothing but that unexplored path before them. 鈥淚t is as though
they think to themselves, 鈥榯here are other possibilities, but I won鈥檛 worry
about them now鈥�,鈥� says Johnson-Laird.
In laboratory tests that mimic this scenario, Johnson-Laird says, many people
also draw no conclusion when confronted with this kind of falsity. The operators
conducting the experiment that led to disaster at Chernobyl may have been in
exactly the same position. According to Zhores Medvedev鈥檚 1992 book on the
meltdown, The Legacy of Chernobyl, they had the following pieces of
information:
鈥淚f the experiment is safe to continue, then the turbines must be rotating
fast enough to generate emergency 别濒别肠迟谤颈肠颈迟测.鈥�
鈥淭he turbines are not rotating fast enough to generate emergency
别濒别肠迟谤颈肠颈迟测.鈥�
From this, they should have recognised that the first clause could be false,
and admitted into their mental model the possibility that the experiment might
no longer be safe. But they didn鈥檛. 鈥淭hey went ahead with the
experiment鈥攚ith tragic consequences,鈥� says Johnson-Laird.
The mental models theory has yet to convince everyone who researches
reasoning and deduction. Ira Noveck of the Claude Bernard University in Lyon,
for example, believes its conclusions may result simply from people鈥檚 difficulty
interpreting the language of the puzzles. At least with the mental rules model
of reasoning, he says, it is easier to work clearly through the mechanisms
behind reasoning. Johnson-Laird insists he has conducted numerous variations on
the basic tests using different wording, and the results come out just the same.
And when people are asked to describe their thinking as they work through the
puzzles, this also suggests that they understand exactly what they鈥檙e being
asked to do.
Ruth Byrne, a mental models researcher at Dublin University who is
collaborating with Johnson-Laird, says the illusions provide a powerful
experimental proof for the mental models theory. 鈥淚t鈥檚 compelling evidence,鈥� she
says. 鈥淚t can鈥檛 be explained by any other theory of reasoning.鈥�
Byrne is investigating how mental models are involved with emotions such as
regret and guilt. These emotions require a deliberate effort to model falsity:
they rely on considering possible alternatives to the real-life consequences of
events. 鈥淵ou couldn鈥檛 explain an emotion like regret unless you were keeping in
mind the way a situation turned out and comparing this with an alternative where
it could have turned out differently,鈥� Byrne says.
Such forced, deliberate 鈥渃ounterfactual鈥� thinking might also be the root of
creativity, she adds. Byrne believes that imagination and daydreaming involve
creating these partially false situations and working through the outcomes of
their models. But that won鈥檛 help you pen a bestselling novel, because most of
us tweak our mental models in exactly the same ways. 鈥淭here is really remarkable
regularity in the counterfactual alternatives that people generate,鈥� Byrne says.
鈥淲hat we seem to find more difficult is creating counterfactual alternatives
that are unlike the ones that everyone else creates.鈥�
Find this elusive ability and you鈥檝e struck gold. But beware: by now you
should have realised that dealing with falsity comes at a price. Guilt, regret
and writing a novel are renowned as some of humanity鈥檚 favourite instruments of
self-torture. At least we understand now why it hurts.