" If you have a correct statement, then
the opposite of a correct statement is of course
an incorrect statement, a wrong statement. But
when you have a deep truth, then the opposite of a deep
truth may again be a deep truth.”
Niels Bohr made this often quoted
remark in the context of the emerging quantum physics and
the complementarity principle he had suggested. The
examples that he used to illustrate his idea were far from
quantum physics, however: 2 x 2 = 4 as a correct statement
and "God exists" as a deep truth. Because of its very
general character, Bohr's idea was even posted as "meeting ground
of science, philosophy and religion." I wonder if
anybody noted that by exalting the quotation as a deep
truth we make it self-denying. On such a shaky
ground I can hardly expect producing anything but a
shallow truism. Yet the idea that fascinated me in my
youth seems such a good seed for an essay!
To face two contradicting true
statements could be a very discomforting and dizzying
experience. What is good for the electron is not quite
good for the mind. If both ideas are of equal stature, the
mind can be suspended between them like the Buridan's ass
that died of hunger, incapable of making choice between
two equal bundles of hay. If an idea is either true or
not, then all true ideas are equally true. But there could
be some way to measure the value of truth to trade one
truth against another.
The Buridan's condition can, in
principle, affect a collective, corporate, or even a
I witnessed the first case of a split
national mind in the Soviet Union when it had not yet been
“former.” The Russian psyche, for example, had to
reconcile two particular ideas:
1. People have personal property and the rest belongs to
2. People have personal property and the rest belongs to
The only way to embrace both ideas was to identify the
people and the state, which would be a big mistake in any
The split went deeper:
1. We have
freedom of speech.
2. Everybody who criticizes the political system is a
1. We have free democratic elections.
2. There could be only one candidate in any election.
And so on.
When people wonder why Russia, more than ten years after
Communism still does not look like a normal country, its
prolonged recovery from a grave mental condition could be
an explanation. As an appropriate metaphor for it,
Although schizophrenia means split mind, it is
not quite what its Greek name might suggest. Its pathology
comes from the split between the mind and the reality.
Rather, schizophrenia is broken mind.
There is a psychiatric condition called split
personalities), but the patient can have only one
personality at a time.
Probably, the best term could be cognitive dissonance,
if only it did not sound so terribly technical.
Interestingly, the concept is almost as old as computer
technology. Not being a household name, it is something we
are very much familiar with because human psychology is
about what we can see with our eyes closed.
Cognitive dissonance looks very much as the true split
mind. It occurs when two or more logically incompatible
ideas have to share the mind like two bears in one den.
Struggling for peace, the mind usually pretends that one
of the bears does not exist or is not a bear but a
In my opinion, an exemplary, although casually recorded,
case is that of the first woman on earth. Yet unnamed at
the time, she quotes God to the serpent : "God hath said,
Ye shall not eat of it [fruit of the tree of knowledge],
neither shall you touch it, lest ye die" (Gen., 3, 3). The
serpent reassures Eve: "Ye shall not surely die," and
throws in more arguments. Eve acts upon the totality of
all contradicting information, observations, and natural
instincts, thus resolving the dissonance, and I see no
evidence that her progeny ever regretted it.
In extreme cases, the mind is in agony. In others, the
result looks more like flipping the sign with OPEN
and CLOSED on a shop door. It is closed for the night but
will be open in the morning.
An example of a trivial cognitive dissonance is the
struggle of two ideas: it is good to drink at a party and
it is bad to drive under the influence of alcohol. This
conflict of ideas can be solved relatively easy and the
sign permanently shows CLOSED to the bad choice. The
technical solution such as a designated driver is also
Hamlet's predicament is a classical example of the grand
cognitive dissonance, alias, internal struggle.
or not to be: that is the question:
'tis nobler in the mind to suffer
slings and arrows of outrageous fortune,
to take arms against a sea of troubles,
by opposing end them?
An easy solution is not to do anything, trust the power
of time, and let the things take their course. That was,
actually, the attitude of the majority of the Soviet
people. Hamlet takes arms and dies.
In Sophocles' Antigone,
written around 440 B.C., the eternal conflict between
law and personal duty is represented by king Creon and
Antigone who do not have any doubts about their respective
stands. It imposes a dilemma on the population of Thebes,
as well as on the mind of king's son Haemon who is torn
between the filial obedience and love to Antigone. The
tragedy ends as a tragedy, not as a Hollywood movie, and
all the good guys die. The conflict was only slightly
rearranged by Shakespeare in Romeo and Juliet. For
the people of Thebes, however, like for the people of
Verona and theater audience of all times, the conflict is
not personal, it is purely abstract. The subconscious
physiology plays little role here and all the cards are on
the mental table.
Literature is powered by conflict. If not for cognitive
dissonance, with its overtones of drama, suspense,
challenge, and risk, we would not have any creative
writing, no epics, no romance, and no detective stories,
Unlike Hamlet, Antigone does not have any doubts. The hero
who reflects and vacillates comes later in history.
One can ponder “to be or not to be” for years, but the
smoker's dilemma requires an immediate decision. In
the struggle between “it is good to smoke” and “it is bad
to smoke,” the choice between wisdom and pleasure is
literally a matter of to be or not to be.
The smoker's dilemma is the most often cited example of
cognitive dissonance. Because of the substance addiction,
however, the somber drama displays in deep physiological
cellars of the brain where mind has little power. It is
really an impasse, the mind is cornered, and there is no
cop-out. There is no such thing as a designated smoker. A
nicotine patch? The love triangle is of the
same nature, but love mercifully turns off the reason and
lets the emotions act.
The mind tries to reduce the discomfort in one way or
another, sometimes, by ignoring the information that
aggravates dissonance or adding weight to the information
that alleviates it.
With the rising din of the twentieth century, dissonance
became a common device of modern art, especially, in
music, painting, and theater. The Picasso's women seen
from both front and back and projected on the plane like
the map of the world (see, for example, Femme
nue jouant avec un chat 3), exemplified the
new dissonant vision, while others (Nu assis aux bras
levés, 1940) seemed like allegories of broken mind,
which was also the forte of the artist
Francis Bacon. Picasso, known as a cruel woman-hater, took
it out almost exclusively on women, while Bacon gallantly
diverted it on himself.
The art of René Magritte, whom I like very much, was based
entirely on the visual dissonance, while Maurice Escher
tried to catch the fleeting moment of transition from one
opposite to the other.
The sharp logical dissonance in
statements referring to themselves, like "This sentence is not true"
generated a massive amount of mathematical research in the
twentieth century. If it is true, then it is not
true, and if it is false, then it is true. Can we resolve
the dissonance? The famous Gödel
Theoremwas bornout of the problem. Its
substance and scope are highly technical and complicated,
but the proof carries grave philosophical implications.
For instance, one can expect examples of logical
statements ('Is secession constitutional?') to arise that
are neither provable, nor disprovable, within a complete
logical framework. One should not be surprised when
the collective mind of the Supreme Court is split.
scientific ideas that have survived for half a century,
keep developing, and even make inroads into politics
I believe that cognitive dissonance is only one case of
a very general situation when a system seems to be in
two incompatible states at the same time.
situation spans, in part:
from the pendulum
of a grandpa's clock
the love triangle, which is not a static geometrical
figure but a vacillation between
two extreme positions,
equilibrium where a mixture of molecules A and B turning
into each othercomes
to a constant ratio A/B (it seems like nothing is going
on, but the equilibrium isdynamic: at
any moment some of A turn into B and an equal number of
B turn into A),
to a tight
election campaign where the pool of undecided voters,
like a swarm of gnats, creates a cloud ofuncertainty,
from the old
sophism about chicken and egg
the problem of what came first in molecular evolution,
properties of a photon, torn by probability between two
to the mind of a
gambler choosing between red or black ofthe
the psychology and psychopathology of stock market.
from the dilemma
of a religious believer who has to choose between the
Bible and Darwin
the dilemma of the prison doctor who has to decide
to treat a mentally ill prisoner on death row
that he could be executed.
range so wide, the word dissonance is hardly applicable.
Nature does not know dissonance: the mind does.
Mind is complex, but there is little more we can say
about mind. In the state of cognitive dissonance, mind
is like a molecule that tries to decide whether it is A
or B. While it is deciding, it is both.
Where a psychologist declares cognitive dissonance,
chemist, like myself, would use the term transition
state for the ephemeral evasive structure
existing for a short time in a chemical reaction and
capable of either returning to the initial stable state
advancing to the final stable state B.
Nothing in the transition state alone indicates which
way it will go. It is the triadof initial,
transition, and final states that determines the
probabilities of the outcome.
A historian would use the terms crisis or revolutionary
situation, describing the time of upheaval and
confusion, but the actual participants had no idea,
while the historian knows post factum how the
events turned out. The presidential election of
2000, with all its bewilderment, presented a colorful
example of a short-living, only hours long, transition
state on a smaller, sub-historical scale. A historical
transition can take centuries, as happened with the
Industrial Revolution, and it can be observed in all
details if the records are available.
In short, it is the moment of transition, emergence,
uncertainty, ambiguity, and gray area between yes and no that decides the
fate of individuals and nations. It is something that
20%, 50% or 80% yes and the rest is
no. Looking back,
everybody can see at least one moment of irreversibility
that changed our lives forever, "point of no return
unremarked at the time in most lives," as Graham Greene,
a great analyst of the dissonance, wrote in the
beginning of The Comedians.
What happens between an offer of a recruiter to a
potential spy and his acceptance (or rejection)?
What happens between the call for help and rushing
between an armed criminal and his victim?
In general, what happens between tossing a coin and its
hitting the ground? Even the theory of probabilities has
no answer. Metaphorically speaking, the mind of the
falling coin is split fifty-fifty.
Suppose, a new reality becomes known
in the form of new event (like a high school shooting),
scientific idea (human cloning), discovery (protein as
infectious agent), social shift (toward temporary and
disloyal employment), political development (scandal),
act of war (God forbid!), or act of God hurling an
asteroid toward the sinful planet.
Often only a minority cares. If an individual takes the
news close to the heart, his mind must take a stand.
Sometimes, the majority is united on the subject.
Sometimes, society splits into parties sticking to two
different opinions, while the undecided are in significant
minority. Sometimes, both sides are just minorities.
Initially, while the news is fresh, everybody knows only
his or her own opinion. The next transitional stage is the
information about the opinions of other individuals.
As soon as the opposite sides are aware of their mutual
positions, their numerical strength, and the implications
of the split, we can speak about a dissonance in the
collective mind. The opposites create each other, leaders
step in the limelight, money is raised, lobbying is
launched, lawyers hired, and the two mental bears start a
wrestling round with a bear hug.
People mostly have no problem with choosing their
positions. It might happen, however, that the individual
choice is difficult.
With my mind perversely attracted to inconsistencies, I
noticed some familiar symptoms in America.
The issue of abortion presented the
biggest problem to me. When, soon after my arrival to
America, I saw for the first time small groups of
protesters with gruesome posters, I could not believe my
eyes. I thought the legal and affordable abortion during
the first three months was one of a few civilized features
of freedom, as I understand it (certainly, whatever you
say about freedom will be a deep truth), allows
everybody to make his or her own decision, especially,
of a very private nature. If there is freedom of
religion, why is there no freedom of reproductive
choice? Yet men, who know neither pregnancy nor abortion
nor the true burden of childcare, dictate women who are
not even their wives or mistresses but complete
strangers what to do or not to do during
pregnancy. All the men can reasonably do is to take a
vow not to perform abortion on themselves and each
dissonance screeches within two pairs of ideas:
Person is a born human.
2. An unborn
human is a person, too.
Religious views cannot be imposed by the government.
views on conception and pregnancy must be the law for
case of split mind concerns violence.
1. The culture of
entertainment demonstrates and glorifies violence.
2. The cultural, religious, and social tradition forbids
violence. Violence is destructive. Or, to
put it differently:
1. We advertise products and behavior by showing happy and
successful people who use them and unhappy clumsy people
who don't. The law forbids violence. We do not advertise
2. We advertise violence by showing around the clock good,
attractive, and successful men and women slaughtering
other people in an elegant and efficient manner.
1. Tobacco is a legal product. Its health hazards have
been in public domain for a long time.
2. Manufacturers of tobacco are sued for the harm done to
While tobacco manufacturers can be sued for making
completely legal products, the makers of violent
Another ear-scratching dissonance comes from the
discussion on guns.
1. The criminal
(or the human nature) kills.
2. The gun
Some cases relate to education:
1. All people
2. All people
can equally succeed in learning
Others complicate the problem of freedom of speech:
1. Everybody is
free to express her or his personal opinion.
should offend others with his or her opinion.
An entire class of utopian expectations or
self-contradicting measures grows from the counterpoint:
1. Men and women are different.
2. Men and women are equal. (Therefore, "his or her", Xena
the Warrior Princess, etc.)
1. Save the caribou.
2. Save the low gasoline price.
1. Limit the tobacco growing to save the smokers from
2. Tax the smokers to pay the tobacco growers to save the
The pure case of national schizophrenia was
recorded by Jonathan Swift as the conflict between those
who break the egg at the large end and those who break
it at the small end:
1. It is
convenient, customary, and natural to break eggs at the
2. The law requires the opposite way of breaking eggs.
strong believer in gun control and the power of numbers,
I wish I could make a case against guns, using math as
Probability has always had a mystical aura in my
eyes. I am crossing the street and the goddess of
probability hovers over me making a quick decision
whether the oncoming car will hit me or stop at the red
light. I live my life, and after a certain age,
probability to die next day is growing faster and
faster, like an evening shadow. And in fact, the car
does not hit me because the probability is low and I die
because the probability is high. The amazing thing is
that whether the car hits me or I live to 100
years, either way it will be justified by probability.
makes us nervous or assured, self-destructive or cautious,
hopeless or energized. Hope is probability. Fear is
probability. An umbrella is probability. It is a powerful
factor in our life, moving millions of dollars and driven
by megawatts of energy. This is awesome, taking to account
that the value of probability can never be more than one
and less than zero. The immaterial probability has a very
intimate relation with energy, but this my private
obsession deserves a separate essay.
Probability is a more agile sister of cognitive resonance:
a rapid swinging between yes and no, so rapid that we
sometimes do not see the extreme positions. Probability is
the fraction of yes
in the superposition of yes and no.
Next follows a primitive example of dealing
with probability, which may well be skipped.
have in mind only one property of probability, which can
also be discovered by using common sense. For the
experiment we need two identically shaped objects of one
kind and two of another kind. It is remarkable
that paper dollars, all of the same size, is the
only category of such objects that we always—almost—have
If we have one $1 and one $20 bills in the left pocket,
the probability to pull $1 is 1/2. If we have the same
bills in the right pocket, the probability to pull $1 is
also 1/2. The probability to draw $1 bills from both
left and right pockets is 1/2 x 1/2 = 1/4. This can be
checked by repeating the drawing many times. In
approximately a quarter of all drawings we will pull $1
from both pockets, provided we put them back in a random
fashion, which is a rather awkward requirement.
To arrive at this conclusion
theoretically, we simply need to list all possible
Evidently, the $1 & $1 combination is only one of
there is event A with probability P(A) and independent
event B with probability P(B), the probability of the
events A and B happening simultaneously is the
illustration tells us something about probability. We
can get the result in many cases without any complex
mathematics, using our common sense and calculating the
total number of all possible events. We need more
mathematics only for more intricate questions.
laws of probability are much harder to dispute than
Darwinism. They can be tested with the same result on
various models 24 hours a day. In Bohr's terms, it
is a trivial truth.
us take the case of gun violence. If the probability
that today a man firmly decides to kill another man in
Murdertown, MU, is
PM (M for murder) and the probability that a
man possesses a gun in the same town is PG(G for
gun), than the probability of a murder with a gun is not
more than the product of two probabilities. PM&G
(Murder & Gun) = PM *PG
. Actually, it is lower, because it should be multiplied
by the probability that the victim is within reach.
this trivial truth tells us is that if PG is very low, PM&G(Murder &
Gun) will be still lower. If PG =0, PM&G
will be 0 even if PM =1. This is
because probability is a fraction and if we multiply two
fractions, the product will be less than any of them:
0.5 * 0.1=0.05. This reasoning might be not so accurate
and even naive, but it illustrates the principle:
probability of two simultaneous independent events
product of their separate probabilities.
on gun possession will have a powerful reducing effect
on the probability of gun violence. If the
violence is reduced, then there is less reason to have
I hope this
is a rational argument. One can find scores of rational
pro-gun arguments, too. It is hard to disagree that in a
violent country one has to protect himself. On the other
hand, in a civilized country it is the government's job
to protect the citizens in a professional manner. For
the sake of variety, it is nice to see an
anti-intellectual and anti-government society still
based on Western values, but this combination is an
ultimate dissonance, a Nu assis aux bras
In my search
for the truth, whether deep or shallow, I decided
to look at the numbers on the Web. I was surprised that
the statistics did not jump on me from the screen. It
was difficult and sometimes impossible to find reliable
I found the
number of gunfire victims surprisingly low: There
a total of 30,708 people killed by guns in the U.S. in
1998. Of these:
* 17,424 were
* 12,102 were gun homicides.
* 886 were unintentional or "accidental" shootings.
* 316 were shooting deaths of undetermined intent
At the same time, the number of traffic fatalities told
people lost their lives in traffic crashes during
in 1998 there were 41,471 fatalities.
does not need to be the driver in order to get hurt in a
crash, the entire population is at risk. The risk to be
killed by car is higher than the risk to die of
bullet. There are dangerous neighborhoods, and there are
It is obvious that the use of cars must be limited
in order to save lives. The murderer does his best to
kill, while the driver does his or her best not to kill
and not to die in a crash, and yet more people die in
crashes than of bullet.
On the second thought, if we protect spotted owl and sea
turtles, why not to protect human fetuses?
Thinking about all that, loosing ground under my feet,
and feeling dizzy like from This sentence is
false, I felt as disoriented as a compass on
the North Pole, where every direction points to the
South. All I could do was to formulate some personal
Niels Bohr was absolutely right: a deep truth is as true
as its opposite. This can be possible, however, because
both are equally irrelevant for basic human needs. The
general course of life is driven by shallow but
practical, singular, and opportunistic truth of the
Whatever the law, there is always a significant
probability that the killer will find a gun, the
unwanted pregnancy will be interrupted, men and women
will be equal at some opportunities and unequal at
others, most people will carefully consider whether to
speak their minds under the circumstances, some people
will learn and succeed more than others, ads and
entertainment will appeal to basic and base human
instincts, religious ethics will not stand against the
pursuit of health and beauty, and the eggs will be
broken at the most convenient end.
Deep or high truth is the truth shared by such a large
number of people that the opposite is shared by a
comparably large number, too. Quite automatically, as
soon as one truth spreads and acquires the status of the
grand truth, its opposite attains the same status by
default, ceases to be a heresy, and its proponents begin
to consolidate the ranks around leaders, worship
martyrs, raise money, and lobby the government.
The necessary condition is, however, that the truth is
really irrelevant to basic human needs, like the
question whether to cross oneself with two or three
fingers, and personal experience does not provide any
clue. On the contrary, it is vitally important to know
that 2 x 2 = 4 in order to keep the personal finances
The absolute majority of people have always believed
that personal security, pleasure, comfort, health,
beauty, and wealth are good. The opposite view remains
heresy, sectarianism, or sainthood. On the
contrary, the deep truth is abstract and open to doubt
People hold on to a pragmatic individual truth
regardless of what other people think. This is not quite
so with a collective truth, otherwise known as deep
truth, which exists only because there is an opposite
Paradoxically, the truth is shallow if an overwhelming
majority of people shares it. A fifty-fifty split
national mind is the perfect certification of the depth
(more government? less government?).
Therefore, the closer the fraction of believers to 50% ,
the deeper the truth. If the ratio is small or large, it
means that one deep truth is less deep than its
On the other hand, a deep truth is only a half-truth.
Does idealism make sense? Why do we want to save the
whales and limit the use of sonar necessary for the
safety of people in submarines?
Ban the submarines! Ban capitalism! Down with the
Youth is a transition state. National schizophrenia is a
transition state. Insoluble contradictions, dissonance,
undecidable measures—it is all, like in chemistry, is an
ephemeral, on historical scale, transition state of
social change. Even the mind-boggling contradictions of
the Soviet Communism were an evidence of an overdue,
frozen transition. Having seen both, I truly believe
that democracy and tyranny are not the logical opposites
but the opposite ends of the single scale, like cold and
heat are simply temperatures below and above the body
Nothing can drive large masses of people in one
direction as effectively as abstract, irrational,
nebulous, and idealistic goals. They turn human
molecules into solid bodies that can perform mechanical
functions of destruction and construction. Nothing can
as effectively resist the flocking instincts as
tightening the screw on basic, almost animal, human
needs. Rich society protects the whales, poor society
tries to survive and eats rats and dogs.
Each time we give to an abstract idea (sanctity, global
domination, democracy, national pride, privacy, even
freedom) a priority over basic human needs (security is
one of them), we move toward the totalitarian end of the
The secret of a totalitarian state, whether Fascist or
Communist or any other past or future form, is that it
starts with idealism, i.e., with a deep truth. When it
becomes evident that idealism works against basic human
needs, the population must choose between a dire
deprivation of human needs and whatever else the
government drives into their minds, so that any flocking
and resistance is out of question, and "whatever else"
is accepted to ease the dissonance. Good-bye whales,
caribou, and spotted owl!
Well, I have arrived at the shallow truism that I
anticipated in the beginning. All that has been well
known, analyzed, and recorded as one of the major
lessons of the twentieth century and is quite trivial.
For somebody who, like myself, has lived through most of
the twentieth century, however, it never fails to stir
the pool of late and futile emotions.
But what about the Buridan's ass? The modern solution of
the problem seems to be that any complex dynamic
system—and animal mind is more than enough dynamic and
complex—experiences fluctuations. No balance is balanced
and no equilibrium is equilibrated forever. Pretty soon
there will be a moment when one bundle of hay will look
bigger than the other. Besides, a gust of wind could
move one closer to the mouth than the other. Thus, in
the 1930's there was a period of hesitation of
idealistic Western intellectuals between the capitalist
and socialist bundles of hay, but the winds of history,
starting with the Communist repressions and
Hitler-Stalin pact, showed that the equality was an
optical illusion. It is hard to blame the idealists in
times when the capitalist bundle of hay was severely
shaken out by the Great Depression.
This is how history is made and our lives are lived.
Something always happens in our lives and in history
because any hot enough complex system is full of chaos
and driven by probability and not certainty, and so we
fall into the trance of our dissonant transition state
and come out of it to a landscape that has changed, and
we ourselves look different in the mirror, notice gray
hair, and this is how life walks, one foot firmly on the
ground and the other in the air, one step at a time,
mostly standing still, and rarely jumping with both feet
above the ground, causing an eerie, electrifying
sensation of losing one's mind.
If we still have $1 and $20 bills, we can conduct
another experiment: show them to a man in the street and
suggest to take one. If we do it many times, the
statistics is easy to predict. The probability that the
man will take $20 will be very high, as compared with
taking $1 or not taking any. Therefore, the fact that
the bills are of equal size cannot deceive basic human
instincts. Well, we still have to run this experiment
before we state anything.
If you asked me what next abstract idea is likely to be
given priority over basic human needs in America, with
potentially destructive results, I would reluctantly
In fact, inequality is the most destructive factor today,
which makes equality/inequality look
like a deep truth, which, nevertheless,concerns basic
human needs of the overwhelming majority. This
paradox resolves if we realize how far the distribution is
removed from 50/50.