Yuri Tarnopolsky
8. On Buridan's Ass

  cognitive dissonance. Niels Bohr. transition state.  history. equality. Buridan's ass.

Use Firefox browser or see  essays-complete.pdf


Essay 8. On Buridan's Ass


" 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 national mind.


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 the people.
2. People have personal property and the rest belongs to the state.

The only way to embrace both ideas was to identify the people and the state, which would be a big mistake in any society.

The split went deeper:

1. We have freedom of speech.
2. Everybody who criticizes the political system is a criminal.

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, national schizophrenia sounds exact.

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 personality (multiple 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 groundhog.

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 available.

Hamlet's predicament is a classical example of the grand cognitive dissonance, alias, internal struggle.

             To be, or not to be: that is the question:
                           Whether 'tis nobler in the mind to suffer
                           The slings and arrows of outrageous fortune,
                           Or to take arms against a sea of troubles,
                           And 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, either. 

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.Picasso1

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  Theorem was born out 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.

The scientific ideas that have survived for half a century, keep developing, and even make inroads into politics deserve deference.

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.

The general situation spans, in part:

from the pendulum of a grandpa's clock

                                    to the love triangle, which is not a static geometrical
                                                figure but a vacillation between two extreme positions,

from chemical equilibrium where a mixture of molecules A and B turning into each other  comes  to a constant ratio A/B (it seems like nothing is going on, but  the equilibrium is  dynamic: 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 of  uncertainty,

from the old sophism about chicken and egg

                                   to the problem of what came first in molecular evolution,
                                               DNA or proteins,

from quantum properties of a photon, torn by probability between two positions,

to the mind of a gambler choosing between red or black of     the roulette,

from mathematical paradoxes

                                    to the psychology and psychopathology of stock market.

from the dilemma of a religious believer who has to choose between the Bible and Darwin

                                                 to the dilemma of the prison doctor  who has to decide
                                                 whether to treat a mentally ill prisoner on death row
                                                 so that he could be executed.

 In the 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 A or advancing to the final stable state B. Nothing in the transition state alone indicates which way it will go. It is the triad  of 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 Russia.

The concept 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 other.

The dissonance screeches within two pairs of ideas:

        1. Person is a born human.
        2. An unborn human is a person, too.

        1. Religious views cannot be imposed by the government.
        2. Religious views on conception and pregnancy must be the law for everybody.

 Another case of split mind concerns violence.

1. The culture of entertainment demonstrates and glorifies violence. Violence sells.
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 violence.

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 the smokers.

While tobacco manufacturers can be sued for making completely legal products, the makers of violent entertainment cannot.

Another ear-scratching dissonance comes from the discussion on guns.

        1. The criminal (or the human nature) kills.
        2. The gun kills.

Some cases relate to education:

        1. All people are different
        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.
        2. Nobody 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 further damage.
2. Tax the smokers to pay the tobacco growers to save the smokers.

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 large end.
2. The law requires the opposite way of breaking eggs.

Being a strong believer in gun control and the power of numbers, I wish I could make a case against guns, using math as an evidence.

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.

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.


Here I 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 on hand.

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 independent events:

















Evidently, the $1 & $1 combination is only one of four outcomes.

If 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 product   P(A&B)=P(A)*P(B).

This 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.

The 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.

Let 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.

What 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:

        the probability of two simultaneous independent events equals
        the product of their separate probabilities.

The limits 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 arms.

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 levés.  

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 data.

I found the number of gunfire victims surprisingly low:
            There were a total of 30,708 people killed by guns in the U.S. in 1998. Of  these:

* 17,424 were gun suicides.
            * 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 me that:

About 41,345 people lost their lives in traffic crashes during 1999,
           in 1998 there  were 41,471 fatalities.

Since one 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 dangerous intersections.

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 opinions.

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 moment.

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 sound.

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 and debate.

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 collective truth.

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 opposite.

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 government!

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 temperature.

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 scale.

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 say:



P.S. (2016). 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.



Page created: 2001                                                     Revised: 2016

  Website: spirospero.net                          To contents                            email
   Essays 1 to 56 :
   Essays 57 to 60: 
   Essay 60: