Yuri Tarnopolsky                                                                                                                                   ESSAYS

Essay 14. On Taking Temperature with a Clock

 temperature. range of variations. music. chaos. order. rubato. Bach. Beethoven. Bartok.

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Essay 14. On Taking Temperature with a Clock

Baron Munchausen  once had to travel by post carriage during a ferociously cold Russian winter.

The winter was then so uncommonly severe all over Europe, that ever since the sun seems to be frost-bitten.     THE SURPRISING ADVENTURES OF BARON MUNCHAUSEN, By Rudolph Erich Raspe,  Chapter VI.

On a narrow road he made the coach blow his horn to warn the oncoming travelers. Not a sound, however, could be extracted from the horn.


Having arrived at the inn, the coach hung the horn on a peg near the kitchen fire.


Suddenly we heard a tereng! tereng! teng! teng! We looked round, and now found the reason why the postilion had not been able to sound his horn; his tunes were frozen up in the horn, and came out now by thawing, plain enough, and much to the credit of the driver, so that the honest fellow entertained us for some time with a variety of tunes, without putting his mouth to the horn - The King of Prussia's March - Over the Hill and over the Dale - with many other favorite tunes; at length the thawing entertainment concluded, as I shall this short account of my Russian travels. (Chapter VI)


Travels and Surprising Adventures of Baron  Munchausen  was originally written in English (1785) by the German author Rudolph Erich Raspe (1736 - 1794). By linking music and temperature, the quoted story gives me a starting point for my own story.

The definition "music is organized sound" is attributed to Edgar Varese (1883-1965), a composer who did a lot to disorganize music by expunging melody and harmony.

Edgar Varese might be right but noise can also be organized, and so are natural and artificial sounds, whether pleasant or irritating. Music is what we call music and sell as music today. Yesterday music meant something different.  Some sound illustrations can be found at The Classical Archives site.

Let us look at three composers, each born a century apart: Bach, Beethoven, and Bartok.

Bach, not just revered by everybody but also admired by many, leaves me, with a few exceptions, cold. Beethoven is, for many reasons, the highest peak in the evolution of music—the opinion I share. Bartok leaves most fans of classical music cold but he is my favorite.

My choice does not represent music as a whole because all three are devoid of romanticism, another powerful branch of musical evolution that I enjoy, too. I prefer music without illusions and sugar, but I love music as a whole, as a parallel world in which a daydreamer can find a temporary shelter from daylight.

Listening to Johann Sebastian Bach (1685-1750) we can hear not only a very regular rhythm but also a rather even distribution of sounds in time. Long pauses and dissonances are absent and sharp dynamic contrasts are rare. The music is well organized, very regular, and even predictable over significant segments. What is hardly predictable is the combinatorial richness of the pieces. There are listeners who worship Bach as the source of heavenly peace, harmony and perfection, others as an ideal of predictability and order, and some, I suspect, put it as an ice pack on the bruised soul. Bach not only creates his own universe, right before our eyes, but also the laws for all subsequent ones. If none of the components of music employed by Bach remains, music ceases to exist to my ears.

Ludwig van Beethoven (1770-1827) departed from the canons. His sound is distributed less evenly and the pauses and long repetitions appear. His music is full of dynamic and orchestral contrasts, complexity, heroic power and tragedy, anxiety, longing, despair, and idealistic beauty. It seems to comprise the full range of human emotions ennobled by intellect, the range so wide that nobody could ever cover his range afterwards. Remarkably, it is still mostly ordered and regular, despite an overwhelming number of innovations. It is about the worldly life, but mostly above its passions.

After Beethoven there was little left unexplored in the classical universe created by Bach. Meanwhile, the Industrial Revolution was turning the world around, and the historically brief but incredibly dense wave of musical romanticism rolled over the nineteenth century world stitched together by steamships and locomotives. There is a relation between both, and as a seed for another essay, I can only note that even the cast flywheels of the early steam engines were embellished as if the engine were Empire furniture, while it was sheer power.

By the time of the WWI,  romanticism—the music of illusions—was gone.

Bela Bartok's (1881-1945) music, as inventive as Bach's and Beethoven's, is nervous, dissonant, irregular, violating all the rules of Bach's Well-Tempered Clavier. It loses a distinct rhythm in the "music of the night" of his slow pieces (for example, in Music for Strings, Percussion, and Celesta), or takes an ominous mechanical beat (for example, in Miraculous Mandarin).  The heavenly beauty and peace disappears from Bartok's music completely, as it disappeared from the world he lived in. The melody is cut into short and unadorned phrases but the rhythmic diversity is rich and intricate.

While Beethoven could find harmony and greatness in the struggle of the individual against the world, Bartok accepted the irreconcilable conflict, with little hope, but no resignation.

It seems to me that Bach talked to God, Beethoven to equals, and Bartok to himself.

All three composers left piano works of pure combinatorial inventiveness: Bach in his Clavier and Inventions, Beethoven in Diabelli Variations, and Bartok in Microcosm (Mikrokosmos). None of the three composers can be called "sweet." Mozart was sweet or, rarely, bittersweet.  

Bach was recognized as a great composer only 80 years after his death, Beethoven's music initially was too hot and passionate for his contemporaries after Mozart and Haydn, and Bartok still grates upon the ears tuned to Beethoven, Schubert, and Chopin.

Dmitri Shostakovich (1906-1975), one of the last big classical composers,  in his latest symphonies and quartets was reminiscent of Bartok, but in general he was much colder. I hear in his palette Bach's monumentality, Beethoven's passion, and Bartok's dissonance intentionally combined in almost postmodern manner. Shostakovich lived in time of fear.

Distinct rhythm was the necessary and sufficient condition of classical music, and it still is in folk and popular music. At its beginnings, music was very rigidly organized, but with time the restrictions loosened a lot. The composer prescribes rhythm as metric pattern consisting of sounds of different duration, accents, and pauses. The composer also marks tempo, traditionally, in Italian, as fast, slow, etc., and dynamic effects.

There is a curious tempo employed mostly by the romantic composers of the period after Beethoven: tempo rubato. In Italian rubare means to steal: duration is stolen from one note and added to another. Rubato makes some notes shorter or longer than the others in the bar so that the total rhythm is preserved.  Rubato, therefore, applies not to the tempo but to its regularity. The following two sequences symbolize regular and rubato tempos by having  the same length but variable segments:

    a     a     a     a     a     a      a   regular
    a      a    a    a       a   a       a  rubato

The effect of rubato is emotional tension and expressivity, the warmth of music, typically represented by Frederic Chopin's Nocturnes.  The irregularity, freedom of composition, fuzziness, abrupt changes or dreamlike fluidity, swinging between joy and sadness, positive attitude to life and its stages, rich chiaroscuro, nuances, and warmth are typical for romanticism and, actually, most of the music starting from Hector Berlioz (1803-69) to Claude Debussy (1862-1918) and Sergei Rachmaninov (1873-1943).

The warmth of the violin and cello sound, so different from the fixed sound of piano, comes from the very design of the violin with its smooth fingerboard that makes the sound less predictable. The performer places his or her fingers with spontaneous or deliberate variations. This variability of the sound is widely used for expressive effects. One of them is vibrato, when the sound fluctuates around a certain tone due to wavelike movement of the finger. Glissando, the continuous sliding of the finger between two tones, can imitate human groan or shriek of joy.

The human voice is the richest instrument, completely devoid of any fixed ordering, but not all singers are able to use the dramatic possibilities of its chaotic potential when technical difficulties and exertion divert most of the energy.

Here are some notes of teachers of music about rubato.

Rubato is a nuance in music with all elusive definition. It is at best learned experientially through listening, analyzing, observation, and imitation, but not necessarily in that order. Even composers editors, and performers have a problem with exactly how this "device" should be used. The "bending of time" will probably not be interpreted the same way by students, teachers, or even advanced performers.

How then, can it possibly be taught? It would be impossible to devise rules for the introduction of rubato for all students or predict when the first magic moment of stretching for expressive purposes might occur.  ( Miriam Byler )

Rubato is not a mathematical concept and cannot be taught by mechanically adding to one note and subtracting from another. The purpose of rubato is to add expression to the music. The key for teaching this concept is the imagination. Each student has different life experiences, background, exposure to the arts, and level of sensitive listening. These either help or hinder the student's ability to imagine. (Sue Shannon )

But of course, rubato is a mathematical concept: it means increasing entropy of a temporal sequence. It means relaxing control over tempo, increasing disorder, and making music less predictable. This is what typically happens with somebody experiencing strong emotions, anxiety and agitation, with a nation in a turmoil, government in a scandal, outraged community, disgruntled employee, collapsing political structure, automobile tire manufacturer with loose quality control, disorderly football fans after their team wins, economy that had lost ground, a lover having discovered betrayal, and any physical system when temperature rises.

In Joseph in Egypt by Thomas Mann, Joseph learns about the interest of Potifar's wife in him.

Joseph's heart—that heart which Jacob, far away, believed long stilled in death, whereas here it was in Egypt, ticking on and exposed to all perils of life—that heart stood a moment still, then, as a heart does, throbbed the faster in order to overtake its lost beats.  (Volume 2, Part The Smitten One, Chapter Threefold Exchange)

 Rubato means that the temperature of the tempo goes up.

Of course, we have to be careful while attributing chaos to a performance. A trained performer can imitate chaos in a cold calculated way. Actors of the silent movies substituted the broken, jolted and exaggerated facial expression and gesticulation for the absent speech. A cursory lover moves in a metronome-like mechanical rhythm, while a refined one improvises variations of the meter and tempo. Computer, like a skilled performer, can only imitate chaos, but I swear that the Microsoft software that I use has some leftovers of authentic human chaos in its nooks, like any rigid, totalitarian, expansionist, and monopolistic system has. Well, bugs are not a Microsoft monopoly, to be honest.

In general, the history of arts can be interpreted as a constant warming up to the temperature when the order dramatically drops: the melting point (see Essay 11).

What is cold and what is hot?

We use GREAT, BIG, SMALL, and TINY with a comparable range of  nouns but there is always a potential number behind the adjectives of size. BIG success means that there is a large number of positive press, sales, attendance, profit, and  small number of accidents and misfortunes of any kind.  These qualities are measurable.

Speaking about emotion, desire, enthusiasm, interest, deal, stock, news, art, feeling, sex, color, debate, character, etc., we use the adjectives HOT and COLD in situations where no thermometer would work.

 What number stands behind the metaphorical heat and cold?

 For most of my life I believed that temperature was one of the cardinal properties of individual and social life and not just a lexical usage. My personal problem with temperature is that I am not an expert in physics and mathematics. As an excuse, I am looking at the temperature outside physics.  A possible good side is that I can find common language with others like myself.

The last half of the twentieth century was spent by some scientists in search for a general theory of complex systems, usually called systems theory, a difficult and fuzzy topic that I would not touch here. The word "systemic," however, is a convenient identifier for the temperature I have in mind (although it has a particular meaning in medicine).

I  believe that very complex systems, for example, humans, whether taken individually or as society, are not good objects  for complete scientific description. The number of human situations and circumstances is enormous because of their combinatorial nature (see Essay 12). Yet there is a lot of built-in order in human behavior.

It may seem that the more order, the easier to describe a complex system, but the following example may perhaps illustrate the arising problem. Suppose, we have separate statistics of house purchases and marriages. We could calculate the probability of the combination of marriage and house purchase by multiplying the probabilities of both. The trouble is that this can be done only for independent events. To find out whether they are independent or not, we have to compare three probabilities: two separate and one combined, which would make our original intent senseless.

This is why we read fiction, memoirs, and biographies: human life is described in them, presumably, as it is, although with most minute detail omitted. True, it can be very far from reality. Nevertheless we can clearly see typical human collisions even in science fiction.

I believe that analogies and metaphors can help understand complex systems. They are major tools of literature and I see no reason why they should be banned from use along with standard scientific approach to aspects, mechanisms, and patterns of human existence. Temperature is among them.

We enter a cold room and turn on the heater. The room thermometer shows the rising temperature because the molecules of air beat against its surface and transfer part of their energy to the liquid in the bulb. The liquid expands and its level in the capillary tube changes. This goes on until the thermometer receives as much energy from molecules as it gives it back, i.e., until equilibrium is reached. The nature of temperature is, therefore, energy. Temperature can be measured in units of energy. Since the mass of molecules does not change, their energy depends only on their speed. The faster they move, the more often they bump into the thermometer and each other.

I do not know what energy is and I am sure nobody can give a universal definition. It is so fundamental that cannot be defined through other things. On the contrary, we can define a lot of properties through energy. We know that energy never disappears and never comes out of nothing. We can measure its change.  We can separate the change of energy into two components: change of order and change of chaos.

 I start here with understanding temperature as a measure of average energy of chaotic events in the system. Thus presented, temperature loses all its specific physical flare except for the word “energy.” Instead of energy we can use the word "effect."  For example, the temperature of the religious, political, environmental, feminist, anti-war, or any other movement can be measured by the frequency of demonstrations multiplied by their intensity and degree of violence. The temperature of the Middle Eastern region is the frequency of  conflicts multiplied by their gravity. The temperature of an area of scientific research is measured by the frequency of publications multiplied by their novelty.

As individuals, we measure the temperature by the information that bombards the bulb of our brain. Unlike thermometer, our brain is what is called an open system: we can lose part or all information next day or even next minute. For the people in the Middle East, however, the input can exceed the loss, and the overheated brain turns to action.

The bulb of the Congress, bombarded by demonstrations and lobbyists, finally reaches the legislative point of no return. A hot research area, on the contrary,  may lose steam because the nature finally has little to demonstrate.

The temperature of love may manifest in the number of gifts and their value. It can be also read from the number of the escapades of the lovers and their eccentricity. Or, if you wish, from the frequency of letters and their length. In a hypothetic case that  the number and length is pre-arranged, the temperature is the rubato of the correspondence: the chaotic variations of the order.

When temperature reaches a certain level, a significant change becomes possible. At a low temperature, the pace of change is slow.

With humans, everything is vague, ill-defined, and fuzzy, but this is why for anything BIG we need intelligence, hard work, and luck in this life. It takes energy to order chaos.

With molecules, everything is simple.

The Figure on the right illustrates what happens with molecules of gas when temperature changes from 0ºC to 900ºC to 2100ºC :   the higher the temperature, the higher the spread of the distribution of energies of individual molecules, the larger the distance between the slow and fast molecules.

We cannot apply observations of molecules to people because life and society are open systems far from equilibrium. We can only draw metaphorical parallels. When it is hot, more of population gets to the extremes, so to speak. The population builds up an army of high energy individuals capable to change the system. When it is cold, the society consists mostly of the middle range units, which was, probably, the idea of egalitarian socialism.

It is still a part of American paradigm that the large middle class stabilizes society. I really don't know whether this is true and what stable society means. Low temperature is what stabilizes anything. Anything stable is cold.

This is how I would describe the temperature of a complex dynamic system in metaphoric (and not scientific) language: it is the range of spontaneity of events.  A zero variability means zero temperature. Temperature is not a measure of order or disorder in the system but the measure of the effort needed to achieve an increase of order. At low temperature, little energy may be needed to maintain order, and at a high temperature, same energy can create less order.  In statistics, the spread of distribution is measured by variance and standard deviation, but I would like to keep the distance of a metaphor.

The words temperature, tempo, and Bach's well-tempered come from the same Latin root meaning the measure of proportion or doing the right thing at the right season. Temperature is the measure of doing the wrong thing at the wrong season, but only if you know what is right.

The power of analogy lies in both similarity it reflects and the difference it is aware of. The difference between society and gas is fundamental, but to explain it would take a lot of dry science. Anyway, the parallel between the physical temperature and the social temperature that I am drawing is limited.  The reason for this is not an absence of general theory of abstract temperature —statistical mechanics is such theory—but the difficulty of defining real live models:

    because of their complexity
    because of incompleteness of our knowledge about them,
    and, paradoxically,
    because they are insufficiently chaotic.

 I wish to stay at the level of metaphor which, unlike analogy, does not even assume any difference. It is simply a link, like in hypertext, and the link may be flawed, irrelevant, or non-existent. Why metaphor works is a separate topic (see Essay 10).

 We can part with the household thermometer here.  We can monitor the temperature in the Middle East with the clock or calendar, recording the number of reports in the unit of time.  The only condition of measuring temperature with the clock is that events are not completely predictable.

There is no temperature without chaos. If the US Congress convenes according to the schedule, it does not matter what the schedule is. But any extraordinary session may mean heat.

Our life is highly ordered in time. Everything is scheduled and organized. We expect a certain predictability of life, without which no happiness is possible.

Is there any chaos in sunrise and sunset?  No, the solar system is very cold on the human time scale and rarely disturbed. But the global weather is heating up, judging by the rising frequency and extent of catastrophic damage. The human activity is blamed but I have never seen any estimate of the price of scaling it down and paying for the global systemic air-conditioner.

Regular, expected, and repeated events have their share of chaos, too. It is difficult to evaluate the temperature of major airlines. The delays have become so predictable that we may see it as cool. The TV schedule is disregarded during major sports events, which is predictable and means no warming. We adapt to the systemic temperature as we adapt to atmospheric one. But it tells us something about the price of order during the warm-up: it is beyond anybody's means.

Western art, apparently, has melted down in the twentieth century. It does not point to any catastrophe because of the memory. The entire history of art is preserved in museums and libraries, and performance art flourishes, but the liquid postmodern culture means that in the ocean of supply one can attract attention only by making big waves and loud screams.

In a solid, cold authoritarian society, like in an ice cube, an individual could establish direct contact only with a narrow circle of other people. In the modern warm and liquid society, like in a spoonful of water, one can, theoretically, bump into anybody. The Internet is regarded as a universal solvent. The same theory, however, tells us that everybody is lost in a global crowd, unless one has enough energy to freeze the liquid around and to build an island with a lighthouse, a bullhorn, and a big paddle to make waves.

In the systemic global warming, the tribal cultures of the tropics offer cool shade and anything solid, except human nature, is made of  ice.


1. The so-called zeroth law of thermodynamics does not define temperature but provides a relation for ordering it. This essay avoids the problem of a contact between different systems and considers only the change of temperature in  a single system over time. The problem of interaction could  be a topic for another essay. Sufficient to say that the art of an epoch tends to come to an equilibrium with its larger environment.

2. "Plato teaches us that, in order to take the spiritual temperature of an individual or society, one must 'mark the music'."   Allan Bloom, The Closing of the American Mind, 1987. New York: Simon and Schuster, p. 72.  Is the rock music hot or cold? I believe it is cold. Bloom's description of American students, whether correct or not, is chilling.                       

3. (2016) Energy is what does not change when something changes in a closed system. But closed systems do not exist in nature.

4. (2016). Presidential Primaries of Election 2016 have the widest range of last remaining candidates that I remember: from leftist dreamer Bernie Sanders to opportunistic demagogue Donald Trump, from urbane, cagy Hillary Clinton to grim, acrimonious Ted Cruz.  The American Society is clearly overheated.

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