A VISIT TO THE BEWILDERING WORLD OF MATH

When it comes to math, I'm on a Neanderthal man´s level. I understand virtually nothing and the more I struggle to understand, the less I do. There must be some brain wrinkles missing, or a defult brain capacity that hinder me from undertstaning much related to algebra and geometry.

Already in primary school, math lessons became a torment for me, not to mention the math homework, which deprived me of time that could be used for other, more pleasureable activities. The first and only time I have been accused of cheating was when I handed in a math notebook while I was in middle school, so the teacher could do the routine check if I had done my homework or not. He then found that several pages were had been filled by my scribblings. However, in between them others had been left blank.

- What is meant by this? For several weeks you have not done some of the homework! I admit that you have done some of the tasks, but far from all of them. What I don´t understand is why you left blank pages between those you solved? Did you try to trick me into thinking you had done all of it? Remember that I am always checking that everything is done, … or not.

I answered:

- Where I have not entered anything, it was because I hadn´t understood what it was all about. When I get older and wiser, I plan to fill them all in.

I was serious, though the teacher probably thought I was crazy, or tried to cover up my laziness. I wonder if I would ever would be clever enough to fill in those pages. It felt like a liberation when, after finishing school, I was freed from the scourge of mathematics.

When I, in the past, did not understand certain things, I assumed that these lacunae were extremely important and thus my ignorance of math haunted me for several years. However, I now realize that for for most of my life span, I have not at all been bothered by my ignorance of those things that I once assumed to be of life changing importance.

I have always found great pleasure in immerseíng myself in music and religion, but that does not mean that I understand the rules governing music and I am far from being a pious and religious person. I cannot play any instrument and do not consider myself to be of any religious persuation, but that does not hinder me from listening to all kind of music with great joy and satisfaction and throughout my life have participated in a wide variety of religious ceremonies, within different contexts and have occasionally been deeply moved by what I experienced.

I assume that religion, like music and math, is related to order and structure. A believer considers her/his religious faith to adhere to a set of rules and provide an explanation of how everything works and is structured. S/he feels included within a system that permeates and controls her/his entire existence. Likewise, religion is a harmonious system where each individual is included as an essential fragment within a structure that provides her/him a sense of belonging, commitment, and peace. Like our existence, some music and even art may appear to be chaotic, though chaos can neverthelss be considered to amount to an ingrediant that after all is part of, or possibly be a reflection of a so far insufficiently known cosmic order governing all creation. 

A harmony of spheres where you and I, as well as single tones, words or numbers, are included as small, but perhaps after all not entirely essential details. Just as our speech reflects a vast universe of relativity and imagination, so are perhaps music and mathematics provide a reflection of a cosmic order we are all part of. Perhaps is math the language that most clearly indicates such a context.

John Napier (1550-1617) was a Scottish aristocat who depised the clinging of stupid priests to unproven dogmas, which they furthermore indoctrinated their parishioners with. Consequently, Napier was an enthusiastic supporter of the Scottish Presbyterians, who did not want to have anything to do with bishops and the Pope. They believed that God was above all that and that the priesthood was an unnecessary and oppressive institution. The only thing that counted was the sovereignty of the Bible and grace through faith in Christ.

Napier believed that the fundamental truths of the Universe were to be found in the Bible. God speaks to humans through His Holy Scripture, but it is important to interpret its content correctly. Just as mathematics can explain and prove cosmic contexts, it could, according to Napier, also be used to clarify the inner message of the Bible. Napier published a commentary on the Book of Revelation - A Plaine Discovery of the Whole Revelation of Saint John. This was an account presented in strictly mathematical terms, with postulates, propositions and evidence, which Napier applied to the biblical text to prove that the Pope was identical to Antichrist and that the world would perish sometime between the years 1688 and 1700. Napier's psyche was, as the case is with many other geniuses, a combination of great talent with quite a lot of madness.

Napier was a mathematical genius and able to express himself in fluent Latin and ancient Greek, the latter was at that time (and even now) quite unusual. Nowadays, John Napier is best known as inventor of mathematical logarithms, which he calculated by using a home-made device called Napier's Bone.

In his book Mirifici Logarithmorum Canonis Descriptio Napier explained the principles of his use of logarithms and presented the first logarithmic lists based on his use of Napier's Bones. The eccentric and rather wealthy Napier preferred to work on his own. However, through his friend John Craig he apparently had some contact with the Danish astronomer Tycho Brahe.

In any case, sometime during the 1590s, Craig wrote a letter to Brahe in which he described Napier's use of logarithms, which was to become of great benefit to Brahe when he, violent and impulsive as he was, in 1597 came on unfriendly terms with the Danish king Christian IV and was forced to seek refuge in Prague. where he was received with open arms by the Emperor Rudolph II. This eccentric ruler and generous patron of art and science provided Brahe with a new observatory in the city of Benátky nad Jizerou, north of Prague, where Brahe in the last years of his life together with another genius, Johannes Kepler, used Napier's logarithms to formulate three basic principles for the planets' elliptical orbits around the sun, as well as they calculated the time it took for each of them to complete its orbit. The logarithms made it possible for them to deal with very large numbers and since then logarithms have been of great importance to astronomers.

Despite this, Napier considered his nutty interpretation of the Book of Revelation to be his most important contribution to the welfare of humankind, and unlike his other books, which were written in Latin, he published his treatise in English so his ”simple” presentation of essential facts could ”effectively illuminate this entire island .”

As I write this, I hear the utterly annoying pigeons cooing on the balcony outside my room. A month ago we cleared away one of their nests and the house became invaded by almost microscopic pigeon lice, which settled in our beds, bit us and sucked our blood. It was therefore with interest that I now read about how Napier's neighbors in Edinburgh told stories about how Napier in order to get rid of pigeons, which irritated to the verge of madness, dipped wheat grains in alcohol that he spread all over his yard. When the helplessly drunk pigeons could not lift off the ground, he rushed out and wrung their necks.

Back to the topic. Logarithms? You who read this probably know more about them than I do. I should probably ask a mathematician about them, but how could he explain it all to a math idiot like me? However, I assume that they are series where numbers constantly increase in a certain sequence. What the word means is not so difficult to understand - the Greek logos may mean ”relationship”, ”plan”, or ”reason”, while arithmosis is ”numbers”. A logarithm could thus be something in acordance with a a sequence like10¹-10²-10³-10⁴, etc., where each number, one by one, is doubled and multiplication thus becomes transformed into addition.

Well, towards the end of his life Napier was visited by the professor of geometry at Oxford University, Henry Briggs, who suggested that he develop his earlier logarithmic tables on the basis of something called the 10-logarithm. Napier explained that he had considered doing so, but that his remaining life would not be enough. Briggs did then on his own compile such a table, which was published the same year Napier died, 1617, containing the logarithms for all integers between 1 and 1,000. Seven years later, Briggs published a book containing "40,000 logarithms, calculated by roots up to the 54th order and results with 30 decimals." I have no idea what that might mean. However, a contemporary astronomer wrote that Briggs' efforts had been invaluable

by reducing to a few days 'work what had previously taken several months, Briggs' work has doubled the life of an astronomer and now spares him from the errors and abhorrence that are inseparate from the execution of extensive calculations.

In 1881, Professor Simon Newcomb sat down in the library at the United States Navy Observatory, which director he was, and opened a logarithmic table. Newcomb had performed a complete revision of the elliptical orbits of Mercury, Venus, Tellus, Mars, Uranus and Neptune and compiled tables displaying how his calculations had been performed. Of course, Newcomb had then used logarithm tables. As Newcomb flipped through the tables in the book on the table in front of him, he noticed that the first five pages were significantly more worn and thumbed than the following pages.

He then discovered that any list involving a large number of figures, like the length of various rivers, death rates, sea depths, incomes, population figures, etc., most numbers were initiated by the number one. And even more astounding – if compiled within a diagram organised in accordance with the initial numbers the resulting curves became almost exactly the same – thirty percent of the numbers began with the number one, seventeen percent of them with number two and then the incidence gradually dropped down to 4.6 percent for the number nine. All in accordance with the curve presented below:

The curve that Newcomb discovered arose from the compilation of figures from virtually any statistical material, regardless if they were generated from human activities or measurements of various natural phenomena, the result became the same. The larger and more varied the range of figures, the closer the numbers of the curve equalled what could be predicted from this so-called Benford´s Law.

That the phenomenon is called Benford's Law was because a physicist named Frank Benford began applying Newcomb's method to compilations he made of price lists, sports scores, areas irrigated by various rivers, electricity bills, and even the street addresses of members of the American Physicists' Association. In total, Benford's lists contained 20,229 different numbers and the curves they resulted in proved what Newcomb had previously come up with. In 1938, Benford reported the results of his research in the article The Law of Anomalous Numbers, published in the Proceedings of the American Philosophical Society.

Deviations from Benford's Law indicate conscious manipulations – or the invention of fictitious figures. In recent years, a growing number of statisticians, accountants and mathematicians have become convinced that Benford´s Law is actually a powerful and relatively simple tool for proving suspicions of all kinds of fraud, such as tax evasion, dishonest audits, even computer fraud, such as the famous trolls, false identities, that Russians apparently used to manipulate the 2016 U.S. presidential election.

Napier, Newcomb and Benford performed their huge calculations of statistical material before the use of computers and calculators. What can now be figured out within a minute or two previously took several years of extremely patient and meticolous calculations. What is also interesting is that all three engaged in these extensive logarithm exercises as a side job.

Napier was intensively busy with the peculiar and self-invented figures he assumed he was discovering in the Bible. Benford was for eighteen years a conscientious and diligent engineer at General Electric's "lighting laboratory" and then for another twenty years he worked at the company's research laboratory. He was an expert in optical phenomena and took out twenty patents for various optical instruments. Newcomb was an astronomer, but also an economist whose theories were highly praised by no less authority than John Maynard Keynes. Newcomb spoke French, German, Italian and Swedish, was for many years an active mountaineer and also wrote several popular science books, as well a science fiction novel – His Wisdom The Defender, a Story. The novel has similarities with the Marvel character The Iron Man, hero in three popular movies from 2008, 2010 and 2013.

Iron Man was originally a Marvel Comics hero created by the author and publisher Stan Lee. This superhero made his debut in 1963 in Tales of Suspense No. 29. In private, Iron Man is Anthony Edward ”Tony” Stark, an American millionaire, entrepreneur, playboy and ingenious scientist. He suffers from a life-threatening chest injury resulting from a kidnapping during which his jailors tried to force him to construct a weapon of mass destruction, though he managed to manufacture a high-tech flight suit and used it to escape from captivity. After that. Tony Stark donned his costume to fight evil forces as The Iron Man.

I do not know if Stan Lee could have been inspired by Simon Newcomb's quite obscure novel, though his Tony Stark does undeniably remind of Newcomb's Professor Campbell, a heroic and skillfull scientist who gathers around him a bunch of loyal comrades and together they fight both the evil of the world and an unreliable manipulative establishment.

Newcomb's novel takes place in the 1940s and tells the story of how the world, through the heroic struggle of a genius scientist, is transformed into a peaceful Utopia. It begins by telling how Professor Campbell, from Harvard University, together with two assistants make two revolutionary inventions. He finds a method for converting aluminum into an extremely flexible material for motorcycles and cars, which he fuels with etherine, extracted from the atmosphere in the form of luminiferous aether, an airborne ether that counteracts gravity. Campbell leaves the university and becomes filthy rich. His second invention is something he calls motes, a kind of aircraft, which becomes the basis of a global network of air transportation.

In secret, Professor Campbell also organizes a group of intelligent and university-educated, young and athletic men, whom he trains to use a mechanical flight suit – a tight-fitting leather jacket fitted with tubes resembling small organ pipes. This is how Campbell describes the first flight attempt with such a flight suit:

The little man began to rise from the floor as the spiritual mediums were said to do a hundred years ago, and was very soon nearly up to the roof, being prevented from striking it and perhaps passing through it only by the rope with which his leg was tied. He could apparently move in any direction he might choose through the air, by a very slight inclination of the handles.  Holding them in one way, he swung round and round a circle having for its radius the length of the rope; holding them another way, he swung in the reverse direction.

With the help of the motes and his rather insignificant army of flying men, Professor Campbell tries to bring about the complete cessation of all global warfare and killing by arms. However, his quest is being thwarted by political, military and journalistic forces which do everything in their power to frustrate his efforts to create a global, permanent peace, while they are trying to get their hands on his highly sophistacted weaponry.

Perhaps it was Newcomb's discovery of Benford's Law, which seemed to prove that there was a solid, natural structure behind the obvious chaos of existence, that made him believe that we could adapt human development to a well-regulated Cosmos, ruled by enlightened scientists. Something I believe will never happen – my own experience tells me that people tends to be intelligent, or stupid, whatever education they might count upon and whatever they do. Of course, knowledge is important, but it does not make us better persons, perhaps more efficient administrators but not morally superior. Take Reinhard Heydrich as an example – he was a handsome man, a sensitive musician, an unusually intelligent person, and at the same time an extremely effective administrator of the mass extermination of Jews and other people who by the rulers of The Third Reich were considered ”unworthy of life”. Something crazier and more bestial is hard to imagine.

It was a short story about a small group of benevolent and eccentric monks striving to achieve the realization of something that could be called a New World Order that made me think about cosmic order, mathematics and religion and write this essay. Arthur C. Clark's Nine Billion Names of God written in 1953 begins with a Tibetan lama, monk/teacher, visiting a computer company on Manhattan. He is interested in buying the company's latest model of the Automtic Sequence Computor Mark V and also for three months hire two computer engineers able to reprogramme the computer for processing words instead of numbers and provide the monks in his monastery with computer printouts of extensive lists.

When the astonished CEO wondered what the purpose of buying such a computer could be, the lama replied that ever since his monastery was founded three hundred years ago, its purpose has been to register every conceivable name of God. After several years of patient counting, meditation and intense thinking, the monks had come to the conclusion that the most comprehensive names consisting of words with less than nine letters and it had been estimated they would amount to nine billion, Compiling and printing all these names by hand would take 15,000 years, even if the most obvious nonsense combinations were ruled out. It was to speed up this time-consuming process that the monastery's lama had now decided to acquire modern computer technology.

When the CEO further wondered what such a strange process would lead to, the lama replied that it all had to do with his religious beliefs and earthly mission. That it was a matter of re-arranging the chaos of existence:

Call it a ritual if you like. But, it's a fundamental part of our beliefs. All the many names of the Supreme Being – God, Jehovah, Allah and so on – they are only man-made labels There is a philosphical problem of som difficulty here which I do not propose to discuss, but somewhere among all the possible combinations of letters, which can occur, are what one may call the real names of God. By systematic permutation of letters, we have been trying to list them all. […] Luckily it will be a simple matter to adapt your automatic sequence computer for this work, since once it has been programmed properly it will permute each letter in turn and print the result. What would have taken us fifteen thousand years it will be able to do in a thousand days.

Arthur C. Clarke's little story about the reclusive computer use of Tibetan monks is probably the reason to why it has now become quite common to publish stories about high-tech educated monks who in the depths of the Himalayas fight evil and try to make the world a better place.

Clarke was certainly inspired by a combination of early twentieth-century speculations about the exkistence of Agartha, an Aryan dreamland nestled among the inaccessible massifs of the Himalayas (the existence of such a secluded ,advanced society found for example a fanatic believer in Heinrich Himmler) and James Hilton's novel Beyond the Horizon from 1933. In 1937, Hilton's novel was filmed by Frank Capra and when the movie was presented in Swedish TV sometime during the early 1960s, it became a great inspiration for me and my friends when we played that we struggled and died in the snow.

Let us now return to The Nine Billion Names of God. After three months, we find the two computer experts during a conversation while looking out over the Himalayan massifs and the Tibetan valleys. The three months are almost over and they are now somewhat anxious. What will their hard work side by side with the patient and kind monks result in?

Everything has worked out beyond expectations. The cumbersome computer had been flown into a nearby primitive, but quite usable airfield. The installation had not been particularly difficult. To the experts' great surprise the monastery had been equipped with modern, diesel-powered generators. They had effortlessly installed a programme that converted numbers into letters and soon the machine was producing extensive lists of God names, all of them with less than nine letters and none with more than three consonants or vowels in a row. The monks had cut the words from the long strips of data printouts and arranged them in extensive books, while mumbling their mantras, the prayer mills had been buzzing around them and prayer flags fluttering in the cool mountain breeze.

However, one of the two experts had recently had a lengthy conversation with the lama and now explained to his colleague that the monks assumed that soon they would have complied all names of God, after that nothing would be the same. They called the ”sum” of the names the Supreme Being, although it was something quite different from a comprehensible creature. It was rather a kind of all-encompassing presence far beyond human imagination. When His/Its purpose for the creation of the earth had been fulfilled, the human race would cease to exist in its present form. The computer expert claimed that the whole thing was blasphemous and obviously dangerously fanatical.

He had asked the lama if it was the Apocalypse, the Last Judgment, he expected to acheive. However, the old lama had smiled benevolently, shaken his head and looked at the computer expert ”in a very queer way, like I’d been stupid in class, and said, ‘It’s nothing as trivial as that’.”

The expert was now worried about what would happen. When the monks had pasted the last name of God in their huge book and nothing revolutionary occurred, they would probably become extremely disappointed and saddened. There was even a risk that the general dissapointment would make the otherwise so kind and patient monks to blame their failure on the computer experts. Accordingly, the two Americans decided that as soon as they had delivered the last computer printout, and before the computer hade been turned off and the monks managed to enter the final name in their book, they had to secretly leave the monastery and board the plane that regularly visited the valley.

A few days later, the computer experts left by sunset, while all the monks were busy entering the last names in their huge books. With two mountain ponies and without saying goodbye, the Americans sneaked out from the monastery. When they had been on the path for a while

George turned in his saddle and stared back up the mountain road. This was the last place from which one could get a clear view of the lamasery. The squat, angular buildings were silhouetted against the afterglow of the sunset; here and there lights gleamed like portholes in the sides of an ocean liner.

He wondered aloud if the computer had finished its run by now and the last name had been entered in the books:

”Look”whispered Chuck and George lifted his eyes to heaven. (There is always a last time for everything).

Overhead, without any fuss. The stars were going out.

Despite its brevity and obvious simplicity, Clarke's short story received considerable attention, not the least in American avant-garde circles where several experimental postmodernist writers have created stories about it. Most striking among them is probably Carter Scholz's short story Nine Billion Names of God, which takes the form of an exchange of letters between a pretentious plagiarist, ”Carter Scholz”, and an editor who has rejected the short story on the grounds that Scholz has ”written” a verbatim plagiary of Arthur C. Clarkes short story with the same name.

The ”author” refuses to accept the publisher's arguments and torments the increasingly desperate editor with a barrage of ”evidence” that his exact Clarke copy is a unique work in its own right. Among other things, he claims that since Clarke's story was written thirty years earlier, it can thus not be the same story as the one Scholz has now ”written”. But… it is in every single detail exactly identical to its model, the publisher claims, whereby Scholz replies that he is of a completely different opinion due to the fact that the time period we now live in is completely different from the one thirty years ago. No one can deny that a story is a child of its time and context. Scholz's short story may seem ot be identical with Clarke's, but since it is ”written” now, it cannot be the same as the ”original”. The editor explains that Scholz's claims are unreasonable, but the stubborn ”author” persists in his madness – he claims that everything is plagiarism and writes the editor a letter in which every single word is limited by quotation marks. The editor says that he gets a headache from reading such annoying rubbish. Scholz then claims that his Nine Billion Names of God is a ready-made work of art like Duchamp's Fountain, and Warhol's Brillo Boxes.

The exhausted editor then offers to buy Scholz's manuscript, as long as he stops tormenting him with his idiotic letters. Nevertheless he adds that it is unthinkable that a serious publishing house ventures to issue such a brazen plagiary as Scholz shameless theft of a wellknown and respected short story written by an established author. However, Scholz is not silenced by that, he writes that the text is a screen behind which a writer hides his true self. ”How in Heavens name might a reader know that?” asks the editor, ”that's exactly the mystery of all writing, its innermost core” explains Scholz. When the editor replies that whatever Scholz s says his text remains a plagiary. The ”author” finally claims that the text came out of a computer after he had programmed it with randomly selected words. He receives no answer – the publisher has gone bankrupt.

This cryptic postmodern fable is entirely in line with other literary inventions by Scholz, such as Kafka Americana from 1999, which he co-wrote with Jontahan Lethem. In this strange book, actual texts written by Kafka are mixed with plagiarism, as well as ”Kafka-stories” written by the two authors, or original Kafka stories provided with alternative endings. Among the stories written by Letham and Ascholz we find we find the latter´s The Amount to Carry, which recounts how the poet Wallace Stevens, the composer Charles Ives and Franz Kafka meet one another during an imaginary Conference for Insurance Executives organized in 1921. An ingenious whim since these three odd geniuses actually worked in the insurance industry. In terms of age, it was not completely impossible that they could have met each other. In 1921, Kafka was thirty-eight years old, while Stevens was forty-two and Ives forty-seven. Kafka and Ives had their creative periods behind them, while Stevens matured late as a poet.

Each of them wanders around the huge hotel, which seems to be a combination of twentieth - century modernism and the increasing comforts of modern times, with Kafka's nightmare worlds and Borge's labyrinths. Scholz is intimately familiar with the three men's different spheres of life and lets their thoughts and lives flow freely in their thoughts. On two occasions they converge – iIes plays the piano in a lobby where Stevens has sits in an armchair with a cigar and redaing The Herald which telling a stories about an Italian political group calling itself fascisti and an obscure demagogue in Munich with a Chaplin-Hardy mustache.

Kafka appears cautiously and discreetly in a doorway. Stevens listens to Ive's music, it appeals to him but worries him as well. It is full of dissonances though it is apparent that these are consciously embedded in a melody based within a Lutheran hymn Stevens heard in in his childhood. The pale man in the doorway whose jug ears and piecing gaze makes Stevens identifying him as as a ”genuine Central European Jew”, suddenly speaks up and declares that he recognizes the melody. He has heard it in Munich ten years earlier, it appeared by the end of a symphony conducted by no less master than Gustav Mahler. Touched and surprised, Ives stops playing. In reality, the symphony was not performed until 1947. The fact is, however, that a year before his death, Mahler had been sent the notes to Charles Ives's Third Symphony and had intended to perform it, but he died the following year, without the project being realized. It soon turns out that the three insurance agents have a lot in common, both taste and trivialities. They meet again during a lunch, but then talk past each other and are soon alone again with their thoughts in the huge hotel's solitary corridors and anonymous hotel rooms. To himself Stevens summarizes the content of both the insurance industry and life in general:

The final belief is to believe in a fiction which you know to be a fiction, because there is nothing else.

Scholz has declared that he wrote his short story after realizing that three of his favorite artists had created their perceptive art alongside their work as hard-working officials. It is a strange, unusually lyrical, empathetic and well-informed short story. A kind of dream play. After reading it once, I read it again several times.

Let us take a look at these strange insurance agents. I have already written about Kafka, so we put him aside.

Wallace Stevens (1879-1955) is one of America's foremost poets. Educated at Harvard and The New York Law School, he spent most of his life as a high-ranking official in the insurance industry and in 1934 he became vice president of the Hartford Livestock Insurance Company. Steven's specialty was to investigate whether an individuals' self-confidence, sense of duty and loyalty was a sufficient basis for economic risk-taking and investments in both individuals and companies. He also wrote about the possibility of insuring against bankruptcy and how to investigate the solvency of company employees.

It may seem somewhat strange that research concerning a company's risk management could be inspiring for a great poet. However, as a matter of fact, Stevens considered writing poetry to be a form of risk management. A good poet has to weigh every word s/he writes against the entire composition and harmonize it with thought and structure. Small mistakes could have catastrophic consequences and ruin what could have been an excellent work of art.

The bureaucrat Wallace Stevens considered himself to be an anonymous cog within a comprehensive system, a way of thinking that characterized a large part of his lyrical output. To pay attention to existence, to realities, to nature and discern the immense context of everything, could be perceived as a kind religion innocent of an almighty, compassionate and personal God.

Towards the end of his life, Stevens struggled with the possibility of reshaping Dante's Divina Commedia in such a way that it reflected our existence as enclosed within a ”Darwinian realm”, where conditions are predetermined by a cosmic force, not a deity, and that a dissolution of the self would not be the end of everything, but a joyous deliverance. Undoubtedly a thought that seems to be closely related to Buddhist ideas.

Stevens was fascinated by art as a means of meditation and an opening to other worlds. He wrote poems about works by Picasso and Klee. His poetry has inspired several artists, among them David Westhead who created an extensive Wallace Stevens Suite.

During his imaginary Berlin conference, Carter Scholz allowed the composer and insurance agent Charles Ives to present his pamphlet The Amount to Carry, which deals with what kind of insurance you may need to protect yourself and your business, and assess how much you ought to spend on an insurance.

In fact, Charles Edward Ives (1874-1954) actually wrote such a work, but he is better known as an American avantgarde composer. In the fifties and sixties, Ives was noticed by bold music innovators such as John Cage and experimental jazz musicians. He was hailed as a pioneer in polytonality, polyrhythm, tone clusters, aleatory/random elements, and quarter tonality.

To my ears, Ive's music can sound both quietly meditative, as well as dynamically exciting. I discovered him through the Swedish essayist Torsten Ekbom's book The Experimental Fields, where he wrote about Ive's strange The Unanswered Question:

Listen, for example, to the strangely beautiful and suggestive orchestral meditation ”The Unanswered Question” from 1906. The piece is made up of three independent layers or sectors that are played out more or less independently from each other. A string quartet placed off-stage plays pianissimi a slowly advancing diatonic chord sequence with a soaring tonality. A lone trumpet intones a five-tone, dissonant motif that reappears unchanged six times. The phrase with its ascending compound second and softly falling third has the question's wondering tone. One can hear the words behind the phrase, something about transcendentalists' wonder at the place of man in Nature and Creation.

All music Ives wrote was characterized by visual imagination, it is a pronounced ”programme music”. Long after he wrote The Unanswered Question, Charles Ives explained that the introductory, silent and impressionistic string suite represented a group of druids ”that understands, sees or hears nothing,” as they are quietly subdued by the sound a lone trumpet loop – The Unanswered Question, which does not explain anything, but concerns The Mystery of Existence. Ives declared that since this question drives development forward it must remain unanswered. During the course of the piece, which lasts less than five minutes, four quarreling flutes (in the version I am listening to there are two flutes, a clarinet and an oboe) break in above the string quartet's meditative flow and according to Ives they correspond to ”the struggling respondents,” but they soon give up and the piece finally culminates in the quiet question followed by silence. Ives characterized his musical meditation as a ”cosmic landscape”.

Fascinated by Carter Scholz's informative and innovative combination of arttistic insurance agents, I came to read his collection of short stories The Amount to Carry where this Kafkaesque story is included together with fifteen other often astonishing stories that challenge time and space. Several of them touch on the theme of this essay - mathematics and cosmic order. For example, The Catastophe Machine which is based on theories developed in the 1960s and 1970s by the mathematicians René Thom and Christopher Zeeman.

Trying to give a simple explanation of what a Catastrophe Theory means that I have to thread on thin ice, since I hardly understand any of it. In mathematics a Catastrophe Theory apparently examines constructed mathematical models within which the value of a variable changes in accordance with rules depending on values ​​that are created by the model itself. Such so-called dynamic systems are generally quite stable and relatively insensitive to influences from external factors, but under certain conditions this state of equilibrium state can change dramatically, often under the influence of extremely small changes in the external factors. With the help of complex mathematical calculations and geometric structures, such sudden changes in dynamic systems, which generally have developed gradually, can be studied and possibly remedied. In these contexts, the word catastrophe refers to a sudden, discontinuous transition to a new, often chaotic state.

As in several other of his stories, Scholzs takes us in the Catastophe Machine into sterile corridors and rooms in research laboratories, apartment buildings and astronomical observatories to demonstrate how we humans often lose control of what our work might actually result in – death and destruction. In The Catastrophe Machine, we meet an odd and misunderstood scientist who has almost innocently ended up in a military-technical, completely emotionally cold, organization, which is translating his ingenious theories about mathematics of loss into a weapon of mass destruction. In his despair, the ingenious scientist exclaims:

– And I who thought I was here to to do math! Don´t you understand that this is mathematics? Pure?”

– Everything pure gets applied, Francis. We deal in the arts of the real.

He is told that everything he has written and calculated belongs to the Organization with which he signed his contract. It has also secretly entered his apartment and without his knowledge copied all his notes and drafts for the book he is writing, which in mathematical terms is intended to describe all historical development.

In the austure vocabulary in the mathematics, a catastrophe is not sudden turn of violence. It is a set of conditions under which a which steady change may cause abrupt effects. At some point in a war of forces, one gives away.

Francis Eckart finds that his own research is classified and he cannot access his writings. What he thought were equations, game theories, a logically constructed fantasy world he took refuge in while suffering from personal problems, may in fact be converted into real nighmare scenarios.

By then the young mathematician has experienced an increasing chaos in his personal life – the death of his mother, his father's severe alcoholism and a painful divorce, but at the same time his experiences have given rise to his discovery of Mathematics of Loss, which he to his despair realized might cause a catastrophe of cosmic dimensions. In this way, Carter Scholz links math to the rules that govern not only our personal lives, but the entire universe.

A pure-minded Buddhist lama would possibly perceive such postmodern fiction as an abomination, especially through its frequent fixation on chimeras, considering life to be filled with alternative possibilities, while sexuality has an overwhelming importance. However, the idea of ​​a universe goverened by strict laws would however not be foreign to him and entirely compatible with the logically based belief system of Buddhism, at least as it was imagined by Arthur C. Clarke's in his The Nine Billion Names of God. which subtly connected mathematics, databases and the basic structure of the universe.

In its original version, Buddhism seems to have been an unusually logical religion. If a pious believer follows the precepts of the Buddha, s/he will reach her/his goal. Although the path to salvation and bliss in Nirvana´s deliverance from suffering involves renunciation, austerity and hard work, the Buddhist is assured of the fact that all this yields desirable results.

As he is portrayed in the scriptures, the founder of Buddhism, Siddhārtha Gautama, was a strict logician who neverthelss was endowed with a certain amount of humor. The Danish religious scholar Vilhelm Grønbech (1873-1948) described him in an unusually sympathetic way:

If there was no more to him than this cold, sharp intellect, we would only admire him and then leave him to his destiny. However, by Buddha we find a face that reflects a soul making him human.[…] The features are characterized by a mild seriousness that excludes all melancholy and hints of sadness and austere seriousness is mitigated by a sense of humor which permeates everything it falls upon. […] He saw himself as something new, not as a warrior, but as life itself. […] His experiences had made him wise, he had a view of life that encompassed its diversity and misery. Then he experienced something that surpassed every vision: all longing and pain left him. It is not enough to state that this new perception of life liberated him, it transformed him into freedom itself.

In Cūḷamālukya Sutta, written sometime between 200 BCE and 100 CE, a story is told of Malunkyaputta, who had set out on the Noble Eightfold Path designated by the Buddha. The cencept is for sure quite well known, though since it illustrates Buddhism's methodic approach to essential insights this path away from suffering might be worthwhile to repeat. Note that the basic principles of Buddhism are generally expressed in different numbers - the three refuges, the four truths and the noble eightfold path:

• Correct understanding of the four noble truths, i.e. i) the truth about dukkha - suffering, dissatisfaction, sorrow, distress, discomfort and frustration. ii) its cause, origin iii) its cessation, ending; and iv) the path leading to to the cessation of dukkha.

• The right intention based on kindness and compassion bringing you to liberation from desire for things that cause suffering for you and others.

• Correct speech includes distancing yourself from all lies and the avoidance of misleading and hurtful claims, as well as gossip and slander.

• Proper action means not harming other beings, as well as refraining from sexually reprehensible acts.

• The right livelihood is to engage in activities that require the right speech and the right action.

• The right effort is to consciously prevent unfavourable perceptions from arising and instead evoke and develop a mindset making it possible to follow the eightfold path.

• Conscious presence means knowledge of how one's own body reacts to emotions, sensory impressions and the insights Buddhist teachings provide you with.

• Proper concentration and meditation equals exercise in and the continous development of dhyana

The word dhyana origintes in ancient Vedic scriptures, the oldest of which were written down as early as 1,500 BCE, it is derived from the Vedic Dhi meaning ”creative vision”. Dhyana eventually came to mean ”deep, methodical and abstract meditation.”

Malunkyaputta had struggled along his cumbersome path towards salvation, but could not really understand what he was devoting so much of his time and effort to. His efforts swere unable provide any answer to the eternal, difficult questions that constantly tormented him, and thus his renunciation and harsh discipline increasingly appeared as utterly meaningless. Siddhārtha Gautama was still alive and to get answers to hiis questions, Malunkyaputta sought out the Master and wondered:

– Venerable Master, as I sat in my solitude, immersed in meditation, the following thoughts rose in my soul: All these doctrines which the Holy One has left unexplained, set aside and rejected – that the world is eternal, that the world is not eternal … the Holy One has actually avoided to answer all these issues. That they remain unanswered displeases me.

Buddha was not at all troubled by Malunkyaputta's disappointment, instead he asked him:

– Say, Malunkyaputta, have I ever told you: Come Malunkyaputta, live a holy life under my direction and I will explain to you if the world is eternal or not eternal … or if the saints exist or do not exist after death?

- No, Venerable Master:

– Accordingly, Malunkyaputta, what has not been explained by me, let it remain unexplained, and what has been explained by me, hold on to what I have explained. And what I have not explained? That the world is eternal and that the world is not eternal… why, Malunkyaputta, did I not explain this? Because it is of no use and has nothing to with the entry into a holy life, nor does it lead to any renunciation of the world … the path to freedom from suffering, to cessation, to peace, to insight, to the highest enlightenment, to Nirvana – therefore I have not explained what you are asking for.

The teachings of the Buddha were practical and logical, there was no room for abstract speculations, only for things that really mattered, which conducted to a throurough change of existence. He explained to Malunkyaputta that his concerns and doubts only caused continued suffering andpossibly death before he had reached the coveted goal of deliverance from suffering.

The Buddha explained his view through a parable. Malunkyaputta's doubts and questions were reminiscent of how a man who had been wounded by an arrow, ”whose tip has been thickly coated with a deadly poison” and was offered the help of a skilled surgeon, though still did not allow him to pull out the arrow and remove the poison until he knew who had shot him, which caste he belonged to, if the bowstring had been manufactured from twisted tendons or any other material, if the bow was made of bamboo or any other material, if the feathers of the arrow shaft came from a heron, or any other bird, if the tip had been smooth or barbed, whether it had been made form iron or ivory. The Buddha stated that such an inquisitive person might die long before the arrow had been pulled out and the poison removed from the wound.

As skeptical as he was of profound speculation, as reluctant was the Buddha to be impressed by miracles. Once an ascetic came to him and claimed: ”Master, your teaching has now perfected my meditation technique and my control of my own body to such an extent that I am able to walk on the water, back and forth across this lake.” The Buddha smiled and wondered, “And what good does that do? And … by the way, there is a perfectly seaworthy boat over there.”

Just as Jesus was a Jew, Siddhārtha was a Hindu. The Kingdom of God taught by Jesus God and The Nirvana by the Buddha found their origins in Judaism and Hinduism and were perhaps even identical with what others had perceived and preached before them. Certainly. the Buddha, just like Jesus, was fully aware of how the Universe was constructed, at least in accordance with to several philoophers of their time had told their audience, and thus they thought it unnecessary to explain such things in too much detail to people who happened to live in the same imaginary world as they did. Jesus's Kingdom of God seems to have been more of a state of mind than a physical place. Siddhārtha, who apparently came from a relatively affluent and highly educated environment, probably regarded the universe as a logical/mathematical construction, possibly akin to what is symbolically represented by Tibetan mandalas.

Hindu philosophy generally speking perceives the Universe as several different, diverse worlds that together build up a multifaceted, yet uniform, Cosmos where each part corresponds to the whole in accordance with mathematically explainable conditions. Probably reminiscent of the motto inscribed on the Grand Seal of the United States – E pluribus unum, by many - one.

Indian cosmology may divided into two variants. The vertical cosmology, Cakravāḍa, describes the arrangement of the worlds in the form of a vertical pattern in which all units are assigned higher and lower positions. Sahasra cosmology, on the other hand, divides the universe into different groupings, a kind of clusters consisting of thousands of millions of individual worlds. Both cosmologies assume that different universes are continuously created and dissolved, ”as Brahman breathes” and this takes place within infinite, cyclical time intervals.

The governing principle of this infinite, cosmic unity follows the same principles summarized by the four Mahavakyas, ”The Great Sayings”, a concise summary of the content of the Indian teachings known as the Upanishads, ” To Sit Down” some of which were written down long before Buddha appeared, sometime during the 400s BCE, others were written down much later. The last of the 108 Upanishads was written sometime during the 15th century CE.

The four Mahayakas are:

• Prajnana Brahma – insight is Brahman, i.e. the supersensible, ever-present and perfected Reality.

• Ayam Atma Brahma – the self (you) is Brahman.

• Tat Tvam Asi – The essence (sat “existence”) is (asi) you (tvam).

• Aham Brahma Asmi – I am Brahman.

We are thus all part of a Cosmic soul/presence, like a drop of water is an undistinguishable part of the sea. Nirvana might be described as a state when we become one with the Cosmos. Accordingly entering a state of Nirvana does not mean an end to our existence, rather a boundless union with, or maybe an ascendant into, the World Soul – the Brahman. The problem is that Buddhism does not acknowledge the existence of any soul, neither a personal one, nor a World Soul, it is a religion that is anātman ”without a self”. According to Buddhism, every human being is a soulless sum of thoughts, feelings, impressions, heritage, and assembled ”palpable” small parts. Nirvana then does not mean an ascension in the Universe but an extinction, a disappearance through the dispersal of all these components. However, several Buddhist philosophers have argued that these ”parts” of human existence do not dissolve and disappear, but constitute permanent parts of the Cosmos, thus they have basically the same view of the Nirvana state as Hindu philosophers.

Accordingly, when our self disappears through our entry into Nirvana, all parts of our ”person” are spread out throughout the Cosmos. Like a drop of water falliing into the ocean. This is perhaps in line with similar views we might discern in Arthur C. Clarke's fable about the Tibetan monks. By compiling all scattered names of God, The Supreme Being, like dispersed letters of a sacred text, or numbers of a mathematical solution, the monks believe they can find a pattern, a plan for the construction of the universe. When this cosmic order appears with the same clarity as the Noble Eightfold Path the monks hope that through their painstaking compilation of the order of the universe they would be able to save/change the entire existence/world and bring us all closer to Nirvana. It was maybe something like that the lama meant when he explained to the American computer expert that what they were trying to accomplish was not the enabling of an Apocalypse , but something that was not so ”trivial” at all. According to Buddhist/Hindu cosmology, the universe/world cannot be obliterated, only changed and this also happens in accordance with a specific, eternally lasting set of rules.

It was possibly speculation about the underlying order of the Cosmos that led Hindu philosophers in the direction of sophisticated, mathematical constructions. As soon as it is possible to reformulate direct observations of our surroundings into descriptions based on relationships between and symbols of ”natural” phenomena, we humans have passed on to a higher stage of knowledge which, if I remember correctly, the philosopher Adi Shankara (788-829 CE)  tried to explain in a simple manner.

If you take an apple and put another apple next to it, there will be two apples. This is completely easy to understand for each and every of one of us. If you then put an apple and a pear next to each other, it will be not only an apple and a pear, but also two fruits. This is our tangible reality.

However … Shankara named the relationship described above as a ”lower reality”. What is then a ”higher” reality? Yes – abstraction. When we reach an abstract sphere we have broken the glass roof of ”reality” and ended up in a completely different dimension than the world of apples and pears. Let us then call the apple one and the pear one as well. When we at this abstract level put them together the result does not become 11, which would have been completely logical, but two 2. How can 1 plus 1 be something as completely different as 2? Well, the equation indicates a new logical context, an abstraction, and according to Shankara a ”higher reality”. That 1 + 1 = 2 is possibly more difficult to understand than that one apple plus another apple become two apples, though abstract numbers do not indicate that a simple summation of apples is wrong, they are just means to bring our thinking up to a ”higher” level.

Let us now say that apples correspond to gods, according to Shankara this is perfectly OK, though the belief in gods does nevertheless belong to a ”lower reality” than the belief that abstract numbers may describe and explain reality as effectively, and even better, as beliefs in gods. If we replace the names of the gods with numbers this does not mean that we change the basic concept – our human existence is governed by contexts and concepts that we can name and replace with numbers. A relationship proving that we are not masters of our existence but only components within an infinite system transcending our comprehension, but which character we nevertheless inmagines by applying mathematics to calculations of how everything relates to each other.

I assume it was such speculations that long before the Europeans could even have imagined it brought the Hindus to the introduction of the number zero as an absolute point of comparison for everything else. Around 200 BCE, the Hindu philosopher Pingala used the word sūnya to indicate the concept we now call zero and around 600 CE the sign 0 had on the Indian subcontinent been established as a symbol for the number zero. However, it was not until the thirteenth century, after much opposition, that the Italian Leonardo Fibonacci succeeded in introducing the concept into Western mathematics.

Another example of the Hindu's early understanding of mathematical comparisons in order to form a concept of the natuers of the Universe and how everything relates to each other is the invention of the game of chess, an almost incomprehensibly refined model of warfare, as well as the dynamics and structure of the universe.

Chess was probably invented during the heyday of the Gupta Empire (280-550 EC) and was then named Chatarunga. The game came to Europe after the Muslims had had conquered Persia in the 7^th century CE and introduced it to Spain, Sicily and Constantinople, while in Africa the Arab version of chess mixed with more ancient board games like the Ethiopian Senterej. Soon chess was played by the Vikings in Scandinavia and Marabouts in West Africa.

Legend states, it was during the regin of a king called Shahram (or Balhait, or Ladava; legends are unreliable) that a ”Brahmin” named Sissa ibn Dahir (or Lahur, Sessa, or Sassa, ibn is the Arab masculine article so it is likely that in its current version the legend has a Muslim origin) invented the game and gave it as a gift to the king, who became so fond of the game that he offered the ”Vizier” (prince, minister, philosopher, or peasant) whatever he asked for as a reward for such a fantastic pastime. The Vizier said that all he asked was that:

You, Most Revered Ruler, place a grain of rice on the first square of the chessboard and then two on its second. Four on the next, then eight and continue to double the number of rice grains you place on each subsequent square, until the board is full.

It seemed to be a modest request, though the king's accountants found that what Sissa Ben Dahir had requested was no less than 18,446,744,073,709,551,615 rice grains, equivalent to the entire world's rice harvests during several upcoming decades. Sissa Ben Dahir had thus demonstrated the marvel of the logarithmic tables that Napier introduced a thousand years later and which now are used to calculate cosmic distances.

Miraculous numerical sequences and relativity-clarifying geometric figures have been used for thousands of years to explain conditions within the universe and make calculations to support planning and construction.

Leonardo Fibonacci was born in Pisa in 1170 but spent his childhood and youth in Algeria where his father during the rule of the Muslim Almohads worked as a merchant with his office in the city of Bugia and Leonardo did not return to Pisa until he was in his thirties. By then he spoke fluent Arabic and was after trading around the Mediterranean well acquainted with the Arabic numeral system (which originally came from India) and position determinations used by Arab seafarers. In 1202, Fibonacci published his Liber Abaci in which he summarized his Arabic arithmetic skills and it is today considered as one of the most important works in the history of mathematics.

The book begins with the phrase ”The nine Indian digits are: 9 8 7 6 5 4 3 2 1 and with these nine digits, and with the sign 0 all numbers can be written,” then follow algorithms for multiplication, addition, subtraction and division and not least the famous Fibonacci Sequence where each number is the sum of the previous two - 1,2,3,5, 8, 13, 21, 35, 55, 89, 144, etc. Although the sequence now bears Fibonacci's name it was apparently also discovered by the Indian philosopher and mathematician Pingala, but it did not come into general use until the 6th century CE.

It is interesting to notice that if you illustrate the Fibonacci Sequence by a geometrical drawing you obtain the following graph:

Or somewaht more elegant:

This is the so-called Golden Section which was known already by Pythagoras (570-495 BC), who believed that everything in the universe could be described through numerical relations and geometric figures and accordingly founded a religion based on this cosmic harmony. Through their great interest in geometry, classical Greek mathematicians became interested in the strange Golden Section, which, for example, appeared in figures such as pentagrams and icosahedrons.

During these COVID-19 times, it may be interesting to remember that many viruses have a capsule shaped like an icosahedron. Of course, the ancient Greeks did not know this, but several of them regarded The Golden Section as a description of a universal relationship and saw it as a norm for the perfect harmony of dimensions and proportions in architecture, painting and sculpture. They also found The Golden Section in several forms and conditions in the nature that surrounded them.

The notion of The Golden Section's presence in the entire universe became even more pronounced during the Renaissance, especially after the Franciscan monk Lua Pacioli (1445-1517) in his work De Divina Proportione, made The Golden Section into metonym for the all harmony found in God's creation. 

The presence of math in the universe has also been used for the production of fractals, a self-uniform pattern that has the same structure at every scale. Natural fractals are, for example, the branches of a tree or the patterns created by river deltas.

The so-called Tree of Life is, moreover, a central symbol in the Jewish Kabbalah, which through speech, numeric and letter symbolism builds up complicated patterns used to describe the universe and which might even serves as a means for an individual to help God,who Kabbalists calls Eyn Sof, "Something that is hidden", in perfecting His creative process. Maybe something akin to the strange activities of the Tibetan monks in Arthur Clarke's short story. Eyn Sof communicates between the different worlds through His ten sefirot, ”emanations”. By becoming deeply acquainted with the different properties and conditions of each sefrirot the Kabbalist tries to find explanations for both the physical and the metaphysical world and thereby become part of the universal harmony that has been divided and dispersed through human egocentrism and childish arrogance.

I had quite early on heard about the Kabbalah since the father of a very good friend and classmate of mine in Hässleholm was quite deeply involved in Jungian metaphysics and the Kabbalah, and when I later was confronted with Noam Chomsky's transformative grammar while studying linguistics at university, I thought I recognized the incomprehensible diagram trees from the Kabbalah and similar incomprehensibilities, which nevertheless could stimulate some of my confusing thoughts about the mystery of life. By the way, Noam Chomsky was certainly well acquainted with Kabbalan. His parents were Jewish refugees from Russia and in addition to being a principal of a Jewish religious school, his father was a linguist and expert in Hebrew.

Generative grammar, at least in Chomsky's version, did in my opinion view grammar in a similar manner as several mathematicians appeared to perceive the Universe, namely as an ordered system which through rules created by the establishment of a certain structure arrange individual sounds so they become to an effective means of communication between individuals expressing themselves through a common language. Accordingly, our way of rearding the world and expressing how we perceive it became subsumed within an almost mathematically predetermined thought structure. I struggled desperately with those, in my opinion, overly complicated linguistic structural trees and silently cursed my profound disinterest in math and utter inability to absorb the miracles of the wonderful world of mathematics.

And it did not get much better when I began studying History of Religions. My friend and professor Tord Olsson had written his doctoral dissertation on Claude Lévi-Strauss, who was interested in complex diagrams and saw them as a means of explaining human thinking. Lévi-Strauss stated that ”I perceive all problems as being linguistic.” Lévi-Strauss combined what he called structural anthropology with mathematical thinking, for example in an early article Les Mathématiques de l´homme, Human Mathematics, which he published in 1954 in the UNESCO Bulletin des sciences sociales and then continued to refine in book after book. Lévi-Strauss argued that in order to understand the basics of human thinking, and thus the society we have created, it is important to study metaphors derived from physics and mathematics, as these sciences examine man's connection with the natural world order.

Lévi-Strauss, who in addition to mathematics also was fascinated by music, stated that ”sounds and numbers are constantly present in the oldest and most mysterious Kabbalistic texts.” He noticed that there was a fundamental correspondence between grammatical rules and mathematical descriptions of reality. In language, through which we express how we relate to and use our position within the universe, it is not the words themselves that carry meaning but how they are combined, as in mathematics where it is the combinations of numbers that give meaning to equations:

It is the combination of sounds, not the sounds in themselves, which convey meaningful data ... [religious thinking] always progresses from the awareness of opposites towards their dissolution.

During the time I studied in Lund, I sometimes worked at a mental institution and there I came across patients who in their desperate efforts to bring order to their mental chaos devoted themselves to counting everything possible. By combining numerical sequences some of them discerned specific messages aimed at them. Because Chomsky's linguistic tree and Lévi-Strauss's diagrams spun around in my head, tormenting and irritating me by obscuring what fascinated me most in literature, art and religion, namely adventure and inspiration, I could not but relate this number hysteria to madness .

The mental disorder of some of the mental patients probably had to do with obsessive-compulsive disorder, a behaviour characterized by constantly repeated rituals, or thought patterns. Such a condition goes by the international name obsessive-compulsive disorder, OCD. Often the compulsive behaviour does not cause the person who suffers from it any discomfort, but may by them instead be considered as a useful and extremely important method to create calm and harmony around them.

The fixation on certain numbers and an almost uninterrupted counting is often referred to as arithmomania and people suffering from such a mental disorder feel a strong need to count everything; their own actions and/or objects they find in their environment. For example, it is common to manically count steps, the number of letters in different words, cracks in floors and ceilings, line markings on streets, even how many times you breathe, or blink. Such manias can develop into the delusion that if you do not do something a certain number of times, for example touching something, then an accident is due to happen.

As in the religious and scientific examples above, a person suffering from OCD may develop complex systems within which values, ​​or numbers, are assigned to people, objects and events in order to arrange them into a larger, even more comprehensive structures. Occasionally, numbers might be linked to previous events and while the victim remembers such incident over and over again, s/he assign special numerical values to them and arrange in the ”Cosmic patterns” they are apt to construct.

I recall several films depicting arithmomania, such as Ron Howard's A Beautiful Mind, which tells about the mathematician John Nash, who for his game theory in 1994 received the Prize for Economic Science in Memory of Alfred Nobel. While studying at a university, Nash neither goes to lectures nor manages to write a dissertation. Nevertheless, his brain works hard to find mathematical formulas to explain things that no one else is pondering about, such as how birds move in a limited space. He becomes increasingly insane and imagines that through his complicated mathematical calculations enabled to trace the behaviour and plans of enemies to the USA and soon fills a number of notebooks, walls and ceilings with calculations in a shed close to his home, where he lives with his wife and children.

The main character Larry Gopnik's brother in the brother Cohen's film A Serious Man, behaves in a similar manner, spending most of his days and evenings writing down carefully constructed equations and geometric figure intended to constitute a book he calls The Mentaculus that will provide a ”probability map of the universe.”

After stumbling around in an incomprehensive mathematical universe I have overtaken by a slightly confused mood. Before I end up on another trail where I run the risk of getting lost in this seemingly endless cosmos of calculations, correspondences and unexpected contexts, I now give up and for now leave the math to go outside and breath some fresh air.

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