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.
- 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.
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.
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.
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.
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