Thursday, November 17, 2005

Where are we in the infinite universe? A theory about coincidences or simultaneous occurrence, and infinity

by Professor H. I. Pilikian

Coincidences or Simultaneous occurrences are puzzling phenomena. Most people have experienced them, and some on many occasions – when you would be thinking of a person, and suddenly he/she appears (“speak of the Devil” they say), or the telephone rings and there he/she is at the other end of the line. Folk wisdom ascribes it to the powers of the Devil, while scientists scratch their heads for an acceptable theory.

On one occasion, I picked up the telephone to ring the London Iranian-Armenian poetess, Mrs. Shoghik Minassian, only to find her at the other end of the line without the telephone having yet rang... she had picked up the telephone to make a phone call herself. In even more of a complex and extremely unlikely version of this – I have dialled the London based Painter from Armenia, Artour Oshakantsi’s number, to discover him at the other end of the line having picked up the telephone with the intention of telephoning me!

Coincidences are the chance occurrence of two unlikely events, seemingly connected, sometimes the same, happening simultaneously, often at the same time, overlapping, and even if not, still unlikely to occur, let alone out of the blue, for no logical reason at all – it is how Matter behaves at the subatomic Quantum level that scientists are still unable but struggling to explain, three quarters of a century after the discovery of the phenomena by the Danish Physicist Niels Bohr (2) and Heisenberg’s Uncertainty Principle (3).


On a less significant mode but even more puzzling was the most bizarre occurrence when on the 3rd of November 2003, having attended a seminar on musical theory, I was on my way in Central London, Queen Square, WC1, at around 8.15 pm, when I noticed at the door of a well-kept house a nicely upholstered wooden chair left in the street, obviously intended for anyone to take. I had never encountered such a surreal sight before (have you?). As an old-fashioned Armenian, I hate waste – my parents’ generation that had survived the 1915 genocide were turned masters of Recycling – A wisdom American Governments still resist learning, in fact they teach their citizens to boast shamelessly that the world-polluting American economy is built on Waste – a mantra the millionaire parents of my first wife would drum into me in my youth every time I would try to eat everything on my plate…

I thought, if I had a car I could take this antique-looking chair home. I chuckled to myself imagining me carrying a wooden chair in the streets, onto the underground, changing trains with it at Finsbury Park station, then on the bus to my home in Barnet – a most surreal scene fit for an avant-garde film. Then I thought no more of it.

An hour later I reached New Barnet train Station, my stop, and as I got off the train I almost bumped into a man carrying in his hands incredibly a… similar wooden chair onto the train!

You tell me, when was the last time (if at all) you saw a man carrying in his hands a big wooden chair taking the train?

Another form of pure coincidence would be winning the fat British Euro Lottery – a matter of impossible luck, just as the first time I visited Istanbul (end of December 2002), the first words spoken I heard in the airport lounge was… Armenian, moreover, Caucasian Armenian. I could not believe my ears. On further investigation, I discovered that an aeroplane from the Armenian Republic had just landed, with a planeful of passengers from the little Armenia the Ottoman Turks had attempted to genocide off the map ninety years ago. For me, from London, born in Iraq of half-genocided parents from ‘turkish’ Armenia, to have been there in Istanbul, the capital of the Young Turk genociders, at that very specific moment when a planeful of Armenians ‘downloaded’, were as likely in terms of probability, as to have won the Euro Lottery!

Control-freaks among the scientists who would want to leave nothing to chance, have tried their damnedest to work out mathematically the possibilities of controlling the vicissitudes of Fortune – the great mystery of the ancients, and the subject of Shakespeare’s ire – he always refers to it as a female, and as nothing but a whore – The good of this world have always wondered with Shakespeare as to why the evil people flourish in the same world and are able to live life happily without conscience, while the good ones (like Othello, and Hamlet) suffer intolerably? Why God does not punish evil in this life?

One of the most interesting books of the Old Testament, The Book of Job could be shown to be an attempt to crack the code of Bad Fortune’s mysteries, its sheer unfairness in devastating a just man, so innocent and holy. The writer’s solution to the crux of unfair fortune is the exasperated religious one – God’s belated intervention (the deus ex machina of the classical Greek dramatists) to restore just deserts. But why let it happen in the first place causing endless misery – Job (like any infant killed in a disaster) never did any wrong – he did not need to be tried…

One could interpret The Gospels equally as a ‘musical’ variation on the theme set by the book of Job – Jesus, like Job, is wholly innocent, Job was God’s man as Jesus is His very son, and yet is doled out the most evil bad luck, this time by totally evil men. Even Jesus himself on the cross finally loses his cool and protests to God – his in-human Father – “Why hast thou forsaken me?”

No suffering in the world, except perhaps by infants, can remotely compare with what Jesus (and Job) had to put up with. And yet those responsible – the warmongers, the Mafia bosses, and the pornographers of this world seem to blossom, and have it all! This awareness has led many a poet and philosopher to loss of faith and atheism.

Few people know, for example, the heart-rending verses of protest against God by the Armenian medieval poet, Frik, or that Karl Marx in his youth was a Christian zealot, had written a thesis on Jesus, advocating the spread of his word to the world so ardently, that he (Karl Marx) could have been mistaken today for a Jehovah Witness…

There is a whole industry in mathematical sciences of Probability Theory (4), the basis of Statistical analyses, attempting to induce respectability to the ancient esoteric arts of prophecy and prediction. This is ironical, because the acceptance of chance is the fundamental conceptual difference between scientific theorizing and religious faith. Religious people believe that all is for a purpose, and that is in God’s mind, not given to man to understand fully, History being the unravelling of that divine mystery. Nothing occurs by chance.

Modern Science rejects this Aristotelian teleology (Christian dogma owes a lot; some would say everything, to the Plato-Aristotle debates in Western philosophy). Scientists believe that all change is due to genetic mutation occurring by chance – quite an infantile concept I must say unworthy of great scientific minds, as causality is proven endlessly daily at all levels of human action and behaviour.

Even Genetic mutation cannot be ascribed to chance if it has to survive environmental change, and adapt to it. As for environmental change – for example, the dilapidation of the ozone layer is undoubtedly caused by the human folly of capitalist polluters seeking blindly cutthroat profits first, last, and in between. They have their own inhuman scientists paid to insist that global warming is a matter of chance! (5)

How then could one account scientifically (not caused by an almighty deity) for impossible coincidences and unlikely events happening, as a matter of historical fact? In terms of religious or quasi-religious faith, the question does not even arise, as the non-scientific mind believes in universal causality – nothing happens by chance, and all events are webbed, or interconnected, and ultimately the deeds of God Himself.

I think the well-established theorem of parallel-lines (6) in mathematics presents a solution and produces an extraordinary insight into the nature of infinity and our place (physical location) in the universe, thus – parallel lines which by definition do not meet run parallel into infinity where they converge to meet (7). A line is the trajectory of a point in motion.

If coincidences are event-points, then their simultaneous occurrence (or meeting) can only take place in or near infinity. It follows that, if the universe (8) is infinite, then our planet specifically (and consequently the whole of the solar system) is physically located very near the edges of the infinity of the universal ontology, resulting in awesome consequences – the main of which is that we are indeed very, very far from the centre of the universe (or God. Medieval philosophers used tautological rationality to identify God to be at the centre of All – thence the Universe – He created) (9).

As we are hovering frighteningly near infinity where, if all points (parallel lines) meet, then we may be next to a most explosive unstable place (energy field), possibly an all devouring Black Hole, which are infinite-energy fields of what is referred to as Dark Matter – still a scientific mystery constituting most of the universe, of which known Matter is thought to be a mere fraction!

But if the Quantum world reflects Infinity and behaves like one – a mini-infinity (10), then ultimately we may be safe, as in spite of all the collisions of subatomic particles within it, Matter is somehow mysteriously still constituted and stable – something science cannot yet explain, but which is perhaps reflected in the psychological construction of the human individual – a mixed bag of explosive contradictions, that may indeed sometimes explode, just as some atoms do. The wonder is that very few do.

If all people exploded at once, it would turn our planet into a black hole! Even during the general madness of the two World Wars, most people, thank God preserved the sanity of matter.



Notes and References



(1) A ‘theory’ is a hypothesis ‘proven’ by facts – laboratory experiments and observation – the deductive/inductive method. The difficulty is that nothing can be proven with finality and certainty. Karl Popper (1902-1994), Austrian-born, a philosopher of science at the London School of Economics, proposed instead the inverted notion of ‘falsifiability’ – a theory must be capable of being falsified by facts… when it is, then a new theory or a ‘paradigm’ (according to Thomas Kuhn [1922-1996], the American philosopher of science) needs to be constructed to replace the old theory, and that is how revolutions occur in scientific thought.

The reason I call mine a theory, and not a hypothesis that is the first rung of an intended theory, is because the mathematics (of parallel lines) upon which my explanations are based is uncontroversial, well-established, and I can take it for granted.

(2) Technically speaking, the Quantum Theory is the definition of Max Planck (1858-1947), the German Physicist and Nobel Prize laureate (1918). He had hypothesized (in 1900) that Energy is emanated/radiated/produced in tiny packages, discrete units he called quanta (from the Latin), something Isaac Newton had already referred to less precisely as the stream of particles in a Light-beam.

More astonishingly, Planck then mathematised a universal constant of nature by attempting to calculate precisely the amount of energy in a quantum of radiation, now labelled as Planck’s Constant (h) = 6.626 x 10 [raised to –34] joule-seconds. The energy content E = h f , where f is the frequency (the number of vibrations per second) of the electromagnetic radiation.

Max Planck had also a highly evolved sense of social conscience, and great courage – he endangered life and limb by criticizing the Nazi regime publicly and suffered some consequences.

Planck’s ideas were given a new lease of life by Niels Bohr (1885-1962), also a Nobel Prize winner (1922), and a man of great conscience – during the Nazi occupation of his country, he fled to Sweden in a small boat, in the darkness of the night, to persuade the King to offer safe haven to all the Jews escaping from Denmark. Although he worked later on the atom bomb in Los Alamos (USA), he was opposed to the secrecy of the project, organizing the first Atoms for Peace Conference in Geneva (1955). Five years earlier, concerned about the consequences of Hiroshima and Nagasaki, he had addressed the United Nations arguing for an “open world” to eliminate all possibility of preparing wars secretly.

After Einstein’s death, Niels Bohr was feted as the greatest physicist alive. In 1912, he had gone to Manchester University where Ernest Rutherford had just discovered the nucleus of the atom and built the model of a mini-solar system – electrons like planets circling the nuclear ‘sun’.

Bohr shocked the world of Physics when in 1913 proposed his own model (based on Planck’s quanta) suggesting that electrons of a nucleus, circle on specified trajectories only, and energy (electromagnetic radiation) is emitted only when an electron jumps from one circulatory level to another. And an atomic nucleus was less like a sun, more like a drop of liquid where molecules collide all the time.

One of Bohr’s children, Aage Bohr (b. in 1922) developed this ‘liquid’ concept further (won the Nobel Prize in 1975) by demonstrating that particles in the nucleus may vibrate and rotate distorting its shape from the expected spherical symmetry into an ellipse.

Based on the latter’s work, I myself would go further and suggest that the ‘spherical symmetry’ is a left-over metaphor from the Rutherfordian concept of an atom that needs to be rejected entirely, being a mere assumption, which then moreover limits the physicist’s vision of a nuclear shape to be related to the image of a sphere. Nuclei in fact I think come in all possible forms and shapes, known (ellipsoids, rhomboids, cones, triangles etc.) and unknown, which explains the infinite variety of material manifestation.


(3) Werner Heisnberg (1901-1976) was a protégé of Niels Bohr, although unlike his mentor he ended up heading the Nazi research for the Bomb. Recent attempts to exonerate him from Nazi crimes suggest that he was secretly subverting the project…

In 1925, Heisenberg had attempted to develop a kind of quantum mechanics (labelled ‘matrix mechanics’ – the unacknowledged pop-basis for the recent Hollywood blockbuster trilogy of ‘matrix’ films starring Keanu Reeves) to rival the classical Newtonian mechanics. Its main focus was the energy levels of the atomic structure, working out the mathematics of the frequencies and amplitudes of the radiation waves absorbed and/or emitted by the atomic system.

What made Heisenberg a world-class intellectual figure (and won him the Nobel Prize in 1932) was his ‘uncertainty principle’ (‘discovered’ in 1927) given I think overrated significance by Niels Bohr. It also fired the imagination of the philosophers struggling with the social uncertainties of the post First World War Europe.

According to the Uncertainty Principle, it is impossible to precisely measure certain quantities simultaneously (that abound in the quantum world). For example, in the Newtonian world, one could ‘observe’ a particle passing through an exactly specified locum (position point), moving with a precisely quantifiable momentum (or speed). According to Heisenberg, this is impossible in quantum mechanics, I would suggest only because of the lack of technology then! Heisenberg arrogantly I think made a universal (quantum) law out of scientific ignorance and inadequacy (his own in the first place).

Einstein, who believed in the objective existence of the physical laws, rubbished Heisenberg’s views uttering his famous injunction ‘God does not play dice in the universe’!

Bohr jumped to Heisenberg’s defence with a self-contradictory circular explanation, acknowledging the physicist’s inability to measure quantities by insisting on its reverse, only to confirm immediately the limitations of the way by which the position and momentum of quanta could be defined, which frankly amounts to the same thing – the inadequacy of technology then to do so!

Bohr philosophised further – that physical quantities are defined by the experimental methods that measured them, that experimenters do effect the results they wish to discover (hence there never can be objective facts!), which although true in especially the social sciences, does not have to be so in carefully constructed experiments – the tendency of a true scientist anyway.

Bohr provided a famously clinching argument – that to describe a living creature completely, one has to know all about its inner workings, which would necessitate taking it to pieces, which means killing it before reaching the full facts!

Once again, strangely, it did not occur to Bohr that such was the failure of culture-specific technology of a time-specific scientific ignorance. Genetic engineering alone today disproves the above – today it is possible to discover the inner workings of a living organism without having to kill it!

Bohr (and Heisenberg) was simply wrong (or right at the time…), even though their ideas laid the foundations of cultural relativism, gay and lesbian theory and/or post-modernism.


(4) Thomas Bayes (1702-1761) was an English mathematician who gave his name to the fundamental theorem in Statistics, relating the probability of an event taking place, to the probability of another event conditional upon it, to have occurred.

For example, the face of a coin with two faces, thrown, would have a fifty percent chance of turning up. Or, for an individual buyer of a lottery ticket, the probability of winning it stands at one over the total number of tickets sold for that particular throw.

The probability of myself (or any Armenian) as an Armenian to visit Istanbul (or any part of Turkey) is one out of the total number of all the Armenians alive in the world.

One could of course mathematically refine this basic idea further (to reduce the chances of occurrence) by arguing that all Armenians would not want to visit Turkey because of bad blood between them, or if they did, they must be healthy or able-bodied (although some airlines make provision for the wheel-chair bound) etc. etc.

(5) Religious sentiment (belief in God) is something so private and personal, that displaying it to all in a public way as American fundamentalists do, amounts to pornography, the equivalent of showing one’s private parts in the London daily Sun newspaper…

However, it is vital to possess and preserve what I call a methodological atheism for scientific research. The scientist may privately feel a powerful faith in a Creator, but he/she would make an inadequate scientist if she/he lacked methodological atheism – the sole path of scientific understanding, and analysis of objective causality, leading to discovery and technological advancement.

(6) Two straight lines are said to run parallel if they are the same distance apart at every point on their trajectories. And if a third straight line crosses them, it cuts each at an angle of the same value.

Parallel lines form the basis of many important geometrical figures called generically parallelograms, like squares, rectangles, and rhombuses.

They constitute also a fundamental element in the scientific understanding of Perspective, which was only decoded in human history as recently as the 15th century, by Italian Renaissance artists, based on the perception that parallel lines converge in infinity, hence in a painting reflecting this conceptually at what is called a vanishing point – usually at the centre of the composition, where the most important element of the painting (like Jesus and the Holy Virgin) is placed – as in The Birth of Mary (1485-1490) by Domenico Ghirlandaio.

The architect Filippo Brunelleschi in Florence was the first (as far as we know) to perform a series of experiments between 1417 and 1420 to teach himself the laws of perspective. Masaccio and Paolo Uccello used Brunelleschi’s mathematical rules to produce the illusion of perspective in painting – depth or three-dimensional feature on the flat surface of the canvas.

In 1435, another architect, Leon Battista Alberti wrote (originally in Latin, subsequently translated into Italian and published in 1436) Della Pittura, a book on painting explaining and adopting Brunelleschi’s methods to achieve the same effects in the visual arts.

It is thought that Dutch and Flemish painters were the first to work out the rules of aerial perspective, subtly noticeable in the work of Jan van Eyck.

The first element that the avant-garde artists of the early 20th century wished to destroy was perspective! What was a hard won mathematical secret unravelled in the Renaissance by hard work was now regarded as irrelevant, and thrown out with the bath water.

What is worth noting (and puzzling) in the history of art is the fact that the problem of perspective emerged only in the aesthetic sensibility of Western art – it was never the concern of any other artistic tradition in the rest of the world – Chinese, pre-Colombian, African, Aboriginal etc. I think the discovery of Eastern art (Japanese prints) by the French Impressionists may have unwittingly triggered the process of the eventual elimination of perspective from Western art.

(7) A simple illustration of this would be to look at the panoramic picture of a road (or rail tracks) running straight into the horizon – you will instantly see the vanishing point, at what looks like the juncture of the two border-lines constituting the road or the track-lines.

The grasp of Perspective (based on the assumption of two parallel lines converging in infinity) is so fundamental that it may be inborn and a Kantian category of the Mind, coded in the primate brain – we use unconsciously our instinctive knowledge of perspective to judge distances, and the relationship of objects in the space we experience them. For example, when you wish to cross a street (ignoring the traffic lights…), if you misjudge the approximate distance of a car racing towards you, you may get run over.

(8) Recent ‘String’ theories derived purely from mathematics and based on Quantum Mechanics arguing for quanta to be string-shaped, assume the existence of many dimensions and universes co-existing in the same space… I consider them to be mathematical-poetry like Heisenberg’s Uncertainty principal (see Note 3).


(9) Classical religious belief demands that God be at the centre of the Universe, of which we are frighteningly far away. It may explain symbolically human folly and evil.

In contradiction, as Man also needs to feel close to God, religion also conceives of the Deity being the whole of the universe, infinity itself, being everywhere at all times accessible to mortals.

(10) One of the great laws of medieval esoteric sciences stated that ‘as below, so is above’ (in some versions ‘as above, so below’) – that the micro-cosmos reflected the macro-cosmos. The concept of the Chinese Box (smaller boxes within larger ones), or the Russian matrioshka dolls, represents a visual representation of similar insights into the natural world and its objective reality.

The End

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