Rippling Circles

Bipolar disorder (formerly known as manic depression) is a serious and enduring illness that can have devastating consequences for those who suffer from it. Such people experience states of intense mania, with symptoms that can include thoughts racing at incredible speed, extreme irritability, inflated confidence, inability to relate to others, decreased need for sleep and food. However, such heightened states will never last; every bipolar sufferer will come down eventually with depression. (See also “What goes up must come down” in: Therapy Today, volume 21, issue 10).  Bipolar sufferers move between mania and depression, sometimes fast, sometimes after periods that are symptom-free. Their most important taskis to manage the triggers that take them up or down; this involves careful management of stresses associated both with work and with emotions, maintaining regular sleep patterns and eating properly as well as taking regular exercise. Psychotherapy can most usefully help to cope with depression; once mania kicks in psychotherapy usually becomes ineffective because sufferers often lose the capacity for self-reflection – this is where medication can help.

There is a fallacy around that suggests a bipolar disorder leads to exceptional creativity. Numerous claims to that effect are circled on the web. Yet what is more realistic is to consider that one can be creative despite a bipolar illness. Every sufferer has a different story to tell about his or her struggle and life with bipolar disorder. You can find a number of short multimedia presentations about the bipolar experience of several bipolar sufferers in the New York Times.

Geert Kliphuis has been living with a bipolar disorder. In this edition of Contemporary Psychotherapy, he writes about his personal experience and of his way of trying to make sense of it by using cosmological concepts created by ancient Middle Eastern scholars.


A Perspective on living with Bipolar Disorder

Geert Kliphuis (In gratitude to ‘Claudia’and Roshdi Rashed)

“…Himmelhoch jauchzend, zum Tode betrübt”…Clärchen to her mother – Goethe, Egmont, Third Act, Scene Two


This is a description of an unusual attempt to handle manic depression. The method I developed has helped me to deal with my own disorder in a more objective, and thus more reliable manner. So far, it is rather successful. That may not last; the method requires constant application, which is not always easy. It appears to work, even though for a few months, I have been taking less medication. I reduced the drugs (mirtazapine, lithium and venlafaxine) to an acceptable minimum because their physiological side effects added to my feelings of depression. The method may perhaps be of help for other patients.

1. Introduction

1.1. Islamic sources from the early Middle Ages

For my work as a novelist, I began reading about the history of medicine in Islam’s Golden Age (± 850 – late 15th century), and discovered the terrific progress made in psychotherapy by physicians like Razi, Ibn Sina (Avicenna), Al-Farabi and Al-Bahlki; and in paediatrics, Al-Tabari, the latter having written the world’s first medical encyclopaedia. Muhammad ud-din Najab (Iraq, 11th century), followed by categorizing and describing the groundbreaking work of his colleagues and predecessors in his psychiatric compendium, The Classification of Mental Disorders. In this work, Najab defined the probable causes and effects of, among others, agitated depression, neurosis, priapism, impotence (nafkhai malikholia), psychosis (kutrib) and mania (dhual-kulb).

In Najab’s days, mental disorders were mostly viewed from a psychosomatic angle and, remarkably modern, from a sociological perspective. As to their psychosomatic causes, the predominant views in Najab’s days were very much in line with the work of Abu Zayd Al-Bahlki who had introduced the concepts of mental health and mental hygiene:

“Human existence cannot be healthy without the ishtibak (interweaving) of body and soul.”

Social causes that catalysed mental illnesses were explained in Nasr Al-Farabi’s treatises, Social Psychology and Model City. Going one step further, in his revolutionary Meanings of the Intellect, Al-Farabi explored music as a therapy and a personal healing experience. At the end of the 10th century, music and mosaics gradually became established therapies in Middle Eastern hospitals. However, the plastic arts in the world of Islam were subject to ‘aniconism’; with respect to the concept of ‘Unity of Islam’; Muhammad, the founder of the religion, had discouraged – but not prohibited – the depiction of living creatures, and thus artists and decorators began to create complex geometrical figures. (Perhaps medieval Islamic mathematics would not have reached such a level of sophistication without aniconism…)

At the same time, Ibn al-Haytham, an influential scientist, began to consider mathematics as an intuitive art (Rashed, 1996, cited in Gould and Cohen, 2000). Al-Haytham had, of course, knowledge of the work of Muhammad Al-Khwarizmi, who had made mathematics accessible with his Compendious Book of Calculations and Balancing, the first comprehensive book on algebra that also had an educational purpose.

Being someone who finds harmony in mathematics, I began to wonder if the beauty of Arabic geometry, and especially spherical trigonometry, might help to make mental disorders bearable. I found that in Muslim Spain, progress was made in spherical trigonometry while Najab’s Baghdad, in those days the scientific and intellectual centre of the world, offered a breakthrough in optics. Therefore, these two disciplines seemed plausible options to explore.

1.2. Spherical trigonometry in Spain

The foundation of spherical trigonometry lay, as in all constructive geometry, in the circle. The Christians said about the circle that “the heart of man is the centre, heaven the circumference.” For the Arabs the circle was not only a spiritual concept but also the core of a mathematical approach to the world around them. The term zero, in western mathematics symbolized by a circle, is a contracted Italianization via zefiro of the Arabic çifr, which means by itself nothing or void. Where Christians considered the circumference a protection against the unknown, the Arabs saw the void as a geometrical, astronomical or even spiritual adventure.

Muslim-Jewish Spain had never really excelled in exact sciences, except medicine (Ibn Rushd aka Averrôes, Maimonides, and, most of all, Al-Zahwari). Andalusia meant philosophy, poetry and translations, especially from Greek and Hebrew. Yet, in the early 11th century, Allah Muhammad ibn Muad, the local judge of Jaén, published his Book of Unknown Arcs of a Sphere. Not since Menelaos of Alexandria, a thousand years previously, had the sphere been the subject of such profound study. Ibn Muad’s book set new standards for the definition of the sphere and introduced methods that freed spherical trigonometry from its astronomical context to become a mathematical discipline in its own right.

Given the ‘planetary’ figure below, one understands why Ibn Muad’s findings in his Book of Unknown Arcs of a Sphere preceded a thesis about the exact height of the atmosphere (On the Dawn or the Twilight and the Rising of the Clouds).

This is a modern version of one of Ibn Muad’s trigonometric figures. It must have been his aim to rotate the sphere in order to displace its north pole on a slightly south-east axis in order to show the dynamics of the sphere, instead of showing it symmetrically, as if on a flat plane.

Ibn Muad made it possible to define the sphere, which, despite being freed from astronomical contexts, reflected for me a physical universe in miniature. The judge, reputedly a man of great wisdom, must have been aware of verses in the Qur’an that were interpreted as an order to help the ill. Verse 5 in the fourth Surah, Nisa (‘Women’) reminds the believer of his responsibilities in both their material and spiritual sense towards people with, what I call, ‘soul pain’:

Do not give away your propertywhich Allah has made for you a means of supportfor the weak of understanding.Maintain them with the profits of it,and clothe them and speak to them words of honest advice.

Yet, Ibn Muad, a devout Muslim, never applied his revolution in spherical trigonometry to the spherical perception some people had of their world.

Neither could he know that the basic structure of his ‘planetary’ sphere, shown above, represents, for some people suffering from manic depression, a system of wheels, which is in slow, constant rotation. (Such is the case for ‘Claudia’, a former fellow patient at a clinic in Tienen, Belgium, and myself.) However, to understand this, we must first see what happens when the world does not rotate but comes to a stop.

1.3. The immobile phase in manic depression

I believe that the euphemistic term ‘bipolar’ describes manic depression only as a roller-coaster experience; it appears inadequate when it concerns the processes of inflation and deflation of the patient’s worldview. A personal example: I find that in a depressed and immobile phase, the world deflates to such an extent that preparing a craved cup of coffee becomes an impossible endeavour. I am unable to perform even the slightest function that may help lift the ban of my immobility. Yet I know that it should be possible. However, the sphere of my existence has deflated to such an extent that the coffee machine seems to be isolated in a parallel sphere, which cannot be accessed. In this deadlock, there are two solutions: either I force my way into the parallel sphere in an act of determination, or I gently inflate my sphere until it touches the sphere of the coffee machine. The first option, when successful, may lead to doubtful satisfaction: I may think indignantly, ‘Okay, but do I need so much effort to make my coffee?’ The second option is more harmonious: I think: ‘Yes, when I do it slowly, I can overcome my immobility and make my coffee.’ Both avenues lead to the same result. However, it seems likely that the patient who uses the first option perceives the coffee as a reward for his determination; the patient who uses the second option will actually appreciate the coffee for its taste. Maybe the latter is important: manic depressed people are in dire need of a good quality of life. The competition with themselves does not contribute necessarily to that feeling; constructive acts of kindness to themselves may well. Self-competing is a constant in their disorder and saps mental energy. With the second option, failing to make your coffee is less frustrating because the mental effort takes less energy: it is easier to try it again.

‘Zenith’ and ‘Nadir’ are the Arabic terms used, mainly in astronomy, for the ‘point above’ and the ‘point below’ in relation to the horizon.

If we assume that the physical universe is a sphere, then we may assume that we live with a spherical perception of the world around us. This sphere has a stable appearance because it is perceived as horizontally ellipsoid (supposedly the shape of the physical universe): our view sweeps a wider distance from east to west than from zenith to nadir.

However, Claudia, the patient at the Tienen clinic, and I perceive the universe as made up from full circles: zenith and nadir lie, geometrically speaking, at equal distances from the centre as the polarities of the horizon, and lack the broad diameter of the ellipse. Claudia told me: ‘When I’m balanced, I’m sitting in the middle of a system of wheels.’ (She added: ‘When I’m not, I’m tied to a wheel.’ We’ll come to that later).

For a ‘normal’ person, this circle seems perfectly stable but Claudia feels that her circular worldview is subject to arbitrary influences. The diameters in the circle rotate, touching all the points between maniacal zenith and depressed nadir. Claudia’s worldview may topple over slowly, leaving zenith, and grind down towards nadir; after a phase of depression it rotates and rises towards the east-west axis for a short span of exhausted balance. Then it spins her to maniacal zenith. That was what she meant by, ‘I’m tied to a wheel.’ To which she had added:

“[The wheel is like] that Hindu-thing, the wheel of Samsara. I’m wrecked and reborn. And every rebirth spells danger. Have you seen that film, Contact, with Jodie Foster? They build a machine to travel to the stars. It consists of three spinning wheels that create an electro-magnetic field. I live in that machine. The vertical wheel is that Hindu wheel. The first time I saw that film, I ran from the theatre.”

Now I understood why her image of ‘I’m in the middle of a system of wheels’ was also reflected in Contact. This is what we have seen earlier, in Figure 2, in which the added vertical circle represents her ‘Hindu wheel’. Still, Claudia is lucky. She is able to identify elements in her disorder and give them a comparative and comprehensible description, and that makes it easier for people to understand her. She gives, what I call, indicators.

Claudia’s indignation at her spherical existence is very much like mine. We both lack that broad base of an ellipsoid worldview. To her, our system of wheels represents all the danger and euphoria of even the metal sphere itself, launched by the system of wheels in Contact to take Jodie Foster to the stars. Typically, all things spherical that were, in her opinion, only superficially understood by others, became the object of her scorn. She once blew her stack at an elderly Belgian man, apparently someone with Buddhist convictions, who had tea in a bar:

“Could you please stop juggling those Yin-Yang balls of yours? They scare me. Man in woman, woman in man, light in darkness, darkness in light. You’re so wrong, my friend! It’s one or the other!”

After my stay at the clinic, I still had no idea how to accept the circle, until a man from a distant past, adherent of a religion quite the opposite of Hinduism or Buddhism, showed me a sphere from a different point of view. I sent one of his drawings to Claudia. She was delighted, in spite – or because – of the sphere being cut in two.

2 Living with the sphere

2.1. Optics in Iraq: Sa’d ibn Sahl

Fig. 6

In CE 984 – which approximates to the Hijri (Islamic) year 374 – Sa’d ibn Sahl, a physicist in Iraq, made a diagram of the first law of light refraction, which is the triangular figure, shown top left. (A modern interpretation of Ibn Sahl’s Law of Refraction: If the ratio of lengths L1/L2 is kept equal to N1/N2, then the rays satisfy the law of sines). Then he applied his findings to an anaclastic lens, that is, a perfect lens without optical aberrations (the demi-sphere – Ibn Sahl’s plano-convex lens, below right). Almost a thousand years later these drawings were discovered in the Millî Library in Tehran by the Egyptian historian of science, Professor Roshdi Rashed, who published the result in 1990.

Claudia and I were thrilled by the drawing of the lens because it shows Ibn Sahl’s correct calculations of the path of a ray of light. In the diagram, the ray is the tiny slanted line, marked – by the letter Sa’d – in the demi-sphere which should, of course, be traced from right to left. It touched us because Ibn Sahl had shown a way into, through, and out of the demi-sphere. In this scientific drawing, Ibn Sahl’s technique touched the spiritual: the fine lines that make up the demi-sphere are drawn by a scientist who becomes an artist, awed by the solution of the mystery. His explanation is written in wonderfully stable and individual handwriting.

For Claudia and myself this is a work of beauty: it frees the sphere from the claustrophobic context in which our circles rotate. Claudia made Ibn Sahl’s drawing a full sphere; she wrote to me: “Hey, I drew the other half myself!” By doing so, she took one more step towards accepting the sphere, and thus gaining control over it.

When I copied the diagram, I realized that my computer could change the demi-sphere, be it irreverently, into a dynamic ellipsoid form:

Fig 7

Now the horizontal axis, from Ibn Sahl’s Point ’Ayn on the right to Point Alif on the left, identified the broad base of the ellipsoid worldview I mentioned earlier. Taking Ibn Sahl’s demi-sphere as a lead, and doubling it, like Claudia, I thought I should project this shape around me, positioning myself at Point ’Ayn. But how?

2.2. A technique for ‘mental naval aviation’

A few weeks later, I saw our neighbour’s cat in our garden; he sat on the edge of the bird-pool, staring at the water. Then, fast as only cats can, he struck with his paw at the surface, and cocked his head intently, watching the water ripple. What I experienced, watching him, is called in German an ‘Aha!-Erlebnis’ (a blast of realization): the cat made ever widening circles. Imitating him, I began to create ripples by dropping pebbles into water and tested them, lowering my head to just above the point of impact on the surface, seeing them expand. I contacted Claudia and, separately, we went to work. After a few months, we compared notes: we were both able to project those ripples in our minds, seeing them flow away gently from our heads, along Ibn Sahl’s ’Ayn to Alif axis, widening our horizon and inflating our spheres. These days, as soon as we wake up, we set them in motion, creating the broad horizon we need to position ourselves. In order to give our life a symbol, which relates to techniques of navigation, I made a proposal to Claudia calling it ‘the aircraft carrier’: when we are in a stable phase, we navigate steadily, the horizon and the level of our worldviews coinciding. In this phase, there is no need for inflation or deflation of our sphere. When the ship is sucked into the maelstrom of depression and we meet, as Claudia says, ‘the Cerberus in my soul’, the horizon is there, diagonally above us, as a reminder of the level we came from and where we will, inevitably, return. In this phase, we may need to inflate our sphere, widening the ripples. When we fly up from our aircraft carrier, like ‘Icarus’ (dixit Claudia), into the high winds of mania, the horizon is still there, diagonally below us, reminding us of the euphoric dangers that we must reduce, for example, by deflating the sphere, limiting the ripples.

In naval aviation, like in any form of flying, a pilot has one particularly important meter on his instrument panel. The official term is ‘artificial horizon’; it is also called the attitude meter, ‘attitude’ meaning ‘position of the body’. Navigating through the rippling circles, with the horizon as our reference, we may just be holding our body – and soul – in the right position. And we can do it, with an intent curiosity, similar to that of our neighbour’s cat.

Geert Kliphuis aka Jay Conrad (b. Netherlands, 1955) is the author of The Mirror City, a novel about Madrid, and composer and performer of Sobre una cama helada, a forthcoming album in Spanish, based on the poetry of Raquel Lanseros.


Rashed, R (1996) Analysis and Synthesis According To Ibn al-Haytham, in C. C. Gould and R. S. Cohen (eds.), (2000) Artifacts, Representations and Social Practice, 121-140, The Netherlands: Kluwer Academic Publishers

Rashed, R (1990) A Pioneer in Anaclastics, Ibn Sahl on Burning Mirrors and Lenses. ISIS, University of Chicago Press

Short biographies

Al-Farabi, Abu Nasr: (Lat. Alpharabius, Iran-Syria-Egypt, c. 872– c. 950) Muslim polymath and one of the greatest scientists of his day. Cosmologist, logician, musician, psychologist and sociologist. An influence on Leo Strauss, the 20th century US-German political philosopher.

Al-Khwarizmi, Abu Ja’far Muhammad ibn Musa: (Baghdad, c. 780–c. 850) Mathematician and astronomer. One of the Banu Musa (sons of Moses, actually three brothers) at the House of Wisdom in Baghdad, founded by the liberal Khalîf, Al-Mamoun. The treatise Al-Kitab al-mukhtasar fi hisab al-jabr w’al-muqabala (The Compendious Book on Calculation and Balancing) was his greatest work and gave the West the word algebra. It was the first book on the subject.

Al-Zahwari, Khalaf ibn Abbas: (Lat. Abulcasis, 910–1013) the court physician of the Spanish Khalîf Al-Haqam II. In the 10th century, Al-Zahwari was considered to be the greatest surgeon in the world. His contribution to modern medicine is impossible to evaluate.

Ibn al-Haytham, Abu Ali al-Hasan: (Lat. Alhazen, Basra 965–Cairo 1040) generally acknowledged to be the founder of modern science. He devoted his life to mathematics, medicine, astronomy and physics. His fabulous Kitab al-Manazir (Book of Optics), which was used by Bacon, Kepler and Da Vinci, was written during his house arrest in Cairo (1010–1021). In 1997, Oxford mathematician Peter M. Neumann finally found an algebraic solution for the notorious Alhacen Problem, from Book V of Kitab al-Manazir. Al-Haytham worked for a long time at Cairo’s Al-Ahzar University (founded 970).

Ibn Muad, Abu Abd Allah Muhammad: (aka al-Jayyani, ‘the man from Jaén’, 989–1079) little is known about this judge (cadi) and confusion exists as to whether the scholar Al-Jayyani may have been the same person. Ibn Muad reportedly also wrote a treatise on machines.

Ibn Rushd, Muhammad ibn Ahmad: (Lat. Averroês, 1126–1198) Spanish-Arab philosopher, expert on the works of Aristotle, which earned him the reputation of ‘The Commentator’. Ibn Rushd wrote a comprehensive encyclopaedia of medicine, and extensively researched smallpox and eye diseases.

Ibn Sahl, Abu Sa’d al-’Ala: (c. 940–c. 1000) Iraqi optics engineer, closely associated with the court of the Abbasids. Credited by the Egyptian historian of science, Prof. Roshdi Rashed, in 1990 for developing the first law of refraction, also known as Snell’s Law, after the 17th century Dutch scientist.

Ibn Sahl al-Balki, Ahmed: 10th century Iraqi pioneer of psychophysiology, and founder of psychosomatic medicine.

Ibn Sahl Rabban al-Tabari, Ali: (838–870) Persian-Jewish (converted to Islam) physician, the world’s first specialist in paediatrics and child development. Wrote the Firdous al-Hikmah (‘Paradise of Wisdom’) or Al-Kunnash, the first encyclopaedia of medicine.

Ibn Sina, Abu Ali al-Hussein: (Lat. Avicenna, 980–1037) the Great Harmonizer. Persian physician, psychiatrist and philosopher, who worked at the astoundingly modern general hospital (see: Razi) at Baghdad. His summary of medical literature in his Al-Qanun was authoritative until after the Renaissance. He also wrote on astronomy, philosophy, mathematics, physics, chemistry, geology and music.

Maimonides: Greek name for Mosheh ben Maimon (1135–1204), or in Arabic, Musa ibn Maimoun; Córdoban rabbi, physician, theologian and philosopher. His most important philosophical treatise is the huge Guide of the Perplexed. Maimonides was a close friend of Ibn Rushd.

Menelaos of Alexandria: (c. 70–140) Greek mathematician and astronomer.

Razi, Muhammad ibn Zakariyah: (Lat. Rhazes, 865–925) Persian physician, specialized in neurosurgery, paediatrics, allergies, immunology and psychotherapy. Was founder – and director, as later was Ibn Sina – of Baghdad’s general hospital, where he had his chemical laboratory to test the faculties of petroleum.

Image: Lights! Lights over there…by Jean Goff