… author, mathematician, inventor. You can check his website, here.
A: It was 1967, London, England. I was 22 years old and already a bit of a geometrician, a ‘techie,’ and an occasional civil engineer. As a ‘forever’ university student I spent half of my summer holidays in Spain and Morocco studying Moorish art and architecture – the geometries of which intrigued me. Somehow or other my geometrical work came to the attention of Aubrey Wolton who was a bit of an orientalist and he invited me to meet him in London, handing me cups of tea over a beautiful middle eastern prayer rug. Aubrey introduced me to a friend of his who was as interested in geometry as I was, particularly Arabian and Moorish geometries. At the time, I did not realize that I had somehow stumbled into a world where new ideas and perspectives were prized and shared…
Aubrey’s friend was Ensor Holiday, a doctor, psychologist, chemist, and mathematician. At the time, Ensor was 64 years old – an age that, to me, seemed ancient (I am now 72 years of age!). Ensor had been given a copy of Albert Calvert’s 1906 Moorish Remains in Spain, and was fascinated by one particular design on page 571, design 151. I later found out that Calvert had ‘picked up’ the design from Jules Bourgoin’s Les Arts Arabes, who, as I found out many years later, copied it from a window grille in the Mamluk-period Sarghatmish Mosque Madrasa (1356) in old Cairo. The design was unique as it was based on an unusual arrangement of ‘close-packing’ circles. Ensor had started creating patterns based on the circles of the Sarghatmish design
Q: Can you tell us more about the Sarghatmish design?
A: The Sarghatmish design patterns had the interesting property of stimulating the visual imagination, I call them ‘perceptual patterns’.
Students of the Madrasa were expected to explore the conceptual ‘levels’ of the window’s design, from the mathematics to the design’s cultural and functional lineage. The design itself is based on a convergence of two Arabic design methods: ‘close-packing circles’ (see Figure Altair 2); and the ‘ray’ system, a system which creates designs based on numerology, particularly the number ‘8’ in this case. The numbers and the rosettes used in the window design have their own purpose. The number ‘8’ for example, traditionally communicates the idea of a transition from ‘Earth’ to ‘Heaven’, and the rosettes symbolize ‘gardens’ and ‘paradise’.
Q: What idea did this stimulate?
A: The patterns later became the bestselling Altair Designs – coloring books where each design could be perceived in an almost infinite number of ways (now available from Wooden Books). Ensor and I worked together for many years. I developed new hi-tech geometries inspired by the Sarghatmish design based on circles and then spheres that change size and position to generate ‘perceptual’ 3D spaces and architectural structures. Altair represents a type of design that literally changes before your eyes. They are designs that conjure images and patterns in the mind’s-eye of a user making whatever is ‘seen’ unique. Altair designs, then, are not like other coloring books – there are no fixed images to color and they serve to stimulate the visual imagination. Figure Altair drawing 3 shows an example where all sorts of image can be ‘seen’ including the elephant who is currently ‘standing in the dark!’
Q: Where else did you friendship with Aubrey and Ensor lead you?
A: Dr. Ensor Holiday had a diverse group of friends and associates. He used to say, ‘If you like someone’s ideas, no matter who they are, just find a way of talking to them.’ However gathered, Ensor’s friends included the theoretical physicist, David Bohm, the anthropologist Francis Huxley (nephew of Aldous Huxley), the architect Richard Burton (grandson of the explorer), the animator Richard Williams, the novelist Doris Lessing, the zoologist Desmond Morris, the psychiatrist Ronnie Laing, and many more – mathematicians, artists, architects – and Idries Shah. I met all of them and became friends with many. It was common practice for the friends to meet and have long discussions, and to share ideas and current projects. The hey-day of all of this, for me, ranged from 1967 to 1976…
One day in about 1970 Ensor Holiday asked me if I might be interested in teaching a number of children over the summer of 1971 at Langton House, an estate near Tunbridge Wells, England. I borrowed Ensor’s mini and drove down to meet the occupants, Idries and Kashfi Shah, and to meet their children Saira, Tahir, and Safia. I was told that Idries Shah liked to be called ‘Shah’, and that’s the name I came to know him by… And so it was that over the summer of 1971 I was living in one of the cottages on the Langton estate and teaching the children including the sons and daughters of some of Shah’s friends in the old school house next door to the main house. According to Tahir Shah I am still remembered for reading stories from the saga of Noggin the Nog – Noggin, the unassuming King of the Northmen.
Q: What was Langton House like then?
A: During my time at Langton meals were either served in the main house with Shah and Kashfi or in the ‘Elephant,’ a dining room named after the story about the elephant in the dark. I was now the ripe old age of 26 years of age – surrounded by people who were mostly much older than myself. Besides the school, the cottages and the Elephant, there was an octagonal structure copied from a building in the Middle East and proportioned to enhance sounds; you could walk around the space with your eyes closed and feel pressure points in the air. I later developed the concept a bit further to design the Nancy Stetson art studio in Boulder, Colorado. I was made most welcome at Langton and felt like one of the family – and my enthusiastic but young ideas were always well received – or at least accepted with a smile (maybe tolerated!).
Q: Abjad is something that has had an influence on you. What is it?
A: The Abjad system is based on the fact that, in some cultures, letters have, or did have, numeric values. This is true for ancient Greek and for Semitic alphabets such as Arabic, Hebrew, and Aramaic. Writing systems such as Arabic and Hebrew originally only used consonants to write words, leaving the reader to use his imagination or the context of a script to add vowels. Such consonantal scripts are called Abjad, or more correctly the first four letters, a-b-j-d. If you look on line you should be able to find an old Arabic ‘root’ dictionary such as Edward Lane’s 1876 Arabic-English Lexicon. The words of root dictionaries are organized by their consonants and then by vowels, where vowels were added to Arabic at around the time of the beginning of Islam but were still secondary to consonants.
Many Arabic words are based on three consonants, called trilateral roots, and these and other consonantal roots are described in Shah’s The Sufis. Shah gives examples of consonantal roots that can have multiple meanings depending upon the vowel sounds you add to them. Vowels and pronunciation marks are some of the tiny letters, dashes and squiggles you can see above and below Arabic consonantal script. Shah’s work on the Abjad system intrigued me as it provided an explanation for the placement of certain Arabian and Moorish Islamic 2D and 3D designs.
Many Arabic surface designs are based on polygons and rosettes that have numeric values: a pentagon (5), a hexagon (6), etc. It appears that in some cases Abjad meanings were applied to ‘numeric’ surface designs, but interpretation can easily be subjective. To confirm an Abjad use then some sort of concurrence is needed, such as a location or a purpose for a building, the type of mathematics used to generate the design, any associated Arabic script. Word meanings derived from a surface design need a fairly high level of concurrence – not just a few words – to have any validity. A number of difficulties arise in ‘reading’ Arabic surface designs, particularly the manipulations of the Abjad system itself – again, as described by Shah. Particular problems arise from, say, a rosette with 16 sides, as there is no letter that has that value. So one falls back on 10 and 6 for which there are numeric-consonant values. Other Abjad system processes such as using multiples of ten of a number (‘5’ can become ‘50’ for example), or changing the order of the consonants, can seem overly manipulative – and that might often be the case but the context of an application can validate an Abjad intent.
Q: Can you give an example of the connection between Abjad and Arab design?
A: I can give you two!
The first is a door. There is a 13th century Seljuk period door in the Ince Minareli Medrese, Konya, Turkey (see Abjad A). Part of the door can be seen in part ‘1’ of the illustration. If you connect the two panels of the door you will see a rosette design composed of five and ten sided rosettes (see part ‘2’ of the illustration). The numeric values are not unusual, as many Islamic designs have the numbers ‘5’ and ‘10’ within them. However, ‘context’ needs to be considered, as this was a door to a ‘tekke’ – a hall where the Mevlevi Whirling Dervishes danced. Using Edward Lane’s Lexicon, the root meanings are as shown in Abjad A: whirling dervishes are called to dance. They meet as arranged. They turn in circles. Their right hand faces up and their left hand faces down. They wear tall hats on top of their heads. They whirl like stars in the night sky. They gather together to dance. They are like thirsty travellers looking for water. As shown in the illustration the design is based on a ‘close-packing’ arrangement of circles placed within pentagonal and rhombic tiles.
Another example is taken from the funerary complex of Sultan al-Ashraf Qaytbay, completed in 1474, which stands in the Northern Cemetery of Cairo (see Abjad B). The Qaytbay dome, shown in the illustration, has a design composed of rosettes with sides 16, 9, and 10. With some manipulation using the Abjad system the numbers 100, 6, and 9 are derived with meanings given in Abjad B (there were no words with a consonantal root corresponding with 10, 6, and 9). Al-Ashraf Sayf ad-Din Qaytbay (1416–96) was originally a slave, who was taken to Cairo and purchased by the sultan: a classic image of a slave is one with a ring around the neck. Al-Ashraf became a member of the palace guard, was later freed, and was then promoted through the Mamluk military hierarchy to become a field marshal, and eventually the sultan. He amassed a fortune during his time with the military which enabled him, when sultan, to exercise many acts of beneficence without draining the royal treasury. If a meaning was intended through the numbers, then the possible Abjad meaning fits perfectly. The design method is based on ‘close-packing’ circles. The dome rests on an octagon – where the octagon represents the traditional transition from ‘Earth’ to ‘Heaven.’ The shape of the dome is that of a tear drop. 
Q: Have you anything to add about Idries Shah and his work?
A: I have to say a few things about Shah’s work – at least from my perspective. I am pragmatic and have always been very logical, sometimes to my detriment. I am constantly curious and inventive and I love being surprised by ideas. I believe that, at the heart of things, Shah was similar to me in these respects. I haven’t read all of Shah’s work and have mostly dipped into chapters here and there – but, even so, I have found many jewels. Tales that have helped me think outside the box, ideas that have made me more aware of the importance of diligence, keeping on my toes, doing my homework, of sharing, and of kindness – all things that are important in an era when many people rely on Twitter and headlines for their news. It seems common for people today to be proud of their opinions over facts and understanding. We should learn from, and be inspired by, ideas of the past – a diamond is a diamond whether or not it is found roughly shaped and embedded in rock.
 To see the latest manifestation of Altair designs see the ‘Crystal Cave,’ published by Wooden Books (Glastonbury, UK) and Bloomsbury Publishing (New York, USA). For a taste of a cultural perspective on ‘perceptual designs,’ see, ‘Mind Doodles,’ published by Park City Publishing.
 For a more in depth understanding, see 3D Thinking in Design and Architecture from Antiquity to the Future, to be published by Thames and Hudson Ltd, April 2018.