I have been working on my latest book, “**The Arabs**,” – a new title in the “**Geometry Through Time**,” series. I’d like to share an idea originally formed in the 1960’s, and that I have been further developing for “The Arabs”; that of the possible use of the **ABJAD** system to store coded messages in Islamic geometric designs.

Arabic script is primarily consonantal in form, the vowels were added later and appear as the many wavy lines and dots you see above and below the consonants. The ABJAD system provides a numeric value to each consonant, so a three consonant word, for example, can have three numbers assigned to it – one for each letter. The ABJAD system also provides a means by which numbers can be manipulated, so that the numbers corresponding to a word can be transformed to correspond to more than one word. For example, numbers can be re-arranged, or replaced by multiples of ten. The numbers, ten, five, and six, can be re-arranged as five, six, and ten, or transformed to become, sixty, fifty, and ten.

It appears that certain Islamic designs were ABJAD encoded to communicate simple messages, give instructions, or convey ideas. It does seem that many designs were encoded deliberately, and not accidentally, with meanings supported by the environment in which the designs appear. In the Alhambra, for example, many designs consist of symmetric repeats of two and three sided rosettes that can be translated into messages of love; meanings that make sense as the Alhambra was somewhat of a “pleasure palace.” I have a prayer rug that, when numbers are counted and translated into consonants, appears to give instructions with regard to positioning hands, head, and body, to pray, whilst conjuring images for a person to reflect upon.

To explore the idea that ABJAD messages are encoded in Islamic designs you need two things. The first is an old arabic root dictionary; preferably published in the eighteen hundreds or early nineteen hundreds. The second is that you will need to understand the geometrical system in the architectural structure, or art and design form, that you are looking at.

An example of a possible ABJAD encoded design appears on a thirteenth or fourteenth century door to a Tekke (Tehk-keh) in Turkey. See the photograph above.

To understand the system used for the design firstly view the door panels as though they are touching each other. The complicated bit is to understand the design system itself, and this takes a knowledge of geometry and some analysis. In the case of the door, the design is based on close packing circles – where the close packing is limited to the area shown in the first line drawing. The master craftsmen then drew in the core numbers in terms of five and ten sided polygons. After that there is more complex development of five and ten sided rosettes drawn within the five and ten sided polygons. The above, three, line drawings show the first steps of the construction. There were, apparently, a number of primary design systems used to embed messages and then a methodology for applying them. To save yourself the work of exploring this idea you can buy my book, as soon as it is published!! From that point you should be able to start to to test the validity of the idea and discover for yourselves if Islamic rugs, walls, spaces, doors, art forms, etc., contain stored messages and ideas. My guess is, assuming the idea to be valid, that encoded designs started to appear from about the tenth century of the Christian era, but it’s possible that the tradition, if a tradition, started well before that. I do know that numbers were used to communicate messages long before ABJAD design applications; in knots tied in ropes, for example. If you have Islamic designs that you’d like me to analyze then please let me see them – or if you have evidence that supports the idea of ABJAD encoded designs, or undermines it, then please let me know.

The door design ends up looking like the drawing on the left below.

Applying the ABJAD system to the design, based on the primary numbers in the design, 5 and 10, and using an old arabic root dictionary we arrive at the following translations:

A Tekke is a hall or monastery known for the dances of the Whirling Dervishes. The Whirling Dervishes are known for a dance where they rotate in a circular fashion, with their right hands facing up and their left hands facing down. They wear tall hats, on top of their heads, and they whirl like stars in the night sky. They are called to dance, and gather together to do so, meeting as arranged. They are like thirsty travelers looking for water. It’s very possible that a symbolic dance arrangement, of the whirling dervishes, followed the positions of the close packing circles that form the foundation of the door’s design.

“The Arabs,” is not just another <geometry book> but, as with all the published and planned titles, in the “Geometry Through Time” series, contains new insights into the uses, and cultural applications, of geometrical systems used in the distant past through to new systems that may be used in the future.

I came to your site via mention of your meeting with Tahir Shah. I am for my sins a maths teacher (13-19 year olds) and have often bemoaned the lack of geometry in our national curriculum in England. I hope to add in some extra geometry to our own school curriculum next year and your site has provided some excellent food for thought on this.

Thanks for your positive thoughts! You might like to track my progress as I prepare for The Leonardo geometry exhibition and workshops. There’s an exhibition section on my website plus posts. I do think we need to make mathematics a logical adventure in the classroom and bring in the “tools” of mathematics on more of an “as needed basis.” I taught Mathematics and ran workshops at the Deepings School in Lincolnshire – pretty much the same age range as you – but this was in the seventies. Best regards, Roger

HI:

this is a very interesting post and I love to read your book. I am planning to focus on my PHD thesis on the topic you just talked about and in more details. I appreciate your help and advice.

Thanks

Nooshin

Thanks for your message but there are many computer generated statements – can you say something specific about your interest.

Roger, I found your analysis of this door fascinating. For a long time I’ve been intrigued by the relationship of patterns (and objects) to the abjad.

I’d like to add that another way of deriving abjad values from panels such as this has to do with the number of discrete shapes they contain. In the case of your ‘elaborated’ door design – the more complex design at the bottom – there are 181 of these (the 1 being contributed by the pentagram in the centre). This can be ‘read’ as the Divine Name al-‘Alim, The Knower (al=31 ‘alim=150).

best wishes, James

Hi James,

Thanks for your idea.

I do have a prayer rug where the number of sides of polygons, and the number of symbols, placed at particular places over the rug, translates to positions of the body for prayer, i.e. position of hands, throat, chest, etc. The rug’s images are fairly abstract but clearly those of a walled area/garden with pools and trees, etc. Where, at prayer, your heart would reflect in one of the two pools. In the case of the rug the highest number is 61 – but there are lots of correspondences of the generated words with the rug and it’s symbolism. So I’d say the numbers communication is valid.

With 2D designs on walls the use the Islamic “Ray” design system to communicate words seems the most reliable. Typically two, three, or four numbers are generated using the system and they easily translates to two, three or four letter words using the ABJAD system. Once a translation has been made then I’ve found that a deliberate use of the ABJAD can only be considered as most likely by the context within which the design appears – as, so often, designs were either copied without any knowledge, or not used to communicate words.

The number 181 is suggestive but the larger numbers worry me as it’s easy to find numbers all over the place and almost certainly some numbers will translate to words accidentally. With bigger numbers you’d need a lot of back up to show that a deliberate use was intended. This line of reasoning is why designs generated using the Ray system seems to me to be more reliable. The ray system not only creates numbers that correspond with typical roots, most commonly try-literal roots, but also creates a primary order to the numbers. Numbers are also used, on occasion, symbolically.

Hope this helps – and thanks for your interest.

Roger, your observations are fascinating – and I’m looking forward to your book!

The abjad is an endlessly absorbing system, not least because of its poetic resonances, and it always seems to be opening up new dimensions. The sense I get is that when artefacts were consciously designed with this in mind, there are numerous layers of meaning. A good example is the octagram device used by the Octagon Press. At one level it can be read as a calligraphic device, in a form of square Kufic, of the word ‘hu’ (He) repeated four times. The abjad value of ‘hu’ is eleven, so we can consider the device to have an overall value of 44. This is reinforced by the fact – and this is a feat of extraordinary artistry to achieve – that it consists of 44 line segments (counting those that meet at the centre as four separate segments) and 44 corners. 44, as Bob Darr points out, is the number of the Divine Name ‘Al Ahad’ (the One). It is also the number of ‘hawla’ (as in ‘la hawla wa la quwwata…’) meaning transformation. There is a very intricate layering here of geometry, calligraphy, semantics and numerology.

Over the years I’ve grown to be alert to numerical connections with the Divine Names (whether those in the traditional lists of 99, or others) because these seem to be clear pointers to the intention behind the place or object. So, for instance, 381 – the number of the Name ‘Shifa’, healer – would be a clue to the use of the place or object for therapeutic purposes. 270, on the other hand, is the number of the Name ‘Kareem’, generous. And I have a beautiful Kütahya plate, which a friend gave me, with a design of vine leaves (in Arabic ‘karm’, from the same root) and grapes, which – as if to reinforce this point – has 270 tiny bunches of grapes.