annular ciphers, keys and decision trees

Annular designs, comprising a set of concentric rings, have been used as keys and ciphers for hundreds, even thousands of years. They arrange and compress information into a compact form that may be  readily portable, for example on paper or light ceramic. Annular designs have been used variously as a secret code, a memory-system, a focus for meditation, a botanical key and a comparator of microbial genomes. 

Why the specific interest? Over the last few years, we have been looking at ways to condense decision trees [1] having many branches, nodes and leaves  into a more compact form. The first attempt, to be described later on these pages, was for a decision tree on environmental risk assessment. Present developments include a decision tree and general guide for use in planning sustainable agriculture and food. 

Browsing a range of sources revealed several devices of this type that were designed for practical usage. Interest arises in the mechanisms by which the user moved from one ring to another. Here is one of them, used primarily as a botanical key.

Ciba-Geigy Weed Tables

A device published 1968 (1975 in English) by the company Ciba-Geigy Ltd, Basle, Switzerland is a classic of annular design. It is a botanical key (Fig. 1). It accompanies a set of exceptional botanical paintings of some major weeds of the world. 

Fig. 1 Photograph of the design from a library copy of the Weed Tables. 

A note attributes text and layout to Ernst Hafliger and artwork to Hanspeter Eisenhut. The design was a supplement to the Ciba-Geigy Weed Tables, a compendium of major weeds of the world. It was found within a box, sat among books in the ‘weeds’ section of the Hutton Institute Library at Invergowrie, Dundee. It was probably bought at the time of the ‘weeds group’ in the previous Scottish Crop Research Institute. 

The key begins in the centre with the seed leaves (cotyledons, one or two), then moves through foliage leaves, flowers, stamens and carpels (Fig. 2) to reach one of the plant families (e.g. Polygonaceae, Chenopodiaceae) arranged on the outer ring. Each family is contained within a segment of the circle defined by radial lines. 

The key would work in the field if it was printed on strong card or something similar, pinned in the centre so that the whole could be moved round repeatedly until the unknown plant being examined could be linked to its family. In that form it would not be that far removed from a mediaeval cipher with independently moveable rings. 

It could also be a great teaching aid in those few remaining places that still teach about weeds. 

Fig. 2 Colours and symbols are used to help the reader navigate through the options from the centre to the perimeter.


The botanical key in the Ciba Geigy Weed Tables works (as do most keys) by radiating from an initial (either-or) choice to traverse a number of options until the final decision is made on the plant family of the (unknown) weed in hand. In contrast, most decision trees begin by quantifying many input attributes, then narrow down the options to one final choice. Both this key and decision trees in general can in principle be worked either way.

The Ciba-Geigy weed key shows that a mass of information and instructions can be arranged into a compact and easily understood guide. Its use of colours and symbols make it appeal to some as a work of art, to be framed and hung on a wall. It lacks some characteristics of decision trees – the capacity for balance and weighing of attributes or  explicit cross links between different branches – though these are not needed for it to fulfill its purpose and could in any case be introduced if a computerised version were made of the key.

This weed key demonstrates (to this writer) a stunning, modern representation of the ancient design of the annular cipher. ‘Modern’ … but this was published more than 50 years ago. The authors, designers, artists and publisher of the Weed Tables viewed weeds as special plants that came to coexist with agriculture, not simply some green stuff that had to be eradicated.

[Descriptions of other designs to follow ….]


[1] For more on decision tree and an example on this web site: Greening with decision trees 

[2] Ciba-geigy Weed Tables. A synoptic presentation of the flora accompanying agricultural crops. Hafliger, E., Brun-Hool, J. 1968. Ciba-Geigy, Basle, Switzerland. First edition in English 1975. The design of the cicular key is attributed to Hanspeter Eisenhut. 

[3] Images used here are phone snaps taken by the author from the copy of the Weed Tables in the James Hutton Institute Library, July 2019.

[4] For an idea of the scope and quality of the illustrations, search online for Ciba-Geogy Weed Tables. The box is still available to buy second-hand. Some vendors show images.

Author/contact: or

form line, form square? … naargh just mix it!

Formal and informal mixed cropping. Mixed corn and mashlum (oats, beans) preferred historically in Scotland, seed mixed not sown in lines or squares. By mid-1900s, covering very small areas of cereal land. Dredge corn from SW Britain.  Unintended mixed grain from volunteer weeds. Mixes grown as a safeguard. Lessons from history.

Archaeological evidence from many landscapes across the globe shows agricultural land divided into geometric shapes. Linear features may have been constructed as drove-ways to move stock from one piece of land to another; or for cultivation by teams of animals dragging a plough that was difficult to turn. Squares or or other shapes with conserved side-length, are preferred when something has to be contained, such as stock animals or valuable crops that can be surrounded by a wall or fence.

Similar features occur when more than one species of crop is grown in a field. Such intercropping or mixed cropping is widely practiced in many agricultural regions. Smallholder gardens will often consist of small blocks, sometimes even single plants, grown close to each other, sometimes under the shade of a tree-crop. Perhaps the most widely observed configuration is that of lines or rows. One species might occupy one or more adjacent lines, then another species then back to the first species, as in the example below of an intercrop of chickpea and sunflower [1]. 

Chickpea field in which lines of sunflower have been sown, Burma (Myanmar), image by curvedflatlands.

Not all mixed crops are grown in formal configurations. Seeds can be mixed in the bag or mechanical sower and broadcast on the land. Two or more species then emerge together to form a mixed stand.

Also, unintended mixtures can occur when seed dropped on the soil by previous crops emerges in a later one (see below). Whether unintended or planned, simple mixtures have been recorded in agriculture since records began.

A new dawn for mixed cropping in Atlantic Europe?

Three factors need to be assessed when considering the (re)introduction or expansion of mixed cropping. One is whether a biological advantage results from growing the species in a mixture: if there is, the grower gets more from the land or resources than they would if the crops were grown alone over the same area. A second is whether the mixture provides a convenience: even without a biological advantage, it might simply be easier for sowing and harvesting to grow two or more crops in a particular configuration, especially if the grower wanted a varied output (e.g. cereals, legumes, fruit, vegetables) from a small plot of land. The third is whether the mix provides a safeguard or security against unexpected events: here, a biological advantage and ease of management may combine to ensure something is produced.  

The type of mixture used in previous times may also be a practical guide to what might still be feasible. In Scotland, and elsewhere in Britain, the most common sown mixtures from the 1700s to the early 1900s were intended for hay and grazing. They were rarely ‘grass only’, but comprised grasses, legumes and other broadleaf species in proportions varying with the intended use [2]. The legumes in the mix, the most abundant being white and red clover, fixed much of the nitrogen used by subsequent grain crops.

Also references are repeatedly made to assorted mixes of corn and grass, where barley or the landrace bere was sown as a ‘nurse’ for the more valuable and longer lasting hay or grazing mixture [3].

Mixed arable crops (no grass) were also mentioned in sources from the 1700s and 1800s, mainly as sown seed mixtures, very rarely if ever as line intercrops. But by the time formal agricultural census began in the later 1800s, sown crop mixtures such as mixed corn and mashlum were grown over a very small area. 

Mixed corn, dredge corn and mashlum

The two most widely grown crop mixtures in the north of Britain go under the names mixed corn or mixed grain and mashlum. Mixed corn consists of two or more cereals, barley and oats for example, while mashlum consists of a cereal and a grain legume, typically oats and beans (Vicia faba). Mashlum reached its 20th century peak during WW2 (Fig. 1). The subsequent fall but continued usage of mashlum was documented on the Living Field web site [4].

Mixed corn or mixed grain appeared as a separate entry among grain crops in the Agricultural Census of 1929 [5]. Its area expanded and contracted over the next 50 years but generally remained less than 0.05% of the combined cereal area (Fig. 1). There is little information of why mixed corn was grown and also why its area was so small. Oat dominated the cereals in the earlier part of the period shown, then gave way to barley and wheat. 

Fig. 1. The areas sown with mixed corn and mashlum in the Agricultural Census for Scotland [5]: mixed corn not identified from other cereals before 1929 and after 1978; mashlum grouped with other forages before 1944 and after 1960. Over the period shown, mixed corn comprised less than 0.05% of the combined cereal area.

Cereal mixtures grown elsewhere in the UK offer some explanation. A mixture of barley and oats named Dredge Corn was a feature of arable in the south west, mainly in Cornwall [6]. Its area was uncertain due the fact it was returned as ‘barley’ before 1919. As the quote at the top of the page implies, it was used as a safeguard, to ensure a reasonable yield under most conditions. It had a place in the crop rotation, sometimes replacing oats, sometimes barley, and was used in particular for a whole crop feed when the soil or the year was not capable of producing a pure crop of quality to sell as grain.  The proportions varied but were typically two parts oats to one barley. Wheat was added in some cases, making a three-part mixed grain.

While it was certainly grown as a safeguard, it was also attributed biological benefits [6]. It was stated to produce more grain than barley alone and generally more than oats alone, oats being deeper rooted and thereby accessing more resource. In dry years, barley grew to fill the ‘gaps’ left by dying oat tillers. The straw was of higher feeding value than the individual crops, due to better overall structure. But perhaps most relevant to the Atlantic climate, the mix was better able than barley or oat alone to withstand the forces of wind and rain to flatten the crop.  Similarly, one source reported that another variant – a mix of white and black oats – gave a greater yield (of straw) than either alone – the stronger stemmed white supporting the finer stemmed black. 

Despite such reports from farmers, there is little hard information on the yield advantage given by mixtures sown on the fringes of Atlantic Europe. They might have given the 1.1. to 1.3 times advantage widely recorded for intercrops, but without the experimental data from the 1920s or earlier, there is no way of knowing. 

Sown as a seed mix in April, no fertliser or pesticide: (left to right, 1 to 4) the bere barley grew quickly (1), then oat pushed through (2), bere matured first (3) and finally oat (4).
The widespread occurrence of unintended mixtures

It is the nature of small-grained cereals – oats, barley, wheat – to drop seed before or at harvest. The seed remains in the soil and, depending on conditions, emerges in a later crop. Today, such crop-weeds are commonly termed ‘volunteers’ [7]. The sown species and the volunteers in effect form a mixed crop (image below for wheat in barley). Other crops also generate volunteers. Those of oilseed rape are the most visible, but potato and field bean (Vicia faba) often produce mixed crops with cereals, though these broadleaf species may be really controlled by selective herbicides today. 

Unintended mixed crops have been a feature of cereal lands probably since domestication. If the intended product was whole-crop cereals to be fed to stock, then they would have been seen as a benefit – free seed. However, they may also create a problem. They are an unwanted nuisance when they have to be separated from the crop, for example when a pure seed-harvest is needed, and they could harbour and carry over disease. Volunteer cereals are not a recent problem: records from the 1500s [8] on oats relate “that they grow amongst wheat and barley without being sowen, as an evil and unprofitable thing ..”.

Maturing barley crop, golden brown, in which volunteer wheat (upright heads, dark grey-green) has established; younger, still green plants growing in the wheel lines.

Mixed corn, and mixtures of corn and grain legumes, have been recorded for centuries in Scotland, and more generally in Atlantic Europe, but their benefits have not been adequately quantified. Where they were grown, it was as broadcast seed mixtures rather than line intercrops. By the early 1900s, they were minor crops. After the 1940s, agriculture was aiming for the high yields promised by intensification: mixtures almost disappeared. 

Current reappraisal of crop mixtures might perhaps examine why in the early 1900s they never became major crops and why they were rarely grown as line intercrops.


[1] Photograph of chickpea-sunflower intercrop taken in Burma (Myanmar). Details on curvedflatlands at Mixed cropping in Burma.

[2] Seed mixtures for hay or grazing from the 1700s to the early 1900s are described in a related article on curvedflatlands: Grass mix diversity a century past.

[3] Crop mixtures are frequently referred to by Andrew Wight in the Present state of husbandry in Scotland (1778-84. Volumes 1 to 6), where one of the components (usually bere or barley)  is most commonly a ‘nurse’ crop, protecting the others, which are usually grass mixes (grasses, legumes and other broadleaf species) to be used for hay or grazing. 

[4] Mashlum, Scotland’s cereal-legume seed mix, still occasionally grown, is described on the Living Field web pages at Mashlum – a traditional mix of oats and beans  and Mashlum no more! Not yet.

[5] Data in Fig. 1 are taken from the online Agricultural Statistics in Scotland one of the Historical Agriculture Publications on the Scottish Government web site. Based on the 1965 census, Coppock created an atlas in which the small area sown with mixed corn was noted with the comment that it was ‘not grown in the great majority of parishes’. Ref: Coppock, JT. 1976. An agricultural atlas of Scotland. John Donald, Edinburgh.

[6] Borlase, W. 1925. Dredge corn. In: Farm Crops, Vol 1, pages 265-269.

[7] Volunteer weeds, derived from crops, and presently common in Scotland  are described at the Living Field web pages on Crop-weeds.

[8] Quote on oat from L’Agriculture et Maison Rustique by Estienne and Liebault, 1593 edition. Further details and origin on the Living Field web pages at: Ready, steady mundify (your barley) and  The Library of Innerpeffray.