Decimal Vs Duodecimal System

I think that duodecimal (dozenal) system would be much more appropriate for architecture and let me explain you why. A big chunk of the design procedure is composed of dividing objects and distances into fractions, which is a mess in the decimal system. For example, we need to divide 20 m long Facade into thirds, which results in those funny numbers with infinite dividers: 6,666 and 13,333. Those numbers are not very useful on the construction site and no producer will make prefabricates in that sizes. We are forced to either use approximations (in this case 6 and 13) or to avoid certain dividers. First option creates some residueg and the second option is not really feasible, as simply too much of architectural design is composed of dividing geometric forms into fractions: halves, thirds, quarters, fifths, tenths, and so on.



Composition of a classical church, in this case squares are divided into rectangles.


Duodecimal system solves this problem by elegantly adding two extra numbers to the counting system. Instead of grouping numbers into tenths, we group them into twelfths.

1       2       3       4       5       6       7       8       9       10       (11)       (12)

1       2       3       4       5       6       7       8       9        ᘔ          Ɛ          10

Technically, number 10 gets a new symbol ᘔ (rotated number 2) and 11 gets Ɛ (rotated number 3). It is actually the oldest counting system, invented in the ancient Sumeria. At that time with the basis of 60 (4 x 12), which is still in use in measuring time. Ancient Sumerians found that this way they could simply divide a unit of crops into thirds and fourths for the purpose of taxation. The Germanic languages still have separate words for 11 and 12, and until the end of 19th century many traders used dozens as their preferred units of measurement.

The argument of having 10 fingers to count, well, it is only partially true. We have 3 bones in each finger, with 4 fingers it makes 12. Index finger is used for counting. Try it, it does work :).



Let’s take a look at dividing into fractions. In the decimal system 1 meter is composed of 10 dm. Let’s divide it:




1/1 of a meter =  10 dm

1/2 of a meter =  5 dm

1/3 of a meter = 3,333333 dm

1/4 of a meter = 2,5 dm

1/5 of a meter = 2 dm

1/6 of a meter = 1,6666666 dm

1/8 of a meter = 1,25 dm

1/10 of a meter = 1 dm


In the duodecimal system 1 meter is composed of 12 dm:


1/1 of a meter =  12 dm

1/2 of a meter =  6 dm

1/3 of a meter = 4 dm

1/4 of a meter = 3 dm

1/5 of a meter = 2,4 dm

1/6 of a meter = 2 dm

1/8 of a meter = 1,5 dm

1/10 of a meter = 1,2 dm

1/12 of a meter =  1 dm

It is quite obvious that we got rid of those infinite  dividers (1,333, etc.) and that almost all numbers are natural numbers. Calculations are much easier, and have almost no residue.

That is why I almost always use as the basis for my plans 1,2 m (and not 1 m), as it is so easy to divide it into fractions. Do I have to extend a road for 1/3? I just add 0,4 m.  And I try to avoid the number 5, as it is a prime number and so non-dividable (numbers as 1’5, 0’5, etc.).

Am I a proponent of the duodecimal system? Yes. Do I think it is realistic to implement it? Of course not.

More on this here and here



Exterior architecture instead of landscape architecture?

In the last weeks I was thinking about the nature of my profession and I think that the name of my profession is set wrong. Well, at least for me, as less than 20% of my projects are about landscapes. The majority of time I am spending on much smaller scales, dealing mostly with urban design, sports and building exteriors. Not much landscape or landscape related issues there. Maybe I should start to present myself more as exterior architect  and not any more as landscape architect.



Angles, those angles

I was having a discussion with my cousin about walls and angles in architecture. To make long story short, it is very suggestable to avoid angles smaller than 90°. At least most of the time, as they minimise usable surface area (and make furiture buying a nightmare).



No design is also design

Last time I had a discussion with Luka, the old colleague. He was telling how Ana Kučan, my menthor and former boss, was discussing during a workshop in Udine how the decision to not do any interventions in architecture is also a design decision. Deciding to not do any design is also a design. Sometimes we are too preocupied to change something realising that a site does not really need any change. Sometimes it is ok as it is.

Interesting thought.

A cheat sheet of the design process in architecture

I wrote this text originally for my architecture students, as they were struggling quite a lot with the design development. Seemingly no one told them how to go from the first concepts to a finished plan. It was also a good opportunity to revise my own knowledge and views on the subject.

There are five types processes of project design: linear, divisions, centralized, cycle, and investigative (here is a brief explanation for all of them). Each of them has its advantages, but I strongly recommend to start with the variant 2: divisions, as it is in my experience the most robust system. I have developed a variation of the system, which bases mostly on my notes from the lectures of dr. Carl Steinitz and dr. Janez Marusic.

Design process can be divided into three phases: Analysis, Vision, and Design. Analysis phase is the imput – here are organised all entry data: site analysis, usage, spatial limitations, and zoning. Key objective in this phase is to define the key problems of the site (is there an important visual axis, are there any unpleasant surrounding elements, a loud side road, or similar). Vision is the new quality your development is bringing to the site, which is then refined in the concept and development phases. The end result is the site plan with graphical representations.

Here is the whole scheme:




Let´s take a look at each step separately, where I will also present what is done in each phase.


1) Inventarisation


To immediately clear the difference between inventarisation and analysis: the goal of inventarisation is to list and organize all of the information from the site, while the analysis shows personal interpretation of the site qualities. Inventarisation is a graphic catalogue of all existing conditions of the site, exactly as they are. For example, roads around the site are divided according to their size, traffic usage, etc. (and drawn on a map).

Most common subcategories are:

  • Traffic: typology of roads (alley, highway,…), typology of traffic (commute, heavy transit traffic, bicycles,…);
  • Land usage;
  • Access;
  • Topography: elevation, slopes, geological features,…;
  • Context: typology of surrounding buildings, shadows, land use,…;
  • Historical development;
  • Exposure to natural elements: insulation, precipitation, temperatures, snow,…;
  • Vulnerability to natural disasters: 100 year floods, earthqakes, …;



Here is an example of an inventarisation. It is a GIS rendering according to some (non given) criteria. Areas are color-coded in an non-discriminator way. Whatever would be the next step, for example coloring the darker areas, is an analysis – a personal interpretation of the site. source



2) Analysis


In simple words, analysis is a personal interpretation of the site and its surroundings. Analysis does not need to be graphic (even though it usually is).  Sometimes a SWAT analysis is enough. The key of the analysis so to define the key problems on the site, and to show your personal position on the site’s current qualities.

Some key bullet points:

  • Exposing key visual elements: points, axis, surfaces (Lynch’s analyis);
  • Defining current site qualities, weaknesses;
  • Giving or taking away the importance of the existing elements (existing buildings, roads, usages…);
  • Areas to keep, areas to upgrade, areas to change, areas to remove;
  • New openings, new closures;
  • Placing the site in a wider context;



Here is an example of an inventarisation. It is a GIS rendering according to some (non given) criteria. Areas are color-coded in an non-discriminator way. Whatever would be the next step, for example coloring the darker areas, is an analysis – a personal interpretation of the site. source



3) Programme


Different types of users demand different typologies of buildings. If, for example, on the site is planned a residential area, it is also very important to determine what type of residents will live there. Usually, the more detailed it is, better it is. Details help, as specific residents demand specific usages; a young family will find important to have bigger, calmer appartments, and the vicinity is a playground, while young students will be satisfied with smaller, darker dwellings, possibly close to bars. Same goes for commercial usage: startups or small companies demand different plot sizes and building typologies than large corporations, retail different than a car mechanic.

Key bullet points:

  • defining types and subtypes of usage
  • defining spatial demands for each type of use



110927_pièces graphiques_cahier A3.indd

Here is an example of an inventarisation. It is a GIS rendering according to some (non given) criteria. Areas are color-coded in an non-discriminator way. Whatever would be the next step, for example coloring the darker areas, is an analysis – a personal interpretation of the site. source



4) Zoning


When the site usages are defined, it is necessary to organize them in a system. Some usages are not compatible and should be separated, while others can be close to each other. Some even thrive in the vicinity. If we take a simple example: It is usually good to separate kitchen and the sleeping rooms (for the odors), or keep kitchen close to the living room. In city planning is usually good to separate  residential areas from industrial zones, and to keep residents close to parks and public transportation.

Some usages are more important and must be placed more to the middle of the site, while others, less important can be placed on the side. In the drawing below is the main stage in the middle of the drawing  (of course), while offices can be somewhere on the side.



Here is an example of an inventarisation. It is a GIS rendering according to some (non given) criteria. Areas are color-coded in an non-discriminator way. Whatever would be the next step, for example coloring the darker areas, is an analysis – a personal interpretation of the site. source



5) Vision


After the analysis we must synthetize all gathered data into a key concept, the main vision for the site. This main unifying idea tries to catch the spirit of the new development, the added value it brings, a new quality to the site. It can also be just a slogan, or someting similar. The main vision solves the main problems of the site and offer some new quality, which is cruicial.



6) Talent


Sometimes it is possible to skip the first four steps and go directly to the vision, ignoring the given situation on the site and start with a brand new development. It is possible, although those plans are rarely better than those which follow a more systematic approach. Analysis is is cruicial in design process, as it helps build a relationship with the site and sometimes it unveils the true and unexpected problems of the site.


7) Concepts


Each vision, can be drawn in different ways. The same idea can be presented in many forms. It can be orthogonal, curved, polymorphic, drawn in circles, or composed of a myriad of forms. The new development can be one megablock, or many smaller city quarters, or a skyscraper. Some typologies fit better to the main idea. The goal is to find which typologies support the main idea the best. In this phase the details are not that important. What is important is to find the rough holding shape, which captures the best the vision. In latter steps is this form refined with all the details.



A mashup of some housing typologies. There is still more. source



8) Variants


Each concept can be drawn in different variants. For example, if the concept is a rectangular building, we can draw in many different ways: with sqare as a base, or the 1:2 rectangle, or 1:4 rectangle, and so on. What is important is the reversibility of the process. If variants seem to lead to a dead end, it is possbile to step back and try another concept.


Some possible variations on a topic of a single city block



9) Result


The end results of the design process can be divided in three groups: Site plan, picturesque representations (isometries, 3D pictures, sections, views), and the supporting graphics (pictograms, sketches, analysis, …). I will focus just on the later, as the first two are quite self-explanatory. The key purpose of supporting graphics is to show the thought process of the architect and to explain the main idea of the development. They tell why your development is different from others and which new quality it is offering to the site. Sometimes is enough to show just a hand sketch. Other time is enough to show (polished) inventarisation, analysis, and zoning  sketches from previous steps (especially those which are relevant and support the main idea).



Architecture ideas are increasingly complex and have to include many aspects: aestethics, structural design, social interactions, energetic and environmental views. Representing all those aspects is perhaps one of the most challenging tasks.

In my experience, it is usually enough if  only one of those elements word-class excellent (either the site plan, representations, or suppotrting sketches). Other elements can be top or middle good, and the whole representation will look ok.



Sometimes is possible to jump a few steps and go directly into developing  a project.  But if you ever get stuck in developing a project, I would consider to simply follow a system. There are many options for that and in the text above I tried to explain one of the possible systems. The steps above usually lead to at least a solid design solution, if not more. The analysis phase helps define the main problem of the development, from which we can extact the vision. The following execution is just trial and error finding the best typology (and other details) for the site.


Even fewer world conflicts

A very nice video about in how pacific times we are living. People often forget that there were never so few armed conflicts as there are right now in the world. The authors, for example, offer a data that the number of peaceful resolutions of conflicts (=diplomacy) have rose from 10% to 40% in last hundred years. They also suggest a few explanations, and I like the most the following:

  • democratisation; democracies only rarely attack each other.
  • globalisation; it is cheaper to buy resources than to conquer lands where they are stored

Facebooking when we are old

Last time I was observing my grandpa sitting on his sofa and watching the news on TV. He has made a habit out of it, as he watches news every day on three different channels, spending in total 1,5 h on them. But it is OK, after 50 years of watching TV news every day, it is his routine. It is actually funny watching him getting angry over different events around the globe. But I have an impression that watching news on TV is getting less and less frequent, especially amongst the youth. And one day, after my regular morning facebooking session, I thought if facebook will be our routine when we grow old? Will we be just sitting there and mindlessly browsing through statuses? Our grandchildren will be looking at us from the corner and giggling how are hooked to this ancient routine.