There is no blue without yellow and without orange.
Vincent Van Gogh
Modelling has been and is an essential and inseparable part of many scientific disciplines, just think about the huge use of modelling in chemistry, where atoms, molecules are represented by graphical models, i.e. the quite famous (at least among chemists) Bohr atom model, with which we can solve the structure of almost all the known substance, natural and artificial. Let’s say that this kind of modelling is a static representation of the matter, but it is not sufficient to represent a different level of complexities, such as the matter behaves in dynamical systems: the swinging of a clock pendulum, the flow of water in a pipe (physical dynamic), the number of fishes reproducing in a lake (population dynamics). Moreover, those static representations, are not useful in analysing the behaviour of intangible magnitudes as prices, which are conditioned and driven by the continual changes in both supply and demand of any particular product (market dynamic) or in cases we should need to analyse the societal or individual behavioural responses facing an unexpected event (behavioural dynamic), just to give an idea of what I meant with different level of complexities..
In all the previous case, mathematics is the perfect tool to help us in describing how a system varies with the spending of the time, or more precisely, as it behaves as ‘function’ of time. And this is why mathematical modelling tools has had a boom, that it is still ongoing, since the birth of computers and computational science: in few decades of the past century, we passed to draw a model using pencils, papers and solving equations with hours of manual calculations, to build it with a computer, with which we can sketch the functions describing the system and the software will take care to solve functions for you.
I used the word ‘sketch’ because, with some of these programs (i.e. google for the terms ‘Vensim’, ‘Stella’, and you will see), functions can be represented by graphical objects corresponding to mathematical variables and/or operators. It is worth to highlight that those graphical objects often recall the shape of subjects that already have a meaning in our mind (arrows = flows, valves = regulators, boxes =stocks) so that, this new language permits 'to write mathematically' in a more intuitive way. And this feature results very helpful, especially for those are not expert of math stuff, allowing a huge saving of time in understanding if a model is catching the system under investigation or not.
The development of this kind of 'drawn-mathematical modelling' is mainly due to an idea of Jay Forrester, by which he revolutionised, during the 60s, the study of the 'dynamic of complex systems', better known as Systems Dynamic. You can find all the information about Jay Forrester, his brilliant mind and his revolution searching in the web, anyway let's keep its name in mind, I will recall him again below.
The success of Systems Dynamic modelling and, in general, of any kind of ‘Models and Modelling Tools’, underlines the high frequency with which our mind resort to model, consciously or unconsciously, to catch the meaning of a complex reality, modelling is an attitude of a rational mind, an attitude that also the famous artist Vincent Van Gogh surely had, as I discovered visiting the Van Gogh Museum in Amsterdam, during an 'off work' moment of the System Dynamic School, I was attended in Delft (Netheralnds) in summer 2016.
Van Gogh was a genius, he invented a really new way of painting, and as you probably know, he has been an almost self-taught artist. He is also famous for having lived an agitated existence, alternating moments of happiness and equilibrium to other blue and irascible moments. Fortunately, he left us proofs about his feelings and his life thanks to a lot of letters he wrote to his brother, Theo. By means these manuscripts we can know him better, anyway in the common imaginations, Van Gogh still remains an icon of one of the most irrational artists in the history of painting. And he seems to think so of himself too:
I put my heart and my soul into my work, and have lost my mind in the process (Vincent Van Gogh)Anyway, if you go in depth in the history of his life and his art, you will find that the previous affirmation describes a feeling that is the result of all, except that an irrational process. And I realised this when I found in the Vang Gogh Museum, his famous ‘box of yarn’, a small Chinese, red lacquer wooden box, that held 16 balls of wool.
I knew some episodes of Van Gogh life from the night classes of the Art school 'L.B. Alberti' (website only in Italian) I attended between 2002 to 2004 in Florence, but I didn’t know the existence of this box before to go to the Museum. But when I saw it, I immediately realised he used this box ‘to model’ the colours’ contrast and combinations for his paintings.
A tool to paint...Vincent has been..in certain sense, a modeller!
Probably I went too fast to this conclusion, as sometimes intuition make you do, but, could I really affirm this?
This fact induced me to investigate more the importance that box could have had in Van Gogh art. Was that box, that modelling tool, really useful for him in understanding a system?
The available information about Van Gogh life report he studied the colour theory of Charles Blanc in 1884, when he lived in Neuman, dispelling the myth that his talent came out of some automatic unconscious well of genius and/or madness.
Van Gogh is also very famous because of the huge production of paintings in a relatively short time: first paintings are dated in 1881 and the latest in 1890, before he died on 29th July of the same year. Take a look at the following graph, which reports the number of Vincent’s paintings as a ‘function’ of time (figure 1):
Figure 1. Van Gogh numbers of paintings as a function of time. The first peak corresponds to the period in which the painter approached the colour theory, and used models of others. The second peak corresponds to the period in which he used the own modelling tool, the box of yarn, and his canvases started to look like textile.Data from Wikipedia, graph by Ilaria.
During those 9 years, he realised around 1000 canvases, culminating in two production ‘peaks’ in 1885 and in 1888. Could it be reasonable to suppose these higher 'production rates' were related to the use of modelling that helped the artist to catch the 'systems' he wanted to represent? Let's see what the facts tell us.
The first peak is in the year 1885, shortly after that Vincent approached the theory of colour using the models of others. Van Gogh quite certainly resorted also the ‘colour wheel’ devised by the chemist Michel Eugène Chevreul, with which he could preview the effect of mix determines tonalities. Probably, this modelling tool gave him a more in-depth understanding of how he could translate what he had in mind on the canvass, culminating in a production of around 150 paintings in the year 1885. We can also note, that from his first paintings of the period 1881-1883, he changed the style, introducing more colours and more contrasts (see the previous wikipedia source and scroll down the images of the paintings).
The second peak in 1888, could be connected with the use of the tool, ‘box of yarn’ (figure 2): Vincent invented is own modelling tool to model the colour combinations, inspired by the work of the weavers he painted in Neunen few years before.
It is Van Gogh’s friend, Bernard, who reported about the existence of this box, shortly after the painter death, and he said it was in Paris he saw the box for the first time, from 1886 to 1888 when Bernard met and worked with Van Gogh before Vincent left to Arles. In the paintings of these years it is clearly visibile the Vincent's famous brushstroke reminding the consistency of a textile. Moreover, with the help of the yarns, he was able to test the combination of colours without waste tempera.
Thus, we can now reasonably conclude the maximum production of Vincent paintings corresponds at the moment in which he approached the colours’ modelling tools. But again, what system did he want to represent?
Analysing the historical changes in Van Gogh, let’s say, ‘styles of painting’, it is in evidence that Vincent mind wanted to go beyond the appearance of the colours, he ran after the colours' potential up to invented an own modelling tool, the ‘box of yarn, to represent the beauty of Nature and of life, let's say very successfully. In a certain sense, the box and the yarns could represent one of the precursors of the RGB colour model now implemented in the representation and display of images in electronic systems, such as televisions and computers.
Van Gogh approach in modelling is not so far from the one from Forrester. Let’s take a look at the following words from Jay Forrester, with which he defines what is a model:
The image of the world around us, which we carry in our head, is just a model. Nobody in his head imagines all the world, government or country. He has only selected concepts, and relationships between them, and uses those to represent the real system (Jay Forrester,1971).
Then we could conclude saying that this is not only the case of Vincent …all what a painter paints can be seen as a model of a real system (material or intangible) and Van Gogh has had the added merit to invent a new modelling tool to do it.
So…is this concept reversible and is a scientist, an economist, and any other of the more 'common' intended modellers.. a sort of painters when modelling an image of the real world?
No easy to answer, I just can say I like to think so...
I wish a good work to all my friends and to have a new year full of inspirations!