The work Movements of a fly on a window between 8 am and 7 pm on one day in May 1967 is a diagram made by the artist and composer Walter Marchetti. In this drawing exercise, Marchetti traced a series of random movements on a surface in a given time; In this way, he schematized and defined with mathematical rigor something arbitrary: the random walk of a fly.
A random walk is, in fact, a mathematical object that consists of a succession of unexpected steps in a designated mathematical space. Its representation uses graphics, planes, or dimensions in vector spaces and has several applications. For example, in mathematical ecology, random walks are used to simulate animal paths to make population dynamics models and empirically support bio diffusion processes.
Other specific cases of random walks are diffusion models, such as the movements of suspended particles in liquids and gases. In this process, the molecules and particles collide with each other, resulting in the seemingly random nature of the movement.
The scientific poem “De Rerum natura” (On the nature of things), written by the Roman philosopher Lucretius (c. 60 BC), would be a relevant text for this discussion. It includes an example of a diffusion random walk in a description of the movement of dust particles. The lyrical nature of the text combines the author’s intention to record the observation of a phenomenon through a poem. Thus, the creative impetus of poetization is found in the face of the methodical contemplation:
“Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways… their dancing is an actual indication of underlying movements of matter that are hidden from our sight… It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.” (p.168-169)
This phenomenon is known as Brownian motion, named after the botanist Robert Brown, who described it in 1827 while observing, through a microscope, pollen submerged in water. Then, in 1900, Louis Bachelier deciphered the mathematics behind this process in his “Theory of Speculation”: the interactions of the multiple particles could only be solved using probabilistic models. Those random movements of pollen were organized into mathematical formulas of probability.
The theory of Bachelier introduced many of the concepts of stochastic analysis and finance. Some market characteristics are predictable precisely because they are random, so the Bachelier model can be used to make probabilistic predictions that, due to the law of large numbers that link probability and frequency, give us information on how long-term market fluctuation will behave.
The theory was developed into a multi-billion dollar global options trading industry.
Thus, a “random walk” may refer to the path of an animal, the movement of a molecule, fluctuations in the stock markets, and also the financial status of a gambler.
In this sense, these phenomena (mathematical and also poetic) whose underlying existence precedes market studies are related to processes that have both technical applications and visualizations. Therefore, I intend to locate the topics described above in the art world, tracing relationships between images, particles, markets, speculations, probabilities, diffusions, and data observation techniques. Thus, the arrangement of lines and strokes in the graphics to represent hidden trends and displacement possibilities establishes connections from which the representation and circulation of images are also possible.
A virtual particle could perform a random path directly on a graph, thus programming the probability that this particle, which starts at one point, will reach a different place after a certain number of steps. These algorithms are applied to determine the object or background labels on each pixel. They are used to convert the data from a digital camera sensor to standard image files, increase the quality of an image (remove noise and pixels, detect and enhance borders) and improve its processing capacity on a computer.
In these dynamics of a digital nature, random walks are used in computer science to sample very large spaces, for example, to choose a random page on the Internet, to make suggestions for accounts to follow on Twitter, or to find similar images on large databases based on their content color and shape (Content-based Image Retrieval).
This system is used in art collections, photographic archives, and image banks in museums. When searching technical data (image, color, and shape) is possible to access the image of artworks quickly. On the other hand, suggestion systems allow artists to increase their visibility, and it is most likely for potential buyers to find pieces on searches according to their preferences.
In this sense, the digitization to which artworks are susceptible off and the advent of file-sharing networks bring changes related to the dissemination and permanence of a piece on the web and in the market.
The financial aspects regarding the art world and the use of images are obvious; platforms that allow quantifying the diffusion and transit flows give art a dimension of participation in quantitative languages, as it happens in any other industry. Just as speculation theories are used as predictive methods, statistical approaches are used to determine trends and make projections in the art market, as if it were a crystal ball.
By Leonardo Da Vinci, Salvator Mundi is today the most expensive painting globally; it was sold for over 450 million dollars to a Saudi prince and later acquired by the Louvre Abu Dhabi through the Department of Culture and Tourism. Although the amount invested in the acquisition of this piece may seem exorbitant, you may consider the added value for the city and the institution in which it is placed and the commercial and marketing impact that it causes: this painting could attract a large number of visitors who would go to the UAE just to see it.
The digitization of artworks could also be combined with models of scientific analysis to shed new light on this particular piece. Using physics-based rendering and computer graphics tools, a team of computer scientists from the University of California investigated how the figure of Christ in this Da Vinci’s work would have been seen through orbs of different materials. Thus, it was determined that the translucent globe in Jesus’ hand does not refract or distort the light that passes through it. The movement of dust particles described in Lucretius’ poem could have also been seen in the light that passes through the orb because it is empty. That is to say, Da Vinci’s glass sphere is actually a bubble.
A bubble is any deviation from a fundamental value. Market bubbles lead to collective behavior since it is not only the management of the companies that determines the value of the shares; it is the most popular story, that is, the perception of them by the host community. Sometimes the survival of an image is determined as much by its aesthetic elements as by its publicity and notoriety. Many museums and galleries have iconic works and a catalog of must-see objects that will become the brand of that given institution.
In the Ecuadorian art scene, the dynamics described above can be exemplified in the 20th-century painter Oswaldo Guayasamín, whose work was (self) promoted as an exportable product. His success in the market was based on the formulation of exoticism, ideological and aesthetic content, and the safe investment value in the stability of an immutable and consistent product. His permanence has been solidified in a museum1 whose name leads to cult associations and in public institutions that solidify his permanence as an icon.
What would be the new iconic pieces for each institution?
Adapting these valuation and market dynamics to digital channels and online searches makes it easier for new artists to become familiar with globalized visual languages and access referential cultural dynamics, thus allowing them to produce in a standardized world. Regarding these virtual environments, the works can be found and displayed in digital formats (jpg., Png.), which causes a paradoxical contrast: either they are accessible and easily located, or they became lost in the torrential search for online images.
The transformations that these tools have conjured result in other types of diffusion phenomena such as the global irradiation of images and information, thanks to the absence of space-time barriers on the Internet. The network allows the integration of different scenarios and contexts regardless of geographical ties: a work could be in one country while the seller lives in another country, the money could be in a different country, and the buyer could live in another country and, therefore lastly, the artwork could be housed in another country.
On the other hand, the internet presence also ensures the availability of a collection of references of different financial aspects: the reports are now available for buyers and investors to carry out analysis to support the market, private and public institutions must provide accountability and explain how the money will be used in cultural investment; there are evaluators, auction house associations or gallery associations with guidelines for codes of conduct. Some countries have these government and market regulations, while others do not (sight). But, as in any industry, a developing cultural scene could become more transparent and professional, or more international, more global, more transactional, more attractive, modern, cool, trendy …
Parting from the conjugation of these actors and dynamics in a scene, the probabilities of displaying an image depend on a series of selection processes and criteria, both of the artists who produce in certain spaces and that of the agents who determine which image it is selected, accepted, exhibited or put in reserve in an institutional space. The random path of a fly in a musician’s diagram is equivalent to actors moving independently under their own random will, in fields of cultural production that are, as Bourdieu described, random, scattered, and devoid of clear direction 2.
Random walks and statistical approaches can be used to determine how an agent would behave in specific spaces or contexts: How likely is it that an image will circulate on a given platform? To answer the stated above, factors of the dynamics of success (understood as visibility and sales) have been studied concerning the music industry (before and after digitization) with the actors of purchase, sale, and speculation. The School of Social Information Studies investigated the success of Japanese popular music between 1990 and 2004, that is, before and after online music sales. As part of the work, they examined different variables: the song producers, the genre of the song (Jpop, short for Japanese pop), the level of sales, or the link of the song to promotional purposes. The study showed that the artist’s fame and their associations with other media increase the success of their songs.
In another case, Ordanini & Nunes investigated the dynamics of songs on the US Billboard Hot 100 singles chart, after which they concluded that after the sale of music online on platforms such as iTunes, there was some deconcentration in the market in a transition from fewer hits by more superstars to more hits by fewer superstars. Finally, the Royal Society of Open Science analyzed songs released in the United Kingdom between 1985 and 2015. It used statistical approaches to determine musical trends and thus identify the extent to which musical attributes contribute to the success of a song. In this study, random paths were used as a predictive method, combining predictions of lists that are created by random sampling of characteristics to explore the probability of future successes using past trends.
Similar studies could be applied in the art world. Using random paths as a predictive method makes it technically possible to create a standard image with serial production means that meet specific selection and acceptance criteria.
Statistical approaches may be used to quantify characteristics and determine trends, combining random sampling created predictions to explore the probability of future successes using past trends. Different variables involved in the dynamics of success can be examined: the level of popularity of the artists, their demographics, their gender, the level of sales, the level of promotion, their nature of legal representation in a gallery, etc.
In the random walks of diffusion, in the market, likewise in pollen in water, liquidity means being easily convertible; it refers to the availability of being immediately exchangeable, that is, how quickly it can be sold. Diffusion models simulate fluid movements by computer and calculate the liquidity of data. The diffusion in the image is manifested both in its processing, production, and distribution. The image will remain suspended between the immediacy of a phenomenon and the quantification of time of its eventual circulation.
1 Capilla del hombre
2 Bourdieu, P. (1993). The Field of Cultural Production: Essays on Art and Literature.
Cheung, G., Magli, E., Tanaka, Y., & Ng, M. (2018). Graph Spectral Image Processing. PROCEEDINGS OF THE IEEE. Retrieved from https://arxiv.org/pdf/1801.04749.pdf
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Interiano, M., Kazemi, K., Wang, L., Yang, J., Yu, Z., & Komarova, N. (2018). Musical trends and predictability of success in contemporary songs in and out of the top charts. The Royal Society Publishing, 5(5). doi:10.1098/rsos.171274
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Liang (Zhanhang), M; Goodrich, M; Zhao, S (2019) On the Optical Accuracy of the Salvator Mundi Retrieved from https://www.ics.uci.edu/~zhanhanl/web_files/projects/salvator_mundi/salvator_mundi-arxiv19.pdf
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zero.void. (2016). Dusty Kid. Retrieved from https://tenor.com/es/ver/dust-dusty-gif-5219397
i Marchetti, W. (1967). Observación de los movimientos de una mosca sobre el cristal de una ventana desde las 8 de la mañana hasta las 7 de la tarde de un día de mayo de 1967.
ii Jordano, P. (2007). Frugivores, seeds and genes: Analysing the key elements of seed shadows. In Frugivory and seed dispersal: theory and applications in a changing world. Wallingford, UK: Commonwealth Agricultural Bureau International. doi:10.1079/9781845931650.0229
iii Esquembre, F. (2012). Ejs Open Source Brownian Motion Gas Model Java Applet. Retrieved from https://es.wikipedia.org/wiki/Movimiento_browniano#/media/Archivo:Brownian_motion_large.gif
iv zero.void. (2016). Dusty Kid. Retrieved from https://tenor.com/es/ver/dust-dusty-gif-5219397
v Cole, L. (2020). File:Stock market crash. Retrieved from https://upload.wikimedia.org/wikipedia/en/2/21/Stock_market_crash_%282020%29.svg
vii Cheung, G., Magli, E., Tanaka, Y., & Ng, M. (2018). Graph Spectral Image Processing. PROCEEDINGS OF THE IEEE. Retrieved from https://arxiv.org/pdf/1801.04749.pdf
viii Anoneditor, Retrieved from en.wikipedia
xi McAndrew, C. (2019). The Art Market 2019. Art Basel.
xii, xv Liang (Zhanhang), M; Goodrich, M; Zhao, S (2019) On the Optical Accuracy of the Salvator Mundi Retrieved from https://www.ics.uci.edu/~zhanhanl/web_files/projects/salvator_mundi/salvator_mundi-arxiv19.pdf
xiii Lewis, B. (2009). The Great Contemporary Art Bubble Update. Retrieved from Docuwiki: https://docuwiki.net/index.php?title=The_Great_Contemporary_Art_Bubble_Update
xix Interiano, M., Kazemi, K., Wang, L., Yang, J., Yu, Z., & Komarova, N. (2018). Musical trends and predictability of success in contemporary songs in and out of the top charts. The Royal Society Publishing, 5(5). doi:10.1098/rsos.171274