OLIVIER BODINI: THE ART OF CODING

Olivier Bodini: My interest in mathematics was sparked at a very early age when I became fascinated by numbers, addition, and multiplication. I found it incredible that such complexity could arise from such simple, natural rules. A number is just an abstraction of grouping and enumerating objects, so why does this richness exist that led mathematicians to create what's known as number theory?

I was a very good math student, which naturally led me to pursue this path, but that's not the only reason. For me, mathematics is a magnificent space for creation, with strict rules, of course, but all the arts are built on rules. I firmly believe that creation needs its limits to flourish; without constraints, you get nowhere.

In fact, my perception of mathematics has always surprised my classmates and continues to surprise my colleagues to this day.

OB: Let me start with music, as the visual arts have more implicit constraints. In Western music, the rules and constraints are numerous. There is the harmonic system (chords), which are limited, and thus the progressions are often organized around tonal schemes like I, IV, V, and I, which correspond to a large part of classical and popular music. The rules also apply to melodic lines, which must adhere to constraints (no repetition of motifs, ascending then descending form, no consecutive fifths, etc.).

Other rules stem from the instruments themselves: their habits, virtuosity, and unique techniques. One does not write for the voice in the same way as for a flute or a piano. There are also rules of orchestration, the combination of instruments, and finally, rules of counterpoint, which is the arrangement of melodic lines with each other. The most famous example is the fugue. Additionally, each work, like a symphony, has its own structure with a sequence of movements: introduction, first movement, minuet, trio, and finale. Each piece is also constructed following a specific form, like the ABA form: a first theme A, followed by a second theme B, and a re-exposition of theme A. I am not even talking about ornamentation or harmonic progression, which are also highly codified.

All these rules impose a significant amount of structure, but they also drive creation by guiding the mind in its creativity. Of course, any rule is, by nature, transgressible. But generally, transgression involves the establishment of other rules. Beethoven transformed the trio into the Scherzo. Schoenberg (1923) broke with the tonal system for the twelve-tone technique. French music at the end of the 19th century shifted from tonal to modal.

This comprehensive framework of rules both constrains and fuels creativity, guiding composers in their artistic endeavors.

In the visual arts, there are also numerous rules: perspective, color, and composition. Art is codified; for example, Cubism, emerging around 1907 with artists like Picasso and Braque, redefined notions of space and perception. The theory of color has traversed the entire history of painting, evolving from the pursuit of harmony in the 17th century works of Le Lorrain to the elegance in Chardin's 18th century paintings and exploring effects from the Impressionists in the late 19th century onward.

Visual art, like music, is guided by established principles that both constrain and inspire creativity. Perspective rules, formalized during the Renaissance in the 15th century, dictate how depth and space are represented on a flat surface, creating the illusion of three-dimensionality. Color theory, significantly advanced by figures like Newton in the 17th century and Goethe in the 18th century, provides guidelines on how colors interact, the emotions they evoke, and how they can be harmoniously combined. Composition rules help artists organize elements within a work to create balance, focus, and movement.

Throughout history, different art movements have challenged and redefined these rules. Cubism, for instance, broke away from traditional perspective to present multiple viewpoints simultaneously, fundamentally altering our understanding of space and form. Similarly, the Impressionists, beginning around 1870 with artists like Monet and Renoir, revolutionized the use of color and light, moving away from precise realism to capture fleeting moments and the effects of light on the natural world.

This evolution in the visual arts reflects a dynamic interplay between adherence to rules and the boldness to break them, driving the continuous transformation and expansion of artistic expression.

OB: My mother was a kindergarten teacher, and she enrolled me in artistic activities such as drawing and music at a very early age. I have always loved creating, and from a scientific perspective, I would say it's a rather intriguing characteristic of humans. Recently, I had a discussion with a colleague in quantum physics whom I had invited to the history and epistemology of science seminar that I co-directed. We talked about how matter—humans, to be precise—because physically speaking, we are merely a collection of atoms, has organized itself so complexly that it possesses a sense of free will and a capacity for creation. This, of course, contradicts classical physics, which posits that all evolutions are entirely governed by the laws of the universe.

Several hypotheses are possible:

1. The universe is entirely deterministic, although unpredictable (chaos theory), and everything is written. Our belief that we decide what we do is an illusion.

2. The universe branches into an infinite number of parallel worlds at every moment, and our universe was just one possible branch on it.

3. Quantum physics contains an element of randomness, of indeterminacy. Our brain, through its complexity, builds itself around this uncertainty. Our creativity is a clever mix of our experiences, our neural structures, and quantum randomness.

I quite like that last hypothesis!

But to return to my first artistic emotions, I must say they were brought about by music. I studied composition and counterpoint at the conservatory in my town and then as an auditor at the National Conservatory of Music and Danse of Paris in Thierry Escaich's class (the famous composer). Music is very close to mathematics, particularly my research field in mathematics called combinatorics, which is the art of combining and counting mathematical structures. I always keep in mind the possibility of returning to musical creation. Everything is connected in my mind and forms a cohesive whole: graphic art, music, and mathematics.

OB: For me, there is no difference in the process of creating a theorem or a painting; only the context changes. Context is a concept that is extensively studied in modern computer science. A piece of software must work just as well on a smartphone as it does on a computer. The software is the same, but the context is different. Creating, for me, works in the same way. In mathematics, you have a theory, and you are led to form conjectures and prove them. It's like assembling mosaic tiles to create a work of art. There is even a book called PROOFS FROM THE BOOK, where Martin Aigner describes proofs that he considers to be masterpieces, to the point of believing they are from a divine book, THE BOOK.

Just as an artist arranges colors and shapes on a canvas to create a visual masterpiece, a mathematician arranges logical statements and proofs to create a theoretical masterpiece. Both processes involve creativity, intuition, and a deep understanding of the underlying principles, whether they be artistic or mathematical. The joy of discovery, the challenge of problem-solving, and the satisfaction of creating something beautiful and meaningful are common to both fields.

AI in art is precisely another context. Artists must embrace all tools, but an artist is someone who will produce something new. Everyone can take photos, but few of us can claim to be art photographers. Once again, I don't believe one can be an artist without having a line of thought. This might be unconscious, but all recognized artists have produced something personal, unique, and recognizable. Often, this stems from an implicit intellectual approach.

AI is just another medium for creativity, a new set of brushes and paints for the modern artist. It offers unprecedented possibilities, yet the core of artistry remains unchanged. The ability to imbue one's work with a unique vision, to convey emotion and thought, is what distinguishes a true artist. Whether it's through traditional media or cutting-edge technology, the essence of art lies in the expression of the artist's inner world and the intellectual journey that drives their creativity.

OB: Two reasons, the main one being the world of NFTs, which presents an incredible opportunity to gain recognition. In my opinion, it has revolutionized the traditional art circuits. I do not have a formal education in fine arts, and it would have been particularly difficult for me to break through without NFTs. I remember reaching out to a gallery five years ago, and they responded by saying, "We only exhibit recognized artists." To which I replied, "How can I become recognized if all the doors are closed from the start?"

The other reason is that my taste in music is extremely conformist, and even though there is currently a resurgence of enhanced tonal music, during my musical studies, the dominant trend was highly conceptual, and I couldn't find my path in it. I am talking about contemporary music, as you understood.

OB: Art galleries play a crucial role in the NFT ecosystem. First and foremost, they serve as a place for curation. While there are many knowledgeable collectors, there are also those who need guidance, and galleries are an ideal venue for this. NFTs have developed at an exponential rate, and it is absolutely vital to structure this space. To me, objkt.com is a genuine incubator of talent, unfiltered, egalitarian, and open. However, it is easy to get lost in the crowd, and gallery owners are there to highlight the most interesting artists.

Galleries are also focal points for more experienced collectors. It's important to recognize that NFTs are based on an ultra-liberal model that has made the market excessively speculative. Personally, I aspire to more academic recognition, which galleries can provide.

OB: First of all, mathematics and computer science form a whole that I do not really distinguish between. The computer science research I conduct mainly concerns algorithms, which is the theoretical part of computer science; I don't particularly enjoy the art of coding.

My team's objective is to apply modern mathematics to the world of art. As everyone knows, AI has entered the art world, yet many questions remain, such as making AI more manageable and, above all, more imaginative. My expertise in random generation leads me to believe that we can make AI-based creation more disruptive than it currently is.

At the same time, with my team, we work on data visualization, and my artworks all stem from this work. Extracting information from massive databases is a very complex challenge, and it is incredibly rich in terms of visuals. Algorithms like Force Atlas have many flaws, and my work aims to produce visuals that are both more expressive and more aesthetic. Lastly, quite incredibly, real data often relies on power laws (scale-free), which turn out to be particularly suited to our visual perception. This has opened up an incredible playground for me, rich in diversity and aesthetic value.

OB: I mean that coding correctly is a discipline of computer science in itself that requires very fine skills. I'm not talking about tinkering with a few lines in p5.js or Python. Computer science is a recent science that has experienced vertiginous development. The art of coding involves mastering a programming language perfectly, knowing how to exploit all its resources, and understanding its weaknesses. You should know that when a program is written, it is first converted by the machine into a binary code (0s and 1s) executable by the machine (this is called compilation). During this process, many optimizations are performed, sometimes quite intricate.

The art of programming is about knowing all these properties of the language. This is not my field of research, and it's not at this level of granularity that I enjoy working. What I love is designing strategies and algorithms, not their efficient implementations. A little anecdote: the revolution in AI is primarily driven by the evolution of computer power and the meticulous coding of neural networks (Pytorch, TensorFlow,...). Training in AI is extremely computationally expensive, but if we look closely, the underlying theory has existed for a long time. The fundamental notion is stochastic gradient descent, which has existed since the 1960s, and the perceptron (the first artificial neural network) dates back to 1957, whereas ChatGPT dates from 2022! But ChatGPT had to wait for TensorFlow and phenomenally powerful machines before impressing people! To summarize, writing code for generative art is fun for me, but rewriting an optimized version of TensorFlow is beyond my skills and my pleasure.

OB: AI is a broad concept that encompasses many things. Let's say we're talking about artificial neural networks. I became aware of AI research very early during my studies. I must admit, my perspective has radically changed over time. In the beginning, significant resources were allocated in French universities to develop AI, with researchers promising spectacular advancements in the 2000s. However, nothing substantial seemed to happen, and it felt more like a scam than anything else.

Then, as machines became increasingly powerful and the datasets for training grew enormously, there was an incredible qualitative leap, say around 2010-2015. Today, AI doesn't really puzzle me; the principles are mathematically quite simple. Instead, it makes me reflect on what we are. Humans have always placed high value on themselves compared to other animals, considering themselves the only beings with a soul in Western religions. Yet, neuroscience shows that our brains and artificial neural networks do essentially the same thing.

We are an organic machine, while a computer is an electronic machine. So either our brain is incomparably richer in neurons than a machine, or we merely imagine ourselves to have special capacities. AI challenges our self-perception much like heliocentrism once removed humans from the center of the universe. This perspective is quite destabilizing, and it is just my personal view. Of course, I respect all viewpoints and do not seek to provoke controversy.

OB: Like in research, you need to know what you are aiming for. Generally, I start by asking myself a question, such as "How do we perceive complexity?" Naturally, we have a limit beyond which we no longer understand, and this gives me a starting point to conceptualize a work of art. However, the questions I ask myself can vary greatly, such as working on gender equality in art, creating by combining existing works, working on dimensionality reduction, and the random generation of structures.

What seems more complicated to me, actually, is maintaining a continuity of style. Sometimes, I think I could create avatars of myself, each exploring a different aspect without muddling the others.

OB: Yes, I believe it's essential for an artist working today to be familiar with the history of art. Understanding the historical context provides a foundation upon which we can build and innovate. To break the rules, you must first master them. In mathematics, it is almost impossible to start from scratch. A researcher friend once told me, "If you come up with an interesting, simple idea, do some literature review—someone has probably already thought of it before you." And that's essentially true!

It's very challenging to find a new and universal concept. I believe more in the art of combining and transforming existing ideas, which underscores the necessity of having an artistic culture.

OB: I don't really like to judge what is good or not in art, as there is so much subjectivity involved that such evaluations can be risky. I am more drawn to certain pieces than others. There is a craftsmanship in the work of an artist, and for generative art, it's the algorithms. I must say that I am particularly intrigued by works where I wonder how the artist achieved them, but this is not my only criterion. I appreciate work on color, originality, and sometimes the message conveyed by the piece.

Therefore, for me, there is no significant difference between generative art and traditional art. It sometimes seems to me that the world of NFTs is a bit immature, and I'm not sure I understand the excitement that certain pieces generate!

OB: I immediately sought out the pieces that seemed the most refined and appreciated by collectors. The title of the exhibition, with its multiple meanings, inspired me to reflect on our current world, which is the foundation of this series—revealing the complexity of our social interactions. We live in a world where the internet and social networks have created a kind of absolute connectivity among all humans, without spatial or even linguistic barriers. What quickly surprised scientists is that instead of fostering harmony among humans, social networks create factionalism and promote behaviors that drift toward extremes. Social networks carry much more hatred than accord; some say they amplify our darker sides.

In the series INTERTWINED WORLD, I wanted to work on a representation of this phenomenon. Each of my works depicts the social behaviors of hundreds of thousands of individuals who organize into groups, connect, and simultaneously separate from others.

OB: Even though I specialize in the random generation of combinatorial structures, the algorithms employed in the series INTERTWINED WORLD are quite unique compared to my usual work. I consider this work to be generative art in a broad sense, meaning art generated from an algorithm. However, in this case, the algorithm requires upstream data and is not autonomous as is often the case in generative art.

There is a long history of graph visualization (i.e., relationships between objects). This history began with William Tutte, a great British mathematician, who in 1963 wrote a remarkable paper called HOW TO DRAW A GRAPH. In this paper, he explained how to draw planar graphs without crossings. The idea is simple and brilliant: he saw the edges of the graph (the links between individuals) as elastic bands, and the entire system became a sort of Rube Goldberg machine that stabilizes in a state where individuals who share many links are close to each other.

However, this algorithm has a flaw: it creates very dense clusters that make the graph difficult to read (and uninteresting). To address this, other researchers thought of making each individual repulsive to others, leading to the development of the Force Atlas algorithm, widely used in graph visualization. However, this algorithm also has its shortcomings. One is that if a group of nodes is not connected to others (known as a connected component), it gets repelled to infinity. To fix this, a general gravity force is applied to the system to pull everything towards the center. But this creates another problem: the center of the image becomes overcrowded (like a forming sun, as Force Atlas is very similar to algorithms used for simulating galaxy and solar system formation).

This is where I come in as an algorithm researcher. Another way to prevent components from drifting to infinity is to curve the space, placing individuals on what we call a compact surface without edges. To be less pedantic, I place the individuals on a sphere (like they are on the surface of the earth). If groups want to distance themselves, they can move to opposite sides of the sphere, but they no longer drift to infinity.

That's the idea behind the algorithm, but from a technical standpoint, these algorithms need to be designed with great agility. Imagine having 100,000 individuals (which is the order of magnitude in my works). Each individual influences all the others (at least by repelling them), so there are roughly 100,000 x 100,000 interactions to compute at each iteration of the physical system. This is colossal, and even with a good computer, it would take too long to stabilize the system. A classic trick is to use a hierarchical data structure called a QuadTree to group nearby individuals. The idea is that if a group of individuals is far from individual A, instead of summing the individual forces of the group, we consider the whole group as a 'super-individual' that interacts with individual A.

Without going into details, this approach makes the algorithm efficient even for sets of millions of individuals. This approach is known as the Barnes-Hut algorithm and is used in astronomy. I have developed another approach based on efficient clustering algorithms, but describing it would be too complex here.

One point I haven't described yet is color. As you may have noticed, I have only talked about algorithms for placing points. To make my work more interesting, I use an algorithm developed by a colleague, called the Louvain method (named after the University of Louvain where he works). This algorithm aims to create groups of individuals (communities) that are assigned the same color. This is known as a community detection algorithm. Again, it is a quite complex algorithm that relies on a notion of modularity (essentially the density of links).

To summarize, each piece in this collection is unique, constructed from real-world data (interactions on Twitter, sales on objkt.com, music listening on Deezer, the NutrinetSanté platform, etc.). The data is collected via APIs (Application Programming Interfaces) that allow querying gigantic databases. Unfortunately, Elon Musk has made Twitter's API paid, making data exploitation from Twitter impossible for most academics, considerably limiting the ability of sociologists to work with relevant real-world data.

OB: I don't know if this difficulty is unique to me or common among all artists, but I find it extremely challenging to have a critical view of my work, particularly in a qualitative sense. This brings to mind an anecdote: both Ravel and Saint-Saëns were deeply disheartened that Bolero and The Carnival of the Animals, respectively, became their most famous works. I believe that every artist primarily seeks recognition from their peers. Bach composed The Art of Fugue, and Beethoven poured his energy into his late quartets. However, I'm not entirely convinced that peer recognition is always a true measure of artistic merit, even though I, like everyone else, strive for it. It reflects the concept of masterpieces within the guild system, where we aim to showcase our technical excellence.

Returning to the question, as I digressed a bit, I primarily used the criterion of selecting pieces that had received more than 300 likes on X (formerly Twitter). I am quite attuned to public opinion. I must also admit that, like many others, I am susceptible to groupthink; when one of my pieces garners very positive feedback, I tend to appreciate it even more!

OB: There is some truth to that. Let's say that the public tends to be a bit conservative in their tastes. On average, I agree with them, but I often disagree on the more demanding pieces. Art is also an education; we cannot ignore the social aspect of art. It is a very strong social marker. When I was young, I found THE ART OF FUGUE very boring, but now I believe it is one of the most important works in music. Nothing in it is simple; it is more a piece to be read on a score than listened to. I am fortunate to be able to hear the music in my head while reading a score. It is a unique experience. Art is an intellectual construction that refers to tangible experiences. I am more sensitive to Western music than to Indian music because Western music is connected to the moments of my life, much like a madeleine in Proust's famous novel.

In my artistic work, I do not aim to break the codes entirely but rather to express myself in a personal language that I hope is universal, even if it raises other philosophical questions... That's probably why I willingly accept the public's opinion.

OB: Linking art to cryptocurrencies has been a tremendous opportunity, but it also presents a major risk. This is one of the reasons that drives me towards galleries. I am not truly convinced by a highly speculative system; I believe more in a fairer, more stable system. I see artists popping up like mushrooms and being consumed like perishable goods. People rush in and just as quickly lose interest.

My goal is the long term. I am focused on a constructive approach, trying to develop an artistic trajectory. I hope that collectors will follow me on this journey.

OB: Don't let yourself be overly influenced! Have a long-term vision and accept the ebb and flow as natural phenomena. I believe that every artist should cultivate their own secret garden. There is some wandering on the path; sometimes we get lost, but we must keep going. I encourage all collectors to look closely at one of my pieces and not to dwell on the fleeting moment of discovery. I had to reduce the sizes of my works for platform reasons, but each piece is a universe in which I invite you to dive.