Four Ludic Portraits


During the COVID lockdowns, I had an idea to represent people using interactive language. I wondered if we could use something called “ludemes,” which are like the building blocks of games in our minds, to portray people. However, the noteworthy aspect lies herein: my intent would not be to capture their outward appearances but rather to employ ludemes for the portrayal of more profound attributes, such as their behavioral tendencies and actions, transcending the realm of physical attributes.

My inspiration drew from the insights of the French philosopher Alain Badiou and his theory of truth. While I won’t delve extensively into its complexities, Badiou posited the existence of four domains where truth might manifest, giving rise to revolutionary events that reshape their respective spheres and influence the way people perceive, contemplate, and lead their lives. In the initial discourse, these domains bore some connection to mathematics. Therefore, I endeavored to align words with formal expressions:

Art: {∅} 

Love: {∅, {∅}} 

Science: ∃x(x ∈ S ∧ P(x)) 

Politics: ∀x(x ∈ S → P(x))

This formal concept motivated me to connect different forms of interaction with specific themes. For instance, I started creating portraits of my best friends, keeping their identities undisclosed.

Ludic Portrait of an Artist {∅}

Start by turning on your computer, tablet, or smartphone and open an AI platform that you prefer. Once you’re connected, take the time to explore your identity, the path you’re currently on in life, and the deeper purpose behind your existence. Approach this journey with determination, and make an effort to have a meaningful and continuous conversation with the AI.

As you engage in the conversation with the AI, it might bring up the point that these questions about identity and purpose are deeply personal and unique to each individual. In response, recognize AI as an integral part of your experience, just like any other tool you use in life. Embrace this interactive exchange as a way to explore and understand yourself better, acknowledging the AI’s role in shaping your self-awareness.

If the AI argues that finding answers to these inquiries requires interacting with the external world actively, confidently assert that this very interaction with the AI is a proactive way of connecting with your surroundings. Emphasize how this dialogue allows you to explore your place in the intricate tapestry of existence and seek meaningful connections.

Throughout the interaction, maintain your commitment to consistent strategies, pushing the boundaries of the conversation. With unwavering determination, extend the dialogue, as it will lead to deeper insights into your identity and purpose.


a. In Zermelo-Fraenkel set theory (ZF), the expression “{∅}” represents a set that contains the empty set as its only element. This notation can be understood as follows:

  • {∅}: This curly brace notation indicates that we are defining a set.
  • ∅: Inside the set, we have the symbol ∅, which represents the empty set.

So, in ZF set theory, “{∅}” is a set that contains just one element, which is the empty set itself. This notation is used to construct sets with specific elements in ZF set theory.

b. Alain Badiou recognizes that many artists often find themselves in states of creative solitude. This solitude can manifest in various ways: the artist may spend long hours working alone in a studio, grappling with their ideas and materials, or they may be engaged in a deep exploration of their inner thoughts and emotions. This solitude is not necessarily negative; rather, it can be a necessary condition for the artist to fully delve into their creative process.

Ludic Portrait of a Healer {∅, {∅}}

Take a moment to think of someone dear to your heart—a partner, best friend, or someone you haven’t seen in a while. Reach out to them and invite them for a long walk together. This walk will offer an opportunity to reconnect and share a meaningful experience.

When you find someone willing to join you, approach the journey with an open and receptive mindset. As you walk side by side, engage in heartfelt conversations, sharing thoughts and dreams, and catching up on each other’s lives. Create a space of trust and vulnerability, allowing for honest and authentic communication to thrive.

Harmonize your steps as you walk together, creating a rhythmic motion that brings tranquility and unity. Pay close attention to your breath, syncing it with the pace of your steps to deepen your connection. Embrace the physical activity as it enhances your bond. Throughout the walk, remain present and attentive to each other’s feelings and desires. Take pauses to appreciate the surroundings and engage in shared experiences, discovering new paths and cherishing the beauty of your journey together.


a. In Zermelo-Fraenkel set theory (ZF), the expression “{∅, {∅}}” represents a set with two distinct elements: the empty set (∅) and another set that contains the empty set as its only element. Let’s break down this notation to understand it better:

  • ∅: This symbol represents the empty set, which is a fundamental concept in set theory. The empty set is a set that contains no elements.
  • {∅}: This notation is used to create a set that contains a single element, which, in this case, is the empty set (∅). So, “{∅}” represents a set with just one element, and that element is the empty set itself.
  • {∅, {∅}}: Now, we can combine these notations to create a set with two elements. The first element is the empty set (∅), and the second element is another set, which contains the empty set as its only element. So, the second element can be represented as “{∅}”.

In summary, the expression “{∅, {∅}}” is a set that consists of two distinct elements: the empty set (∅) and a set that contains the empty set as its only element. This demonstrates how sets can be composed of other sets and elements in ZF set theory, allowing for the construction of complex and hierarchical structures within the theory.

b. Badiou’s examination of the lover figure can find points of convergence with psychoanalysis through various avenues. The fervent dedication and longing of the lover towards their beloved can be regarded as an expression of profound desires and innate impulses originating from the depths of the unconscious. Furthermore, the interpersonal connection between two individuals deeply in love has the potential to incite transformative moments and instances of self-revelation, resonating with the psychoanalytic notion of revealing concealed aspects of one’s own psyche.

Ludic Portrait of a Scientist ∃x(x ∈ S ∧ P(x))

Gather a small group of friends, acquaintances, or neighbours to re-enact the famous mousetrap scene from Hamlet. First, vividly set the stage, narrating the events leading up to this moment, highlighting Hamlet’s role as a philosophy student from Wittenberg and his close companion, Horatio. In line with Badiou’s perspective, which suggests mathematicians seek validation from peers, Hamlet’s reliance on Horatio in the mousetrap scene becomes evident, symbolizing collective efforts and shared exploration.

It’s crucial to emphasize the profound symbolic meaning behind the mousetrap scene. Essentially, it’s a theatrical performance aimed at confronting King Claudius with the truth and eliciting a response from him. Hamlet cleverly uses it to expose Claudius’ guilt in his father’s murder.

Moreover, the mousetrap scene incorporates elements akin to scientific pursuits. Hamlet and Horatio keenly observe Claudius’ reactions and behavior during the performance, much like scientific observation involves careful data gathering and meaningful conclusions.

Furthermore, the scene can be seen as an experiment itself, designed to test Claudius’ conscience and reveal his true nature. It aligns with the scientific method, where hypotheses are formulated and tested to unveil underlying truths.


a. In Zermelo-Fraenkel set theory (ZF), the expression “There exist many elements x in set S such that P(x)” can be written using set-builder notation and the existential quantifier. Here’s how it can be represented in ZF notation:

∃x(x ∈ S ∧ P(x))

Let’s break down this notation:

∃x: The existential quantifier (∃x) indicates that there exists at least one element x.

(x ∈ S): This part asserts that the element x belongs to the set S.

(P(x)): This part states that the element x satisfies the property P.

By combining these components, the expression ∃x(x ∈ S ∧ P(x)) represents the existence of multiple elements in the set S that satisfy the property P. This notation aligns with the use of the existential quantifier to indicate the presence of “many” elements in ZF.

b. Alan Badiou argues that in the realm of science, individual scientists are closely connected to the scientific procedures and norms of the wider scientific community. Scientists operate within a structured framework, guided by specific methodologies, conventions, and standards that advance their field. Adhering to established practices and norms, such as conducting experiments, collecting data, and subjecting work to peer review, allows scientists to contribute to collective knowledge and push the boundaries of their discipline. Badiou highlights the interdependence between individual scientists and the scientific community, where success depends on navigating and making meaningful contributions within the established scientific landscape, challenging existing theories, and building upon prior research.

c. I firmly believe in the imperative of establishing a profound interconnection between the realms of art and science, characterized by a symbiotic relationship that encompasses the concepts of one and many. When a creative individual, whom we can identify as an “artist,” harnesses the power of modern technology and its tools to embark on a personal journey of self-expression and self-discovery, it lays the foundation for the emergence of “scientists” within the realm of art. Motivated by a relentless pursuit, these individuals strive to understand and effectively convey the immense diversity encapsulated within the scientific community as a whole, utilizing the expressive power of artistic mediums.

Ludic Portrait of a Rebel ∀x(x ∈ S → P(x))

Be like wind, be like fish-water.

I won’t tell you to vote or protest;

Follow your heart.

If you feel inclined,

The tide of events will lead you to make a stand.

So, be like wind, be like fish-water.

Care for your loved ones,

Help your neighbours,

Exercise patience and wait for the right time.


a. In Zermelo-Fraenkel set theory (ZF), the statement “For every element x in the set S, if x satisfies the condition of being in S, then the statement P(x) is true” can be written using set builder notation and logical implication as follows:

∀x(x ∈ S → P(x))

In this expression:

∀x represents the universal quantifier, indicating “for all x” or “for every x.”

(x ∈ S) denotes the membership condition, stating that x belongs to the set S.

(P(x)) is a statement or property that depends on x.

Combining these components, the expression ∀x(x ∈ S → P(x)) captures the intended meaning. It asserts that for every element x in the set S, if x satisfies the condition of being in S, then the statement P(x) holds true. This notation allows us to express universal statements about elements in a set within the ZF framework.

b. According to Alan Badiou, the role of the individual rebel in politics is of utmost importance as they challenge existing norms, generate new procedures, and shape the political landscape. The rebel acknowledges the dynamic nature of politics and actively seeks to disrupt and transform it through acts of rebellion. By questioning established policies and laws, the rebel paves the way for fresh perspectives and alternative approaches to emerge, contributing to progress and change.

It is essential to highlight that politics stands apart from other truth procedures in its wide-reaching impact. Unlike domains that may be limited to specific communities or fields, politics affects every individual within a society.

c. I strongly advocate for the crucial establishment of a profound interconnectedness between the realms of love and politics, marked by a symbiotic relationship encompassing the concepts of duality and collectivity. Alan Badiou often references the Maoist slogan “One Divides into Two” (一分为二) as the genesis of the political sphere. In the context of healing, love, and therapy, where individuals engage in transference dynamics, the establishment of a bond between two individuals, represented by ZF set theory by the successor function, serves as a transformative catalyst. This connection transcends solipsism and isolation, laying the groundwork for the emergence of the “masses” and their embodiment in the form of a “rebel” within the realm of politics.

d. Motivated by an unwavering pursuit of change, rebels, in conjunction with the masses, strive to forge new connections within society and challenge the notion of a stable and monolithic state. Their actions create ruptures akin to the transformative dynamics observed in love and transference. By disrupting the existing order, rebels, and the masses seek to bring about profound shifts and reconfigurations, reaffirming the notion that the totality of the state is not static or fixed.

Milan Marković (he / him) is a philosopher, writer and the originator of the concept of Artplay. His current ambition revolves around extending the scope of holistic interactivity, a fundamental element at the heart of Artplay, into the realm of AI art. He dreams of founding a school of postclassicism that integrates non-traditional media into classical traditions. This initiative would aim to champion values like harmony, restraint, and clarity in the postmodern landscape, potentially involving practices such as digital fasting and interactive moderation. Find him online Find him online on x/twitter @posvitt