*** L.I.F.E. Project Workshop *** Oct 20–28, 2025 - - "The Infinite, the Infinitesimal and the Imaginary" - -
Submitted by Valentina Desideri on Wed, 2025-07-30 14:06
Workshop piloted by Gabriel Catren
with the assistance of Manuel Eguía, Jonathan Lorand and Emily Roff, at PAF.
L.I.F.E. Project
In this workshop, open to any curious mind and body, we will explore the fundamental concepts of one of the central chapters of modern mathematics: differential and integral calculus.
Calculus, as we know it today, is the culmination of an intellectual journey spanning more than two millennia and drawing from diverse geo-cultural traditions. Within the confines of the Western canon, this journey begins with Zeno’s paradoxes (5th century BCE), which questioned whether continuous motion is possible, since it seems to require completing an infinite number of intermediate steps in finite time. Because motion and change defied intelligibility, Zeno argued that only what is unchanging can truly be said to exist, a claim that shaped two millennia of scientific and philosophical thought. Yet philosophers and scientists continued to ask: Can motion and change be grasped rationally, or are they nothing but fleeting illusions?
Over the following centuries, Greek mathematicians like Eudoxus and, later, Archimedes turned to what seemed like a feat of mathematical magic to calculate the areas and lengths of geometric figures. Their method broke problems into infinitely many vanishingly small parts, solved them individually, and then ‘integrated’ the results into a finite solution. Yet magic is never without a pact with something beyond: in this case, it invited into mathematics the unruly guest of infinity, both the infinitely large and the infinitely small. While endless progression (like counting) is, to a certain extent, intuitive, the notions of actual infinity (an infinite totality existing all at once) and infinitesimals (nonzero quantities smaller than any finite magnitude) pose indeed deep mathematical and philosophical challenges.
In the 17th century, Newton and Leibniz independently synthesized these ideas into the calculus we know today. While its computational power has far exceeded early expectations and underpins modern physics, its foundational concepts—the continuum, infinity, and the infinitesimal—remain open to both philosophical and mathematical inquiry.
In this workshop, we will introduce core concepts such as functions, limits, derivatives, integrals, and series. To do so, we will first revisit and deepen one of our earliest mathematical abilities: counting, though this time venturing into what the mathematician David Hilbert called Cantor’s paradise, a realm teeming with infinite infinities, arranged in an ecstatic, never-ending ascension. From there, we will trace the evolution of number systems, from whole numbers to numbers that are “less than nothing,” numbers that are not “rational,” continuous number systems that can be endlessly divided, and finally to “imaginary” numbers that complexify the linear order of previous systems with a lateral twist. Along the way, we shall toll the bells of PAF to unveil the elegance of Fourier analysis, a theory that allows us to synthesize sounds of any timbre from ever-ringing pure tones. If time allows, we’ll close with a brief glimpse into the beauty of differential geometry.
The lectures will be given by Gabriel Catren with the assistance of Manuel Eguía, Jonathan Lorand and Emily Roff.
About the L.I.F.E. Project. The L.I.F.E. project is an experimental scientific education initiative carried out at PAF since 2018. It aims to collectively explore new ways of producing, sharing, and enjoying scientific thought — and, amid the current state of the world, of putting it at the service of life.
Practical Information
The workshop will take place at the Performing Arts Forum (Saint-Erme, France) and will start on October 20st (arrival day) and end on October 28th (departure day), 2025. The workshop consists of four working days (October 21st, 23rd, 25th, and 27th) interspersed by three “free” days (October 22, 24th, and 26th) during which the participants will have the time to rest, to work through the new material, and to participate in the related activities that we shall propose.
Dates: Arrival on October 20st; Workshop from October 21st to 27th; Departure on October 28th, 2023.
Location: Performing Arts Forum (PAF), Saint-Erme, France.
Cost: Accommodation (sliding scale 18€ – 25€ per night) ● Meal expenses (16€ per day including breakfast, lunch, dinner, and coffee) ● PAF membership: 20€ per year ● Tuition fee: 50€ ● The kids’ rate is calculated as: age × 1€ per night for accommodation, plus age × 1€ per day for meals (a disclaimer must be signed upon arrival).
If you would like to attend but are currently unable to fully or partially cover the cost, please don’t hesitate to write to gabrielcatren@gmail.com; we will do our best to find a way to make your participation possible.
Accessibility: We are continuously working to improve accessibility at PAF. For mobility access, the ground floor includes a bedroom with a toilet, as well as another bedroom with a wheelchair-accessible shower and toilet. Kitchens and workspaces are also available on this level. If needed, we can provide pictures and measurements. If you have any additional accessibility requirements, please let us know—we will do our best to make it possible for you to participate. For more details please find our current accessibility rider working document here.
Linguistic accessibility: The lectures will primarily be held in English. However, we are strongly committed to fostering linguistic pluralism and to exploring strategies for overcoming prevailing forms of Anglocentrism. Languages other than English will therefore be warmly welcomed as alternative channels of interaction throughout the event.
PAF is a self-organized space with no permanent staff. All participants are expected to take part in the various tasks that sustain our collective life, such as cooking, cleaning, and other forms of shared care. Since we aim to counteract the separation of scientific work from the conditions that make it possible, the communal and material dimensions of life at PAF are considered just as important as the lectures themselves.
Reservations are mandatory and should be made by writing to contact@pa-f.net. The workshop is limited to 40 participants, and we ask everyone to commit to attending the entire duration of the workshop. Please include in your email any info regarding accessibility (if you do not have the financial conditions to participate, if you come with children, if you have mobility requirements, acute allergies, etc.), as this will inform the roomplan and help to better organise the workshop for everyone.
Important note: Cancellations after registration create significant additional work for the organizers (e.g., managing emails, updating the waiting list, etc.). We therefore kindly ask you to be as certain as possible of your availability before reserving your place.
For any questions that you might have, you can write to Gabriel Catren (gabrielcatren@gmail.com).
