A human-being-ist* dissidence of Topology applied to human movement
I invite you to experience Topological Walking, a practice where each step becomes continuity, each turn a meaningful twist, and each variation a bodily homeomorphism. For those who live among structures, invariants, and abstract spaces, walking in this way offers the possibility of feeling—in one’s own body—what one studies with the mind. Discover how topology, far from the blackboard, can become an everyday, holistic, and deeply stimulating movement.
Walking is one of the simplest and, at the same time, most profound acts of human existence. But it is also an art that we can elevate if we look at it from new perspectives. On this occasion, I propose an intellectual, physical, and emotional experiment based on the five fundamental principles and guidelines of the WALK-RWD SYSTEM (Post THE FUNDAMENTAL PRINCIPLES OF THE WALK-RWD SYSTEM): combining walking with topology, that surprising branch of mathematics that studies shapes in their essence, without being confused by their deformations.
From this union, a powerful and accessible concept is born: Topologesic Walking.
1. Poetic-scientific definition of Topologesic Walking
Topologesic Walking is the practice of moving by incorporating the continuous, fluid, and transformative principles of Topology, in order to understand space not as a neutral territory, but as an intimate extension of the body and of the mind.
It is walking without ruptures, with awareness of the natural deformations of movement, and with a special sensitivity toward the invariants that sustain us: the axis, the breath, the intention.
It is a human-being-ist dissidence: a gentle rebellion that extracts from mathematics (1) its deepest structure to apply it to the essential art of being a walking human.
2. Manifesto of Topologesic Walking
- Space is not traversed: it is gestated.
Each step is a way of creating continuity in the world.
- Every deformation is welcome.
Turning, leaning, stretching: the body changes without losing its essence.
- Human invariants are sacred.
Breath, body axis, presence: they are maintained even when the rest varies.
- Continuity is an ethic.
Walking is the experience of linking without breaking.
- Open paths liberate.
Letting a walk transform spontaneously is part of its beauty.
- Convergence is an internal destination.
We walk to gather scattered thoughts, emotions, and perceptions.
- Torsion is a reading of space.
Gently turning the body is reading the world in 3D.
- Space does not contain us: it dialogues with us.
Walking topologesic is perceiving proximity beyond distance.
3. Initial Exercises
Exercise 1: Walked Continuity
Camina 5 minutes maintaining this thread in your mind:
“Each step is born from the previous one and prepares the next.”
Do not allow your attention to jump; maintain continuity.
Exercise 2: Corporeal Homeomorphism
Walk while gently altering your posture: lean your torso, rotate your shoulders, lengthen your stride slightly. Do it without losing your axis. Discover your own elasticity.
Exercise 3: Open Set
Go out without a fixed route. Allow for spontaneous detours, changes of direction, small explorations. Feel the freedom of that which is unbounded.
Exercise 4: Mental Convergence
Choose a confused or heavy thought. Every 100 steps, simplify it. Walk until it converges into a clear idea.
Exercise 5: Torsion of Space
Walk incorporating micro-turns of the torso: to the right, to the left. It is not dance; it is a reading of invisible space.
4. A brief philosophical history
Topology was born from the question:
“What remains when everything changes?”
That is also the background of human walking.
From the ancient Greeks who walked to think, to the monks who made walking a form of meditation, there was always a topologesic intuition: movement changes, but walking remains.
Topologesic Walking rescues this ancestral idea and unites it with a 20th-century mathematical conceptual framework, creating a bridge between abstract reasoning and everyday bodily experience.
A philosophy of space lived with the feet, not just thought with the mind.
5. A program to convince those who do not walk
- Walking is no longer physical exercise: it is topologesic exploration.
When walking ceases to be an obligation and becomes a discovery, resistance diminishes.
- Space becomes interesting.
Topology allows one to see the world as a living system of continuities and deformations.
The walker feels curiosity once again.
- Walking orders the mind.
The concept of “convergence” is very attractive to those living with stress or mental overload.
- It does not compete nor demand speed.
Topologesic walking is democratic and kind to any body.
- It makes every walk unique.
By incorporating variations, torsions, open routes, every walk is unrepeatable.
- It creates emotional connection.
Seeing the world as a continuous space that is gestated with every step is deeply motivating.
Note: “Serhumanista” in the original text is a play on words combining “Ser humano” (Human being) and “Humanista” (Humanist). It has been translated here as “Human-being-ist” to preserve the coined nature of the term.
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Final Invitation to the Reader:
A Topologesic Call to Get Moving
If you have reached this point, perhaps you are still part of those who look at the act of walking with certain distance, disinterest, or anticipated fatigue. This invitation is for you.
But now I do not invite you to walk “for health,” “for sport,” nor “out of obligation.”
I invite you to walk topologesic.
Topology —that mathematics that breathes continuity, flexibility, and essential structure— can offer you a completely different entry point into movement.
Perhaps you did not walk before because no one offered you a perspective that felt intimate, meaningful, or stimulating.
Today I want to give you several.
1. Walk because no step is a rupture
Topology teaches that everything is held together by continuity.
Walking this way avoids the sensation of abrupt effort:
each step is born from the previous one as a natural prolongation.
There are no jumps, no demands, only a quiet thread you can follow.
2. Walk to allow yourself to deform without changing your essence
The body does not have to be “perfect” nor “aligned.”
It can stretch, lean, twist gently.
In Topology, deformations do not alter identity.
Let that idea liberate you: your form can change without you losing yourself.
3. Walk like someone entering an open set
An open set is one that does not impose rigid limits upon you.
That is how your walk can be: without a mandatory route, with living options,
open to detours and surprises.
Freedom is the best motivator for those who have avoided walking.
4. Walk to experience your own internal space
Topology reminds you of something profound:
space is not a passive container, but a continuous dialogue with you.
Every time you walk, the world rewrites itself around your body.
It is beautiful to feel it for the first time.
5. Walk to converge
If your thoughts scatter, if your spirit fragments,
if your mind fills with confusion,
walking allows for what mathematics calls convergence:
a process where things draw near, order themselves, become clear.
A ten-minute walk can achieve more than you imagine.
6. Walk because you do not have to compete with anyone
Topologesic Walking does not demand speed, distance, nor records.
It does not ask for athletic bodies.
It does not ask for iron will.
It only asks for presence, a body that lets itself move, and a gentle intention.
7. Walk to experience the torsion of the world
Turning the torso slightly while advancing, changing the angle of your gaze,
perceiving how space stretches or contracts around you…
this is not gymnastics: it is a topologesic reading of the environment.
It is discovering a dimension that was always there, but which you never inhabited.
8. Walk because life needs continuity
Continuity not only sustains mathematical figures; it sustains human lives.
When you walk, even for just a few minutes, you reinstall the continuity
that stress, haste, or sadness have fragmented.
It is a silent repair.
9. Walk because it is a humanistic act
Topologesic Walking returns you to your natural condition:
being a human in dialogue with their world, with their space, with their history.
Walking is not moving away, it is returning to yourself.
10. Walk because you can start now
Without special clothes, without goals, without apps watching you.
Just stand up and take a step.
That step is already topologesic valid:
it creates continuity, gestates space, deforms without destroying,
and opens a new set in your life.
So I invite you, reluctant reader,
to convert your next walk into your first topologesic gesture.
Discover that space does not wait for you: you create it with your steps.
When you find the courage to go out, even for a few minutes,
you will verify that it was not the body that was resisting…
but the lack of a meaning that now, finally, you have.
And that meaning is summarized by the essence of this new practice:
Topologesic Walking:
the art of moving without losing your continuity,
and of transforming yourself without ceasing to be you.
(1) Loya Lopategui, Carlos, & Loya Pinera Rodrigo, Sensitive Mathematical Model (SMM). Towards an Architecture of Sensation, Perception and Emotion in AI, EMULISA, Mexico, 2025: “The leap proposed by the MMS is not technical, but anthropological. Based on this model, AI ceases to be a responsive tool and becomes an agent that feels, interprets, and collaborates from a mathematically structured emotional axis. And this transforms everything: the way we heal, create, walk, build homes, form communities, cultivate affection, resolve conflicts, and understand ourselves,” p. 231. Available on Amazon, Kindle Edition: https://www.amazon.com/dp/B0GJJLPTPV