The Straight Lines of the Mind

You know the old adage: "There are no straight lines in nature". It is so often observed that the saying seems to be trite. But I was thinking about this today from a slightly different perspective. And the more I thought about it, the more it unsettled me - not as a matter of geometry, but of perception. Straightness, I realised, might exist only in the human mind. The universe curves, folds, warps, and weaves - everything. Perhaps it is only our perception that insists on flattening it - smoothing it into lines we can grasp, into sequences we can track, into stories we can tell. If that is true, then the ramifications are quite far-reaching. The adage does a lot more than suggest that we won't find a straight line in the woods or in a river. It is indeed possible that "straightness" of lines is a complete illusion - one that we humans have constructed to make sense of our universe. And it may be the reason why we keep missing the mark on so many things - from having a grand, unifying theory of physics all the way through to perfecting the art of practical self-defence. Maybe what we take as "trite" has such deep ramifications that affects every aspect of how we understand, and interact with, the universe.

The Straightening Instinct

To explain what I mean, I have to set out the fundamental parameters that define human perception: each and every one of us is born into what we might call a "local frame of reference". By that, I mean that our senses have evolved to interpret the narrow patch of reality necessary for survival - the surface beneath our feet, the distance to a predator, the arc of a thrown stone. We were never built to sense the rotation of galaxies or the vibration of quantum fields. So our nervous system learned to approximate: to straighten, to smooth, to simplify. While it might have great utility on a local frame of refence, this ultimately becomes a limiting factor when we start to try to examine the world through a wider lens - one that looks beyond the local frame of reference. This applies to any level of deeper analysis or prediction - from formulating theories in physics to deciding on strategies for fighting or combat training: what we take as "absolutes" are often nothing more than these approximations.

When we look at a mountain, we see an outline, not a fractal. When we trace a coastline, our minds draw a continuous contour - though, at every level of magnification, that contour would dissolve into smaller and smaller irregularities. The eye imposes an illusion of continuity; the mind turns discontinuity into order.

Straightness is not a flaw in perception but its shorthand - a trick of compression that lets us navigate a world too complex to see in full resolution. The mind turns infinities into finite approximations, as a cartographer draws a straight border on a curved Earth.

The Fractal Beneath

But nature resists simplification. At every level, the world reveals self-similar patterns - branches, coastlines, mountain ridges, lightning, lungs, neurons. They repeat, diverge, repeat again — infinitely, recursively, beyond any finite description.

A fractal never resolves into a perfectly straight segment, no matter how far one zooms in. Straightness, then, is not an attribute of reality but of perception. The curve, the fold, the infinite recursion - these are the world’s native grammar. Our “straight” lines are the equivalent of baby talk: a crude translation that lets us handle what we cannot pronounce.

Every smoothness we perceive - every apparently continuous curve - is an act of mercy by the brain, a kindness of cognition that keeps us from drowning in detail.

The Human Lens Revealed

Jason Padgett provides a striking example. After a traumatic head injury sustained during an assault, his perception of the world fractured into discrete frames. Motion appeared as a sequence of tiny steps, surfaces revealed underlying geometry, and circles - even at infinite resolution -showed themselves as jagged assemblies of straight lines. Padgett’s experience demonstrates that our normal perception smooths out the underlying structure, rendering a continuous, comprehensible reality from a fundamentally discontinuous world.

Jason Padgett's TED talk

Padgett began to draw what he saw, producing intricate geometric sketches of fractals and polar integrals, unknowingly mapping the mathematics of motion. He described how circles, when viewed through this new lens, could never be perfect - because even at infinite resolution, their edges are always zigzag. “Perfect circles literally don’t exist,” he said. His condition, later identified as acquired savant syndrome, arises when damage to one area of the brain disinhibits latent capacities elsewhere, unlocking hyper-systematised forms of perception. In this way, he glimpsed the raw scaffolding of the world - the geometry we normally smooth over.

There is actually a martial resonance here: just as fighters train to sense subtle shifts in posture, timing, and momentum, Padgett’s brain - injured though it was - attuned to the underlying patterns of motion and structure, perceiving what others instinctively smooth away. Perception, like combat, is a calibration between immediate survival and insight into deeper patterns.

The Local Paradigm

This smoothing is not only spatial but temporal. We perceive not just in space, but in sequence. We live inside what might be called a local paradigm - a reality filtered through proximity and immediacy. Our brains compress information logarithmically: we notice small differences when things are near, but large differences only when they are far. The same applies to time. We experience the present sharply, the past dimly, the future as possibility.

We are local creatures, bound to a narrow aperture of space and time, yet we continually mistake this aperture for the whole of reality. Science has widened that aperture - telescopes, microscopes, accelerators - but even those instruments feed back into the same perceptual system. We have widened the window, not escaped the house.

The Speed of Causality

From this follows a deeper thought: our very experience of time may be a by-product of this straightening instinct.

The speed of light is really the speed of causality

Consider Padgett’s assault. The timeframe of the attack - the thugs’ movements, the strike to his head - is irrelevant to the cause itself. The blow that triggered his altered perception is the causal act, completed in an almost immeasurable instant. Its effects - new ways of seeing, drawing, understanding - unfolded gradually, yet the cause existed fully once the strike was inflicted.

Causation, unlike motion, is effectively instantaneous. “X caused Y” does not refer to the interval between X and Y; it refers to the establishment of a necessary relation, once and for all. We might fire an employee and only months later experience the consequences, but the cause itself was complete at the moment of decision. In physical terms, the speed of instancy is bound only by the maximum rate at which information propagates - c, or the speed of light - yet for practical understanding, causation itself transcends temporal measurement. The universe, once a causal relation is established, exists in that truth immediately.

In this sense, the speed of light represents not merely a universal constant but a cognitive limit - the speed of causality. It is the fastest rate at which information, and thus experience, can traverse our perception. It defines the boundary between sequence and simultaneity: below it, cause and effect; beyond it, both collapse into one. So it is important to understand that,  unlike what our local frame of reference tells us, light does not "travel through the universe"; it is the universe in its instantaneous form. To a photon, no time elapses along its path - it exists everywhere along that trajectory simultaneously. The distinction between “before” and “after” exists only for us, the slower observers.

Perhaps the speed of light is really the speed of perception - the rate at which finite consciousness translates the timeless into the sequential, the infinite into the measurable. It is not the limit of reality, but the limit of us.

Infinity and the Finite Mind

Infinity cannot be felt. We can symbolise it, but not inhabit it. Our minds evolved for finitude: for the bounded, the graspable, the near. To imagine infinity is to push perception beyond its native resolution - like zooming into a digital image until the pixels show.

And yet the universe is pixelated in its own way: quantum fields, discrete energy levels, Planck lengths and times. Between the infinite divisibility of the fractal and the discreteness of quantum mechanics lies a paradox - the world is both endlessly detailed and fundamentally granular. What bridges these opposites is perception itself, which smooths, interpolates, and stitches continuity out of quanta, curves out of lines.

The straight line may be the mind’s unit of meaning, just as the atom is matter’s unit of form. Both are simplifications of something deeper and less linear.

Beyond Straightness

If this is true, every act of understanding - scientific or artistic (including martial) - becomes an attempt to reintroduce curvature into our straightened world. Physics bends our notions of space and time back into the fabric they came from. Art bends intuition into new geometries of feeling. Music, unfolding linearly but resolving harmonically, might be our most natural bridge between sequence and simultaneity.

To think beyond straightness is to think fractally, relationally, holographically - to accept that the world is not composed of objects moving through space, but of interactions expressing patterns. We do not live in space and time; we live as space and time, folded into the geometry of perception. (In the martial context, I have addressed this previously in discussions about the importance of understanding dimensionality in the martial arts.)

The Mirror and the Map

To map such a universe, we draw straight lines, because that is what we can draw. But the map is not the territory. Our equations, diagrams, and languages are projections of the infinite onto the finite. They are not wrong - only partial.

Perhaps enlightenment, in whatever form, is not the gaining of new information but the loosening of the straightening instinct - the willingness to perceive without compressing, to experience without linearising. When that happens, the distinction between inside and outside, subject and object, before and after begins to soften. The mind’s lines start to curve.

The Infinite in the Finite

And yet, paradoxically, it is through these straight lines - through mathematics, art, and language - that we approach the infinite. A musical scale is made of discrete notes, yet from them arises continuity. A poem is written in finite words, yet evokes endless feeling. An attack, once launched is singular, but at that moment the possibilities in response are infinite. It is for this reason, I believe, that when the character for "kara" in "karate" was changed from its homonym "唐", meaning "Tang" or "China" (for political reasons), the character chosen was "空" meaning "empty" - not in the sense of being "vacant" but in the sense of "as empty as the sky", i.e. infinite.

The straight line and the curve are not enemies but collaborators: the line giving form, the curve giving depth. The mind simplifies so that consciousness can engage the infinite one fragment at a time.

When I think of the speed of light now, I no longer imagine beams racing through space. I imagine the boundary of awareness - the line at which causality, perception, and time converge into one brilliant instant. Beyond it, everything is simultaneous; within it, everything is sequential. We live inside the gradient between the two.

Coda

Perhaps that is what we mean by consciousness: a straight line moving through a curved universe, translating the infinite into experience, the simultaneous into story. The universe may already be complete - every photon, every pattern, every possibility already present - but we, bound by the speed of causality, can only read it word by word, line by line.

And yet, even in that limitation, there is wonder. For the straight line, though finite, remains our bridge to the infinite - the thread by which the universe allows itself to be known. It's no small wonder that the journey of karate begins with the straight punch, the journey of music begins with the linear sequence of a scale. Understanding the limitations of our perception does not mean we can dispense with these stepping stones to greater understanding - it just means we can't afford to treat them as destinations.

Copyright © 2025 Dejan Djurdjevic