William Crane, Line & Form (1900)

I always felt like pixels are an approximation of reality, and vectors are a reconstruction. It is the job of artists to reverse engineer reality into their medium of choice.
Rafaël Rozendaal and Jürg Lehni, Compression by Abstraction: A Conversation About Vectors¹

In a digital universe, there is a fundamental difference between curves rendered as pixels, and those plotted as geometric vectors. In the first instance, a smooth shape is split up into small elements that appear continuous, but are actually discrete. In the second, a mathemetical formula is used to draw a line between different points that apply direction and tension to its shape. This difference in rendering curves runs along the digital drawing toolbox. There are so-called ‘bitmap manipulation tools’ (Gimp, Photoshop) on the one side, and 'vector drawing tools' on the other (Inkscape, Illustrator).

At the output stage most digital (mathematical graph) drawings will end up being rasterized (applied to a screen grid of pixels). In order to be visualised on a screen or printed on paper, curves are translated into dots or screenpixels. Of course there are exceptions: vinyl cutting machines, cnc milling machines, 35mm film laser subtitling machines, pen plotters and cathode ray tube screens will maintain the curved nature of the drawing right until the end.

The dominance of the discrete pixel in the digital universe contrasts with the presence of vectors in an analog world, where movements and shapes are generally understood as continuous (mathematical) curves. And also here there are exceptions and ambiguities. Mathematically, a straight line is "just" a specific case of a curve. But if we change to a quantum scale, we can understand a line as waves moving in space, but also as tiny particle interactions.

It seems that when shapes are deposited or visualised, pixels usually dominate. When a movement is being expressed, whether by a human, a plant or a machine, vectors are more useful.

Interestingly, in Compression by Abstraction: A Conversation About Vectors¹, one of the rare texts we found which tackles the issues between bitmap and vectorial modes, Rafaël Rozendaal and Jürg Lehni refer only briefly to ‘movement’ and tend to their conversation about imagery and contrast despite the title.

JL: [...] did you ever explain vectors to your mother?
RR: No, I never tried. I think it’s something that is hard to explain to someone who doesn’t really use computers to make images.
JL: I wonder how you ended up more or less limiting yourself to this format. Was there first a fascination with the idea of pure form and its abstract mathematical representation, or was it more a question of what tools were available at the time?
RR: As long as I can remember, I’ve been drawing. I enjoy converting thoughts into lines. I have an affinity for “abstraction in service of reproduction.” What I mean is that in order to make images that are easily copied/transmitted, artists have invented different ways of simplifying. Think of Egyptian reliefs, Japanese woodblock prints, early Mickey Mouse, early video games. In all these cases the medium forced artists to simplify. Vectors are honest about the fact that they are computer imagery. It is clear that they are made on a computer, they’re not trying to be real. I would describe my work as “lossless image compression by making human decisions.” I don’t let a digital camera decide how to compress an image, it is my choice how I convert thoughts and perceptions and feelings into lines. Isn’t lossless a beautiful idea?
I always felt that using a computer, we should not try to depict the world in ways that were possible before, like photography and video. We should find new ways of depicting. [...] I’m trying very hard to explain why I think it is better. I just feel like bitmaps and Photoshop filters and pixel displacements and mpeg compressions are trying to be something they are not. But that doesn’t really make sense, you can use them in a way that is truthful. But when I see textures in 3D renderings I just feel like they are trying to be something they are not. Does that make any sense? Vectors do have their limitations. It is really difficult to make something look dirty. Everything always looks clean. [...]
RR: Is antialiasing a more truthful rendering of a vector shape on a pixel screen, or is it a lie?
JL: I can see how you could think of it as a lie, because it is using different shades of a color at the border of a shape to trick the eye into thinking there is more definition to the image. But at the same time, if you would print the shape at really high resolution on a paper, and then take a digital photograph of the printout at lower resolution, you would get very similar "blurred" borders. In that sense, I would call antialiasing (and even more so, subpixel rendering) a very convincing trick. One can also argue that any rendering of such pure information into a grid will be a lie, since it will be imprecise. An antialiased version of the same shape would then just be a more convincing lie. In that logic, I can see how an aliased version is then so obviously a "lie" that it is more approachable, likable.
Rafaël Rozendaal and Jürg Lehni, Compression by Abstraction: A Conversation About Vectors¹

In addition to how useful they can be in their intended use cases, we find that curves are simply more interesting than pixels. They are abstracted geometric shapes that flow from intentions. They have direction and the ability to express ideas. While they may be numerically complex, they relate intimately to the inherent discreteness of computation. They take full advantage of how computers can serve imagery. Curves have the ability to be close to movements, and open up non-binary conversations between digital and analog spaces. As shareable numerical objects, they are more open to collaboration and allow actual reinterpretation. Curves seem to be rawer expressions of vision, somehow more natural, more honest.