INFINITY IS SILLY
The linear perspective represents infinity. In a one point perspective drawing, the vanishing point is infinity.
When you think about the fact that infinity is represented on your paper with a pencil dot, it seems rather silly. The infinite compression of space/time is shown as a dot on a piece of paper is completely incomprehensible. Yet we dutifully place this dot without thinking anything about the transition between the humble objects that we are drawing and the infinite narrowing of space time.
Link to a previous post on this subject here.
And in the one point perspective system, there are really two infinities. The one that is represented by the dot on your paper, and then the one that is directly behind your head. The one behind you is an infinity that gets infinitely larger, whereas the one on your piece of paper gets infinitely smaller.
All of which means that in a one point drawing system, there are two specific directions of infinity. A one point perspective creates a linear infinity. Which is also silly. Our commonly understood model of infinity is spherical, rather than linear.
In spherical infinity, our commonly understood model is where your head is at the center, and then space / time extends forever in every direction. In spherical models, it is almost as if you are carrying around infinity in your head. Or at least infinity starts at your head. Which is of course silly as well.
Yet is is fun to contemplate infinity, and how our mental images and drawings are a fundamental part of this understanding. Rest assured that the problem of infinity has occupied the mind of humanity for quite some time. Writers and philosophers as far back as 600 BCE were considering space, time, atoms and the essential continuity of our perceptible world.
In this discussion, what we are interested in is the visual models of infinity. Hopefully this discussion triggered powerful mental images in your head. Link to a previous post on this subject here. So when you are drawing your next one point perspective, it might at least be fun to consider the implications of infinity on your piece of paper. What you are really showing is all of the space behind your object to infinity.
Our consideration of infinity is simply to point out some of the limits of human perception and understanding. We cannot understand infinity. Yet we try to get at the concept of infinity when we make our drawings.
Your description and analysis of one-point perspective is how I’ve always thought about it.
I had a great plane geometry teacher. The first day she started off by taking a piece of chalk (keep in mind, this would be the early 60s) and drove it into the board, chalk bits flying. “This is a point but it’s not THE point. What you see represents what you can’t see.” Chalk flying again as she drew a very long line. “This is a line but it’s not THE line. I understood that immediately and have always been aware of representation. As magical as the illusion of linear perspective is, it is a representation but it’s not THE representation.
Your point about scaling and our position relative to the surface and distance has the resonance of large insight.
Thank you.