Axes, dimensions, observers, and the role of inner perspective.
As a girl, one day while standing on the side of a cliff looking out over the water, I experienced a huge perspective shift, and it was overwhelming. It also helped me understand how we all see things differently even within the same exact physical universe, and to more deeply notice how things relate to one another.
I was looking at the horizon of the ocean, and in a split second, the water no longer appeared as a horizontal expanse, it instead appeared to be a vertical wall of teeming, wiggling molecules.
In this oddly psychedelic moment, I continued to perceive everything as 3 dimensions, but the axis of the water had completely changed. What had been lying down like a blanket across a bed, now felt like it was instead ‘up’ like a curtain on a window. And just like any horizon should, the top of this “wall of water” appeared at eye level.1 And because this sight was completely different, yet still included a sense of distance, my brain interpreted the mass of water as skyscraper high — like a huge wave headed to shore. Frightening.
I knew what I was seeing was wrong, but the emotion of seeing a huge mountain of water affected me emotionally nevertheless. I never saw things the same way after that, nor took anything I saw for granted, knowing a perspective shift can take the exact same thing and change it from something like a peaceful ocean to a terrifying tidal wave.
How an observer’s perspective can change how we see, measure, and interpret the world.
Making realistic visual art requires measurement, understanding materials, and hand-eye coordination. Realism also requires an viewer that can compare different objects, or different parts of an object, then accurately reproduce differences, proportions, and angles. This can be accomplished by using a technique called “sighting.” It is most often used when looking at a 3 dimensional object and translating it into a 2 dimensional representation like a painting or a canvas.
The Geographer
by Johannes Vermeer2
Rule of Thumb: how to make something look real
Have you ever seen an artist holding up their thumb in front of their subject? As long as they consistently hold their thumb at arm’s length, the artist knows they can trust their own thumb to help them understand the subject in proportion to itself. For example, a head = one thumb knuckle high, and a torso = 2 knuckles high, and so on. When the artist translates what they measured, they can represent the object most accurately.
Another sighting technique is to hold a pencil or stick up to match it to angle of the object we are rendering. Doing this can help us render an accurate “view” of something in 2D and how it relates to the other objects it shares the scene with. These sighting tools can be used while you are looking at anything, and help you translate what you see into a fairly accurate representation of the thing in a lower dimension.
An artist is a seer, a point of view, a measuring stick, and the memory that holds all these parts in proper relationship.
The artist is also an emotional association-maker, and keeper of the perspective too. We value this when it feels true, even if odd or fantastical.
Painting of painter Vermeer and his subject by Vermeer titled “The Art of Painting.” [learn more]
Look Book Example
Take for instance, this book on a table. One flat thing on another flat thing, parallel to the ground. My head is above the book, looking over at it. The bottom spine of the book is closer to me, and the upper right hand corner of the book is furthest away.
To make a realistic drawing of this book, I’d need to understand the angles the book in relation to my eye. Here, you can see the line of the bottom of the book is tilting upward as it recedes into the distance. If you were to draw it in 2D, this angle would be just like the forward slash.
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Laying down the line
Drawing lines to match our perspective is easy when using a tool like sighting, but we might not get to see that forward slash shape without using the tool. Prior to scientific “sighting,” people often represented shapes as much how they thought they should look as how they actually saw they looked.3
So, to help illustrate, what if instea first showed you a forward slash? Would you ever first say it looks like the angle of the bottom of a book on a table? Probably not.
You are much more likely to see a line like this as something more like a ladder leaning against a building, or maybe only as a written glyph. Let’s right now, though, imagine it as a ladder.
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So I want to encourage you to look at this little purple ‘ladder’ for a moment, really look at it, and feel it in space in relationship to you.
Can you now, imagine that line morphing into becoming the bottom of the book? See if you can follow that transition slowly in your minds eye, while keeping your eyes trained on the line.
What did you feel like, when you visualized that shift? Did you notice your chin dropping a little into your chest, maybe? Did you feel the teeniest bit woozy as you felt your position shift in relationship to the line, even if nothing in your body moved at all?
This is the relationship between observer and observed. And it can be downright (no pun intended) visceral.
Science Someday: because what else can I do here but pivot to physics?
I would love to start writing about quantum mechanics here, but that’s really pushing this essay’s subject matter to the nth degree. And, I’m an artist and writer, not a physicist. But if I were to explore how particles (nee ‘things’) shift behaviors in their relationship to the observer, I might want to investigate how different kinds of artists see and represent things in their art, and what feels most true to them in their best moments?
So here are my physics-connected questions. If only to ask for a good physicist to help me create some kind of experiment:
- If relational tools like ‘sighting’ help someone make good representations of 3D in 2D, is it possible to devise some tool4 that can unravel 2D back into 3D? What’s the math on this?
- If a 3D axis can seem to shift to an observer (me in the water wall example above), can a 4D axis appear to shift too? What would be that experience be like?
- Making great art often involves emotion, a seat of perspective, questions of meaning, and visceral experience with imaginative expression. These holistic elements appear to affect the value of the art.
- Is there a parallel in quantum mechanics? Is there a way for a maker/observer of quantum experiments to include more holistic properties an create a more valuable outcome? If art were to inform that science, what would we learn about reality that we don’t already know?
Yeah, email me if you have any ideas on how to experiment with this. Or just send over your questions and comments elizabeth@mommess.com
- In the Renaissance, painting ‘in perspective’ became one more groovy way that artists could represent things. It begat a much more realistic set of paintings and has affected our perception ever since. In perspective, the horizon line is always at eye level. Description here: https://archive.artic.edu/sciarttech/2d1.html ↩︎
- From The Essential Vermeer ↩︎
Just putting this awesome Matisse here as an example of perspective shifts. Although Henri Matisse could draw realistically, many of his best works include mixed up representations like this one. It’s a round table and round fruit… all drawn round (although, the table would actually appear as an oval if one were aiming for realism!) ↩︎- I remember once reading a piece about how Adobe Photoshop makers were consulted to unscramble a face of a criminal, who had used the software’s ‘swirl’ tool to obscure his identity in an image he disseminated. Adobe was able to take an image of a pea soup face and retro-engineer by thinking the tool backwards to identify the guy. They un-swirled him into order. They could create the past order from present chaos because they made the tool. Side note, he was identified and arrested. ↩︎
