The Congress of Intersectionality between Virtual reality and Psychedelics [CIVP]
Goal: to create dialogue within two different communities who have the potential to create a breakthrough in our methods of communicating to each other with a visible language and establish a space a few times a year, where people can gather and discuss the impacts of psychedelics and IT- specifically EVR [electronic virtual reality.]
MIRRORS & SYMETRICAL TEXTURE REPITITION
Euclidean 3D space has fundamental limitations that seem like they are impossible to even imagine in any other way. For example, an equilateral triangle always has 60 degree angles in its inner corners.
Not only does it seem impossible to create an equilateral triangle in any other way, it seems impossible to even be able to imagine how such a triangle would even look like, since even the limits of the imagination seem to be bound by the laws of Euclidean geometry. Look at the triangle above and try to imagine it with each side being the same length, but the angles being a number different than 60 degrees.
What if I was to say that it is not only possible to imagine it, but even possible to draw it? How can that be? This is where hyperbolic curvature comes in.
What is hyperbolic curvature?
The simplest way to describe hyperbolic curvature is that is is what happens when the dimensional plane in which a shape exists is folded through the space of a higher dimension. For example, if one was to draw a triangle on a piece of paper that is curved inwards, one would have a triangle with negative hyperbolic curvature of the 2D space that it is drawn on. This is known as H2, meaning that the 2D plane is curved. The dimensionality of the plane corresponds to the number that appears after the H, so even if the piece of paper is being folded through 3D space, the hyperbolic curvature is two dimensional.
So how does this relate to being able to draw an equilateral triangle that has angles that are different than 60 degrees? This is something that is easier to show than it is to explain:
Even though the lines appear to be curved with a 3D interpretation of that image, the lines would still appear straight to a “Flatlander”. What is a Flatlander? A Flatlander is a hypothetical being that lives on a 2D plane and it only able to perceive two spatial dimensions. Using a Flatlander’s perspective of 3D space will help us understand how higher dimensional geometry might appear on a lower dimensional plane, and how higher dimensional spaces might be imagined within the limitations of lower dimensional perspective.
Imagine that the Flatlanders live on a piece of paper that is falling. What we perceive as an up/down space would be perceived as time from a Flatlander’s perspective. For example, if the piece of paper that the Flatlanders live on passes through a tetrahedron, the tetrahedron would appear as a triangle that pops into existence, grows in size, and then disappears. A Flatlander’s perspective of up/down space is limited to only one point of up/down space, and does not extend beyond the infinitely small thickness of the 2D plane that they live on. Thus, their perception of tetrahedral geometry in relation to up/down space can only be perceived through changes of 2D geometry over a period of time. Using this perspective of how things would be for a Flatlander, we can think of how the spatial extent of objects in 4D space can only be perceived via changes in 3D geometry over a period of time from a 3D spatial perspective.
Even if a Flatlander might not ever be able to see an actual 3D cube, they are able to see an approximation of what a cube looks like with a drawing of a cube on their 2D plane. Most Flatlanders would see a hexagon with a “Y” in it or two squares joined together (depending on how the cube is drawn) rather than a drawing of a cube, since their perspective being constrained to two spatial dimensions makes it difficult to understand how this drawing portrays a simulation of what a 3D space looks like.
The Dimensionality of Human Visual Perception
One thing that most people take for granted is that human visual perception is actually 2D, and that the perception of 3D space is created via a series of sensory illusions that create a simulation of 3D space that is accurate enough to allow humans to be able to navigate a 3D world. There is only up/down and left/right in the visual field, and any perception of forward/backward space is due to having an awareness of how certain patterns in 2D space correspond to changes in 3D space, such as things getting bigger if they are closer and smaller if they are further.
When light hits the retina, the resulting data inputs occur on a 2D plane with negative hyperbolic curvature. The retina is not flat- it is curved inwards along with the spherical shape of the eyeball. The hyperbolic curvature of the retina is what allows for the 2D space of visual perception to be able to incorporate 3D geometry and creates the ability for forward/backward space to be perceived via interpolations of the 2D visual plane, like distant objects appearing smaller and closer objects appearing larger. The hyperbolic curvature of the retina allows the brain to be able to calculate the forward/backward distance of where the light is coming from. Although things like balance and proprioception allow for the perception of 3D space, the hyperbolic curvature of the retina as well as the way the brain processes the data inputs from the retina allow the visual field itself to appear to be able to accurately fit 3D geometry within it, or in other words, allow for accurate depth perception.
[Insert drawing to make this easier to explain]
The Dimensionality of Human Time Perception
As discussed earlier with the example of the Flatlander perceiving up/down space in 3D as a linear progression of points that we think of as “time”, what humans perceive as “time” is also the result of only being able to an infinitely small point of the space of the dimension above, and the space of the dimension above can only be seen as a progression of changes of 3D space from one point of time to another. Time is not something that is objectively or tangibly different than space (as Albert Einstein had discovered over a century ago), but rather something that is the result of the subjective perspective of only one infinitely small point of space within a dimension as a linear progression of points where movement through the 4th dimension can only be seen via the changes of 3D space over periods of time. Just like how a Flatlander sees an MRI scan like perspective of 3D geometry without being able to easily imagine how the changes of 2D space in time might look like in the form of 3D geometry, humans are constantly seeing 4D objects pass through 3D space, but are only limited to an MRI scan like perspective that makes it difficult to imagine how the changes in 3D space over periods of time would appear spatially in 4D.
For all we know, there could be 3D drawings of 4D geometry present in everyday life, such as the tesseract above, which is a 4D version of a cube. However, we might not be aware of it even if we are looking straight at it. Just like how Flatlander would perceive a drawing of a cube as two squares joined together or a hexagon with a Y in it and be unable to see the “cube” that a human would see, we might be seeing 3D drawings of 4D geometry everywhere but only have an awareness of its 3D spatial properties, and are unable to see what would clearly appear to be a drawing of a 4D shape to a 4D creature. Looking at the tesseract above, it’s difficult to perceive it as anything other an inner cube that is spinning within a distorting outer cube from our perspective, even though it would be obviously apparent at an animated 2D drawing of a 4D shape we don’t have a word for to a 4D creature.
However, there are ways to read between the lines and transcend seemingly fundamental constraints of Euclidean geometry that might help us understand what a 4D shape might actually look like in a way where we can perceive it as a 4D shape, and see past the lower dimensional plane that it is drawn on, kind of like if a Flatlander was to be able to understand how a drawing of a cube is actually something other than just a hexagon with a Y in it.
What Happens if a Flatlander Takes Psychedelics?
When people describe their psychedelic experiences, they are often described as being “higher dimensional”. Although most people seem to assume that this only is a metaphor for its profound nature, it may actually be true in a literal, mathematical sense as well. In order to be able to more easily describe how this might be the case, we will use an example of how it may appear from a Flatlander’s perspective.
According to the hypothesis presented in Psychedelic Signal Theory by James L. Kent, psychedelics produce their effects on perception by causing a phenomenon in the multisensory cortex (the part of the brain that pieces together multisensory perception) called recurrent excitation. Recurrent excitation is the phenomenon of neurons firing in a frequency that is out of sync with the frequency that is usually present. This creates a feedback effect where perception from past perceptual frames persist into the future’s perceptual frames. The visual aspect of this can be easily understood by even somebody who has never taken psychedelics as the tendency for the brain to cause afterimages to become vividly retained for a longer time than usual without the need to stare at one spot for a long time. The afterimages do not get erased as they normally would, and stack up into the upcoming perceptual frames. This leads to visual effects like trails or tracers, and in higher doses where the afterimages stack up over a longer period of time, the afterimages recursively stack up in a manner that leads to the fractal geometry that psychedelic experiences are well known for.
Since the perceptual input from the past is retained into the future, this means that perception of changes in 3D space extend beyond just the present moment in time can be seen spatially in one’s visual field, and the constraints of only being able to perceive infinitely small points of 4D space are transcended.
In order to understand how something as seemingly insignificant as afterimages can allow for perception of higher dimensional space, think of what would happen if a Flatlander on psychedelics saw a tetrahedron while they are tripping. As the 2D plane that the Flatlander lives on passes through a tetrahedron, the afterimages of the smaller triangles persist in the Flatlander’s vision as the triangle grows. Once the 2D plane reaches the bottom of the tetrahedron, the recursive stacking of afterimages would allow the Flatlander to be able to see a trail of small to big triangles with lines that show the vector of movement through 3D space that would look something like this:
[insert better drawing later]
If you consider that the up/down space of the tetrahedron is being drawn from a forward/backward perspective, the triangles getting closer and closer together show how knowing things like how the differences in size within 2D space that is used by the human brain to perceive the differences in distance in 3D space between the middle and the edge of the tetrahedron can be used by a Flatlander to understand how the position in 3D space can be inferred from the 2D drawing. The lines appear due to the point of 2D space where the corners meet forming a visual trail that forms a line along the 3D vector the movement through 3D space (which would normally be perceived as time for a Flatlander), which draws the ridges of the tetrahedron. In order for a Flatlander to be able to see something other than a series of triangles with a Y in it, they would need to understand how 3D spaces can be drawn in 2D, like knowing that things get bigger if they are closer, and smaller if they are further.
Even if a drawing of a 3D shape in 2D space may look convincingly 3D, whether it is on a computer screen or in the human visual field, it is nonetheless still only 2D. The 3D appearance is only a convincingly persistent illusion.
One of the reasons why drawings of 3D shapes look so convincing to humans is because all of human visual perception is essentially a 2D drawing of 3D space. This give humans an innate ability to subjectively “add” the perception of extra dimensions to lower dimensional projections of higher dimensional shapes, even if the actual higher dimensional shapes are not able to be seen directly. Thus, if one extrapolates the same aspects that allow 3D space to be seen on a 2D input, it is entirely possible to gain an awareness of 4D space by paying attention to specific patterns of changes within 3D space. However, the patterns of changes within 3D that are required to “draw” 4D are difficult to portray in “real life” 3D space due to the limitations of Euclidean geometry. Not only that, but due to the fact that human visual perception is only a 2D drawing of 3D even if one is seeing “real life” 3D space, it’s actually more useful to use drawings that create illusions within 2D space to depict 4D. Since human vision is already 2D, one is not really “going down a dimension” by using a 2D plane to draw projections of higher dimensions. Not only that, but the lack of “real life” 3D space within the 2D plane that is used for the drawings allows some “cheating” of the limitations of Euclidean 3D geometry that need to be transcended to be able to show spatial 4D.
The Dimensionality of Virtual Experiences
One of the limitations of drawings is that they are unable to utilize changes in space over time as a means of depicting spatial changes in higher dimensions, since drawings are static and cannot depict changes in perspective within the illusionary 3D space present in the 2D drawing. For example, let’s compare a static drawing of a cube vs. an animated GIF of a drawing of a cube.
This may appear unmistakably as a cube for those who are familiar with 3D space, but for a Flatlander, it’s difficult to know exactly where the change in 3D space is precisely occurring among the two diagonally joined squares since it is only drawn from one vantage point in 3D. By incorporating changes in time into the drawing, one can show movement in the illusionary 3D space of the 2D drawing:
Although it may clearly look like a rotating cube to a human, the Flatlander’s first impression of this animation would be similar to how a human might perceive the animation of the tesseract.
There is an “inside square” that only looks like a perfect square from a head-on perspective. As soon as the shape rotates within left/right space in a manner that leads to changes in the forward/backward space that does not make sense to a Flatlander, the lack of a forward/backward perspective leads to the perception that the inner square becomes distorted in a way where its connection with a distorted outer square can be seen as it “exits” to the right (or left, depending on which square one is focusing on), and the inner square that is outgoing to the right somehow seems to re-integrate itself into a new square that is incoming from the left.
Note how the direction of the rotation can look different depending on which square one is focusing on- stare at this animation for long enough, and you might find that the rotation randomly changes direction whether one is focusing on the “front” square or the “back” square.
In order to understand why a Flatlander’s perspective of the direction of the rotation can only go one way, we only need to look at the tesseract GIF again:
Just like how the rotating cube features an inside square that only appears as a perfect square from a head-on perspective in 3D, and then “exits” and becomes distorted and somehow feeds itself back in via the outside square into the incoming square, the tesseract likewise features an inner cube that only appears as a perfect cube from a head on perspective in 4D, and then “exits” and does this strange distortion process within the outside cube where it somehow feeds itself back in as the incoming cube. Just like the inside square moves to the right and the outside square moves to the left in the cube GIF, the inside cube moves right and the outside cube moves left during its rotation through left/right space that leads to changes in its 4D spacial positioning.
If one pays attention to the apparent 3D positioning of the corners of the tesseract, it becomes evident that such an object cannot possibly exist in “real life” 3D. The manner in which the corners appear to travel in opposite directions in forward/backward space yet still appear to able to connected via what appears to be an inward direction in forward/backward space is an example of how replacing the spatial dimension of a higher dimensional drawing that is missing from the 2D plane it is drawn on with time, can allow for drawings of 4D geometry that our vision still interprets as being 3D, but since the tangible presence of the Euclidean limitations of one of the spatial dimensions is absent on a 2D plane, aspects of 4D space that would not be able to be modeled in real life 3D can be modelled as an animated 2D drawing of a shape that appears to have spatial properties that are impossible in real life, Euclidean space. Since our visual perception is so highly prone to “adding” a forward/backward dimension to 2D drawings, this allows for the illusion of 3D shapes that are impossible in Euclidean 3D space.
This is what allows virtual reality to be the best medium for replicating the spatial properties of dimensions higher than 3D. It is due to the combination of several things that allows for VR to uniquely be able to depict higher dimensional spaces that go beyond the limitations of Euclidean 3D space:
- The lack of a tangible forward/backward space that removes the Euclidean limitations of that space
- The ability for human visual perception to “add” a forward/backward space even if it does not tangibly exist
- The ability for VR to depict changes in perspectives over time that create the illusion of 3D within a 2D medium
- The ability for VR to replicate the illusions that the brain uses to perceive forward/backward spaces by incorporating the changes in 2D that correspond to those present in human visual perception, leading to the realistic perception of being able to move through a 3D space
- In particular, the combination of the realistic impression of movement through 3D space that includes forward/backward space but the lack of actual forward/backward space allowing for things that are impossible in real life, like walking all the way around an impossible triangle and having it remain impossible no matter which way you look at it from
Even if a tangible forward/backward dimension is removed in VR, the brain’s processing of visual information will add it in anyway, and the removal of a tangible forward/backward space can be used to show drawings of 4D space within a 2D plane that require the absence of limitations of a tangible forward/backward space that the brain automatically “adds” back in, which results in the perception of spatial phenomena that is impossible in tangible 3D that nonetheless appears to include impossible looking higher dimensional spatial 4D connections within a space that appears realistically 3D.
How Does This Tie Into Psychedelic Experiences?
- Celestina Aurora Madry
