Notes by Katie Poon
Vision of 3D Object in 2D World: References to "Flatland" by Edwin Abbot
If a sphere passes through a 2D plane/world, those "creatures" living on the 2D world would see a circle.
Intuition, or mental imagery, is hard while conceptual understanding is easy.
You can write calculus in higher dimensions with equations but can people perceive it in their minds?
Like vision
has all properties of image
size, location, resolution, color, etc
viewpoint specific
aided by motor action
interference/integration with vision (If you concentrate on one image, you will not detect other images)
free manipulation of perception qualities
size, orientation, location, color, etc
all possible physical operations
divide and assemble
new perceptual dimension
new color? new spatial dimension?
drawing analogue to 3D space- drop to 3D to see what the object looks like then imagine it in 4D
experiencing 4D space directly
limitation of sensory organ: 2D retina
mental limitation?
claims of success: Davis P.J. & Hersh, R., & Marchisotto, R.A (1995) Rucker, R. (1984) Seyranian, G.D (2001)
We show 3D slices of random 4-simplexes
study for 2 minutes
adjust for length
Conclusions
people can make 4D judgements
Conclusions
people can make orientation judgements
not based on calculations
imagery: 4D or 3D movie?
Can we do more complicated tasks?
3D/4D geometrical properties
mental rotation/viewpoint change
rotate 4D object and observe from a different angle
navigation and mental maps in spaces of different geometries
curved 3D spaces
navigation in 4D
Are there better presentation techniques?
slicing vs. projection
parallel vs perspective projections
"thicker" 3D slices
difference cues for 4D depth (brightness, density, patterns, etc)