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?

### Mental Imagery "Visualizing in the mind's eye."

#### Visual Imagery

• Like vision

• has all properties of image

1. 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)

#### Mental Rotation Function: Flexibility and Limitations

##### Flexibility
• free manipulation of perception qualities

• size, orientation, location, color, etc

• all possible physical operations

• divide and assemble

##### Limitations
• new perceptual dimension

• new color? new spatial dimension?

#### Ways to Obtain up Intuition

• 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)

#### Our Experiment

We show 3D slices of random 4-simplexes

##### Basic Property: distance judgements
• study for 2 minutes

Conclusions

• people can make 4D judgements

##### Angle Judgements

Conclusions

• people can make orientation judgements

• not based on calculations

• imagery: 4D or 3D movie?

#### Future Projects

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