Definition: A one-dimensional world has no height or depth, only length.
Movement: An organism in a 1D world moves linearly, forward and backward.
2D World
Definition: A two-dimensional world has width and length.
Movement: An organism in a 2D world can move up, down, left, right, and anywhere in between.
Composition: Comprised of an infinite series of 1D worlds stacked upon each other.
3D World
Definition: A three-dimensional world has depth, length, and height.
Composition: Made of an infinite series of 2D worlds stacked upon each other.
4D World
Definition: A hypothetical world with a fourth dimension in addition to depth, length, and height.
Perception: Inhabitants would see 3D objects in their entirety, similar to how 3D beings view 2D objects.
Composition: Made of an infinite series of 3D objects.
Visualization: A basic shape is a tesseract, which is challenging to visualize in 3D.
Perception of Dimensions
2D Organisms: Would perceive a 2D slice of a 3D object. Example: perceiving a sphere as a circle.
3D Organisms: Perceive 3D objects in two dimensions. For example, we see a sphere as a circle without light and shading cues.
4D Organisms: Would perceive all parts of a 3D object simultaneously.
Misconception about the 4th Dimension
Common Misconception: The 4th dimension is time.
Counterarguments:
Time is non-spatial.
Every dimension includes time, implying it wouldn't be a separate spatial dimension.
Moving near the speed of light causes time dilation but doesn't equate to traveling through a spatial dimension.
Curved Dimensions Theory
Curvature: Some physicists suggest dimensions are slightly curved, so moving continuously in one direction would eventually bring you back to your starting point.
Example: A 1D line could theoretically form a circle. A 2D square could form a sphere, and similarly, our 3D space could be part of a 4D curved space.
Implications: The 3D world could be within a 4D world, continuing infinitely.
Infinity Problem: It remains unclear if there is an end to dimensions or if infinity is possible.
Conclusion
Summary: The presentation explores the idea that spatial dimensions build upon each other, from a simple line (1D) to complex tesseracts (4D), challenging our perception and understanding of space and its infinite possibilities.