Difference Between 3D and 4D

Every object occupies some space. But the dimension varies.

Dimension is an attribute for an object which defines the position of the target object. It tells the extension or presence of the target in a particular direction.

For example, a point has no dimension.

A line occupies only one dimension. It extends in one direction only.

A simple plane occupies two dimensions. For instance, a plane surface can extend in any of two Cartesian coordinates.

Every object in this world occupies three dimensions, i.e. length, width and depth.

3D vs 4D

The difference between three and four dimensions is that three dimensions can be easily perceived, unlike the fourth dimension which is difficult to feel and observe.

Three dimensions (3D) is all about the presence (extension) of the object of the target in x, y and z-axis. The world we live and the object around us are visualized by us in three dimensions (3D).

It has become possible for us to visualize the three dimensions with the help of data collected and recognized by our sense organs. Knowledge on three dimensions can be traced back to the seventeenth century where it started sprouting with the invention of the Cartesian coordinate system.

Whatever we experience comes under the space of three dimensions. But researchers have long assumed the existence of another dimension in addition to the third dimension which they termed as the fourth dimension.

The debate on the fourth dimension started when Jean Le Rond D’Alembert mentioned this term in the late eighteenth century. The fourth dimension refers to time which cannot be seen or felt.

Comparison Table

Parameter of Comparison	Three Dimensions	Four Dimensions
Definition	Refers to the extension or presence of the objects across the three Cartesian co-ordinates	Refers to the extension of the three-dimension space which is a mathematical concept of time and space.
Parameters	Length, breadth(width) and height	Length, height, width(breadth) and time
Visualization	Can be felt and experienced	Cannot be perceived easily
Origin	Early seventeenth century	Late eighteenth century
Proof of Existence	Three-dimensional space has been proved both in theory and in reality.	The fourth dimension is a concept which has not been demonstrated in actual reality.
Mathematical Parameters	X, Y and Z axis	It consists of four dimensions in which time has been added as a virtual axis.
Example	Cuboid	Tesseract

What is Three-Dimensional Space?

Three-dimensional (3D) space refers to the existence of an object in the three spatial axes. In other terms, it is the number of independent parameters needed to define the location of a particular object in space.

Knowledge of three-dimensional space had been conceptualized at a very early time period.  Every object around us is three-dimensional in nature.

All these objects possess length, breadth (width) and height. The world we live in is visualized in three dimensions.

The degree of this visualization depends on the individual’s ability to perceive these dimensions with the aid of one’s senses.

The representation of three-dimensional space in mathematics is defined by the three Cartesian coordinates. i.e. x-, y- and z-axis. All three axes are mandatory for defining its position or existence.

For example, a square plane can be defined by either of the two axes in the coordinate system, i.e. x-y plane, y-z plane or z-x plane whereas all the three axes are necessary for validating the existence of cube. The volume of the cube can be found only by the data extracted from all the three axes.

What is Four Dimensional Space?

Four-dimensional (4D) space is something unique. It still exists as an abstract which gained more attention when Einstein published his works on the theory of relativity.

The fourth dimension is a modified version of three-dimensional space with the addition of time as the fourth imaginary axis. As per Einstein’s theory, every object falls under a specific frame of space and time.

Time is not treated as independent quantity, rather it is related to space.

This means that any alteration in the space would have a profound effect on time as well. Under this assumption, the working of the universe differs completely when time is assumed to be a dimensional parameter.

Here the effect of past, present and future get nullified as the space changes relatively to time.

Tesseract is a good example of understanding the fourth dimension. Tesseract is the presence of a cube in the fourth dimension.

When a cube is perceived to be extruded in a direction perpendicular to the existing three-dimension, the tesseract is formed. The below gif would give an idea on tesseract from a three-dimensional perspective.

We feel difficult to perceive as we could sense only from a three-dimensional perspective. Scientists are trying to their best to demonstrate this abstract in reality which could take some time to get materialized.

Main Difference Between Third and Fourth Dimensional Space

1. Three-dimensional space specifies the location of a particular concerning three co-ordinates (axes). The fourth dimension is a conceptual one where time is added in the three- dimensional space which acts as an additional virtual axis.
2. The three-dimensional space consists of length, width(breadth) and height. Time is added as the fourth dimension.
3. We live in the world of three dimensions. The concept of four dimensions was formulated from Einstein’s general theory of relativity which remains as an abstract.
4. The geometrical example for three-dimensional space can be a cuboid, cube, sphere etc. Tesseract is a classic example of fourth-dimensional space.
5. A practical example can be additive manufacturing. The addition of material to its perpendicular base results in 3D printing.
   When this 3d print starts reacting to the changes in the environment, it can be termed as 4D printing.

References

1. https://link.springer.com/article/10.1007%2FBF00762914
2. https://www.sciencedirect.com/science/article/abs/pii/0010448591900839