# The 4th Dimension: Where Science and Imagination Collide

By: Molly Edmonds & Desiree Bowie  |

Most of us are accustomed to watching movies in 2D; even though characters on the screen appear to have depth and texture, the image is actually flat.

But when we put on 3D glasses, we see a world that we could walk in. We can imagine existing in such a three-dimensional world because we actually live in one. But for someone who's only known life in two dimensions, the third dimension would be impossible to comprehend.

And that, according to many researchers, is the reason we can't see the fourth dimension, or any other dimension beyond that. Physicists work under the assumption that there are at least 10 dimensions, but the majority of us will never "see" them. Because we only know life in 3D, our brains don't understand how to look for anything more.

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## What Is a Dimensional Space?

A dimensional space, in mathematics and physics, is a way of describing the different directions or coordinates in which objects can exist or move. It's a mathematical concept used to understand and visualize the positioning and movement of things in our world.

In our everyday world, we often use three dimensions: height (up and down), width (left and right) and depth (forward and backward) to describe the location of objects. These three dimensions create what's called 3D space.

However, in more advanced mathematics and physics, dimensional spaces can have more than three dimensions, and they help scientists and mathematicians understand complex phenomena like quantum mechanics, string theory or data analysis in higher dimensions.

These higher-dimensional spaces are harder to visualize because they go beyond our everyday experience, but they are essential for solving various problems and studying intricate systems.

## Looking Beyond This Dimensional Space

In 1884, Edwin A. Abbot published a novella that depicts the problem of seeing dimensions beyond your own. In "Flatland: A Romance of Many Dimensions," Abbot describes the life of a square living in a two-dimensional world. Living in 2D means that the square is surrounded by circles, triangles and rectangles, but all the square sees are other lines. One day, the square is visited by a sphere.

On first glance, the sphere just looks like a circle to the square, and the square can't comprehend what the sphere means when he explains 3D objects. Eventually, the sphere takes the square to the 3D world, and the square understands. He sees not just lines, but entire shapes that have depth.

Emboldened, the square asks the sphere what exists beyond the 3D world; the sphere is appalled. The sphere can't comprehend a world beyond this, and in this way, stands in for the reader. Our brains aren't trained to see anything other than our world, and it will likely take something from another dimension to make us understand.

## The Fourth Dimension

But what is this other dimension? Mystics used to see it as a place where spirits lived, since they weren't bound by our earthly rules. In his theory of special relativity, Einstein referred to time as the fourth dimension, but noted that time is inseparable from space.

Science-fiction aficionados may recognize that union as space-time, and indeed, the idea of a space-time continuum has been popularized by science-fiction writers for centuries (e.g., Ray Bradbury's "The Martian Chronicles" or Joe Haldeman's "The Forever War").

Today, some physicists describe the fourth dimension as any space that's perpendicular to a cube — the problem being that most of us can't visualize something that is perpendicular to a cube [source: Duke University].

Researchers have used Einstein's ideas to determine whether we can travel through time. While we can move in any direction in our 3D world, we can only move forward in time. Thus, traveling to the past has been deemed near-impossible, though some researchers still hold out hope for finding wormholes that connect to different sections of space-time.

###### Beginnings of the Concept

In the early 19th century, mathematicians and thinkers began to explore the idea of a fourth spatial dimension beyond our familiar three dimensions (depth, width and height). August Ferdinand Möbius was among those who pondered the possibilities of this additional dimension. One of the intriguing aspects of the fourth dimension is that in it, a three-dimensional object could be rotated in such a way that it would appear as its own mirror image, a concept that challenges our intuitive understanding of space.

The tesseract, also known as a hypercube, is a common visual representation of 4D space. It is an extension of the concept of a cube (a 3D object) into the fourth dimension. While it's challenging to visualize in our three-dimensional world, mathematicians use diagrams and models to help convey the idea of a tesseract.

Later in the 19th century, mathematician Bernhard Riemann laid the foundations for true four-dimensional geometry, providing a mathematical framework for understanding and working with higher-dimensional spaces. This work became fundamental to later developments in mathematics and physics, particularly in the study of curved spaces and the theory of relativity.

## Types of Dimensional Spaces

In mathematics and physics, we encounter various types of dimensional spaces beyond our familiar three-dimensional world.

1. Zero-Dimensional Space (0D): Often referred to as a single point or a singleton, this space represents a single location or value with no spatial extent or degrees of freedom. It is the simplest and most abstract of all dimensional spaces, serving as a foundational concept in mathematics, especially in set theory and abstract algebra.
2. One-Dimensional Space (1D): This is the simplest dimensional space, represented as a straight line. In a one-dimensional world, objects and entities can only move along a single axis (like a timeline), limiting their spatial freedom to one dimension.
3. Two-Dimensional Space (2D): This space includes coordinates that cover a plane, like a sheet of paper. It's used for mapping and analyzing objects' positions in two directions.
4. Three-Dimensional Space (3D): Our everyday space involves three dimensions: height, width and the third dimension of depth. The interaction of these dimensions allows us to describe the physical world and how objects move within it.
5. Four-Dimensional Space (4D): In physics, time is often considered the fourth dimension, essential in understanding space-time in Einstein's theory of general relativity.
6. Euclidean n-Dimensional Space (nD): It's a way of thinking about space that goes beyond our usual three dimensions. This space can have any number of dimensions (n), where distances and angles between points are measured in a consistent, familiar way.
7. Vector Spaces: These spaces can have any finite number of dimensions and are fundamental in linear algebra, which plays a vital role in physics, computer graphics and engineering.
8. Hilbert Spaces: Infinite-dimensional spaces are used in quantum mechanics to describe the state of quantum systems.
9. Function Spaces: These spaces involve functions as their elements and are used in various mathematical and scientific disciplines.
10. Manifolds: These spaces that look like Euclidean space near every point but may have a different overall shape.
11. Phase Spaces: Used in physics to describe the complete set of variables needed to predict the future behavior of a dynamic system.

## Why Is It Important to Understand the Fourth Dimension?

If we can't use the fourth dimension to time travel, and if we can't even see the fourth dimension, then what's the point of knowing about it? Understanding these higher spatial dimensions is of importance to mathematicians and physicists because it helps them understand the world.

String theory, for example, relies upon at least 10 dimensions to remain viable [source: Groleau]. For these researchers, the answers to complex problems in the 3D world may be found in the next dimension — and beyond.

###### Applications in Math

In mathematics, particularly in geometry, comprehending higher-dimensional spaces, including the fourth dimension, is fundamental. These spaces expand problem-solving capabilities, although visualizing them challenges our conventional three-dimensional thinking. Concepts like hypercubes enable mathematicians to explore these abstract spaces.

In geometry, the fourth dimension plays a vital role in visual representation. It extends beyond our everyday experience, challenging our ability to grasp complex spatial arrangements. While we can't directly visualize four-dimensional space, math provides tools for representing and comprehending it, expanding our geometric understanding.

###### Applications in Physics

In physics, the fourth dimension, as time in space-time, forms the cornerstone of our comprehension of physical laws and predictions. The theories of modern physics, like Einstein's general relativity, rely on this concept. Accurate predictions about the behavior of objects and events demand the inclusion of time as the fourth dimension.

In fact, time as the fourth dimension is crucial for reshaping our understanding of gravity in the context of general relativity. It describes gravity as the curvature of space-time by massive objects, deeply intertwined with the fourth dimension. Neglecting time in this context would make explaining gravitational phenomena very challenging.

###### Everyday Applications

In everyday life, tasks, such as navigation and communication, heavily depend on our grasp of time as the fourth dimension. Technologies like GPS and accurate time-keeping systems rely on this foundational understanding, enhancing our daily lives.

Moreover, the concept of the fourth spatial dimension prompts profound philosophical inquiries into the nature of time and reality, challenging our perceptions and encouraging contemplation about our place within the universe.

###### Applications in Cosmology

Lastly, in cosmology, the fourth dimension is pivotal for unveiling the history and evolution of the universe. It assists in studying significant events like the Big Bang, cosmic expansion and the formation of galaxies and stars, providing invaluable insights into the cosmos.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.

### Sources

• Cole, K.C. "Escape From 3-D." Discover Magazine. July 1993. (May 3, 2010) http://discovermagazine.com/1993/jul/escapefrom3d237
• Goudarzi, Sara. "You Can't Travel Back in Time, Scientists Say." LiveScience. March 7, 2007. (May 3, 2010)http://www.livescience.com/technology/070307_time_travel.html
• Groleau, Rick. "Imagining Other Dimensions." The Elegant Universe, NOVA. July 2003. (May 3, 2010)http://www.pbs.org/wgbh/nova/elegant/dimensions.html
• Jones, Garrett. "Fourth Dimension: Tetraspace." 2000. (May 3, 2010)http://teamikaria.com/hddb/classic/
• Overbye, Dennis. "Unbreakable: He's Still Ready for His Close-Up." New York Times. May 12, 2002. (May 3, 2010)http://www.nytimes.com/2002/05/12/weekinreview/ideas-trends-unbreakable-he-s-still-ready-for-his-close-up.html