# Visualizing 4D Euclidian Space: A Book for Mind-Boggling Effects

• Hornbein
In summary: The book is based on the 19th century mathematics of William Clifford. Math is death in the marketplace so the book contains none of that, just the effects. What surfing would be like, what pizza or automobiles would be like, things like that. There is a website occupied by the five or so mathematicians who are interested in this so I got one of them to approve of the manuscript. I've earned a masters degree in math from a fancy university and the math is quite simple, basic linear algebra, it's just a question of how to visualize the results. The main difference is that according to Clifford things in a four dimensional universe rotate quite differently. The exotic rotation of a 4D Earth would have
Hornbein
Decades ago I read that it was impossible to visualize a four dimensional Euclidian space. I decided to try to do that. It isn't possible to see a 4D space as a native would -- we don't have 4D hardware -- but through various tricks one can do better than nothing. So I wrote a book about the results and had it illustrated.

The book is based on the 19th century mathematics of William Clifford. Math is death in the marketplace so the book contains none of that, just the effects. What surfing would be like, what pizza or automobiles would be like, things like that. There is a website occupied by the five or so mathematicians who are interested in this so I got one of them to approve of the manuscript. I've earned a masters degree in math from a fancy university and the math is quite simple, basic linear algebra, it's just a question of how to visualize the results. The main difference is that according to Clifford things in a four dimensional universe rotate quite differently. The exotic rotation of a 4D Earth would have big effects on everyday life and climate. In 4D a rifle would offer no advantage over a musket. Be assured that I don't claim any such 4D objects could exist, it's strictly a pedogogical tool, an intellectual exercise. If you can't imagine what everyday objects would have to be like in a 4D universe, then can you say you really understand 4D?

When it got to the point of advertising the book I found out that I couldn't stand doing that, so I decided to give it away free. I've had a few readers, but it would be nice to have more than five. It's not about our universe so it isn't physics. There are no characters or plot so its not what people would expect from science fiction. The world building community might be interested but having an extra spatial dimension is radical. This would be for people who want to have their minds boggled. What would you suggest I do to find those few who would be interested?

Last edited:
“but it would be nice to have more than five.”

I’d be happy to make it 6.

Seven, even. Or 7, odd? I have read and enjoyed books describing the mathematics inherent in M.C. Escher's paintings. Your book sounds interesting, more so with underlying equations.

Research on standardized testing supports the theme that some people 'think geometrically'; i.e., possesses innate ability to spatially locate objects, to mentally rotate surface asymmetric n-dimensional objects to form sets, etc. If these results accurately measure 'geometric' or 'topological' mental ability, innate or acquired; such people might be able to visualize multiple physical dimensions more readily than those lacking this hypothetical ability.

Sounds interesting.

What did you use to generate the visualizations?

If you can render it with (say) GeoGebra or Glowscript
and then embed the visualization in your book (in epub?),
It could attract more attention.

https://wiki.geogebra.org/en/Embedding_in_Webpages
See https://vpython.org/presentation2018/noinstall.html
(e.g. https://www.wired.com/2015/04/dare-change-numerical-calculation/ ).

Some examples of GeoGebra that may be of interest
https://www.geogebra.org/m/yvNYFtFS (someone's visualization of geometric algebra)
https://www.geogebra.org/m/GXtFTDTW (someone's assignment on non-euclidean geometry)
https://www.geogebra.org/m/c4wHSCSj (someone's book on Escher and hyperbolic geometry)
https://www.geogebra.org/m/pr63mk3j (my recent visualization of light cones)

Last edited:
robphy said:
What did you use to generate the visualizations?

If you can render it with (say) GeoGebra or Glowscript
and then embed the visualization in your book (in epub?),
It could attract more attention.

https://wiki.geogebra.org/en/Embedding_in_Webpages
See https://vpython.org/presentation2018/noinstall.html
(e.g. https://www.wired.com/2015/04/dare-change-numerical-calculation/ ).

Some examples of GeoGebra that may be of interest
https://www.geogebra.org/m/yvNYFtFS (someone's visualization of geometric algebra)
https://www.geogebra.org/m/GXtFTDTW (someone's assignment on non-euclidean geometry)
https://www.geogebra.org/m/c4wHSCSj (someone's book on Escher and hyperbolic geometry)
https://www.geogebra.org/m/pr63mk3j (my recent visualization of light cones)
I used a from-scratch Python program to simulate the seasons and climate of a 4D planet. This drew the results as graphics, but I felt that the results were too sophisticated for the book. I didn't want to exclude people who don't like or can't read graphs. Instead of such abstract results I hired artists to make drawings of 4D superhighways, animals, houses, and so forth. I presented the exotic and esoteric subject matter in as down to Earth a fashion as I could. I figured that even if reader didn't understand a word, they might at least like the illustrations.

I'm also pretty chary of anything interactive. Who knows whether it will work on Windows 7 or whatever? Then there's what happened to Java. A friend have a very nice website that depended on that. When Java was killed the website went with it. I'll stick with PDFs. Even that isn't perfectly safe, but what can you do.

Last edited:
I have sent personal messages to the three responders with a link to the book. Just making sure y'all know.

gmax137 and Klystron
:raises hand hopefully:

Have you thought about publishing it as an e-book on Amazon (or elsewhere)? I hear they have a pretty streamlined process for doing that. Setting the price even just to a few or a dozen bucks might recover some of the costs you seem to have incurred in hiring the artists. But more importantly, it would be publicly available, open to reviews, and subject to search queries and algorithmic recommendations. I'd be sure to buy it myself as it sounds like my kind of jam.

Hornbein said:
When Java was killed the website went with it.
What? Java's dead? I am so out of the loop post-retirement.

Klystron said:
What? Java's dead? I am so out of the loop post-retirement.
Yeah. It was very insecure, and Sun lost interest.

Hornbein said:
I'm also pretty chary of anything interactive. Who knows whether it will work on Windows 7 or whatever? Then there's what happened to Java. A friend have a very nice website that depended on that. When Java was killed the website went with it. I'll stick with PDFs. Even that isn't perfectly safe, but what can you do.

The internet is full of things that come and go. .. e.g. Flash, Java, ...

I was enthusiastic about VRML for visualizing electromagnetism and relativity.
After VRML dropped off, I stumbled on VPython back in 2001 or so.
I was hesitant to invest effort in something that might also drop off.
But I kept on with VPython, which has evolved into https://glowscript.org/ (using Javascript... which can be embedded in a webpage) and VPython in a Jupyter notebook.

Some Physics simulations that started as java or flash (e.g. https://phet.colorado.edu/ https://www.falstad.com/ ) have moved to Javascript and HTML5 (some using CheepJ and other similar methods).

Good luck.

## 1. What is 4D Euclidian space?

4D Euclidian space is a mathematical concept that extends the traditional 3-dimensional Euclidean space by adding a fourth dimension, known as the "w" dimension. This dimension is usually represented by the letter "w" and is perpendicular to the other three dimensions (x, y, and z).

## 2. How can we visualize 4D Euclidian space?

Visualizing 4D Euclidian space requires us to use our imagination and think in abstract terms. One way to visualize it is to imagine a 3-dimensional object moving through time, which represents the fourth dimension. Another way is to use mathematical tools such as projections and rotations to represent 4D objects in 3D space.

## 3. What are some real-world applications of 4D Euclidian space?

4D Euclidian space has many applications in fields such as physics, computer graphics, and engineering. In physics, it is used to describe the behavior of particles in spacetime. In computer graphics, it is used to create more realistic and complex 3D animations. In engineering, it is used to model and analyze the behavior of complex systems.

## 4. Is it possible to experience 4D Euclidian space in our everyday lives?

No, it is not possible to experience 4D Euclidian space in our everyday lives because our brains are limited to perceiving and understanding the world in 3 dimensions. However, we can use visual aids and mathematical concepts to help us understand and visualize 4D space.

## 5. How can learning about 4D Euclidian space benefit us?

Learning about 4D Euclidian space can benefit us by expanding our understanding of the world and how it works. It can also improve our critical thinking and problem-solving skills by challenging us to think in abstract and multidimensional ways. Additionally, it has practical applications in various fields, as mentioned earlier.

Replies
11
Views
2K
Replies
0
Views
2K
Replies
9
Views
2K
Replies
1
Views
2K
Replies
25
Views
893
Replies
5
Views
3K
Replies
3
Views
702
Replies
20
Views
3K
Replies
4
Views
1K
Replies
19
Views
3K