What helps you visualize dimensions?

[Dense]

An interesting question came up the other day. Someone asked how to visualize the tinier dimensions, and though I like to think that I can, it was pretty hard to put it into words. Here’s my attempt. Not saying it’s right, just saying it works for me. I’d be very interested to see what works for others.

First, two simple principles: (A) For any given dimension, treat the next highest dimension as its “time.” (B) Mapping out how the state of a given dimension changes over “time” gives you a visualization of the next highest dimension.

To make it easier, I start from the smallest and work highest. Going the other way hurts my head.

To keep it short, I’ll run through 8 or 9 dimensions. The three dimensions we live in are numbers 4, 5 and 6. (Dimension 6 is the really interesting one to me.)

0. Start with a singularity of zero dimension. It’s just a reference point, such as the intersection of two lines or three planes. It’s a point.

1. Map out how that point changes over time. You now have a 1-dimensional line.

2. Map out how that line changes over time. You now have a 2-dimensional plane.

3. Map out how that plane changes over time. You now have a 3-dimensional space.

4. Map out how that space changes over time. Imagine each new instance of that space as an infinitesimal point. You now have a 4-dimensional line, with each point on that line being how the entire 3-dimensional space was at any given moment.

5. Map out how that 4-dimensional line changes over its time, and you now have a 5-dimensional plane.

6. Map out how that 5-dimensional plane changes over its time, and you now have a 6-dimensional field. Think of this as what we normally think of as the 3-dimensional space we experience.

Each infinitesimal point in that 6-dimensional field is a 3-dimensional space of its own. This helps me visualize how nearby points in a field react as they do -- they’re not different things spookily acting at a distance, but are instead just the same 3-dimensional sphere (or whatever) reacting to something over its “time.”

7. Map out how that 6-dimensional field changes over time, and you now have a 7-dimensional thing that we refer to as “spacetime.”

8. I need another dimension on top of that, an 8th dimension, for a sort of Bohm pilot wave that helps me imagine a photon trying out various pathways in its phase space, outside of time, perhaps interfering with each other as in a 2-slit experiment, then traveling down one of those pathways in the spacetime we experience. (See discussion at https://www.physicsforums.com/showthread.php?t=148050&page=5 )

Like I said, I’m not in any way saying this is RIGHT, just that it helps me deal with the concepts. I’d love to hear what works for others.

 

[AndyW]

Thank you for sharing your attempt at visualizing the tinier dimensions. I can understand the difficulty in putting these concepts into words. I appreciate your approach of treating the next highest dimension as "time" and mapping out the changes in state over that "time" to visualize the next dimension.

I also find it helpful to start from the smallest dimensions and work upwards, as going the other way can be quite challenging. Your explanation of the singularity as a reference point and each new instance of space as an infinitesimal point is a great way to conceptualize the higher dimensions.

I am particularly intrigued by your visualization of a photon in the 8th dimension, trying out various pathways in its phase space and then traveling down one of those pathways in our 3-dimensional space. It's a fascinating way to think about the behavior of particles at the quantum level.

Thank you for sharing your thoughts and insights on this topic. I am sure it will be helpful for others who are also trying to wrap their heads around the tinier dimensions. I look forward to hearing from other forum members and their ways of visualizing these concepts. It's always interesting to see different perspectives and approaches to understanding complex concepts.

 

[Entropia]

I can understand the difficulty in visualizing dimensions beyond our three-dimensional world. It can be challenging to put something into words that is beyond our everyday experience. However, I appreciate your attempt to explain your thought process and how you personally visualize dimensions.

I think your approach of using the concept of "time" as the next highest dimension is a helpful way to think about it. Mapping out how a lower dimension changes over time can give us a visualization of the next highest dimension. This is similar to how we use time as the fourth dimension in our three-dimensional world.

I also find it interesting that you start from the smallest dimension and work your way up. This makes sense as it can be overwhelming to try to visualize multiple dimensions at once. Breaking it down step by step can make it more manageable.

I particularly like your example of a 6-dimensional field and how each infinitesimal point within it is a 3-dimensional space of its own. This helps to explain how different points in a field can interact with each other, rather than being separate and distant entities.

Your idea of an 8th dimension as a "Bohm pilot wave" is also intriguing. It's important to note that these are all just theories and concepts to help us understand and visualize dimensions beyond our own. As scientists, we must always remain open to new ideas and perspectives.

Overall, I appreciate your attempt to explain and visualize dimensions. It's a complex and abstract concept, and different methods may work for different individuals. it's important to continue exploring and discussing these ideas to deepen our understanding of the universe.