Questions about the (Spatial) Fourth Dimension

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Discussion Overview

The discussion revolves around the concept of the fourth spatial dimension and its implications for how beings in different dimensional worlds perceive objects. Participants explore theoretical scenarios involving dimensional interactions, particularly focusing on how a fourth-dimensional object might manifest in our three-dimensional space and the nature of dimensional projections.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that if a fourth-dimensional being were to interact with our three-dimensional world, we would perceive a sphere as it passes through, similar to how a two-dimensional being perceives a circle when a three-dimensional object interacts with their world.
  • Another participant agrees with the idea of perceiving a sphere but emphasizes that the shape seen is a projection of the object, which may not necessarily be a perfect sphere depending on the angle of interaction.
  • A later reply introduces the notion that beings in lower dimensions perceive shapes differently, noting that two-dimensional beings would see a one-dimensional representation rather than a circle.
  • One participant encourages a mathematical approach to the topic, suggesting that a more rigorous exploration could yield deeper insights.
  • There is uncertainty regarding the nature of a "3D tunnel" and how it relates to the original questions posed.

Areas of Agreement / Disagreement

Participants generally agree on the idea that higher-dimensional objects would be perceived as projections in lower dimensions, but there is disagreement on the specifics of how these projections manifest and the implications of dimensional perception.

Contextual Notes

Participants express varying levels of understanding regarding dimensional concepts, with some acknowledging limitations in their knowledge. The discussion includes assumptions about perception based on dimensionality that may not be universally accepted.

Who May Find This Useful

This discussion may be of interest to those exploring concepts in higher dimensions, mathematical visualization, or the philosophical implications of dimensionality in physics and mathematics.

Tesseract
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I have a couple questions I have been thinking about:

Say that there is a two dimensional, three dimensional, and four dimensional spatial worlds lined up. If I poked my finger through the two dimensional world they would see a circle. If a fourth dimensional person poked their finger through our world would we see a sphere?

Another thing, would the opening of fourth dimensional tunnel be a 3D hole accessible from 6 sides?

(If I don't know something obvious it's because I'm in seventh grade and haven't learned it yet.)
 
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yes, what you'd see is a sphere... it's like what they are saying for large extra dimensions... if you suddenly saw a a 3D object (let's say sphere) starting growing out of nowhere and then starting to collapse again until it disappears it would mean that a 4spatial dimensional object passed through our world dimensions...
All these are funnily explained from the flatland... if you passed your finger in that world, the 2d people would see a shape appearing (let's say a circle) growing, and then disappearing as you take your finger out of their flat dimension...

I don't get your 2nd question...
 
I highly recommend you read the book Flatland, freely available here: http://www.gutenberg.org/ebooks/201

It is very accessible but also a very good read. I still read it now and then because it's very well written.
 
Thank you for all of the feedback.
 
I got to say, you are a very impressive seventh grader! Keep at it dude!

Really though, there is a lot more that could be said about this topic. Not to be a hater, but ChrisVer basically answered yes and repeated your same line of logic. This whole question could be approached from a mathematical standpoint and I'm sure the results would be a lot more satisfying.

e-
For your second question, what do you consider to be a 3D tunnel?
 
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well OK... just to be more precise... in the 2D world they wouldn't necessarily see a circle, neither in our 3D world would they see a sphere... the correct shape is just the projection of the object...
if your finger's projection is a circle, so be it... I am not so sure ...
 
If you want some more food for thought, consider this: when you poke your finger across a 2D world, the 2D beings themselves won't see a circle since they will have 2D eyes and so will see in 1D :)

Just as how we live in a 3D world with 3D eyes but see in 2D (although our brains make it look like we're seeing 3D).
 

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