4th spatial dimension thought experiment

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Discussion Overview

The discussion explores the concept of higher spatial dimensions, particularly the fourth spatial dimension, through thought experiments and analogies involving lower-dimensional universes. Participants examine how beings in different dimensions perceive their realities and the implications for understanding dimensions beyond our own.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that in a 1D universe, perception is limited to a point, while in a 2D universe, perception is limited to a line, and in a 3D universe, perception is limited to a plane. They question whether a similar limitation applies to perceiving a fourth dimension.
  • Another participant argues that a 2D creature would struggle to construct a 2D model of their surroundings due to topological constraints, while a 3D universe can support complex visual data processing that might allow for the creation of a 4D model from 2D images.
  • There is a mention of the book "Flatland" by Edwin Abbott as a relevant resource for understanding these concepts.
  • One participant raises a question about the ability of a 2D creature to perceive depth from a 1D image, suggesting that information about depth exists even in lower dimensions, similar to how humans perceive 3D from 2D images.
  • Participants discuss the necessity of brain circuitry in addition to sensory organs for perception, highlighting the challenges of visual data processing in a 2D universe, where electrical circuits would face limitations due to crossing lines.
  • Links to free books about life in a 4D world are shared, indicating interest in further exploration of the topic.

Areas of Agreement / Disagreement

Participants express various viewpoints on the limitations of perception in different dimensions, with no clear consensus on the implications for understanding the fourth dimension. The discussion remains unresolved regarding the extent to which beings in lower dimensions can perceive higher dimensions.

Contextual Notes

Participants acknowledge the complexity of visual data processing and the potential limitations imposed by the physics of lower-dimensional universes. There are unresolved questions about the nature of perception and the necessary conditions for constructing models of higher dimensions.

greggnog
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TL;DR
Theorizing that a 4th spatial dimension doesn't exist.
I know I'm completely wrong about this, but it's been a really fun thought experiment for me. I clearly have no physics training, so apologies for basic mistakes, incorrect terminology, etc.. I would love a deeper explanation of what I'm getting wrong!

So in a 1D universe, you see in 0D (a point), in a 2D universe you see in 1D (a line), and in our 3D universe we see in 2D (a plane). But in our world, our brains have enough information to turn the 2D images we see into 3D interpretations. So it appears that we are seeing in 3D.

The same could be true in a 2D world: I may just see a line, but objects on the 2D plane have varying levels of distance from each other. My brain on a 2D plane could therefore have enough information to expand the 1D image into a 2D one in the same way that this happens in our 3D world. So in this 2D world, why can't we expand this perceived 2D image into a 3D one?

We can't do that because the information is missing. There are an infinite number of possibilities for what that third dimension might look like, so our 2D brains cannot construct a 3D image. There is no third dimension in this 2D world. So back to our dimension: could the same be true? We see in 2D, we interpret that to 3D, but we lack the information to see the fourth dimension. Does that mean that there is no 4th spatial dimension in our 3D world? Or maybe we are in a higher dimension universe and humans just can't see the N-1 dimensional picture?

Anyway, it was fun to think about!
 
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A 2D creature would have a hard time constructing a 2D model of what he was seeing because visual data processing would be severely restrict by the topological constraints of 2 dimensions. Even a simple flip-flop circuit would need to have separate signal paths share the space where they crossed.
In contrast, a 3D universe easily supports any visual data processing - and in the right circumstances, given suitable a priori information and well-planned scanning techniques, could create a 4D model based on a series of 2D images
 
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.Scott said:
A 2D creature would have a hard time constructing a 2D model of what he was seeing because visual data processing would be severely restrict by the topological constraints of 2 dimensions. Even a simple flip-flop circuit would need to have separate signal paths share the space where they crossed.
In contrast, a 3D universe easily supports any visual data processing - and in the right circumstances, given suitable a priori information and well-planned scanning techniques, could create a 4D model based on a series of 2D images
Thanks for the reply, Scott! Can you explain a bit more why a 2D creature would have trouble constructing a 2D image? It seems like in their 1D vision the information about another axis of depth exists. Like if I hold up a 2D circle and look at it from the side, I see a 1D image but the data that parts of it are further away than others is there. This seems to be exactly what happens in our 3D world: I see a 2D image, but the data about the depth of each plane is there so I can construct a 3D visualization.
 
You need more than a lens and retina to see. You also need brain circuitry. If you look at any electrical schematic, there will be lots of places where lines cross. In a 2D universe, you would need some way to keep those lines from shorting out. If the Physics of that 2D universe provided a way to do this, then you're all set. Otherwise, your circuits will be very primitive.
 
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.Scott said:
You need more than a lens and retina to see. You also need brain circuitry. If you look at any electrical schematic, there will be lots of places where lines cross. In a 2D universe, you would need some way to keep those lines from shorting out. If the Physics of that 2D universe provided a way to do this, then you're all set. Otherwise, your circuits will be very primitive.
I hadn't even thought of that! Thanks again, Scott!
 
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