4th spatial dimension thought experiment

[greggnog]

TL;DR Summary

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!

 

[.Scott]

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

 

[jedishrfu]

Checkout the Flatlands book by Edwin Abbott for starters:

https://en.wikipedia.org/wiki/Flatland

 

[greggnog]

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.

 

[greggnog]

Checkout the Flatlands book by Edwin Abbott for starters:

https://en.wikipedia.org/wiki/Flatland

Love that premise! Thanks for sharing, I'll check it out!

 

[.Scott]

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.

 

[greggnog]

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!