Questions about the (Spatial) Fourth Dimension

[Tesseract]

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.)

 

[ChrisVer]

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...

 

[micromass]

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.

 

[Tesseract]

Thank you for all of the feedback.

 

[Hertz]

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?

 

[ChrisVer]

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 ...

 

[hddd123456789]

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).