Could 2-D & 3-D & 4-D atoms interact?

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Edwin Abbot's "Flatland," published in 1884, explores a two-dimensional world inhabited by polygons and circles, where a three-dimensional sphere interacts with the two-dimensional characters. This interaction raises questions about the possibility of different spatial dimensions intersecting and how atoms from these dimensions might interact. In a creative context, the discussion revolves around a superhero character capable of transitioning from three-dimensional to four-dimensional space. The implications of such a transformation include potential changes in size and physical properties, with suggestions that if atoms remain unchanged, the character could face catastrophic consequences. The narrative emphasizes that while dimensional interactions can lead to intriguing concepts, they often require suspension of disbelief, as the focus should remain on storytelling rather than strict adherence to scientific accuracy. The conversation also touches on the potential for body horror in such scenarios, although this is not a favored approach for all creators.
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Most of us have probably read Edwin Abbot's "Flatland," which was published in 1884.

https://www.gutenberg.org/cache/epub/201/pg201.txt

In this novella, sapient and motile polygons & circles inhabit a two-dimensional world. Late in the story, a sapient sphere presents itself to the two-dimensional characters. As it passes through the plane, the 2-D characters see the sphere as the edge of a circle that appears out of nowhere, grows larger then smaller, and then disappears.

In modern terms, we have three-dimensional atoms interacting with two-dimensional atoms.

Sometimes I write about my own original superheroes for my own amusement. One of my characters has the power to take on the characteristics of a four-dimensional creature. Obviously, I could make a comic-book character any way I wanted to, given the prevalence of pseudoscience in the genre. (Arc-reactors, anyone?) But I would like to write this character with as little handwaving as possible.

So, my question should read "Is it possible for atoms that have different numbers of spatial dimensions to interact, assuming that spaces with different numbers of dimensions can intersect each other?

Also, when my character switches from 3-D to 4-D, what happens to his/her/its size?
 
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I don't see why not. The narrator did it in Flatland.
He simply interacted as a cross-section through Flatland.

There was another story, whose provenance I forget, wherein a 4D creature did the same thing in our 3-dimensions. The hero stabbed the creature through the foot, pinning it to the ground so it couldn't leave the 3D dimension.

BTW, I stumbled across this list of reading material:
https://www.theguardian.com/books/2020/jun/03/top-10-four-dimensional-novels-mark-blacklock-hinton
Some are apt, some are not.I didn't actually read this article but just the blurb gave me idea of a Flatlander donning a "skinsuit" that would make his 2D body have a thin 3D dimension, allowing him to enter the 3D world without harm and interact as a 3D shape.
 
Lren Zvsm said:
Also, when my character switches from 3-D to 4-D, what happens to his/her/its size?

If the character's atoms have the same diameter and properties in 4D and are somehow rearranged so that the character becomes 4D then the character's height is about three millimeters. Their surface area goes up by a factor of three hundred. (I have a thread about this in this subgroup.)

If the character's atoms are not rearranged then they flop to the ground while all their bodily fluids flow out into the new dimension.
 
A lot of setting sci-fi rules comes down to what you want to do with your characters and story. Edwin Abbot wanted to talk mathematics, and sidestepped into some social commentary. As Hornbein suggests, dimensional interaction lends itself to body horror. I'm not into that, but some people are.

I can't imagine the addition of an extra dimension being anything but devastating to the lower one. Since they have zero in the missing dimension, their mass is zero relative to the higher dimensional object. Even on the atomic scale, that is going to be a mess. It's probably best to hand wave it all away, as Edwin Abbot does, and stick to what your story is about.

 
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A map of a four-dimensional planet is three dimensional, so such can exist in our Universe. I made one and posted a video to the Internet. This is all based on William Kingdon Clifford's math from the 19th century. It works like this. A 4D planet has two perpendicular planes of rotation. The intersection of such a plane with the surface of the planet is a great circle. We can define latitude as the arctan( distance from one plane/distance from the other plane). The set of all points...

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