Four dimensional objects

[Magical Realist]

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"A Klein bottle is a one-sided surface with no distinct inside or outside, meaning you could travel along its surface and end up back where you started but on the opposite side, like on a Möbius strip. It's a closed, non-orientable surface named after the mathematician Felix Klein. Unlike a sphere, it has no volume.
The Klein bottle's history begins with German mathematician Felix Klein, who introduced the concept in 1882 as a one-sided, non-orientable surface, a "bottle" with no inside or outside, existing ideally in four dimensions but representable in 3D. Inspired by the Möbius strip, it's formed by joining two Möbius strips along their edges, creating a seamless, boundary-less object that challenges our 3D intuition, captivating mathematicians, artists, and thinkers for over a century as a symbol of the infinite and the impossible."
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"Have you ever considered how a four-dimensional being would appear to you if it suddenly came into your room?

I think they would resemble flesh-colored balloons constantly changing in size. We would see disconnected blobs of flesh, some attached to claws, teeth, lips, eyes, or hair. Let me tell you why.

Think of it this way. Consider a two-dimensional world resembling a sheet of paper. How would you appear to the inhabitants of such a world if you tried to interact with with them? The 2-D creatures would only see cross-sections of you as you intersected their universe. Your finger would look like a flat disc that grew in size as you pushed it through their world. Your five fingers might looked like five separate circles. They would just see irregular shapes with skin boundaries as you entered their world. Similarly, a hyperbeing who lived in the fourth dimension would have a cross-section in our space that looked liked a bunch of skin blobs.

A 4-D being would be a god to us. It would see everything in our world. It could even look inside your stomach and remove your breakfast without cutting through your skin, just like you could remove a dot inside a circle by moving it up into the third dimension, perpendicular to the circle, without breaking the circle.

A hyperbeing can effortlessly remove things before your very eyes, giving you the impression that the objects simply disappeared. The hyperbeing can also see inside any 3-D object or life form, and if necessary remove anything from inside. The being can look inside our intestines, or remove a tumor from our brain without ever cutting through the skin. A pair of gloves can be easily transformed into two left or two right gloves. And 3-D knots fall apart in the hands of a hyperbeing, much as a 2-D knot (a loop of string lying on a plane) can easily be undone by a 3-D being simply by lifting the end of the loop up into the third dimension."---Clifford Pickover https://sprott.physics.wisc.edu/pickover/fourth.html

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[...] Think of it this way. Consider a two-dimensional world resembling a sheet of paper. How would you appear to the inhabitants of such a world if you tried to interact with with them? The 2-D creatures would only see cross-sections of you as you intersected their universe. Your finger would look like a flat disc that grew in size as you pushed it through their world. Your five fingers might looked like five separate circles. They would just see irregular shapes with skin boundaries as you entered their world. Similarly, a hyperbeing who lived in the fourth dimension would have a cross-section in our space that looked liked a bunch of skin blobs.

A 4-D being would be a god to us. It would see everything in our world. It could even look inside your stomach and remove your breakfast without cutting through your skin, just like you could remove a dot inside a circle by moving it up into the third dimension, perpendicular to the circle, without breaking the circle.

A hyperbeing can effortlessly remove things before your very eyes, giving you the impression that the objects simply disappeared. The hyperbeing can also see inside any 3-D object or life form, and if necessary remove anything from inside. The being can look inside our intestines, or remove a tumor from our brain without ever cutting through the skin. A pair of gloves can be easily transformed into two left or two right gloves. And 3-D knots fall apart in the hands of a hyperbeing, much as a 2-D knot (a loop of string lying on a plane) can easily be undone by a 3-D being simply by lifting the end of the loop up into the third dimension."---Clifford Pickover https://sprott.physics.wisc.edu/pickover/fourth.html

While such examples are necessary to illustrate how the two contrast, there's no guarantee that a 4D being would be composed of excitations or particles belonging to quantum fields (like ours). It might be worse than dark matter, and not even be able to interact gravitationally with the "stuff" in our 3D realm. In that scenario, it would pass through our world without having an effect on us and without acquiring awareness of us, and vice versa.