Are we already in the fourth dimensions?

[zero]

We can keep going back and forth on this zero, but really, I don't see how anything 1D can be seen.

Yes, I've noticed. Rather than merely repeating things already said, why not step back to more carefully examine the concepts we are investigating?

Simply, you can't see something with zero thickness in our dimension, or in any other dimension.

Don't be so hasty to make such overreaching remarks. The fact is we can see objects that are three dimensional, even though they have "zero thickness" in any number of orthogonal additional dimensions. Is a 3D object in the shape of a cube invisible to you because it has "zero thickness" in a fourth, fifth, sxth or higher dimension? Of course not.

Do not forget that the notion of "thickness" is also ambiguous without context. It has a dimensional component to it, so when you just say "zero thickness" by itself, you are not communicating clearly or effectively. In other words, the objects visible to me in 3D space have a left-to-right thickness, a top-to-bottom thickness, and a front-to-back thickness. Any object I can perceive, whether by sight or by any other sensory means, must have this "thickness" in three orthogonal directions. However, it can also have zero thickness in infinitely many other orthogonal directions, without that being in any way an impediment to my perception.

The vision of a 4D being is debatable.

Anything is debatable; but when it comes to geometry, theorems follow as the logical consequences of initial postulates. My purpose here, however, is not to "debate," but to explain.

[zero]

According to your pattern, a 1D creature would see a 0D point, which I'd say isn't possible, or logical at all.

OK. Then let's discover what is standing in the way of comprehension.

I suggest turning the lights out for a moment.
Set aside vision and consider things from a tactile sensory perspective. If all the lights are out, you cannot see anything, but you can feel items in your environment. When one 3D object touches another (both embedded in the same 3D manifold), the area of contact or boundary between them is 2D. Likewise, when a 2D object touches another (both in the same 2D manifold), the contact or boundary is 1D. And finally, when a 1D object touches another (both in the same 1D manifold), the contact or boundary between them can only be a point.

Now let's turn the lights back on.
Vision involves the stimulation of receptors by some mediating influence. In our 3D experience, this means molecules in our retinas are stimulated by photons of light. In a sense, the photons create a kind of "long-distance" touch from one 3D object, the one we see, to another 3D object, what we see with. Our field of vision is 2D as a direct result of our three dimensional nature: the photons "touch" the object in front of you, then they "touch" the surface of the retina internal to your eye. Traveling from object X to viewer Y eliminates one dimension, leaving the other two remaining to form our field of vision.

If we suppose light of some variety can exist within a 2D manifold, the same analogy applies. Because 2D objects touch along a 1D boundary, this extends to the "long-distance" touch of a 2D photon from the 2D object to the 2D viewer. The eye receptors will be spread along a line, creating a 1D field of vision.

This is a matter of logical necessity.

[zero]

Finally, Hugh, here is an exercise to help if you find yourself stuck on this "zero thickness" kick.

Instead of thinking of 2D items as having zero depth in a third dimension, try giving them infinite depth in a third dimension. For a 2D universe on the surface of a table just take each 2D object within it, and extend it endlessly up and down. The freedom of motion is exactly the same either way. It is in this respect an isomorphic mapping between arbitrary 2D objects and specially restricted 3D objects.

Now you have infinite thickness instead of zero thickness in a third dimension, but the two models behave just the same from a logical point of view. Does this make sense to you, or should it be spelled out in more detail for clarity?

[scruffy63]

umm has anybody thought that maybe these 1d 0r 2d beings might not use conventional "eyes"? we all know we our eyes are limited in what we can see so maybe their "eyes are so limited that they don't use them. Maybe they have mastered the use of their "3rd eye". I don't know maybe they see each others soul/mind. who knows.

[zero]

Since no one knows, we're simply discussing a "what if"' that assumes something analogous to our own vision -- similar yet VERY different because of the different number of dimensions.

In the book Flatland, the king of the 1D creatures located others by the use of sound (as otherwise there would be no way to "see" more than two: those on either side of him). Lineland is a very constrained place indeed when it comes to moving around.