Flaw in "Flatland"

[Jay]

I'm a new guy with a question.

When the sphere took the square out of Flatland and brought him into Spaceland, he showed him a cube. However, since the square's eye's were two-dimensional (flat), how could he see up or down? And how could he see more than a line of vision, even though he was in Realmspace?

Similarly, if we were taken into tetraspace, would we still only see planes, instead of entire solids and their insides?

[Aale de Winkel]

mentally I think

I think that when I (as a trionian) would somehow find myself in Tetronia (ie some tetronian world) I would be able to easily change my trionian viewpoint from {x,y,z} {x,y,w} {x,z,w} and {y,z,w} and must somehow mentally make the connection that those views represent the same object.
My trionian perception can only view one of the above mentioned views at a glance, being able to shift quickly from views can be very helpfull in establishing my mental picture.
You might imagine having 6 seperate pictures of mere squares with colored edges, when those same pictures are on a single sheet, it will be more easily to view them as representing the same cube, certainly when they are layed out in the way a papercube can be constructed from them (ie the 3,1,1,1 layout or simular)

As a tronian I can percieve 3d object at a single glance, be it that I can only see three faces at once of say a solid cube

[alkaline]

Yes jay you are right, flatlanders would only see lines and we would only see planes. The being that moved us to the higher dimension would have to rotate us around to see different angles on objects. If he pointed us back at 3d objects, we could indeed see the insides of them, but only one plane at a time. So, if we were looking at a person, it would be like looking at some kind of successive cat scan of the body as our view traversed it. We couldn't see the insides of 4d objects, though.

[Keiji]

If a flatlander is pulled into realmspace, there are 2 possibilities:

1. His whole plane is moved
2. He is taken out of his plane and extruded a small amount.

Obviously the latter happens in this case, so as he becomes three-dimensional, he can move in three dimensions and see two. The same would happen if we were taken out into tetraspace.

[alkaline]

bobxp, it seems that you are assuming that the flatlander is given 3d thickness when he is pulled out of planespace. In the book Flatland, i think the flatlander was still a flat 2d being when it was brought into realmspace. But even if the flatlander was given a small 3d thickness, it wouldn't be able to stand up on its own - it's like trying to stand up a playing card on its edge. Also, in order for an eye of n dimensions to see one dimension higher than usual, it would have to grow cones & rods in that new dimension, you couldn't just stretch the existing ones.

[Keiji]

No the light can travel in more directions so they can see more

[alkaline]

In order to sense light at any particular point, you need a light sensor there. Since a flatlander's light sensors are arranged in a line, they couldn't see any wider than a line even if the light was there. The flatlander would need parallel lines of light sensors in order to get any width to their vision. This is a matter of the magnitude of light sensors in the eye - a flatlander only has so many light sensors, and thus only so many neural pathways into the brain from those light sensors. It is not something you can adjust to in an instant.

[sup2069]

Yes jay you are right, flatlanders would only see lines and we would only see planes. The being that moved us to the higher dimension would have to rotate us around to see different angles on objects. If he pointed us back at 3d objects, we could indeed see the insides of them, but only one plane at a time. So, if we were looking at a person, it would be like looking at some kind of successive cat scan of the body as our view traversed it. We couldn't see the insides of 4d objects, though.

While reading your post, it reminded me of the movie "Hollow Man". Where the CGI would slowly show his skin invis'ing away to reveal his muscles, nerves etc. etc. to show his bones then nothing.

It would be nice to be able to see 3rd dimensional slices of people without slipping (into) the fourth dimension. You would be the best doctor in the world. Imagine a gunshot victim coming in to the ER. You could take a few seconds glance and know where the bullet was and what was damaged! ( The few seconds delay would be you shifting your vision in infinite slices till you viewed the body. ( Just like you mentioned with cat scans) But much faster.

EDIT: I know it sounds like I have discovered something new, but I tend to get out of hand when it comes to writing. I pour my thoughts out while im writing

[Aale de Winkel]

It would be nice to be able to see 3rd dimensional slices of people without slipping (into) the fourth dimension. You would be the best doctor in the world. Imagine a gunshot victim coming in to the ER. You could take a few seconds glance and know where the bullet was and what was damaged! ( The few seconds delay would be you shifting your vision in infinite slices till you viewed the body. ( Just like you mentioned with cat scans) But much faster.

I doubt very much that tetra-vision would be the same as x-ray-vision.
Tetronians will not be able to see within a trionian body, they see the lightrays reflecting of a body just in a direction more then we trionians do!

I can imagin me having some trength (tetridth) which I can't see because of my limitation to tri-vision, this view puts several discussions here in a different light.
The flatlander simply became aware of his height (? or whichever tridth) when he was pulled into realmspace, but his view would still be limited to bi-vision. Being able to switch viewpoint might enable him to imagin those views combined as a single object.

combining a few things here:
an n-onian feel the (<=) n-dimensional forces, coming from objects they share (<=) n-dimensional space with.
the statement above includes the statement that being limited to n-dimensional vision they can only view (<=) n-dimensional object they share space with.

[sup2069]

I doubt very much that tetra-vision would be the same as x-ray-vision.

Sorry for poor thread back there, I was not referring my vision to tetra-vision. I was merely putting it in a way for me to see-through anything in 3rd space. Instead of being pulled into 4th dimension, pointed to a 3rd dimensional object to be able to see through it...I was dreaming it would be nice to have that ability in our realm to see through any object if you focused.

But even if the flatlander was given a small 3d thickness, it wouldn't be able to stand up on its own - it's like trying to stand up a playing card on its edge.

So in order for us to walk around in tetraspace, we would need tetra legs in order to move around? Since our realmspace bodies would be considered thin by tertraonians, we would need 4D thickness?

[alkaline]

So in order for us to walk around in tetraspace, we would need tetra legs in order to move around? Since our realmspace bodies would be considered thin by tertraonians, we would need 4D thickness?

We would need an extra leg or two to give us balance in the new dimension. The problem is that we would need to be able to control this leg with our brain some how, and it would have to be connected to our nervous system in some way. I'm not sure that we would necessarily need 4d thickness, but we might me a little too fragile in the 4d world so it would be best to give us more thickness to make us more robust. We might also be so light that we flutter away in the wind - so we'd have to be weighed down; but then, we wouldn't be strong enough to move with a 4d weight attached to us. This is beginning to sound hopeless.

[sup2069]

The problem is that we would need to be able to control this leg with our brain some how, and it would have to be connected to our nervous system in some way.

Easily done! Well if you was a tetraonian doctor it would be simple. Assuming here that they have far superior technology, they could grow arms, legs and eyes for us and implant them for us. Our old eyes instead of being removed, could be ( lets say) upgraded. By using fourth dimensional cones in rods in our eyes. Of course we would need a new complete nervous system to handle these new body parts.
You could go to sleep in your bed, a tetraonian doctor would slip you out into his 4d operating room. A few hours you wake up and perceive the tetraonian world as they do!


In the end it would be best to just be transformed into a tetraonian !

[mahtlaxgoalie]

The problem is that we would need to be able to control this leg with our brain some how, and it would have to be connected to our nervous system in some way.

Easily done! Well if you was a tetraonian doctor it would be simple. Assuming here that they have far superior technology, they could grow arms, legs and eyes for us and implant them for us. Our old eyes instead of being removed, could be ( lets say) upgraded. By using fourth dimensional cones in rods in our eyes. Of course we would need a new complete nervous system to handle these new body parts.
You could go to sleep in your bed, a tetraonian doctor would slip you out into his 4d operating room. A few hours you wake up and perceive the tetraonian world as they do!


In the end it would be best to just be transformed into a tetraonian !

Then wouldnt our bodies need to be in the 4th dimension? bob couldnt just put a 3d eye in fred cause freds body is not in the right dimension.

[sup2069]

Then wouldnt our bodies need to be in the 4th dimension? bob couldnt just put a 3d eye in fred cause freds body is not in the right dimension.

Yes, that was the point of getting the upgrades. It would be impossible to reinsert yourself back into realmspace.

As far as the eye, I didnt say installing 4d eyes, I said upgrading. But of course that would cause problems coming back. You would feel blind when your added 4d vision would vanish. It would be like Fred with a 3d eye ball going back to flat land only to have to view lines again.

[Neues Kinder]

I know you stopped talking about this years ago, but I couldn't help but state my opinion on this.

It is impossible to be pulled out of realmspace and pulled into tetraspace. First, to be given 4D bodily implants, we would have to be pulled out of our world into Tetronia (I really love that name) first so that we're in the right dimension to do it. But the problem is we can't get pulled out of our world until we're given tetridth so that we can exist in their world. But we can't be given tetridth before we are pulled out because we are not in the right dimension to do so. And we can't just magically obtain 4D thickness as soon as we step out, because we don't have any preset 4D shape that we would be given. There are many possibilities of the form we would be given if we would build up off of our form if we would somehow step into tetraspace, just like if you pulled a triangle out of planespace and it obtained tridth (I think that's the correct term), it could turn into a tetrahedron, or a cone, or a triangular prism, or a rectangular pyramid, or a pentagonal pyramid, etc.

I'm not saying this to try and spoil your fun, I'm just stating what I think on the matter.