Seems 2d but is 3d

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Seems 2d but is 3d

Postby anderscolingustafson » Sat Mar 29, 2014 9:56 pm

I was just thinking if there was a conscious life form that had a length of about 3m and a width of about 50cm but it was only one cell tall then only 2 of the 3 dimensions would be available for signals to travel through the nervous system as each neuron would only have neighbors along the width and length but not the height so even though the life form would be 3d it would only be able to tell that it had two dimensions and so it would feel 2d. While in order to be truly 2d an organism would need to have 0 size in one of the three dimensions an organism could feel 3d so long as one of its dimensions was equal to or less than the size of the individual units of its brain. If there were an organism that was 3d but its height was only one cell thick then looking at the macroscopic level the organism would look 2d as its 3rd dimension would be too small to be seen with the naked eye but when looking under the microscope it would be possible to see all of its 3 dimensions.
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Re: Seems 2d but is 3d

Postby quickfur » Sat Mar 29, 2014 10:18 pm

This is basically the underlying premise of string theory. I wrote about this here (it's in the last 4 paragraphs).
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Re: Seems 2d but is 3d

Postby ICN5D » Sat Mar 29, 2014 10:35 pm

That's kinda sorta how we perceive the surface of the earth. Without aircraft, of course, we are stuck to the ground. There are still 3 dimensions, but we can only use 2 of them on the grand scale of long distance travel. Same even goes for time as our 4th degree of freedom. We can meet someone at east 21st street and second avenue on the 11th floor, but that's still not enough information. We need to address when to meet them. But, of course, we cannot walk backwards through time, we just have to wait for the cycle to repeat. These two unusable dimensions are passively guiding us, where we still have control with the coordinates, be it climbing a mountain, or waiting in the same place for a while. But, we cannot fly or go back to the past.

SCUBA diving is a neat experience for us land dwellers, especially when you get down to 80 or 90 feet. There is so much water around you, it tends to blend in with your surroundings and you lose sense of it. It becomes your natural medium that you move and dwell in. Spending even 30-45 minutes down there retrains your instinctual movements into 3D thinking. For once you can actually "fly" up to that giant propeller, or hover above the ground at will. Going even deeper, you cannot see the surface, so it becomes a kind of outer space. One of the cooler dives I did was a "blue water" dive, where we went out to 1,000 feet deep, and went down only 60 or so. We tied ropes off to our tanks, so we could hang there above the vast emptiness below. Looking straight down, all you saw was this incredible deep violet color, not blue. And, all the neat little pelagic creatures pulsing by.
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Re: Seems 2d but is 3d

Postby ICN5D » Sat Mar 29, 2014 10:37 pm

quickfur wrote:This is basically the underlying premise of string theory. I wrote about this here (it's in the last 4 paragraphs).


Yep, we're supposed to be higher dimensional, but we only perceive our 3 extended directions. The garden hose universe!
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Re: Seems 2d but is 3d

Postby quickfur » Sat Mar 29, 2014 10:59 pm

It's interesting that when navigating in full 3D (e.g., scuba diving, or playing games like Descent), it's very easy to lose track of where you are unless you maintain a single unchanging axis, such as the vertical axis. Gravity provides the most natural reference in this regard. But remove that, and suddenly you're confronted with the full freedom of 3D, with 3 spatial dimensions to fly through, and 24 possible orientations while you're flying through it. :P Most people lose their sense of direction when this happens -- I know I do.

This is probably why I have a lot of trouble actually navigating in 4D -- the ground is fully 3D, so after a while I lose track of my orientation (even while maintaining a constant 4D vertical direction!), and all the (3D ground) directions become jumbled up to me, and I get completely lost. Visualizing 4D objects while standing still in one spot, with a fixed target object, is one thing, but really "seeing" 4D when moving around (like in John McIntosh's excellent 4D Blocks game), is a whole 'nother can o' fish. It will challenge how much you actually have a grasp on 3D (not even to speak of full 4D without a fixed vertical axis -- 192 orientations you can be in :lol:).
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Re: Seems 2d but is 3d

Postby ICN5D » Sun Mar 30, 2014 3:45 am

Hmm, what are these 24 orientations you speak of? Are they different combinations of facing directions plus moving directions, plus inverted orientations?
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Re: Seems 2d but is 3d

Postby anderscolingustafson » Sun Mar 30, 2014 4:08 am

I was thinking about a situation in which there are two see through slabs that are only 1mm apart and some top soil is put between the slabs with and then some plant seeds are planted in the soil between the slabs and some insect eggs are put between the slabs. What I wonder is how having only 1mm to grow in one of the three dimensions would effect plant growth and how it might effect the growth of insects. If the seed of a large tree was planted between two slabs that were 1mm apart so that it had only 1mm to grow in one of the three dimensions but plenty of space to grow in the other two dimensions how might the tree grow? Would a butterfly be able to function and survive if from the moment it hatched as a caterpillar it only had 1mm to grow in one of the three dimensions but all the space it needed to grow in the other two spatial dimensions and if so how might it grow?
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Re: Seems 2d but is 3d

Postby quickfur » Sun Mar 30, 2014 4:15 am

ICN5D wrote:Hmm, what are these 24 orientations you speak of? Are they different combinations of facing directions plus moving directions, plus inverted orientations?

Consider yourself standing upright somewhere in 3D space, with your arms stretched out sideways. There are a couple of vectors that determine your position: (1) which direction you're facing (the front vector), (2) which direction your feet are pointing (the down vector), (3) which direction your head is pointing (the up vector), (4) the direction your back faces (the back vector), (5) the direction your left arm is pointing, and (6) the direction your right arm is pointing. These 6 directions may be mapped to the 6 faces of a cube, or equivalently, the 6 vertices of an octahedron. You could, for example, label the vertices of the octahedron as F, D, U, B, L, R in the respective order of the above vectors. Now the question is, how many ways can you orient an octahedron in space? This is equivalent to the number of (primary) orientations you can have in space.

For example, if you spin the octahedron around the L-R axis, you'll find 4 orientations, where you face forward, up, back, or down, but your arms remain pointing in the same directions. You can also spin the octahedron around the U-D axis, where you'll find that you face forward, left, back, right, with your arms changing from L-R to B-F to R-L to F-B (then back to L-R), but your head and feet continue pointing the same way. Each of these represents a distinct orientation of your body in 3D space. There are many other such combinations, which, if you work it out, corresponds with the rotational symmetries of the octahedron (equivalently, the cube), which we know are 24 in number. Note that all of these are distinct orientations without changing your location in 3D -- you're just spinning in-place.

So, to fully specify your configuration in 3D space, you require first a 3-vector that specifies your position, then you have to specify in which of these 24 orientations your body is. Of course, these 24 orientations represent the 24 principal orientations in 3D; it doesn't include combinations like rotating 45° to your left, then spinning 72° up, etc.. So you see, 3D isn't quite a simple as you may have thought. :D

Of course, in real-life we usually don't think of these 24 orientations, because gravity for the most part confines us to a fixed up/down direction, so that fixes the U/D vectors to 1 out of 6 possible directions, which effectively divides the 24 orientations by 6, resulting in the 4 familiar directions forward, backward, left, and right. These directions correspond to the 4 orientations of a square in 2D, which reflects how our floor is essentially a 2D surface.

Now in 4D, the floor becomes 3D, so there are 24 orientations you can have just by standing in one spot on the ground! We find this confusing, because in 2D, the 4 orientations are in a 1-to-1 relationship with the facing direction, so we are used to thinking that our orientation on the floor is equal to which direction we're facing. This is no longer true in 4D, because of the 3D floor! In fact, if we're floating in 3D space, then we'll realize that we can actually be in 4 different orientations without changing which way we're facing: to see this, consider looking straight forward, but your legs could be pointing down, up, left, or right. In 4D, therefore, while standing on the same spot on the ground, there are 24 possible orientations, divided into 6 groups of 4, each group of which represents one facing direction. So even while facing the same direction in 4D (and keeping your head pointing up and feet on the floor), you still have 4 distinct orientations you can be in. Or, put another way, you can spin your body around in 4D while standing on the same spot, and facing the same direction, without changing the latter. :)

Now, this is just when you maintain an upright orientation in 4D... if you're floating through 4D space, then suddenly you discover that you have a lot more distinct orientations, because now your up/down direction can point in any of the 8 directions of the tesseract, and each of these directions have 24 orientations as I described above. Which means there are a total of 24*8 = 192 possible orientations. :lol: (Which means that if you're walking around in 5D, you'll have to keep track of 192 different orientations you could be in! And if you're floating around in 5D space, then it's a whopping 1920 possible orientations. :mrgreen: )
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Re: Seems 2d but is 3d

Postby Hugh » Tue Apr 01, 2014 2:06 am

quickfur wrote:So even while facing the same direction in 4D (and keeping your head pointing up and feet on the floor), you still have 4 distinct orientations you can be in. Or, put another way, you can spin your body around in 4D while standing on the same spot, and facing the same direction, without changing the latter. :)

Thanks quickfur! This relates directly to the Visual Reorientation Illusion experience that people have!

I'm going to quote it in my VRI thread http://hddb.teamikaria.com/forum/viewtopic.php?t=401 and talk more about it there. Thanks again!

P.S. For me this quote is like "seems 3d but is 4d" :)
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