Effects of going into a spherical portal in the human body
I'm working with a fiction idea where people use portals to get around. How these portals get made and where they go doesn't matter right now; I'm interested in the geometry of the whole thing, and how it would affect people going inside it, since that's not something I've seen explored, even in fiction that has spherical, 3D portals.
Basically, the portal is a sphere that exists in both ends at the same time, with the same size. Each point on one end of the portal corresponds to a given point on the other end, at the exact polar opposite of the sphere. So, say, assuming compass bearing means the same thing at both ends (I don't think that'd hold in the fictional universe, but just for the sake of explanation), if you walk into the south side of portal A, going northwards, you would go out the north side of portal B, still going northwards.
OK then. Now, considering the surface of the portal you're going into is a curve rather than a flat surface, how would it affect you to go through it? Thinking a bit about the geometry of it, I've come to the following conclusions. I don't really have much time to draw schematics now, might do it later if it's hard to visualize.
1) You'd go out the other way rotated 180 degrees, relative to the axis corresponding to the "normal" line of contact into the portal. So, if you just walk in while upright, you'd come out the other end upside down. If you go in horizontally belly-up, you'd come out horizontally belly-down. If you drop into the portal from above (what I think is probably the best option), you'd come out the other end still right-side up, only facing the opposite direction. Otherwise (and except for point 2 below), it wouldn't affect your general shape (e.g. you shouldn't be mirror-flipped or anything). However...
2) You'd suffer stretching forces, along the axis of movement into the portal, that would be stronger the further you get from the normal line of contact (or, alternatively, the more inclined you are relative to the surface). For that reason, you'd want the portal to be as large as possible, so its surface is effectively as close to flat as possible, and move into it while perpendicular to the sphere for the same reason, to minimize your contact surface. So, a portal that's about just as big as you can fit into might turn you into a red splotch on the other end, and would be a really bad idea (except, say, for just observing the other side, as light-waves and air particles wouldn't really be affected).
That's about it, from what I can picture. Can you get what I'm getting at? Is there anything I'm getting wrong? And can you think of any other consequences of going through that portal? Thanks!
Re: Effects of going into a spherical portal in the human body
I think I get what you're saying, and it sounds pretty cool. Some questions/considerations below.
Is momentum conserved when you pass through the portal?
If someone jumped up into the portal from below, they'd appear above it but (due to gravity) probably fall back into the portal and wind up where they started. Right?
(That isn't an objection or anything bad. An amusing side-effect, perhaps.)
The stretching forces sound neat. I'd think a lot of the tech would be focused on making portals safe for the intended purpose. E.g., maybe room-sized ones for human transport. But how big would you need to move a ship (space or nautical) without it tearing into scrap metal.
For a person entering, would entering via a diving motion (hands forward as if diving into a pool) negate most of the stretching pressure since, as the person is more of a point, the portal is more like a flat surface with respect to them?
I also wasn't clear on what you meant about air and light particles. Does air naturally move through the portal? Would a poison gas? Differentials in air pressure? (If no to air, what about liquids, such as a portal in or underwater?)
I could see some psuedo-science/supertech justification for only solids (or liquids/gases inside solid containers, like a human body or a metal cylinder) working through the portals. Stretches belief a touch, but not too bad.
If you want light to not pass through (which I guess would be necessary for the sphere to be visible as a sphere instead of just seeing the other world)... well, that seems easier to explain away even if air or water would pass through the portal.
EDIT: on air/water, I could see stating the the portal gives a certain amount of resistance. That resistance is enough that air and liquids at normal pressure don't pass through it, and I guess light bounces off it to make it visible.
Re: Effects of going into a spherical portal in the human body
Quote:
Originally Posted by
JeenLeen
I think I get what you're saying, and it sounds pretty cool. Some questions/considerations below.
Is momentum conserved when you pass through the portal?
I don't see why not. I mean, I guess it would be hard to go through otherwise.
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If someone jumped up into the portal from below, they'd appear above it but (due to gravity) probably fall back into the portal and wind up where they started. Right?
(That isn't an objection or anything bad. An amusing side-effect, perhaps.)
Yes, they would. So, for people going into the portal from below (which I can see happening in some situations), they'd probably be spooled in through a cable or something so they don't fall back in. I guess crossing the portal is hard enough on your body that you don't want it happening twice in quick succession :smalltongue:
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The stretching forces sound neat. I'd think a lot of the tech would be focused on making portals safe for the intended purpose. E.g., maybe room-sized ones for human transport. But how big would you need to move a ship (space or nautical) without it tearing into scrap metal.
I suppose that's more a question of materials strength than anything else. Well, that, and remembering that there are people inside the ship that might not like to be treated like silly putty. Either way, for any given macroscopic object (or person), I'm guessing you probably need a portal many times bigger than what's going through.
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For a person entering, would entering via a diving motion (hands forward as if diving into a pool) negate most of the stretching pressure since, as the person is more of a point, the portal is more like a flat surface with respect to them?
Yes, that's how I envision people entering the portal. Make yourself as close to a straight line perpendicular to the portal's surface as possible.
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I also wasn't clear on what you meant about air and light particles. Does air naturally move through the portal? Would a poison gas? Differentials in air pressure? (If no to air, what about liquids, such as a portal in or underwater?)
I could see some psuedo-science/supertech justification for only solids (or liquids/gases inside solid containers, like a human body or a metal cylinder) working through the portals. Stretches belief a touch, but not too bad.
If you want light to not pass through (which I guess would be necessary for the sphere to be visible as a sphere instead of just seeing the other world)... well, that seems easier to explain away even if air or water would pass through the portal.
No, the way I see it, the portal just means space continues seamlessly from one place to another. So air, light, water, and anything else would move through normally. Which is why pressure differentials are something significant to be taken into consideration, yes. The chamber where the portal is generated is carefully pressurized. Opening a portal into water or anything like that sounds like a bad idea. However, opening portals into deep space (after emptying the chamber into as hard a vacuum as possible) is not only feasible, but actually a staple of modern astronomy in this fictional universe :smallbiggrin:
Re: Effects of going into a spherical portal in the human body
Anything going through would end up quite a bit broken.
The contact lens shaped contact patch would be pushed inside out by the transition, which would have strange geometrical effects. Things on the tangent point would be moved 2*1-(cos(arcsin(ratio of object radius to sphere radius))) forward relative to the furthest parts of the object. If your sphere is 10 times the size of the object, the disruption would be 2.5% of the object's radius. If your sphere is only three times the object's size, 27%. Some rather in-depth googling gave me the figure that a femur can bend 3.75% before breaking (depending on the individual), so your sphere would need to be more than 5.2 times the maximum width of a passenger to keep from breaking their strongest bones.
If I was using it in a story, it would be less than a meter in diameter, and used for transmitting water, gasses and information, It would only be used as a means of transportation by the most desperate, or as an attempted murder weapon. The portal would leave extremely distinctive concentric cylindrical breaks and tears along axis of travel, looking almost like rings in a tree.
Re: Effects of going into a spherical portal in the human body
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Originally Posted by
SirKazum
No, the way I see it, the portal just means space continues seamlessly from one place to another. So air, light, water, and anything else would move through normally. Which is why pressure differentials are something significant to be taken into consideration, yes. The chamber where the portal is generated is carefully pressurized. Opening a portal into water or anything like that sounds like a bad idea. However, opening portals into deep space (after emptying the chamber into as hard a vacuum as possible) is not only feasible, but actually a staple of modern astronomy in this fictional universe :smallbiggrin:
So the portal isn't actually a visible thing (like the Stargate portal in Stargate), but a coterminous location. Is it "invisible" then, or just you see what is on the other side when you look at it, as light still passes through? That is, the portal as a portal is invisible, but you can (in most cases) detect it because what you see there isn't what is around the portal?
That sounds pretty consistent and cool.
Depending on how easy it is to generate portals, weaponizing them would be something to consider. One portal in space and another on a city street means a lot of destruction.
Re: Effects of going into a spherical portal in the human body
I'd lean towards "The portal is co-terminus with both spaces". So, if you enter the portal going north, and turn left in the middle, you'll come out the portal coming west. Because the portal exists in 3 dimensions (including all the other dimensions it travels through), your orientation on entering matters less the your orientation upon leaving. With a "flat" portal, you can only enter and leave, not reorient in the middle. With a sphere, you can. So, someone who dove through (with velocity and direction) would go straight through. Someone who stepped more slowly (and knew the portal was there) could reorient.
Re: Effects of going into a spherical portal in the human body
So what you're describing is called 3d point reflection.
Several thoughts:
- We can't actually enter the sphere. Once you hit the surface, you're reflected to to the surface of the other sphere, travelling out of it.
- It get's worse than mild stretching. A flat plane reflected and teleported through the sphere in this manner would be torn apart and wildly reshaped. When the center of the plan strikes the sphere's surface, it's teleported. As the plan travels further into the portal, the new portions are teleported even further back, warping the shape entirely. I suspect you'd want a sphere on the order of miles in diameter to avoid killing anything sent through it, maybe larger; it would be incredibly bad if the neurons in your brain were suddenly separated after being teleported 0.6mm apart. Here is an image I made of a 2d version of the sort of thing you're talking about.
- Because it's 3 dimensional, the point reflection does a little more than just rotate you. A 2 dimensional point reflection rotates you, but a 3d point reflection is like a planer reflection on top of a rotation around the normal of that plane. Reflections also caus weird problems because of chirality. Look at the first image I linked. Look at the left pyramid, imagine the red dot is the top, and purple dot is pointing north. Notice how the orange dot is to the west while the green dot is to the east? The opposite is true of the right pyramid. You can't super impose those reflections, they're geometrically different. Doing that to a human would cause weird problems, like your right arm suddenly being on your left side.
EDITED
DOUBLE EDIT
A more intuitive explanation of point 3 would be this: draw a dot on your left hand and go look at your reflections hands. The dot will be on your reflection's right hand, not the left.
TRIPLE EDIT
I think I'm actually wrong about the reflection. Because you don't actually enter the sphere, but teleport straight to the surface of the other portal, it's more like being rotated around the axis of your direction of movement and the projected onto the surface of a sphere.
Re: Effects of going into a spherical portal in the human body
Quote:
Originally Posted by
Spojaz
Anything going through would end up quite a bit broken.
The contact lens shaped contact patch would be pushed inside out by the transition, which would have strange geometrical effects. Things on the tangent point would be moved 2*1-(cos(arcsin(ratio of object radius to sphere radius))) forward relative to the furthest parts of the object. If your sphere is 10 times the size of the object, the disruption would be 2.5% of the object's radius. If your sphere is only three times the object's size, 27%. Some rather in-depth googling gave me the figure that a femur can bend 3.75% before breaking (depending on the individual), so your sphere would need to be more than 5.2 times the maximum width of a passenger to keep from breaking their strongest bones.
If I was using it in a story, it would be less than a meter in diameter, and used for transmitting water, gasses and information, It would only be used as a means of transportation by the most desperate, or as an attempted murder weapon. The portal would leave extremely distinctive concentric cylindrical breaks and tears along axis of travel, looking almost like rings in a tree.
Quote:
Originally Posted by
crayzz
So what you're describing is called
3d point reflection.
Several thoughts:
- We can't actually enter the sphere. Once you hit the surface, you're reflected to to the surface of the other sphere, travelling out of it.
- It get's worse than mild stretching. A flat plane reflected and teleported through the sphere in this manner would be torn apart and wildly reshaped. When the center of the plan strikes the sphere's surface, it's teleported. As the plan travels further into the portal, the new portions are teleported even further back, warping the shape entirely. I suspect you'd want a sphere on the order of miles in diameter to avoid killing anything sent through it, maybe larger; it would be incredibly bad if the neurons in your brain were suddenly separated after being teleported 0.6mm apart. Here is an image I made of a 2d version of the sort of thing you're talking about.
- Because it's 3 dimensional, the point reflection does a little more than just rotate you. A 2 dimensional point reflection rotates you, but a 3d point reflection is like a planer reflection on top of a rotation around the normal of that plane. Reflections also caus weird problems because of chirality. Look at the first image I linked. Look at the left pyramid, imagine the red dot is the top, and purple dot is pointing north. Notice how the orange dot is to the west while the green dot is to the east? The opposite is true of the right pyramid. You can't super impose those reflections, they're geometrically different. Doing that to a human would cause weird problems, like your right arm suddenly being on your left side.
EDITED
DOUBLE EDIT
A more intuitive explanation of point 3 would be this: draw a dot on your left hand and go look at your reflections hands. The dot will be on your reflection's right hand, not the left.
TRIPLE EDIT
I think I'm actually wrong about the reflection. Because you don't actually enter the sphere, but teleport straight to the surface of the other portal, it's more like being rotated around the axis of your direction of movement and the projected onto the surface of a sphere.
Thank you guys for the insightful analysis. Especially the formula governing the stretching. I'll have to take a look at it more in-depth later, but I imagine that, even with a rather large portal (like, house-sized), it's got to do some damage, especially to the nervous system. I was thinking that people would enter the portal at high speed to minimize exposure time, but that might be actually worse, as the rapid stretching might be physically traumatic.
And I hadn't given much thought to the physical appearance of the portal, but the fact that it doesn't really look like anything other than a distorted view into the other side might be an advantage in situations where it needs to be concealed, especially if a very large portal is in order (as seems to be the case).
Thanks a lot for the insight, folks!
Re: Effects of going into a spherical portal in the human body
If the portal is required to be the surface of a sphere, then I think a rigid object like a bone just wouldn't pass through unless the sphere was very large. It would be much more useful if the portal were faceted like a diamond. You could pass through a single facet, but not through an edge.
Re: Effects of going into a spherical portal in the human body
You would definitely get issues. Interestingly, probably not the ones you might think, and not quite as dangerous as you might think (though still pretty messy). Conservation of energy considerations would crop up. Basically, as people have said, changing the geometry will result in some pretty large stresses, and energy needs to come from somewhere to account for them. Imagine pushing a metal cube half way through. Symmetry arguments imply that the plane along the center of the cube will be warped to the surface, so the energy required will be the same as that required to distort 2 half cubes so that one side of each is flat to a sphere, which is quite a lot. Consider how difficult it would be to bend the a 10x10x5 cm block of steel by 1/10 of a mm. Forces come about because of energy gradients, and they will get very high. That means truly staggering forces are required to push rigid objects through the portals, which is both a bug and a feature. Getting stuff through it will be difficult, but it does mean that if somebody tries to put their head through a portal they would probably break their neck from the forces required before they shattered their skull, and they are unlikely to be able to get that much force. If they ran at it head first it would be no more dangerous than trying to go through a wall head first.
Where it gets to be very messy is if somebody manages to get partially through it. Rigid material would mean large energy gradients, and hence large forces, but most body tissue is not particularly rigid. It is entirely possible that a person could get stuck at a minima, where something like their knees are at the threshold, but their bones refuse to cross.
You could have the portals being 'smart' and introducing external forces to counter the ones that come about naturally from the stress gradients. That would get you back to casually pushing things through and them disintegrating from stresses as you do so if they are not pliable enough, but requires energy input and also introduces a whole host of interesting failure modes. If you are going to use them for brutal fiction this might be the type you would go with.
One nuance that might become important is that reducing the radius of the portal with a rigid body partially through will increase the stresses, and require more energy. Conversely, increasing the radius or reducing the curvature would be a source of energy. To get a real idea of what happens we need to know how much energy is invested in a given surface area of portal, and how it changes with shape. If not much energy is required per unit area of portal then the minimum energy solution might be that the surface of the portal moves to reduce it's curvature rather than significant stresses being applied at all. If the energy of a portal with a flat face 10x10 cm somewhere on it was only 100j more than a perfectly spherical one then a steel cube 10cm each side could go through if you threw it at it at >5m/s, without significant stresses on the cube. Instead of the cube deforming, the portal does using the kinetic energy from the cube (which slows to a crawl as it goes through, before being flicked out the other side as the portal returns to spherical). You might still have problems with materials like glass, that are very rigid but not very strong, but people should be fine, except in extreme osteoporosis cases.
TLDR: the 'shredding' problem can be resolved if the surface of the portal is more like the surface of a water droplet; naturally spherical but will deform to be flatter if required to avoid stresses.
Re: Effects of going into a spherical portal in the human body
Quote:
Originally Posted by
Fat Rooster
TLDR: the 'shredding' problem can be resolved if the surface of the portal is more like the surface of a water droplet; naturally spherical but will deform to be flatter if required to avoid stresses.
Hm. That's a very interesting thought. I always thought a hole across spacetime would be uniformly spherical because... I don't know, it just seemed obvious to me. But maybe a deforming portal might actually make more sense, at the very least because of how gravity interacts with spacetime (though it sounds like that should be a completely unnoticeable effect for, well, roughly people-sized things). Ah, what the hell, it sounds really cool to have it react to stuff crossing it. I'll give that some more thought.
Re: Effects of going into a spherical portal in the human body
Quote:
Originally Posted by
Fat Rooster
Spoiler: Spoilered to save space
Show
You would definitely get issues. Interestingly, probably not the ones you might think, and not quite as dangerous as you might think (though still pretty messy). Conservation of energy considerations would crop up. Basically, as people have said, changing the geometry will result in some pretty large stresses, and energy needs to come from somewhere to account for them. Imagine pushing a metal cube half way through. Symmetry arguments imply that the plane along the center of the cube will be warped to the surface, so the energy required will be the same as that required to distort 2 half cubes so that one side of each is flat to a sphere, which is quite a lot. Consider how difficult it would be to bend the a 10x10x5 cm block of steel by 1/10 of a mm. Forces come about because of energy gradients, and they will get very high. That means truly staggering forces are required to push rigid objects through the portals, which is both a bug and a feature. Getting stuff through it will be difficult, but it does mean that if somebody tries to put their head through a portal they would probably break their neck from the forces required before they shattered their skull, and they are unlikely to be able to get that much force. If they ran at it head first it would be no more dangerous than trying to go through a wall head first.
Where it gets to be very messy is if somebody manages to get partially through it. Rigid material would mean large energy gradients, and hence large forces, but most body tissue is not particularly rigid. It is entirely possible that a person could get stuck at a minima, where something like their knees are at the threshold, but their bones refuse to cross.
You could have the portals being 'smart' and introducing external forces to counter the ones that come about naturally from the stress gradients. That would get you back to casually pushing things through and them disintegrating from stresses as you do so if they are not pliable enough, but requires energy input and also introduces a whole host of interesting failure modes. If you are going to use them for brutal fiction this might be the type you would go with.
One nuance that might become important is that reducing the radius of the portal with a rigid body partially through will increase the stresses, and require more energy. Conversely, increasing the radius or reducing the curvature would be a source of energy. To get a real idea of what happens we need to know how much energy is invested in a given surface area of portal, and how it changes with shape. If not much energy is required per unit area of portal then the minimum energy solution might be that the surface of the portal moves to reduce it's curvature rather than significant stresses being applied at all. If the energy of a portal with a flat face 10x10 cm somewhere on it was only 100j more than a perfectly spherical one then a steel cube 10cm each side could go through if you threw it at it at >5m/s, without significant stresses on the cube. Instead of the cube deforming, the portal does using the kinetic energy from the cube (which slows to a crawl as it goes through, before being flicked out the other side as the portal returns to spherical). You might still have problems with materials like glass, that are very rigid but not very strong, but people should be fine, except in extreme osteoporosis cases.
TLDR: the 'shredding' problem can be resolved if the surface of the portal is more like the surface of a water droplet; naturally spherical but will deform to be flatter if required to avoid stresses.
I love this idea - it both solves the object destruction problem end evokes beautiful imagery with big waves and small ripples going around the portal when an objects goes through. If I get the chance to run some fantasy or SF games I will totally steal this idea.
To add something else to the thread: how would those portals behave when they are created? Essentially while being spherical, they do not have an inside in any practical sense. I would imagine the portal when created starts from a point and grows pushing everything away. If both ends are in the air, then there is nothing interesting happening, but put one end inside a rock and the other end starts spitting stone while it grows.
Re: Effects of going into a spherical portal in the human body
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Originally Posted by
Radar
To add something else to the thread: how would those portals behave when they are created? Essentially while being spherical, they do not have an inside in any practical sense. I would imagine the portal when created starts from a point and grows pushing everything away. If both ends are in the air, then there is nothing interesting happening, but put one end inside a rock and the other end starts spitting stone while it grows.
Yeah, pretty much this. The portal starts out subatomic (essentially point-like, or as much as quantum physics might allow anyway), and then is grown up to its desired size, shunting whatever's caught on its surface to the other side as it grows. Stuff (hopefully just air molecules, but who knows) would cross back and forth repeatedly as the portal catches up to it during growth stage.
As for the inside of the portal, as I understand it, it literally does not exist anywhere at all. The portal is just a continuity between two regions of spacetime. The sphere-shaped region that should be inside of it is just something like a defect on the structure of spacetime that exists as long as the portal does. There is no space there, so any question along the lines of "what does it look like in there" has no possible answer at all.
Re: Effects of going into a spherical portal in the human body
Quote:
Originally Posted by
JeenLeen
So the portal isn't actually a visible thing (like the Stargate portal in Stargate), but a coterminous location. Is it "invisible" then, or just you see what is on the other side when you look at it, as light still passes through? That is, the portal as a portal is invisible, but you can (in most cases) detect it because what you see there isn't what is around the portal?
That sounds pretty consistent and cool.
Depending on how easy it is to generate portals, weaponizing them would be something to consider. One portal in space and another on a city street means a lot of destruction.
It would probably look somethig like this, according to wikipedia
I'm pretty sure what he's describing is a wormhole
Also, if this is the case the angle you enter from affects whether your direction gets flipped*, as made more clear by this diagram with the space around it bent so that the einstein-rosen bridge can be shown straight
Imagine how the green arrow would change for different angles of approach. As you can see, if you approach from the side you wind up heading back the way you came. If you approach from between the ends you end up in a loop. And if you approach from the far end (as in the diagram) you bypass the intervening area between the two mouths.
*I think. Provided that the addition of a third dimension doesn;t change the behavior shown in the diagram in some non-obvious way.
Re: Effects of going into a spherical portal in the human body
Quote:
Originally Posted by
SirKazum
Hm. That's a very interesting thought. I always thought a hole across spacetime would be uniformly spherical because... I don't know, it just seemed obvious to me. But maybe a deforming portal might actually make more sense, at the very least because of how gravity interacts with spacetime (though it sounds like that should be a completely unnoticeable effect for, well, roughly people-sized things). Ah, what the hell, it sounds really cool to have it react to stuff crossing it. I'll give that some more thought.
Symmetry arguments have a lot going for them, and they point to spherical. Spheres turn up a lot in cosmology for a reason, so your intuition is pretty solid. The idea that a portal would be something that you could push is not particularly natural, given that the whole point is that you go through it, but it does work out well.
Gravity might be a bit of a stumbling block (or opportunity), if you want very hard sci-fi. Portals across the surface of the earth would be fine, as the energy requirements would be pretty small, but the difference in energy between an object being on earth and at pluto is considerable. That energy has to come from somewhere. The easiest solution in my mind is to draw the energy from the portal, resulting in it's rapid contraction (and subsequent problems from high curvature making progress require large forces). The machinery in charge of maintaining the portal then immediately pumps the required energy back into the portal, maintaining it's size.
Velocity behaves pretty similarly, though at this point I think you need to be talking about more advanced relativity than I know.
Where this becomes an opportunity is that you can use changing gravitational potential as a powerful energy source. Imagine two stars orbiting each other but in an eccentric orbit. They spend some time close together, then far apart, and so on. An object at their mutual center of mass will just sit there, but will alternate between being close to 2 stars and far from them. If we have a portal at this point, and we pile lots of stuff to this point when the stars are close it will be like moving stuff from pluto to earth, liberating a huge amount of energy. The gravity of this stuff will slow the stars slightly as they move away, drawing energy from their orbit. When the stars are far apart moving stuff out of the portal will be like moving stuff from pluto to pluto. When the stars come back in, this stuff not being there will mean they don't accelerate down the same way they were decelerated going out, and we have harvested energy from their orbit.
Other conservation laws might start to bite, though I don't know exactly how. Again more advanced relativity than I am capable of.
Quote:
Originally Posted by
Bohandas
It would probably look somethig like this, according to wikipedia
*I think. Provided that the addition of a third dimension doesn;t change the behavior shown in the diagram in some non-obvious way.
That image implies that there is a more gradual bending than the OP is suggesting. You can see that light is bent that does not go through the portal, which would not happen given the proposed effect occurs strictly at the surface. It is a wormhole, but curvature is much less smooth than standard.
The distortion works out exactly the same as if you are considering refection on a sphere, only it is 'reflecting' the other side. It would look like a really weird marble.
A third dimension fixes the flipping problem that the direction change is required for in 2 dimensions, as objects passing through are reflected in 2 axis (rather than 1 in the 2D case), maintaining handedness. You would maintain direction of travel, but be rotated through 180' in that axis. OP already caught that one. :smalltongue:
