I'm here to talk about 3D vision.
"3D" = 3 dimensions: an ordinary picture has height and width, but real life, and 3D pictures and movies, also have depth.
When you see a picture, you can show depth.
I've shown some depth here, and you know that some things are supposed to be farther away than others in the picture. In general, your brain tries to make sense of what you see, and it uses all kinds of clues in a picture to figure out how far back or how far forward different things in the picture are. But even so, this doesn't really pop out at you the way a 3D movie does, does it? Nevertheless, sometimes your brain keys off of the visual clues and assumes things about a scene in ways that interact with the pop-out effect.
As you play with the viewmasters, notice the 3D pop-out effect. Has everyone here experienced that "pop-out" effect at some time in their lives? You get it in real life all the time, and through special movies or viewmasters. Your ability to get the pop-out effect is almost like being able to smell or taste or see colors - it is almost like a whole sense modality in itself. But how does your visual system, your eyes and brain, do this? If you look at an ordinary picture of a car in front of some trees, you just sort of know that the car is closer than the trees, but you don't get the pop-out effect. Moreover, you can get the pop-out effect even with images that are purely abstract and don't give you any clues from their subject matter about what objects "should" be in front or in back of other objects. So it isn't just a case of knowing that parts of the picture are in front of other parts.
With color, the photons of light actually have different wavelengths, and your retinas detect this, and your consciousness interprets these differences as "colors". What is it in the physical world that your eyes and brain can detect that gives rise to this pop-out effect?
Here is a wrong story about that. What if, when light reflects off something and heads toward your eye, it ages along the way, so that your eyes can detect that some light is staler than other light. The fresher light would be interpreted by your brain as coming from closer things, and the staler light if reflected from things that are farther away. Now this is not at all what is going on here, but what is it about the light that clues your brain and/or eyes into creating this pop-out effect?
Here is a clue: notice that the effect goes away when you close one eye. Try it with the viewmaster.
The short answer is that your brain is amazing. We don't have two eyes just so one eye can be the backup eye in case we lose the other one. Because your eyes are set some distance apart on your face, each eye has a slightly different view of the world, and your brain uses the differences between the two images to figure out how far away the things you are looking at are, and it uses this information to put the two images together into one single image with the impression of depth built into it. Being able to see with two eyes like this is called binocular vision from "bi" meaning two, as in bicycle, and "oculus", meaning eye.
Try this right now. Hold your arm out in front of you while holding a pencil, and look at me. Make it so the pencil is right in front of me. Now close one eye. Where exactly does the pencil end up relative to me? Now open that eye and close the other one. Now where is the pencil relative to me? See how it jumps around as you switch eye to eye? OK, now bend your elbow and bring the pencil in closer to your face and do the same experiment. Besides being bigger in your field of vision, the pencil jumps a lot more from side to side as you switch eyes. So here is the main thing: things that are closer to you are more shifted from side to side in the separate images that your eyes send to your brain, and things that are farther away are less shifted. The closer something is to you, the more different it is in the two images your brain receives from each of your eyes.
Looking at this diagram, you can see that the left eye sees the back object to the left a little bit, while the right eye sees the back object a little to the right.
Objects that are closer are shifted to the left in your right eye's view (relative to the background) and shifted to the right in your left eye's view (relative to the background). In other words, from each eye's point of view, closer objects are shifted toward the other eye relative to the background. They are squeezed inward, toward your nose.
In still other words, objects that are farther away are seen by the left eye as being shifted to the left (relative to the foreground), and are seen by the right eye as being shifted to the right (relative to the foreground). So things that are farther away are shifted, in each eye's view, away from the other eye, that is, each eye sees background objects as pushed away, out, toward the periphery of you field of vision.
This way in which nearby objects appear to be displaced relative to their backgrounds by your two eyes is called the parallax effect, and it is the basis for 3D vision.
Notice that the viewmaster disks have 14 cels in them, for a total of only seven pictures. That is because for each picture, there is a separate left and right image.
Over a century ago, in the Victorian era, devices such as this were extremely popular.
Every parlor had one, and thousands and thousands of stereo slides were sold. The 3D effect was discovered in 1838 by an Englishman named Charles Wheatstone. He is the first one to figure out how the mind puts the two images from the eyes together to create the impression of depth. The device I just handed out, however, was invented by Oliver Wendell Holmes, an American.
The trick with the OWH viewer and the viewmaster is that it shows you a slightly different image to each eye. If you look closely at the OWH slides, you can see this. look at the edge of an object in the foreground, and see where it intersects with the background in each of the two images (Like where a person's head meets clouds in the sky behind). You will see that in the left image it doesn't line up in exactly the same way that it does in the right image. You can see the same thing with the viewmaster if you look through it and close one eye then the other.
Look at these with the viewer, and then without it. See the pop-out effect? See how the apparent nearness of things in the images correlates to the amount by which they are offset in the two images?
Now based on this, what can we guess about how these images were created? If you were walking in Boston and you saw a person taking pictures for a viewmaster or a OWH viewer, what about him or her or the equipment would tell you right away that that is what they were doing, that would be different from ordinary photography? How could we take such pictures?
There must be two images, offset from each other just as the human eyes are. So they make special cameras with two lenses, and two shutters, really two entire cameras but with one button so that the shutters click simultaneously.
Some people are very into this kind of photography as a hobby, and collect these cameras. They aren't made much anymore, so the old ones are prized by collectors and enthusiasts. There are lots of web sites dedicated to this with tutorials and galleries of peoples' work.
Now I made some of the slides I've passed around myself, without one of those fancy cameras. I did it with a cheap, easily constructed rig.
You have to push the buttons at exactly the same time, especially if anything in the frame is moving. And some care has to be taken in cropping and mounting. And even cheaper and easier way of taking such pictures is the so-called cha-cha method.
Note that when I shifted my position between shots, I shifted more than the distance between a normal person's eyes.
The 3D effect would be exaggerated: the difference between the two images would be greater than it "should" be, and things that were nearer would seem even nearer than they are. This ends up making scenes of streets, for example, look like models.
Do you see how the 3D effect goes away when you look at the slide where the images are the same with the viewer? And how the effect is exaggerated when you view the image where the foreground and background images are displaced more from each other in the left and right images? Look at the three slides (same, different, more different) without the viewer and see the differences (or lack thereof) between the left and right images.
So the main thing about 3D vision is that each eye sees a different image, each from a slightly different perspective. With the viewmaster and the OWH viewer, we had two entire images side by side, and the device showed the left one to the left eye and the right one to the right eye.
All the other techniques that give us the 3D effect are just tricky ways of delivering one image to one eye and a different image to the other eye.
Main take-home messages:
If you look at the world through a green lens, green things disappear, and when you look at the world through a red lens, red things disappear.
To achieve the 3D effect, you put take your two images (one for the left eye and one for the right), and you make one of them red, and the other cyan, and put them right on top of each other. When you put on the glasses, the eye with the cyan lens only sees the red image (which appears black) and the cyan image disappears, while the eye with the red lens only sees the cyan image (which appears black to it) and the red image disappears. Your brain gets the two different (black) images and puts them together as before. The drawback is that you only perceive a black image, so you are limited to black and white pictures.
A 3D image produced in this way is called an anaglyph image.
These are called phantograms and they combine two illusions in one. First, they are red/cyan anaglyphs, but they also play games with perspective so that when you view the image from about a 45 degree angle, the stretching of the image on the page combined with the 3D effect combines to create a 3D image that seems to rise up off the page.
Draw or write on the pads with an ordinary pen, and look at the result with the red/cyan glasses on. Do you see the pop-out effect? Your writing appears to float above the page.
The grid is the background, and there are two grids, one in red and the other in cyan, slightly offset from one another. With the glasses on, you see your writing on a black grid with one eye, and on what your brain thinks is the same black grid with the other eye, but the writing is shifted a little relative to the grid. Your brain puts this together and assumes that the writing is some distance closer to you than the black grid in the background.
Another way of tricking your brain into interpreting something as 3D without the binocular parallax effect is through motion parallax, or wigglegrams. The term "wigglegram" is not a real word (yet) in the dictionary, since the phenomenon has only recently been invented. You all know what an animated GIF is? When you have a digital image on a computer, the image itself is stored as rows and columns of pixels. Some image formats allow for multiple frames all stored in the same file, and when displayed, the frames are shown in sequence with a delay, so you see an endless loop of animation.
If you make an animated GIF in which the frames alternate between a left eye image and a right eye image, even though both eyes see the animated GIF at the same time, it will seem 3D, as if you were rapidly moving yourself side-to-side while viewing. Such animated GIFs used to simulate 3D are called wigglegrams. Some people even take old stereograms and turn them into wigglegrams.
I want to show you an example of a sort-of 3D effect that has nothing to do with the parallax effect. This is a good example of how your brain will try to see things as 3D even without really doing the pop-out thing. There are situations in which your brain supplies the 3D effect even though both eyes are seeing the same image. You don't just go by the parallax effect and the differences between the images seen by your two eyes to interpret things as poking in or out. Your brain will try to interpret things as best it can in the absence of clues. Sometimes this will fight against the parallax pop-out effect, and sometimes it will enhance it. Stare at this for a while, like a minute.
Did you think of it, and thus see it, as oriented one way, then after a bit it suddenly flipped the other way? No actual parallax 3D effect, both eyes see the same image, but your brain insists on overriding the lack of 3D and imparting a 3D interpretation anyway, even flipping between mutually contradictory interpretations.
Each picture in the book is animated. As you know, animation works by showing you different images, one after the other, quickly, like a movie or a flip-book. Let's say you had a movie of me throwing a frisbee, and there were six different snapshots of me, A-F, as I go through that motion. If you put them in a flip book and flipped the pages, you would have a very short animation of me throwing the frisbee. But for this book, what Rufus Seder did is he sliced each shot up vertically, and took one thin strip from A, then one thin strip from B, and so on, and after he had thin strips from A-F, start over with another thin strip from A. In this way, all six shots are interleaved. Then, if you slide a mask over the whole thing that only shows you each sixth vertical strip at a time, you first see only the strips that make up shot A, then only those that make up B, etc. and you seem to see motion. The drawback is that for six shots, five sixths of the image is blacked out at any time. This gives the impression of watching a horse through a thick grating.
So this kind of thing lets us see different images depending on where the mask is as we slide it over the page. We can use this technique to achieve a 3D effect if we use only two images, one left eye image and one right eye image, and we raise the mask a little bit off the page so that each eye sees the correct image. This is tricky in that you really have to have your head positioned just right to view it properly and get the pop-out effect.
How does this work? This is an example of what is called lenticular printing. It works in a way similar to the way the images in "Gallop!" work, but with an improvement. There are still multiple images, cut into vertical slices. But instead of masking off all the slices except for those belonging to one frame and leaving them blacked out, you put a series of long lenses (called lenticules) over the whole thing. Then, depending on what where your eye is, the lenticules will pick up and magnify all the slices from just one frame and you will see only that image. Then if you move your head a little, the lenticules will pick up and magnify all the slices from a different frame.
Rufus Seder, who did "Gallop!", also creates huge public murals with lenticular glass tiles over them, so that you see scenes in motion as you walk by on the sidewalk.
However, you can arrange the images so that if you look at the lenticular picture straight on, one eye gets one image and the other eye gets the other image - and that, remember, is what you need to achieve the 3D effect.
Can everyone cross their eyes? OK. Look at these shapes and cross your eyes. Can you make yourself see four shapes? Then as you cross your eyes even more, the two in the middle get closer together, until they overlap and you can see three shapes. The one in the middle is the overlap shape, red square and green triangle together. Try to focus on that middle shape.
This middle overlap shape is made of the image of the left red square as seen by the right eye and the right green triangle as seen by the left eye. If you stare enough at the middle overlap shape, your brain will try to put it together into a single image. You can use this to achieve a 3D effect if you put the left eye image to the right and the right eye image to the left and view them through crossed eyes.
The middle overlapped image is made of the two images, left and right, merged together by your brain into one 3D image.
Most stereo images are of more or less familiar scenes, or at least scenes that contain familiar elements. So your brain could be picking up on clues in the context to decide what to pop out or pop in. Now take a look at this:
In the 1950's, the random dot stereogram was invented: a scene of completely random dots with no context or pattern whatsoever. The right and left image are different, however. In one, a section has been shifted in such a way as to achieve the parallax effect, and you should see a shape stand out from the background. There are no trees or cars or people to clue you in as to what should be in front or in back, so we have proof that your brain can do this trick purely using the parallax effect.
This effect was commercialized quite successfully in the 1990s with the "Magic Eye" books and posters. These consisted of Autostereograms like this one:
What you do is try to stare through the image as if you were focusing on the distance beyond the poster. It can be hard to do. Some people (like me, for instance) find it easier to cross their eyes, as before with the cross-eye 3D effect, resulting in the 3D going the wrong way. What you want is the so-called walleye effect, not eyes crossed. You see that there is a repeating pattern here - what you want is to trick your eyes into seeing two different versions of the pattern, but putting them together as if they were the same one. Then the tiny variations between the two versions of the same pattern get interpreted by the brain as the parallax effect, and a 3D image emerges.
Christopher Tyler, the guy who invented these autostereograms, that do not require the use of a stereoscope, had worked with Bela Julesz, the guy who, decades before, had invented the random dot stereogram. There was a time when these posters were in every dorm room in every college around. There were best-selling books of these things.
Sometimes you can be confused for a moment as you accidentally try to do the autostereogram effect on some repeating pattern, like a window screen, or a repeating pattern of holes over a speaker or something. It takes a moment to focus and line the right holes up with each other in both eyes.
Now what about "The Hobbit" and other 3D movies? You have to wear special glasses, like these
As we know, the 3D effect depends on showing one image to one eye and a different image to the other eye, but how do the glasses help accomplish that?
First, we know the movie must be shot with special movie cameras with two lenses, like the still photo 3D cameras.
To understand how this works, we will have to talk about polarization.
To be perfectly honest, I don't understand polarization completely myself, but it kind of works like this: you may know that light may be thought of as a wave (note: "may be thought of"). As it turns out, this wave can have a certain flatness, or two dimensional character.
As the wave travels, in addition to going in a certain direction, it can be oriented this way, or that way (rotate the wave).
A polarizing lens can only let light in that is oriented the right way, like this cooling rack
If the light strikes the lens, it will pass through only if the lens is lined up with the orientation of the light wave.
Most light from regular sources like the sun or lamps around the house scatter light in all directions, with all orientations.
It won't get through if the lens is oriented "wrong", but only if it were oriented "right". So what if you were wearing glasses with polarized lenses in such a situation?
Everything would go dark if your head were tipped one way, and light if you tipped your head the other way (90 degrees off).
What if you had two polarized lenses?
If they are lined up, they are just like a single polarized lens, but if their polarizations are at right angles, they block all light.
As I said, most light in our environment is messy light, polarized every which way, but certain sources of light are polarized. Many kinds of reflections, for instance, especially light reflected at an angle off a surface that is not mirrorlike, like a road. Much glare is polarized, which is why polarized sunglasses are so popular for driving. It is not so much that they dim the light and make it darker, but they cut down on the glare. As you get the polarized lenses passed to you, take one and look around the room and rotate it and see if any reflections get cut out.
Also, LCD displays on calculators, watches, and computer monitors are polarized and will disappear if you look at them through a polarized lens the "wrong" way.
So how does polarization help us see "The Hobbit"? 3D movies in the old days used two projectors, one for each eye's movie, and one had a polarizing filter going one way, and the other had a polarizing filter offset 90 degrees from the first one. You would wear glasses with polarized lenses like the ones I passed out, with the left eye's lens oriented to completely block the right image and let the left image in, and the right eye's lens oriented to completely block the left image and let the right image in. The problem is that you had to keep your head perfectly level for it to work.
There was another interesting problem these movies had. As a film gets passed from movie theater to movie theater, it gets banged up, and it is a perfectly normal thing for projectionists to have to cut frames out and splice films together. You ordinarily don't even notice, maybe a tiny jump from time to time. But with the old 3D movies, there were two entire films: the right eye film and the left eye film. If they were out of sync, even a little bit, the film was pretty unwatchable - headaches, that kind of thing. So any frames cut from one film had to be matched by cutting exactly the corresponding frame from the other one.
Also, since movie screens reflect a lot of light but not like a mirror, they tend to scatter it, destroying the nice consistent polarization needed for the 3D effect. So there must be special screens that will preserve the polarization as the light from the projector is reflected off the screen and into your eyes.
Besides the polarization along an axis, like the wire cooling racks, there is circular, or spiral polarization. Think of the light wave not like a 2D wave, but a corkscrew. It can twist to the left or to the right. You can have a lens that will block left handed spiral polarization or a lens that will block the right handed polarization. That way you can tilt your head and still have the glasses work perfectly. Newer technology has also solved the problem of the inconvenience of two separate films and two simultaneous projectors. "The Hobbit" was one one single film, with right eye images alternating with left eye images in quick succession. There was an electronically controlled spiral polarizer on the lens of the projector that switched back and forth many times per second between left hand and right hand spiral polarization, in sync with the frames being projected so that the right eye frames got polarized one way and the left eye frames got polarized the other way.
Real 3D, the technique used in today's 3D movies.
A mirror will reverse spiral polarization.
When you look in a mirror wearing the glasses and close one eye, then the other, the open eye can't see itself (the glass is opaque) but it can see the closed eye. The light from the skin around your open eye passes through the lens with polarization A, gets reversed to B by the mirror, and is screened by the A lens. But the light from the skin around your other (closed) eye, polarized by its lens to to B, gets reversed to A by the mirror, and gets through the A lens to your open eye.
When they shoot a live action movie in 3D, they must use special cameras with two lenses, effectively shooting two movies at once: one for the right eye and one for the left eye. But for a digital cartoon, there is no camera. The scene being "shot" exists in the computer, in a big data structure they call a "model". The computer "knows" about this scene from all angles, and the film makers get to decide what angle they want the actual shot that goes on the final film to be from. The camera is imaginary, and they get to decide where they want the camera to seem to be. So it is pretty easy for them to take the same scene and generate a left eye version, then change the "camera" angle a little bit and generate a right eye version. This is how they were able to create a 3D version of the original "Toy Story", even though it was not originally in 3D. They still had the old computer data that generated that movie hanging around, and they just got it to print out from a different angle.
BTW: the TV ad for that had Buzz Lightyear looking through the Real 3D glasses and saying how wonderful the 3D was, but he was toy-sized and the glasses were full human sized, so he was only looking through one lens. It made for a cute ad, but he would not have actually gotten any 3D effect that way, would he?
Another way of achieving 3D in TVs or video games is called alternate frame sequencing. Instead of having an electronically controlled polarizer polarizing each alternate image in opposite ways, you just show the images unpolarized, alternating right eye image, left eye image, very quickly. That is, each lens is electronically rendered completely opaque, alternately, in quick succession. The viewer then wears glasses that have an LCD shutter on them that actually blacks out each eye alternately in perfect sync with the images being shown so that the left eye is blocked when a right image is being shown and the right eye is blocked when a left image is being shown. Of course the glasses must be able to react very quickly, completely blacking out then going completely clear many times each second.
As you may imagine, with both the "The Hobbit" style using polarization and alternate frame sequencing, since each eye only sees half of the images being shown, the film has to show at least twice as many frames per second as it normally would in order to not flicker noticeably.
Look at this artwork with the Chromadepth glasses on, and note that it gives you a 3D effect.
Recall that the pop-out 3D effect relies on showing each eye a different image, and we have seen a bunch of clever ways of doing that. How do these glasses do it? There is only one image here, and there is nothing particularly special about it - it has not been prepared or created in any special way like the red/cyan anaglyph was, or the lenticular cards were. It is just an ordinary image. The trick is all in the glasses themselves.
People like to say that it breaks light apart, but I don't like that terminology, because the light was never one thing to begin with. It was never "broken". White light, rather, is a jumble of lots of colors. What a prism does, really, is sort the light, like if you gave a pile of Legos to a toddler and told her to put the blue ones in one bucket, the white ones in another, and the red ones in another. A prism does this by bending light, like a magnifying glass. But a prism bends different wavelengths, or colors, different amounts. The prism separates the colors out by bending some more than others so you get a smeared-out spectrum from red to purple.
The chromadepth glasses are made of many, many micro prisms, so different colors get shifted different amounts. But in the left eye the prism is oriented the opposite of the way it is oriented in the right eye, so while in the left eye blues are shifted to the left of the reds, in the right eye, the blues are shifted to the right of the reds.
Remember our parallax effect: if the right eye sees things more to the right of where the left eye sees those same things, then the brain assumes that those things are in the background. Since the blues are seen by the right eye to the right of where the left eye sees them, the blues are popped in relative to the reds. The red seem to pop out, floating above the blues.
Do you see the 3D pop-out effect? How do you suppose this works? This called the Pulfrich Effect after its discoverer, Carl Pulfirch in the 1800's. Interestingly, Carl Pulfrich never experienced the effect he discovered directly himself: he was blind in one eye, and as we know, you only get the 3D pop-out effect by showing each eye different images, so a one-eyed person lives in a visually flat, 2D world. Pulfrich experimented on other people to discover the Pulfrich effect.
Obviously, one eye is darkened, so right there we are showing different images to each eye. But so what? What does that have to do with the parallax effect?
It turns out that the optical system in humans is wired up in such a way that dimmer signals make it to the brain more slowly than bright signals. Usually, both eyes see things equally dimly or brightly, and the signals from the eyes are in sync with each other. But with these special glasses on, one eye is dim, and its signal to the brain is delayed, but the other eye is clear, so its signal is not delayed. Again, so what? Think about what happens when your left eye is covered with the dark lens, and you are looking at something moving from right to left. The right eye will see it at a certain point, relative to the background, but the delayed left eye will see it a little behind where the right eye sees it. The visual system in the brain doesn't know about the delay, so it will try to put the images together anyway, and it will end up thinking that the right eye sees the object to the left of where the left eye sees it, relative to the background.
This is where the parallax effect kicks in. Refer back to the parallax diagram on the board When we see something pushed to the left relative to the background in the right eye and pushed to the right relative to the background in the left eye, the brain interprets it as popping out, that is, closer to you than the background. What happens if look at an object moving in the other direction, left to right? The same thing happens in reverse. The delayed left eye now sees it a little behind because of the delay, so the left eye sees it to the left of where the right eye sees it. When the left eye sees something pushed to the left, and the right eye sees it pushed to the right, your brain thinks it is farther away, and interprets it as pushed in.
In general, then, given that with the Pulfrich glasses you could have the dark lens on either eye, and objects can move right-to-left or left-to-right, things seem to pop out or forward that are moving in the direction of the darkened eye, and they seem to pop in or back that are moving in the direction of the clear eye.
Put the glasses on with the dark lens over the left eye. The video shows a carnival ride where people are riding in swings around a central hub. It works incredibly well - the people in the foreground, going right to left pop right out at you, and the people going back around in back, left to right, pop in. It only works, however, for something like that, where the things that you want to pop out are all going left to right, and all the things you want to be in the background are all going right to left. Also, this is something of a cheat, because even in ordinary 2D, without the glasses on, you know, and expect that the people in front are in front, and the people behind are behind. Nevertheless, I, at least, definitely feel that I get the real pop-out effect.
This device is called a pseudoscope. It feeds the left eye the right image, and the right eye the left image. It basically swaps the eyes.
Your brain will still try to put the images together into a single image with depth, but it will have everything exactly backwards. As a result, it will think the buildings are behind Mr. Mittens and Godzilla, not in front of them. Things that are supposed to pop out will pop in instead, things in the back will seem to be in the front and vice versa.
Now the pseudoscope doesn't work as well as you might think, because your brain is pretty smart and doesn't just go by the parallax effect to decide what is in front of what. Remember the Necker cube? Your brain really wants to interpret things as being whatever way seems to make the most sense to it. This is one of those cases where the natural way for your brain to interpret the scene conflicts with the parallax effect. You know that the guy is in front of the house, and it is hard to convince yourself that the house is in front of the guy, and there is a perfect guy-shaped hole in the house with the guy showing through it. The pseudoscope works best when viewing things that don't have a whole lot of other clues about what is supposed to be in front and what is supposed to be in back, like this shiny bowl. As you look at it with the pseudoscope, you can convince yourself that it bows in instead of out, or if you are looking at its concave side, that it bows out instead of in.
With this slide, it is easier to see that what should be in front pops back, or in, and vice versa.
Actually, there is an entirely different way to make a pseudoscope. Consider this:
What happens here in terms of our parallax effect?
It turns out that a right-angle prism flips whatever you look at through it. So if you put one in front of each eye like so:
You will see each image flipped: writing, for example, appears backwards.
With this slide, it is easier to see that what should be in front pops back, or in, and vice versa.
My final toy is this:
The lines of sight between the mirrored concave surfaces are such that the object in the mirascope gets reflected just right to achieve the parallax effect.
As you play with it, close one eye and then the other to see how each eye is getting a different image to achieve the 3D effect.