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VR Definition, History - Part 3 — Transcript

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0:01[Music]
0:16Let's go move on. So now let's talk
0:20about an interesting question that's um
0:22that will be important uh for us in as
0:26we understand our cardboards but also
0:28it's important for movies, computer
0:29games and virtual reality. So how many
0:32frames per second is enough? In this
0:34video I have only two frames per second.
0:38So do I perceive motion? Yes. Is it
0:42continuous motion? No, I can't see
0:45frames.
0:47So the answer is then how many frames
0:50per second is enough
0:53is related to how our brain perceives
0:56motion. So that's actually related to
0:58neuroscience and we'll talk about it
1:01later in class in more details what
1:02neural structures will detect motion in
1:04our brains and how the eyes detect
1:06motions together with the brain. Uh but
1:10I have a question for you. What do you
1:12think is frame uh frame rate that is
1:16enough to perceive continuous motion now
1:18then?
1:20So we said at two frames per second you
1:23perceive motion but it's not continuous.
1:26So what would make it continuous? What's
1:28the threshold?
1:32And thank you for answering. The correct
1:34answer is not 24. Although this is a
1:36standard 24 is standard for for movie
1:39for movies in movie theaters but
1:41actually the answer is 12.
1:44So people study these concepts very
1:48carefully. How many frames per second is
1:50enough for various things. So um to
1:53perceive a motion is two frames per
1:56second. to perceive motion as
1:58continuous. So not to see individual
2:01frames. It should be the minimal of 12
2:03frames per second. Of course, the more
2:05the better, but it's the minimal of 12.
2:09And we'll learn later why exactly the in
2:12movies we have 24, not 12. Now, how many
2:15frames per second is enough then to
2:17watch movies comfortably. See that's
2:19another thing because there's other
2:21issues like jutdder or flicker that will
2:24appear even though the motion is
2:26continuous but you can see then this
2:27transition between the frames that is
2:29annoying
2:30not necessarily individual frames but
2:32the transition will be result in this
2:35flicker or jutter. So then uh in movie
2:38theaters the screens are quite far away.
2:40So 24 frames per second was set as a
2:43standard but on on TV usually most of
2:47TVs today have 60 frames per second but
2:49the content may be 24 or 30 or 60. Uh on
2:53a phone usually starting with 60 these
2:56days and in VR it's an open question.
2:58Starting with 90, that's the minimal
3:00recommendation of frame of frame rates.
3:03But we'll show you that if you raise
3:06frame rates, there still may be issues
3:08just because the screens are so much
3:11closer to our eyes. But also with the
3:13way we interact with the environments,
3:15there's tracking that has never been the
3:18issue for movie theaters or for uh 2D
3:22screens, uh computer screens or phones.
3:24So you can interact with the
3:25environment. So the environment has to
3:27react fast enough as you move your head.
3:30So that will drive this frame per second
3:33requirement in VR even higher.
3:36But it all depends so all it depends uh
3:39on this on the hardware uh
3:41specifications on distance to the screen
3:43and on perceptions or on our neural
3:45structures. And we'll talk about it more
3:47in details. But now I'll just talk I I
3:50showed this slide for you so that you
3:51know what is it that you'll expect in
3:53this course. What what questions will we
3:55answer in this course? Is there any
3:57advantage done in VR technology to bring
3:59out immersive experience of sense of
4:01touch? I think professor manan would be
4:04a very good person to ask this questions
4:06and he'll um he'll have lectures uh
4:09later towards the end of the course. So
4:13um I don't work with touch as much as
4:16they do. So please ask it later.
4:22Okay. So let's let's continue.
4:25Similar evolution of computer games may
4:27be relevant to virtual reality. And
4:29again computer games can be simple can
4:32be extremely realistic
4:35uh but they can be portable on phones
4:38again simple right. So the question is
4:41how much um
4:44how much effort do you want to put into
4:47your um into your game into a computer
4:49game and what's the goal? So if realism
4:52is gold that's great but if
4:54entertainment is gold then you can get
4:56away with very very simple solution and
4:59still u generate huge crowd right like
5:02uh angry birds or Minecraft
5:06so what is the goal is the goal
5:08entertain or capture attention in some
5:10way then you can reduce the cost of
5:13production so it's very important okay
5:17so now let's really talk about virtual
5:20reality
5:21So, so far, if you think about it, we
5:23really taught about staring at
5:25rectangles. Our phones, TVs, computer
5:27screens, they're rectangles. They're 2D
5:29rectangles. So, when did something more
5:32immersive or 3D start? Which system was
5:35the first one? So, Sensorama is maybe
5:38the first one, but we've never heard of
5:39it. It's just like a sphere spherical
5:42image. They didn't provide tracking
5:43really. Um so probably the the the first
5:48virtual reality or the big big big leap
5:52with respect to this 3D immersive
5:54environment was Ivan Sutherland's sword
5:57of Damocles. So this is considered the
6:00first functional VR headset.
6:03It was built in uh 16 1968
6:08and uh uh it already had to use the
6:10power of modern PCs at the time because
6:14uh it had tracking. So there was a big
6:17computer the um in this room the size of
6:21the wall that did all of the
6:22computations and there was tracking. So
6:24there was sensors that would sense the
6:27emotions to generate to to reproduce the
6:29environment uh appropriately on the
6:32world. So it's um it had tracking.
6:37Ivan Sutherland is considered to be the
6:38pioneer of VR because of that. But if
6:41you look at what exactly is shown, it's
6:44just more like AR. So this very simple
6:47cubes are projected on the world but
6:49they attract, right? They attract. It's
6:52a very very simple system. about the
6:54groundbreaking at the time. So starting
6:56the season and up to the '90s, there was
6:58a huge hype around VR because of all of
7:01these advances. So the first commercial
7:03products uh appeared VPL company uh
7:07popularized the gloves and headset.
7:10However, there were always problems at
7:12the time with cost, resolution, latency,
7:15and content. So something that we still
7:17talk, right? We still have problems of
7:19cost, resolution, latency, and cont. We
7:21don't have latency anymore though, but
7:22content and the headsets being heavy,
7:25bulky, and expensive. But at that first
7:28wave, they were much heavier, much much
7:30bulkier than what we have now. So then
7:34the first commercial VR game ever
7:36released was by Nintendo Virtual Boy in
7:391995.
7:41And guess what? This device together
7:43with the game,
7:45the content was red and white. So it
7:49didn't even have colors, red and white
7:51content and there was no tracking. So
7:54you had to put it on the table and and
7:55just attach your head and view the
7:58content through through the headset.
8:01So this really effectively marked the
8:03death of VR in the '90s and nobody ever
8:06wanted to touch VR until the Palmer's
8:09prototype in 2012 because the the
8:12thinking was that if Nintendo can do it,
8:14nobody can do it.
8:16Uh however there were I have to uh
8:18mention that there were military
8:20headsets that were on the order of
8:22thousand tens of thousands of dollars
8:25but uh again they were bulky and heavy
8:27and low resolution and very expensive
8:30and there were caves. So caves is very
8:32interesting thing they stayed around in
8:34academic circles. They're extremely
8:37expensive. So like a cave like this
8:38would be a million dollars to set up.
8:41Um, and it's a projection system on the
8:44walls with tracking. So, there's sensors
8:47that would track your body and upgrade
8:49the projection on the walls accordingly.
8:51And in order to have stereo, you had to
8:53have polarized glasses for that. Like
8:55you could see that this guy was wearing
8:57polarized glasses.
8:59So, uh, the question is, are we in we
9:02are in the second wave of hype in VR?
9:05And is it going to stay around? It seems
9:07like it's going to stay around with this
9:08cheaper and better, lighter and less
9:11expensive headsets,
9:13but still we we lacking content.
9:16So, okay, we are done with this um
9:20introduction lecture, but I want to talk
9:24I want to jump to the next lecture. Then
9:27I want to go
9:30let me see.
9:33So I want to
9:36since we have time I want to go in
9:38chapter two the bird's eye view and talk
9:41about the hardware and maybe start with
9:43human senses and sensors because this
9:45chapter is so long that um we'll have
9:47only two more lectures to cover it but I
9:50wanted to start today then so we will
9:53jump into chapter
9:56two but I want to ask you just some
9:59review so that to wake us up kind of for
10:02the next chapter.
10:04So realistic graphics is this is
10:05essential for immersion in VR or not.
10:12We just covered it. So
10:15release
10:17answer
10:19is realism important for immersion.
10:23So what if it's not realistic
10:25environment? What is it if it's a
10:26cartoon environment in VR or
10:30or something else? I don't know, very
10:33simple kind of or what if it's not even
10:36an environment? I'll we'll we'll show
10:37you some examples like some of you tried
10:39sites in VR that's not really any kind
10:43of realistic environment but you're
10:46you're interacting with something.
10:49So are you immersed or not?
10:56So the correct answer is false. Right?
10:58Realistic graphics is not essential for
11:02immersion. You can be immersed in a
11:04cartoon world. You can be immersed in uh
11:07unity generated world. That's not
11:09necessarily uh realistic.
11:12Right? So the correct answer is false.
11:15Very good. Now the first ever VR headset
11:18was released by Nintendo together with
11:20the game Virtual Boy. Is that true or
11:22false?
11:26It was false. Right. The first ever
11:29VR headset was uh done pro much earlier
11:34before. So Ivan Sutherland's headset you
11:37can call that maybe the first ever. It
11:40wasn't really released but there were uh
11:42other ones like VPL companies headsets.
11:46Okay. So false. Very good.
11:49I put those questions because so many
11:51students get it wrong on the exams. I
11:53think um
11:55I don't know. Just wanted to make sure
11:57that we get it right. So, as you
12:00probably can already see that without
12:02understanding human senses, it's
12:06impossible to design good and
12:08comfortable VR systems because it's very
12:10important what is it that we see, how we
12:13see it, and how the brain processes this
12:15information. Uh VR systems are supposed
12:19to trick the human senses, right? So,
12:21it's very important to know what is it
12:23that you're tricking. So, let's start
12:24with a simple question. How many senses
12:26do humans have? That's one question. So,
12:29how many senses do humans have?
12:45So, I see some of you are answering in
12:47chat. Median chat. It's harder to read
12:48there. Please join um slider.com. just
12:52uh just use this QR code and you will
12:55get to slider.com
12:57and you can answer those questions and
12:59put your questions there too in Q&A.
13:03Okay, so see I see many many is good.
13:06It's not five, it's not six.
13:09And again, this is one of the questions
13:11that some students don't get right on
13:13the exam and I want you to get it right.
13:15If you studied perceptual psychology
13:17then you know that the correct answer is
13:19not five is not six and the correct
13:21answer will be the boring answer it's
13:23more complicated than that right so the
13:25qu the answer is it's just more
13:27complicated
13:29the reason is that the senses are
13:31related the in in perceptual psychology
13:34definition are related to receptors that
13:37receive that information and there are
13:39so many there are more than 10 we'll
13:41have a whole table but let me just give
13:44this a demonstration So on this picture
13:46on the left here I picked one organ. So
13:49sense organ for each sense that is
13:52relevant to virtual reality. So here is
13:54the eye for seeing things. Ear for
13:57hearing, ear for the sense of balance.
14:00There you go. So there are receptors in
14:02our ears that will determine where we
14:04are in with respect to space to help us
14:06balance. So that's not the um one of the
14:11five senses that we usually talk about
14:13in mainstream, right? So that's why it's
14:16so it's much more complicated than that.
14:18Here for we we pick touch for the sense
14:22of touch. Sorry, we pick skin for the
14:25sense of touch but also skin can detect
14:27the sense of pressure, pain and
14:30temperature. Right? So there are many
14:32other receptors there not only for the
14:34touch. Nose is for smelling. Notice
14:36there is no tongue here for tasting
14:38because we don't do VR for tastes. Uh we
14:43there's some prototypes for VR for
14:45noses. So there's some smells together
14:47with other sensory information. But most
14:50of the things that we are really
14:51concerned is the eyes, the ear and the
14:53sense of touch in virtual reality as we
14:55can do today.
14:57So uh let's see. So these are the only
15:01ones that we know how to interface
15:03really well.
15:04But even not all of them like the sense
15:07of uh the the vestibular system we don't
15:10know how to inter interfere too much.
15:13Okay. So how do senses work? How do
15:16senses u measure things? So there as I
15:20said there are the special cells that
15:22are called receptors that do the
15:24measuring. So in the eyes for example
15:26like in this video um there is the photo
15:29receptors on the back of our retina that
15:31absorb the light
15:34and do the sensing. So here's the video
15:36that shows it how it's done. So we also
15:38have receptors in ears sound receptors
15:41and position receptors for vibar system
15:43in the ears. There are also um uh
15:47receptors on the skin. So in the ears
15:49there's little hairs actually that move
15:52and they with the bending this
15:54appropriate signal is sent to the brain.
15:56But what's important is that the signals
15:58are sent to the brain for processing. So
16:00that's very important
16:02and I now because of that now I want to
16:05compare human senses to engineered
16:08sensors.
16:09So here how we can think about it. So
16:13the divi if for the devices that humans
16:15engineer we call them sensors and if
16:18it's something that naturally evolved on
16:21our bodies then we call them senses or
16:24sense organs. So the sense organ if it's
16:26we talking about a particular part of
16:28the body or sense if we're talking about
16:30receptors. So we will actually use these
16:34two words sense human sense and sensors
16:37interchangeably because they're kind of
16:39doing the same thing for the purpose of
16:41our class. So uh and they're both used
16:44for tracking so to speak. So what is the
16:47difference now and similarities between
16:49human senses and engineered sense
16:51source? So here on the right I have some
16:53sensors like um say cameras,
16:56microphones, thermometers, right? They
16:58do some kind of measuring of the real
16:59world around them and then they send the
17:01information to the some kind of central
17:04processing unit maybe CPU. So I have a
17:06question for you.
17:08What are the similarities between the
17:10human senses and the engineered sensors?
17:14So maybe you can think of it and then
17:16I'll I'll give the definition of how
17:18we'll define those two in our class.
17:26Oh yes, I forgot to mention that we
17:28switched to another slide. So the code
17:31has changed in slider. You're right. It
17:33did change. I forgot to warn you. Right.
17:36Right. Whenever we jump from one slide
17:37to another, there will be a change in
17:39slider.com and you need to scan the the
17:42code again.
17:47Yeah. So it both sensors and senses they
17:50sense the environment or they um get
17:54that information from the environment in
17:56some way to the processing unit. So um
18:02so here's the definition then a sensor
18:04sense is a transducer that uh transforms
18:07the physical world energy whatever it's
18:10measuring into a signal of some kind and
18:13for the engineered devices the signal
18:15will be the digital signals and it's
18:17sent via uh wires to the CPU while for
18:20the human senses it's the neural signal
18:23that is sent via neurons to the brain
18:26right and what would be the examples of
18:28energy Well, whatever they're measuring,
18:30right? The light chemical reaction
18:33energy or audio waves like air pressure
18:36waves or temperature whatever whatever
18:38is measuring. So why uh why is it
18:41important? Why do we talk about sensors
18:43and sensors? Well, it's all related to
18:45tracking. So we'll talk a lot about
18:47these things here because we need to
18:50understand tracking systems. So we need
18:52to interfere with what people see, touch
18:56or whatever we are interfering with
18:58hear. Um so that will be called then
19:01tracking, eye tracking, head tracking,
19:04uh hand tracking, body tracking,
19:05whatever. So in order to have high
19:08quality tracking, we need to understand
19:12how the senses or sense organs move with
19:15respect to the world so that we send a
19:18proper signal. So say in the real world
19:20if I want to see something closer I move
19:22my head closer right or if I want to
19:24hear something better I turn my ear
19:27towards the source of the sound. So we
19:29need to figure out in how many ways this
19:32uh transformations can happen so that
19:34the virtual worlds react appropriately
19:37in realistic ways because if if they're
19:40not then it the experience will be
19:42uncomfortable cause fatigue eye strain
19:45nausea vomiting whatever. So it's very
19:47important to for tracking to understand
19:49in how many different ways. So let's see
19:53um in how many ways uh the um sense
19:57organs can move in space and these
20:00senses can move this this changes the
20:03way they can change in the world they
20:05are controlled by the brain and the
20:08number of ways in which the sense can
20:11move with respect to the world is called
20:12the number the degrees of freedom. Okay.
20:15So the space of all such changes then is
20:17called configuration space and the
20:19dimension of this configuration space is
20:22called the number of degrees of freedom
20:24for that sense. So I want to count the
20:28in how many different ways with respect
20:31to the world can our sense organs move
20:33and relevant to VR. So we'll talk about
20:36eyes and ears for now. So I have a
20:39question for you. How many degrees of
20:41freedom does the human eye have? So
20:43again in how many different ways can it
20:45move in the space? So and what is the
20:49dimension of that space of motions? So
20:51for human eye
20:543 9 2 6 and I'm asking you the questions
20:59to think about it and then of course
21:00we're going to answer this question. So
21:02what about the human hand?
21:05How in how many different ways?
21:08How many different ways can can we touch
21:11things and feel something different you
21:13know so how in how many different ways
21:16can we move our hand so that the
21:18sensation is different because if you're
21:20creating VR for hand then the world
21:22should react to all these changes and
21:24give you different stimulus so it's much
21:27much yeah who said 360 exactly it's more
21:30like hundreds of degrees of freedom
21:33oh very good so we have some haptics
21:35experts here very good many. So the good
21:38answer is many. Okay.
21:44So how do you perceive time? We will not
21:47talk actually you know what maybe we'll
21:49have a little bit of that but time is a
21:52tricky thing because I don't think we
21:54really truly know how we perceive time
21:56but I can give you I will give you time
21:58illusions in the future. So there's a
22:00lot of thing tricky things about time.
22:02Some things we just completely some
22:05things that happen we completely erase
22:07from our memory. So we'll show you.
22:11Okay. Engineered sensor electronic.
22:14Yeah. It's electric signal that is sent
22:16via brains. Yep. Um
22:19okay. So
22:25we'll start with the ear. So now we'll
22:27answer this questions. We'll start with
22:28the ear. So in how many different ways
22:31we can place the human ear in the world
22:34so that we hear things differently and I
22:37wanted you to think of a single source
22:38of sound and how could I position my ear
22:42to hear it differently and I saw that
22:44you showed you answered in many
22:46different ways but let's finalize the
22:47answer and I put a video of a cat here
22:51because cat and other animals can bend
22:54which way their ears are pointing which
22:56will change the sound how it sounds And
22:59we humans we can't our ears are rigidly
23:02attached to the head and therefore the
23:05way uh you try sound for humans is
23:08different than it would be for cats and
23:10that's a a serious distinction. So oh
23:14yeah I didn't ask you. So how many
23:15degrees of freedom do you think the
23:17human ear has? So that's different from
23:20eyes.
23:25Okay. So let's let's now answer our ear.
23:30So there is head position right as I
23:33move my head in three different ways
23:35along three different axis um then along
23:38X Y and Z that will be three degrees of
23:41freedom and then I can rotate my head
23:43around the same axis. So the total
23:46number of degrees of freedom for ear is
23:49six. So that's very good. And um now
23:53let's do I. So for eyes, there's
23:56suddenly a change. The eyes can rotate
23:59in eye sockets. So that's kind of like
24:01the cat ears can rotate in their
24:04sockets, but our ears can't rotate in
24:07sockets, but the eyes can. Therefore,
24:10there is the usual the same for as for
24:14the ear. There is head position, head
24:15orientation for eye uh degrees of
24:19freedom. But then eyes can rotate in the
24:21obvious two directions in the direction
24:24of a yes up and down or sideways for no
24:28right but there is also the third
24:32rotation so I put two plus here this
24:36that is torsional and it's demonstrated
24:39and what 154
24:42here so there is a torsional component
24:45of the eyes rotating in their sockets
24:49Do you see that? So as we do this kind
24:52of motions, our eyes rotate torsionally
24:55which means that we see the world
24:57differently. So think about it. What
25:01does it mean, right? Do we have that
25:03kind of interface in our VR devices
25:06because the real world would respond and
25:08would be projected differently on our
25:10retinas as our eyes rotate tortionally.
25:14But do we provide that in VR devices?
25:17Not really. Right.
25:22Okay.
25:25Yeah.
25:29Well, yeah. I guess I I I'm most excited
25:32about next generation VR headsets where
25:35it will be this um retinal
25:39uh retinal displays. They're much more
25:41exciting to me. And um yeah, so I'm much
25:46more interested in advanced optics, but
25:49we'll see what happens. Apparently in
25:502027, there will be a lot of new
25:52headsets that will have that technology,
25:54good technology, not like Holo Lens 2,
25:56which is already kind of there, but not
25:58as exciting yet. Okay. So now, uh let's
26:03then count all of the degrees of freedom
26:05for the eyes. As I said already, head
26:07position three, head orientation three,
26:10rotations of eyes in sockets, that's
26:13two. And this is per eye. So each eye
26:16will have two more for yes and no, but
26:18also torsional maybe. So 2 point
26:20something. Then eyes can dilate. So
26:23there's additional internal changes that
26:25the eye can undergo such as pupil
26:29dilation and accommodation.
26:32And um dilation is something that you
26:34get to experience during the eye exam.
26:36So that just how much light the eye
26:38allows. But then accommodation is
26:41something very important.
26:43So uh we can refocus on objects as they
26:46get closer or further away. And what
26:49happens is that the silary muscles
26:51inside of the eyes, they squeeze the
26:53lens effectively increasing the diaper
26:56or the magnification power of our lens
26:58inside of the eyes. So we can see things
27:02um clear at different depths at
27:04different focal def depths.
27:08Um that is effectively another degree of
27:10freedom and uh as we get older we lose
27:13this uh power of the muscles. Uh so then
27:16we need reading glasses and but for
27:19example very very young children they
27:21can see things much much closer than
27:23young adults like you guys.
27:26But anyway, so if you add this all up,
27:28you you get about 10 total degrees of
27:31freedom. But how many um degrees of
27:34freedom does the Oculus Quest or
27:36Cardboard have or they how many they
27:38provide? How many they track? Right? So
27:40that's the question. How many degrees of
27:42freedom does the Oculus Quest 2 have?
27:48Six. Right? It says the degrees of
27:50freedom headset.
27:54So that's very good.
27:56it says so it only provides
27:59um head rotation and head position up
28:03down sideways or rotation of the head
28:05that's the only things that are tracked
28:08if you move your eyes around uh there is
28:10no eye tracking in Oculus Quest 2 what
28:13about VR cardboard and viewer that we
28:15will be using in this class how many
28:18degrees of freedom uh can be tracked I I
28:22degrees of freedom can be tracked in VR
28:24cardboard board only three right there
28:27is no six
28:29only three and the three degrees of
28:31freedom that can be trapped in
28:33cardboards are just orientation so if
28:35you go up and down the world will not
28:37change if you move sideways the world
28:39will not change there will be no
28:40parallels as you move sideways or
28:42forward
28:44uh our phones cannot do tracking without
28:47additional camera um so without
28:50additional sensors essentially so the
28:52only the IMU sensors that or on any
28:55phone will only provide three degrees of
28:57freedom tracking which we don't have.
28:59Okay, so let me summarize. This is the
29:01last slide. So the definition of degrees
29:04of freedom of senses and how it's
29:06connected to virtual reality. So here's
29:09the definition. In how many
29:12degrees of freedom is in how many ways
29:14can the brain control the sense organ to
29:16experience the world differently. Right?
29:20And the space of all such configurations
29:23is called configuration space and the
29:25dimension of it is degrees of freedom.
29:27And it's essential for understanding
29:29tracking or designing tracking systems
29:31that we will design in this class. So we
29:33will need this for um for designing
29:37tracking systems. Okay.
29:40So next time we'll start with hardware.
29:43We'll continue with hardware. Sorry.
29:44We'll uh go into what is the hardware
29:47that we have in common uh headsets. But
29:50now I'll take maybe questions and we can
29:53finish.
29:55So is vision pro the latest VR? No,
29:58there's uh other things that vision pro
30:01is not even a good one. So uh I think
30:04Quest 3 is it out? I'm not sure but
30:06that's the one that we're excited. It's
30:08like a low a cheaper high-end HMD that
30:12is coming out that is everybody's
30:13exciting about Ready Player One movie
30:16possible. Uh not yet. What is Quest 2?
30:20Uh Quest 2 is a high-end HMD that we do
30:23not have in this class. But in
30:24traditional courses that I teach at
30:26University of Olu, we usually distribute
30:28those to students.
30:31What is vection?
30:33Vet is the illusion of motion when there
30:37is no motion. So when you're in VR and
30:39there is a lot of optic flow if you feel
30:42suddenly like oh I'm moving
30:44um it's not necessarily that it will
30:46make you vomit right away. So vection
30:48and nausea are not necessarily the same
30:49concepts but it's this illusion of
30:52motion like when you don't move in your
30:54chair but you feel like you're moving in
30:56virtual space that's the that's fashion.
30:59Can you explain how to measure degrees
31:01of freedom? You need to figure out
31:02what's the configuration space. So where
31:04can in how many different ways and where
31:08can say the eye move and uh looking at
31:12that space you can compute its
31:15dimension. We maybe we'll go more
31:17through this. Okay. So
31:22or you know what let's open a discussion
31:24on discord as well. So that will be
31:26good. It's a little bit of a
31:28mathematical notion. So you really need
31:30to think of a space of all
31:32configurations of some object
31:37configuration space. So you can Google
31:38what a configuration space is and how to
31:40define it for different objects and then
31:44that is the answer. Do you have examples
31:47of non-invasive BCI using VR
31:51interface
31:54brain computer interface? Is that I'm
31:57not sure. I'm guessing this term and
32:01non-invasive
32:03brain computer interface.
32:05Oh, yeah. Yeah. Yeah. Of course. Yeah.
32:08No, I don't know any any of those. I
32:11clearly it's not my area.
32:14But
32:16a good question. We can we can look up
32:18together. I can ask my colleagues. I
32:20don't think so. I think they need to put
32:22the electrodes inside. Oh, but although
32:25now I think they maybe there are some
32:27electrodes that can be like in EG caps
32:29that can measure a lot more of brain
32:31activity. But no, I I really don't
32:33that's not my field. So uh but I
32:36definitely can ask and we can Google
32:38together. It's 7:15. Yes, it's time to
32:41finish. So we are done.
32:44Please I'll try to again I'll try to
32:47answer all the questions later after
32:48lecture. I'll go through this unanswered
32:50questions and put them on Discord. So
32:53goodbye.
32:56[Music]

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