Good evening, friends of the inner sanctum. This is your host to welcome you through the squeaking door. Ah, our cast assembled here in a highly unique manner tonight. The angineau flew in the window. Did anyone whisper which window? Ha, ha, ha, ha. Another nimble member of the cast crawled out of the studio woodwork. This creep said that he simply loved popping up where least suspected. Ha, ha, ha. Oh, unforgettable character. Meet him once and they'll haunt you right to your grave. Ha, ha, ha. But seriously, every last one of them is really and truly wrapped up in his work. Like a, shall we say, ascorpion. Hmm. Ha, ha, ha, ha, ha, ha. Tonight's inner sanctum mystery, Hangman's Island, was written by John Robert and stars Mason Adams in the role of Regan, with else with Eric as Wilma. We're on an island somewhere off the Florida Key. Hangman's Island, a bleak ruin of marsh rubble and scotch pine trees. It is sometime between night and morning, cowering in the marsh crawling on all fours like a giant ant.  He crawls like a hunted animal with the taunting voice of the hunter exploding in his brain. Regan!  Regan! Ha, ha, ha, ha, ha.  I know exactly where you are, and I watch you, and I take this island. Ha, ha, ha, ha. And the morning has come for you. Just one more hour, Regan, and it will be morning. One more hour... up there in the sky. I can see a gold ball, the sun... burning up the night. Ha, ha, ha, ha. A gold ball in the sky. A gold I'm gonna guess. It all began the day I got the feeling that Fats was about to dust me off part company.  I could tell he didn't want me around to help him count it. I could use five. Who couldn't kid? Hey, you're not hinting you think I've got five. You've got that well fed look the last couple days, huh? Lobster dinner look. You're talking from hunger kid.  Hand me that necktie, huh? Steppin' off? Yeah. Regan. Why? I've been thinking. We haven't done so good teamed up. Our luck's been all bad. So? So we ought to face up to it. And part company, huh? Yeah.  You going alone? Sure. No hard feelings. Sure. No hard feelings. Fats had some swindle cooking and he wanted a hog. I followed right behind him to a shack on the wharf that furnished cheap piano music and heaping plate of fishing ships. I was right behind a paper thin partition and watching Fats and a blonde doll sitting over a lobster dinner. The doll had hair as golden as anything in the mid. He was the last aim in the world you'd expect to make a pitch for a roly-poly fatso crock. I didn't catch your name the other day, Goldilocks. Wilma. Your mind made up? I have. What's the other half of you holding out for? More on the line. How much more? The same slice in advance. You're expensive, friend. Down at the heel pan, Handler. You'll find another slice in this envelope. How about the rest of the instruction? You'll find them written on this. How long have I got? When you're finished, we'll meet again. Fats was cooking a fancy dish, all right? Early that night in the wormy room we shared, I waited till Fats was asleep. I had to find things out fast before daylight brushed me out of his life. I went through his pockets. Fats had a bankroll, all right? More dull than he'd ever seen outside of his dreams. A thousand dollars in yellow-backed gold notes, the kind of treasury he'd called in back in the 30s. And all soiled and damp like they'd been buried somewhere. In another pocket I found the note the girl had slipped. It was a map of an island drawn by hand, like a treasure map with arrows leading in from a beach and pointing to what looked like a cave somewhere in the middle of the island. A map read Hinckley's Island, a treasure map right out of a kid's storybook. There was a big star over the last arrow where the cave showed. A star that yelled pot of gold at me so loud my pulse jumping made enough noise to wake in Fats out of dreamland. What are you snooping around my clothes for? What's the gun for? Yo, double-crossing roll-up, lover.  Who's joking, kid?  Just one of us.  You don't know what it's about. I can read maps too. And I can cut off gold back. Regan, it's not your kind of a pitch. This isn't petty larceny. It's something small-time. What's the pillow for? What are you going to do? Yes. Regan, don't. We'll go together. I'll split the roll with you. I'll go, Fats. I couldn't trust you alive anymore. So long, Fats. See you in the next world. I could feel the warrants blow out of him like escaping steam. And then he grew cold. He came out the back door then rode across Cracodile Creek into the Everglades. I dumped him. I didn't have to wait him down or worry that he might float to the mainland and be discovered. Not a chance. Not in Cracodile Creek. I read the map again. Hinkley's Island, four miles out in the ocean. Made my way to a boat landing. I wanted to go after the money at once. It had to be hidden treasure. What else? I wasn't beating my brains out, figuring what were the exact terms of Crocker's deal with the blonde. Or what else lay behind me? I was too hot-dubbed. The boat landing the ocean was acting up. I signed Red Peterson's boats for a higher day or week. I knocked for Peterson. Yes? I want to rent a motor boat. Tonight? Tonight. My skin, I'll cover the liability. Where are you figuring on that? Hinkley's Island. Hangman's Island? I said Hinkley's Island. What made you say Hangman's Island? Because that's its name as we know it. What would a young fella like yourself be wanting with Hinkley? Why, is he poison? They've got the brand of the devil, Hinkley. Now, you've got me interested. Exactly who is Hinkley? Hinkley used to be a public executioner, a hangman, somewhere in the islands. Five thousand in gold every time Hinkley threw the trap and sent a man swinging to eternity. How'd he come to settle on the island? He bought it and retired to it twenty years ago. Brought a young bride in the islands to settle there with him. Nobody's seen hide a hair of the bride ever since that first day, twenty years ago. Has anybody around here ever seen Hangman's Island? Not the easiest. It's worth your life to try. Hinkley's got barbed wire all around it. Nectric voltage, it'd burn you to a crisp if you touched it. Cracked by hermit, huh? You... You can have your money back. Land's drier and safer. I said I wanted to rent a boat.  The seas were calmer and the lightning had quit as if someone had pulled a mast to switch. A midnight moon was peeping through. I covered the four miles to the island straight as an arrow and ran the motorboat up on a sandbar that opened into a short rocky beach. I had company on the sandbar. Another boat. I got the map out to figure my course when I sound like the death cry of an animal broke the air. It was a human cry, a man. I looked following the direction of the screen and then, in the distance, outlined high against the sky, a man was hanging from a tree with a crossbar that looked like a gallows. He was hanging by one foot face down. I started forward toward him before I could stop to see him. What an idea, friend. You're having a chance in the world of reaching him. Who are you? Burnside, Lieutenant Burnside of the Coast Guard. Is that a uniform? It's still Lieutenant Burnside of the Coast Guard. What do you mean I haven't got a chance of reaching him? The island is a big booby trap. You've got to get through electrified barbed wire to get anywhere.  And quick sands, cleverly covered over, and camouflage.  McEvoy there walked into one of the simpler devices. Steel-jawed animal trap. Swung him into mid-air, hanging by one heel. Who is McEvoy? He's my sidekick. I mean, was. You get stranded on that sandbar? Yeah, yeah, I lost my bearings and ran up on it. Well, that map you were reading a minute ago, let's see it. Maybe I can set you back on your course. How do you know it was a map? I guess.  I'm doing more than shaking my head. I see. You mean to shoot that gun? If I don't get some straight talk, I'm fast. Okay, straight talk. That map you're carrying, what if I told you the map is the biggest booby trap of all? I'd laugh out loud. The girl palmed off a similar map on a couple of characters a month ago in Key West. They run at a boat in school for Hangman's Island and... And what? That's all. They never came back. You'll probably run into them in one of the line plates. Or under their quicksand, Tucker. Don't believe me, huh?  I've got goldbacks, mister. A pocket full of them. This says you're just trying to scare me off. The goldbacks are the bait. The girl snitched them from Hinkley's savings. Why would she bother just to get them away? Some insanity of hers. Let's just say that the golden-haired siren baits men to their murder for reasons of their own. You, um... Still pushing ahead? I still want to know who you really are, Mr. Burnside. You're still Lieutenant Burnside of the Coast Guard. We've been watching the girl. We came here to arrest Hinkley for the murder of those two men who never returned a month ago. I'll let Hinkley identify me for it. We are no tricks, Burnside, or I'll show you. Adjust this rock. I'll hit one of those wires and start the bell ringing. How was it? Lieutenant Burnside. This is Hinkley.  Strangled by his own blood rushing to his head. Ha-ha-ha-ha. Your next Burnside. Believe me now? Sure. Crazy. I believe it. Then give it up and don't hamper me. I've got enough to do. I have to tangling with Hinkley. Put your gun down. No! I'm in it for the whole ride. How far can you get? Right to the star on that map. Okay, Burnside. Turn around. You're regretting. I might regret giving you a break. Better turn around. Burnside fell like a slaughtered ox. Somehow I didn't have the heart to drill him. It was one murder I wasn't up to. He'd be out cold, stay put until I worked my way to the cave on the map. Luck. Lady Luck couldn't give me the horselab, not after what I'd done chasing her. She couldn't. She stayed with me as if I was somebody special. I'd pass an arrowed marker on the map an inch closer to the cave and a landmine would blow a shower of sand and rock into the air. Just 20 yards away, maybe 30, but I stayed alive and unhurt. I was brushed live wise and started bells ringing in a jangling chorus, but I pushed on like a foot soldier crossing no man's land. Inch, inch, yard. Seemed ours, but I made it. I made it on my hands and knees. I made the cave. Only it wasn't a cave, really. It had a heavy door with polished brass fittings tooled into an opening. An eerie yellow light shone from a square little window. It looked like a, like a mausoleum where the dead were put to rest. I went in with my gun drawn. It was a mausoleum casket in awe. Sitting solemnly in mourning clothes like a high priestess of the black arts. With the golden girl, Wilma. You. Where is he? The fat one. I'm reek and set to do them for him. Any objection? Not if you have the steel at me. I have the steel. I'm here in the cave with all the booby trucks. I'm right here. Yes, you have the steel for the job. Job? What do you mean job? You don't know. Not exactly. I guessed that Hinkley has a fortune hidden. A gold horde maybe. And you're betting he loses it to whoever has the steel to take it from. You made that kind of a deal with me. It's a joke. Your guess is so funny. Who has no gold horde? Come again? I said there's no gold, no fortune.  Look, sister, don't play Captain Moss with me. I killed a man. I crawled here in my hands and my knees. I'm covered with blood and sweat. I followed that map. I died with every arrow. Now I'm here at the end of the rainbow. Don't kid. I can't help what you imagined. I imagined a pot of gold. I looked at that map. I imagined a pot of gold in my brain radio back shore. You can go to it, boy. Where is it? Where's the gold? You're hurting me. Try lying on your losing arm. Where does the loony hermit keep you? That's the gold you... Casket. The gold's right here in this cave, just like the star in the map shows it. It's not casket, is it? Why not see for yourself? Sure. Sure, I'll see for myself. What do you see? You. You're in there. Lying with your arms, folding on your chest. Dead. Is it me? Sure. The exact image. Face. Figure. Size. Beautiful. And the hair, Regan. Golden. Like yours. As golden as anything in the mint. There's your gold, Regan. Just that. No more. What kind of crazy... Who is she? She was my mother. She's not a day-old, isn't she? Just carefully preserved. She died at exactly my age now. The idea wasn't preserving like that. Hinkley. She's his... Hagan got it. He pretends she's alive. Agents. But she never really died. And you... You're Hinkley's daughter. And you...  Yes, I hate him. Coast guard man on the beach said you were a siren luring men to their death here. Wrong.  You'll have to kill Hinkley now. He knows you're here. He's overheard our whole talk. This cave is wired and Hinkley listens.  Where are you going? Wilma, come back! You can't go! Wilma, come back! Right under my nose she disappeared as if she'd floated through the walls.  I didn't have any choice.  Hagan.  I was in the devil's backyard. All right, my old Peter's in a sad. I tried to crawl back to the beach infantry style of my hands and knees. Not the lady luck was small. She couldn't desert me now, not now. The bullet? Not me right in the stomach. A rifle shot from somewhere. I couldn't fight back. The bullet got you. I'm freaking out. I can't crawl in. Inch. Inch. It seemed hours. I passed a hat sitting on the edge of a lime pit. Just a hat. Whoever owned it had tumbled in.  The landline went off my 30 yards away. The whirling dust caked my clothes. Chips of flying rock hit me in the face. In the morning I'll come for you, Hagan. Just one more hour. One more hour. Something had happened to Hinckley. Two shots in the scream.  I looked up over the island. There was an old man. Hinckley. He had to be Hinckley. Hanged by a hill faced downward. It was Hinckley. Caught in his own movie. It was Burnside's Hinckley. Just lost control of the situation. One hour. Don't bother coming. The last poor Regan. Out cold and no gold. What a story. A crazy hermit, booby trapped. The gallows quicksand. A mausoleum, a blonde witch. An informant tells me that Dracula was scheduled to appear on page 25. But the author fell into a lime pit on page 24. Moral? There's some jittery Joe out a homely hint of how to keep from going cold.  Okay, friend. When bitten by the gold bug, don't yell Eureka. Be cautious. Play safe. Y'all help. Goodbye. Pleasant dream. Intersanctum came to you through the United States Armed Forces Radio Service. The voice of information and education.


Okay so good afternoon everyone and welcome to this lecture and I think I should start right from so from the previous lecture so where we basically when we left which last last time I was I only managed to introduce just a bit to the topic and what the time I'm interested in and why it's difficult for neuroscience cognitive neuroscience to study time so really what is the range of interest what what is the process we are interested in and why it is important to to study and now today I hope to be able to go in deep into this neuroscience of time and I will start really we're still in this introductory bit I'm not haven't started yet the the modeling and the empirical evidences that I will bring in favor of against all these models that I'm presenting we're still in this introductory bit where today I hope I will tell you about the task so how do we study actually so what are the tasks we use to investigating time perception duration perception and what is the variable we measure and what are the properties of duration perception in what if there is any so any general property that species and and tasks share okay so perception one of the really a common task we use is depicted in a very schematic way in the slide that you have that is here so you this is called two force two interval force a choice task and is basically what you do you present the subject with two different sensory information that let's say two sounds or two visual images and those images have you presented in sequence you have first you present the first duration so the sound that has a duration t and then after a variable amount of time you present a second duration that is t plus or minus a delta t and then you ask the subjects to compare so you said okay which one of the two sounds that you just heard was longer according to you and then the subject press the key normally you you it has the possibility of choosing one of two one of two response keys so if first was longer you press monkey and if second was longer second key and in some circumstances you provide feedback to the subject so you just tell the person whether it was correct or wrong of course using or not to feedback has an impact on what you do right so there are certain certain experiments you want to the subjects to learn and to improve by using the feedback in some subjects in some cases you don't want to have this interference with the feedback so the subject does the task without really knowing if it's performing good or not and what I would like you what I like to stress here is that there are so in this what we call this is a trial okay and when you run an experiment you use multiple trials because you want to sort of average then out the performance of your subject right because you need a lot of you know you need numbers you need a lot of observations in order to have a reliable uh to perform reliable statistics on on on on the subject's performance and also because you want to get rid of the normal variability that you have in behavior right so let's say in one trial the subject was a little bit distracted in the second trial it was drowsy in the third trial it was there was some environmental noise that interfered with the with the perception of what you were supposed to attend so there are lots of uncontrolled so variables that might have influenced the subject's behavior and you want to get rid of it by just repeating by collecting data lots of data in order to then have a reliable measure of what the performance of this person was okay so you do this multiple times and uh what I also would like to to to stress is that each of this moment in the trial has a has a certain requirement for the subject okay so has a specific task for the subject let's let's try to to dissect this so in the first place so the subject has to perceive something or hear something and he has to extract the temporal information from this sensory event okay so this is let's say we call it the encoding of the temporal information the extraction of temporal information that's the only job he has to do the subject or and and while you encode while you extract this temporal information you need it to store it somewhere right so and it's possible that of course while you're encoding you just keep it in this working memory we call it so it's like a short time memory where you just store is a temporary storage of this information then the second stimulus appears so you have stored the past information then you have a new information coming so uh you again extract temporal information from this second stimulus you have to keep it memory as well and once the second information as elapsed the second duration as elapsed what you do you retrieve from your from your memory from your storage space the previous information you do a comparison between so because your task is to to to compare them so you have to compare the two stimuli and make a decision and then express your decision by responding with a key press okay so there are from the cognitive point of view there are different things happening during this single trial if you want for example let's as you can as you can see right so while i'm appreciating the second stimulus and i have to retrieve for memory past information making a decision responding preparing to respond so there are lots of cognitive things on right so if you want to get rid of all this let's say interfering information so if you are not in let's let's imagine that you are just interested in the encoding of the temporal information and you don't want you want to get rid of the confound of memory storage memory retrieval comparison decision you just you can have a different type of task you can get rid of one of the stimuli so you you get rid of the memory load in the whole experiment and run an experiment where you have for each single trial a single interval so basically you just present a single interval in any in every trial and you ask the subject to compare this single interval with single duration better with a reference that you built up over time so this reference which is like let's say in a storage that it's more stable it's a long term memory you can ask the subject to build in while doing the experiment or you can provide this template duration before starting the experiment right so you have a sort of training phase where you just present this person with a sound of 200 milliseconds repeatedly so beep so the subject gets acquainted with this duration and then in the proper task in the proper test you just present duration that either longer or shorter than this template the subject has in his head okay and and in this way you get rid of the memory load that he has to really that the memory load in every trial and and it's just a single you focus more on the encoding rather than all this memory aspect of the task i give you an example okay this is what we i presented yesterday right so this is an example where you have two stimuli to care about right so the first and the second beside which one was longer and in this case was the second was longer this is again an example but yeah so this task so the subject already knows what is the task before it starts right you you have a face of a familiarization so before starting really the testing phase you show and you explain what they have supposed to do yes yes so but say how is this representative to how people behave when they do not know in advance what is the task i mean performing the same task but they don't know it in advance i so they learn it right am i i think so they they can learn it and for example this template can be built over time right of course it can but i'm asking how different is the initial stage of the performance i mean with the stage performance it would be very different and you can you you have to run a totally different analysis you have to because normally you are you tend to this is something we don't do frequently it would be like using this patient approach for example and try to see whether how does it change your performance over time you have to do that you have to consider the trials over time and see how your performance changes according to the fact that the subject is building up expectation and it's making a statistics of the environment right so he has to sample this information and for example something that you will see later so if i present the subject with a bunch of durations the subject performance tends after a certain amount of time tends to to collapse towards the mean so it's a sort of if i ask you to if i present you with 200 400 600 800 milliseconds your performance and you ask okay reproduce this but i'm not i'm saying i'm not presenting this duration all at once but trial by trial so the subject basically is building a template and it's building a statistic so what is basically the range of duration i'm dealing with and in order to optimize the behavior it relies a lot on on prior knowledge you know so he builds a prior which is basically probably the mean of the sample that is handling and he tends to converge to this mean of the distribution so he's so he tends to perceive the incoming information as more similar to the average rather than it actually is this is an important concept because the brain doesn't doesn't take just simply it doesn't take passively snapshot of the world around us the brain makes statistics of the environment and what the what you perceive what each of us perceive it's really the result of this this statistical approach to the environment so what i the incoming sensory so and this now this was something relatively new material so before we tend to have really to to to consider every single trial as a distinct uh uh as an isolated element and we just analyze how the the subject behavior now the brain gets this information independently from what was previously presented and what was previously done by the subject now this approach of seeing things more dynamically and so consider your perception and your behavior in light of what you saw before and what you did before what you perceive before it's a new approach so this contextual effect and has been now we start so there are lots of studies that study this contextual effect we call it so you build spatial and also temporal statistics of the world and this influences your behavior yeah no that's fine thank you yeah and but normally what you do in a more classical approach you don't look at this trials over time you just took a snapshot of the subject performance by looking at the median or the mean of the performance over trial okay unless you're interested in learning then learning studies normally compare how was your performance before the learning after learning they do this my question was essentially exactly on this point so what is the cognitive load of paying attention to a particular stimuli yeah if it is heavy then the selection on what you perceive and what you don't perceive yeah can change absolutely can change it can change a lot can varies a lot and you can measure it this is because you can measure how your performance so how you you behave in trial and and look at n minus one and n minus one and you go back in trials and see how much your performance has been influenced but what was was presented to you uh minus uh five trials before on according to what was your performance five trial before of course the influence is very strong for what you did before much more than of course the the the the backwards you go the less is the impact of what on the current trial yeah but that's interesting sure and another yeah yeah yeah just wanted to know if if there is any dependence on the frequencies how do we cancel them the frequencies of what uh like when we play two different sounds and the answers might differ on on the frequencies the you mean the frequency of the pitch so the frequency of the sound or the frequency of so how closing time are the two stimuli no no the frequency of the actual time so actual sound the pitch yeah you normally for example if you okay sure and this is something that we you can manipulate you can see how if if if this is your in experimental question you can body the pitch of the sounds and see you have some condition in which uh the pitch is x and some condition where the pitch is y it's something different but you normally and so if this is your manipulate your experimental manipulation you should control that and have different trials and normally you have an equal number of observation for each frequency you want to test okay if you have a specific hypothesis you know I don't know that the the higher the pitch the longer the time okay or the lower the pitch but this is actually has been studied and I will show data on on on this especially on moving motion or anyway frequency of of the motion in and of moving dots of clouds of dots but normally if you're not interested in this manipulation so so you don't want to change you're not interested in understanding what's the impact of a sensory feature of your stimulus on time perception you just keep the sensory features equal across all your trials so you want really to control so you want to manipulate only the variable of interest then in this case is only time okay you don't you're not interested in manipulating sensory features so the features should be constant across trials should shouldn't vary so you're welcome and there are two also ways you can you can explore time and this comes to a question that someone yesterday asked was something that we said at the really end of the talk so you can measure time as a filled duration so like you present something on the screen and has an onset stays there for a central amount of time and has an offset or you can measure empty intervals so a time an empty time between those two flashes okay so in this case you minimize the impact of the sensory information but you ask the subject just to judge the empty time between two events which are often two flashes i'll give you an example with this okay um excuse me excuse me i couldn't understand the difference between feedback and response okay the the the response is the subject has to just decide he has two keys on the keyboard or a keypad there are two buttons and has to say which one was so in every trial after seeing those two stimuli which one was longer and has to press one either one of the two keys according to whether a judge is the second as longer or shorter than the first one the feedback is something that appears on the screen it could be that you see this cross here maybe a feedback is when this cross on the screen gets read after you respond you you know if your response was correct or incorrect so if it was incorrect the cross turns red if it was correct it turns green okay okay so this is a feedback so you you tell them what they how was their performance okay but this has an impact okay giving a feedback or not giving a feedback has an impact on your behavior you learn quickly of course with feedback i see but even but even without you you manage very well to do i will show you an example of this two-forced choice interval what i haven't done okay it's very brief i don't know if you if you manage to see it i will show it again which one was longer you have to judge really deep the empty time between the flashes do you know which one was longer i'll show it again i think the second was longer but now i'm over trained uh subject so here an example no for example you can use a tea of 200 milliseconds and the so the teas we call it the standard duration so the duration that you keep constant across trials no and this the comparison duration is the duration that varies okay and it could be shorter like could be 50 milliseconds 100 milliseconds or 150 milliseconds or longer so it could be 250 300 or 350 okay so this is the range for example it's a pretty narrow but this is actually something that the subject can discriminate okay so this is what you manipulate you just keep one fixed and you change the order okay but of course you have to make sure that the subject cannot respond to the task by just seeing the first stimulus okay that's why you want to make the second stimulus either longer or shorter because otherwise subject you see if the second is always longer it's always shorter you of course you subject can easily then perform the task without paying attention to the two stimuli and an example of field duration it's this one where you don't have intervals empty intervals so you don't have these four flashes but you have just two bright discs displayed on the screen okay which one was longer it's really hard to tell I think it was the first one I think people easily I mean okay we tested I mean personally I work we work with young students so we we don't test the aging people so we really work with in a young range and some of the subjects when they come they really say oh no this I'm not gonna do this it's too difficult but in the end after a couple of trials they really can do it very well okay so okay this is a single interval so it's the same okay this is a different task so here you have different here you change for example this is an experiment where what you manipulate it's not just the time but is also the special position of the duration in the visual field but this is an example of single interval it's very quick so basically the subject has for every flashing disc it has to decide whether the duration of this disc was longer shorter than a previously acquired template this is something we tested already something that we are doing for fMRI but this will go later because it's a complicated experiment where we try to bind space and time okay but this is for me just to tell you okay let's try to see it again and see if you can see the difference in duration between okay this is more quickly quickly quick yeah this was definitely longer than the first I think yeah you can appreciate this subtle differences between but this is a single interval so every time the the stimulus flashes on the screen is a different trial so you are supposed to give an answer so now the video goes on and on but you are supposed to give an answer each time the stimulus appears oh sorry I just didn't want to I wasn't meant to okay so what you measure it's uh what you measure here what okay this is a way we sort of look at the data so what you have in the y-axis is the person touch so the number of times the subject respond longer so the judge so so when he has to compare the two stimuli it it said longer he said or she said longer okay so personal percentage of longer so this is the percept of the subject and on the x-axis you have the the physical duration really okay so the physical time and the the dots are really the the the mean of the subject performance for example and what you do you just fit a function okay so logistic function and then what you measure is there are two things you can measure the one you can you measure the accuracy so you measure for example uh uh basically uh when how so what is the value of the physical stimulus that leads to uh uh 50 accuracy so which is basically 50 means being a chance if you have if you have two possibilities right uh and this is called point of subjective equality which is sorry uh which is really a measure of a bias so because it tells you when so which value needs to have the physical stimulus for you to be judged equally either longer or shorter so it's the point where you judge the two durations the same okay and if you have a if you if for some reason you have a distortion of time this point of subjective equality should be shifted towards the left or towards the right okay because it means that something so if it if it let's say this red point it's here then it means that something that that was presented for uh less than 200 milliseconds you judge it as if it was equal to 200 milliseconds so it means that you uh you're you're perceived duration you you you have a temporal uh overestimation of the duration no because remember sorry here I didn't say something important that your standard stimulus so the stimulus that never changes is 200 milliseconds no and you have durations that are either shorter or longer to that okay so if at the point of subjective equality shifted uh towards the right then it means that something that it's uh 250 for example millisecond that is physically longer has been perceived as if it was equal to 200 milliseconds so then it means that your your duration has been so your perception has shrinked okay so you your you you tend to underestimate time so it's a measure of accuracy a measure of bias but then you can use another measure which is called the just noticeable difference which is basically the difference between 75 and 50 accuracy and this just noticeable difference it's a measure of how precise is your temporal system so what is the the the minimum difference between the two stimuli in order for you to reach 75 percent of accuracy okay it's a measure more of sensitivity and the two things can be um basically dissociable no so you can dissociate the two things so the J and D it's basically the steepness of this curve the the the the the the yeah the flatter so it means that you are you the less precise you are whereas you can have a curve that is equally steep so your J and D is good but you have the the curve is just shifted in one direction and in this case you can have a bias in one or the other direction so it means that your your your your your sensitive enough to duration but you systematically judge for some reason the duration to be either longer or shorter than they physically are those tasks that I presented to you are really on the perceptual side because what you'd need to do it's just to perceptually match two stimuli okay but there are tasks that are more in there are a stronger motor component you remember yesterday I I mentioned you this I gave the example of the language no so and the fact that in language is very important the poses are important no so for how long a certain syllable is pronounced for and that's in a case where time you need time you need to perceive time accurately but you also need to produce time accurately when you make a movement and that's why we also tend to measure the accuracy of your motor timing system in the lab and we do it with like with the task that we call reproduction of time and I show you an example of this so what you just briefly described so what you do you present a subject first a stimulus so there is still a perceptual component in the task because you have to extract temporal information in what you in what you see or what you hear and then you have to translate this temporal information into a precise motor action so you have to reproduce the duration that you just perceive so by pressing a key for example holding the key down and release the key when the key press that you made has had the same duration of the of the duration that you just perceived okay so in this sense you do a translation of a percept into you translate a perception into a motor action but he has you know he has a temporal component in it so okay this is a duration then you have a go okay the burst of white noise it's a go signal for you to start a reproduction this is the second trial what you have to reproduce is the duration of the first beep that the tone the pure tone very brief so with the with your with your finger you just press and release okay and of course so here you have really to rely the only you have to rely on your your proprioceptive we call it information so you have to the only information is just the sensation that you have by pressing the key down holding it and releasing it so that's the only feedback you have to reproduce but subject can do that and we have I will show you data on that so this is really a reproduction task another yeah I can show you yeah that's okay these are schematically are two different types of reproduction where the degrees of timing motor timing is different in the first case is what I just described to you so you have rather than a sound you have a this square on the screen then after a variable amount of time you have a queue in this case is the word noun that appears on the screen and then what you are have been asked is just to press a key hold the key down and release it when you think that the duration that you reproduce match the duration that you just saw in this case when the subject presses you give an extra information so because there is something appearing on the screen and when you release the key immediately the the the information disappears so in this case you have an extra information that helps you out with the task in the second example you still have first a duration to appreciate and then you have a second stimulus on the screen the second stimulus it's in principle stays there forever what you have to do you have to press the key to stop the second duration in order to and you you you stop when you think that the two duration matching time okay so this is a it's slightly there is no translation somehow but just a very precise motor moment motor act sorry here's like tennis eating the ball at the right time so you want to stop the presentation of the second stimulus when you think it matches your perception the the perception of the previous duration uh yeah and what you see echo matthew so if you look at what you see is that what you measure is okay sorry i'll just go gradually okay so what you measure in this case is the reproduction of the duration so for how long the subject press the key okay so and what you do you just normally in this case the subject have to reproduce two durations 300 and 1.2 seconds okay and what you do you you you just take the the the the time the subject press the key you subtracted from the physical duration okay so and this means that zero means that you perfect you are a perfect clock so that the performance was perfect all the positive values means that you press more than you should have negative values you you means that you press less time so that you underestimate time okay and what happens is this so that you tend to press more so you overestimate the shorter duration and you underestimate the longer duration don't care so don't pay attention to the different colors of the bus this is something irrelevant for now it's just uh there are different experimental conditions but i don't want to go into it because it's too much of detail at this level it's just uh just what i want you to appreciate is that you have okay in the y-axis the accuracy measure according to this index and you have the different experimental condition in the x-axis so the physical time was 300 or 1.2 seconds so you have overestimation for short and under estimation for long and this is the same if i plot this is a different experiment where i have this objective duration on the x-axis so here i ask subjects to in certain blocks of trial i ask them to reproduce 300 something that it's a 400 and something in 600 in certain blocks of trials in other blocks they have to reproduce 600 one second 1.2 and here is the subjective duration okay so if the subject is a perfect clock their performance should lie on this diagonal okay so all so and the their bias is measured so how you measure how distant they are from reality from this diagonal and also here you can appreciate that they tend to overestimate so here the a bit the shorter 400 and 300 here it's and they tend to be more veridical for 600 the same it's here so you have 600 is a little bit more underestimated here here it's more or less veridical and here you tend to underestimate duration so this is the famous convergence to the meaning of the distribution so the subject yeah can you tell what is the difference between blue and the red curve okay are two different so the blue and the red are two distinct experimental blocks so subject per force so subject is asked to reproduce duration in two different temporal contexts in one case they handle 300 450 and 650 so when they do this they do this task for let's say 70 70 times okay and then you just you stop with this and you ask them to do the same type of task but this time the range that they have to reproduce is likely bigger so the shorter duration of the range is 600 milliseconds the intermediate range in this case is a bit more than 800 and or 800 I think and the longest is 1.2 seconds so the task is exactly the same is just the range their handling is different thanks so and this is it tells what I was telling you before that the subjects so the perception of the subject is driven by the context okay so there is a big influence of the context and the subjects tend to converge to the mean of the distribution uh they are handling in these different blocks because okay I observe these two points these two points are the same physical duration so you give you you ask the subject to reproduce 650 milliseconds but you ask to reproduce this duration in two different contexts in one case the range is small and and he has a smaller mean value in another case is a bigger range and the subject perceived the same physical duration has different because the context has changed this is something that to follow up of Matteo's question and my answer that the perception it's not something uh frozen and static but really depends on what you perceive before okay it's really influenced by the context in which uh in which you're you're you're you're perceiving things so the environment matters and the the brain builds statistics of the environment and the way we perceive is influenced uh by that okay and this is uh just the same it's the performance of the same experiment but this time uh it's uh it's uh rather here the subject had had a feedback so they hear a sound and when they produce the sound they hear a second sound so they have a cue that help them to reproduce duration and indeed if you appreciate they really tend although they have these subtle biases they tend to be closer to the to the to the perfect clock whereas if you don't provide any feedback to this object so you do what i show you before so with the the sounds that you just start you you you you hear a sound peep you have a cue and you just have to press all the key down and release without any other help apart from the sensation of your key press you tend to be less close to the to the reality so you're you're very you're more distant from this uh ideal clock okay but even though and so and generally what it's graph is telling me is the subject overall tend to overestimate more so they tend to press more than these physical durations are but if you look at relative differences so if you look at the differences between the different points you still see that the pattern is exactly as it was before so you tend to have this regression we call it to the mean and this context effect but this was a sort of regression from what was my goal was to show you the tasks and how we measure the performance and something that i want to to tell you about the performance of the subject so there is something that it's always there no matter uh the task you use to measure duration perception no matter the sub no matter the subjects you are doing your experiment with so no matter if you're using animals or if you're animal animal that are not humans or human animals you tend to see the same pattern and this pattern is called scarlet property so it means that basically that if you this is exactly what i show you in the reproduction okay this is the the you show something that lasts eight seconds and you ask participants to press a key for eight seconds okay or for 20 seconds so this is an experiment that works with much longer range that i'm normally work with so it's a very it's a multi-seconds range of time but still the task is the same and so and if you basically plot the performance so the plot the the time the subject presses and this is over time and you see basically that on average subjects is very close to the reality of the target so eight seconds in this case 20 seconds in this case and then if you look at the the variance so the variability uh on a trial by trial basis you see there is a certain variability no but in this variability it's greater you see the the width of the Gaussian curve it's wider for 21 seconds rather than eight seconds so basically this means that and if you basically normalize the two curves so if you divide everything by the target interval that you are using you basically can superimpose the two Gaussian so because this tells you that the the the the variability of your temporal performance scales with time it follows Weber's law we said a special case of Weber's law and this is something very typical even if you are so if i'm asking to you to judge the the pitch of two sounds okay or the weight of two objects so a lot of this is a sort of feature that is in your sensory system and it's it's there no matter the the type of judgments you are to make so that really your your your ability to discriminate a certain things changes with the range you are really uh that you are handling so if you have to discriminate one kilos with two kilos you feel the difference but if you have to to say the difference between between 20 kilos and 21 kilos it's still one kilos difference but you are less you are you'll be worse in discriminating this one kilo difference if you have to if the target is 20 kilos and it's the same for time right so your variance scales with the really target interval that you that you have to and this is an example still the same super so the the same curves and this is for example this is taken from a study that studies aging people and people that have parkinson disease that is a disease that causes you problems in motor coordinations and is often linked to deficits in your dopaminergic system in specific brain areas in your especially in in in structures of the brain that use dopamine as a neurotransmitter and those are often subcortical regions like the basal ganga but even prefrontal cortex and this is basically uh the the the the the the performance with patients that are on dopa so where they are they taking dopamine and this is when they are off dopa so when they basically don't take this dopaminergic drugs and basically as you see this color properties doesn't hold anymore so the the the behavior it's much doesn't fall the the Weber laws as it should be normal people and this is just according to these people just to prove the importance of the dopaminergic system to the the capacity of telling time okay the temporal precision and now i'm showing something similar in animals right to show that even animals show the color property so this is exactly the same reproduction task that i show you before but this it's monkeys who have to do that okay monkeys are of course are trained for a month to do this task and here is a we will see in detail this experiment in the following lectures and basically here the monkey is trained to associate different cues like so different colors okay so red and blue with different durations in one case is 800 milliseconds in other cases a second okay and the shape of the q so whether it is a square or a triangle they have to use different factors so different body parts to to give an answer so to reproduce time in one case they have to make a circuit so meaning they have to move their eyes to a target and in in another case they have to really keep press they have to really use a lever to their finger to press and to reproduce the duration in that case the reproduction so basically there is something flashing on the screen so but an important thing is this bit so basically they have to so they have to get ready to to perform this is the trial initiation then there is something flashing on the screen that in case of they have to make that tells the monkey where is the target of the eye movement and then this is really the time they have to produce so this the monkey has to hold the response so differently from what I said you before so here they don't have to press hold and release here they have to refrain from moving from moving and for a certain amount of time in case the the q was red they have to wait at least 800 milliseconds before making the eye movements if it was an eye movement trial or they have to wait 800 milliseconds before do a key press if it was red or a second and a half if it was blue the q and so they how they do they learn they learn through reward basically so they are they get reward only if they waiting it's the waiting time before making a movement it's as if it is supposed to be right and so they learn to do this and I can see you see now this is really the production interval of the monkey so you see on the y-axis is really the the production and this is the number of trial they basically they they they they perform so you see an each dot is a trial so it's actually response and if you see here summarized the distribution of their responses in blue is the longer range in red is the short is to 800 and you see you know how so it's greater the variability in the longer range rather than the short range you see and these are the first our top is one monkey bottom row is a second monkey monkey studies of course the record from a limited number of of animals right it's just too in cognitive neuroscientists use a greater number of subjects because then we run statistics on on the group okay so we sample it depends what type of experiments you are you are performing but normally if you just measure behavior and you don't record any brain signal you need at least 20 people even 25 30 40 even okay of course the greater is the sample the the more representative of course of the population is what you what you see okay so you can make your you know you are more confident in making some assumptions that refers to the population from which the sample is is taken okay so if i'm sampling young i can say something i can make inferences about the the the young aging the young exactly the perception of time in the in the younger people but i think i'm it's i'm supposed to stop now right yeah so i have a question yeah see what is the i mean what is the origin of this color property or let let me so does it has to do with the fact that i mean the the the information uh uh information limits essentially in storage capacity of uh say how how many bits you can use to to do this task and then how you should use most efficiently these bits yeah well it must come from uh the limit the limitations of your yeah of your of your sensory systems not the the grain that your your sensory system can handle right so because if you if yeah i think it's what you say this more or less could be the case that this is the reason why but it is since it's so common across sensory feature is not just something typical about time it's something that even if you have to estimate the length of a segment no you have to judge if something is a is a half a centimeter or a centimeter and a half it's the same so again for pitch it's probably due to read the the the limitations of our of our of the incoming of the information you can handle at once it must be like like something of that sort but i don't know i'm not aware if someone has it must be some someone who has tried to answer these questions but it's interesting i can i can browse and check if someone has studied that the origin of the scallop but any model that wants to try to explain how time works in the brain that has to face this issue of being able to replicate the scallop property although the scallop property okay the scallop property study is taken as a very general rule no that holds across across across tasks across speeches but indeed if you go in deep and look at the literature you realize that for example it doesn't hold for durations that are below Mateo below below the the 100 milliseconds so already if you under 50 milliseconds this doesn't hold all durations that are above two seconds or the the the scallop properties sort of start failing it's not so obvious okay because the scallop property is taken as a proof sometimes of the fact that the clock is universal okay but indeed the failure of the scallop properties on the other hand are taken as a proof that okay listen but this might not be so universal this law and so let's say depending on the sensory modality you are using the the you will see it will present some experiments that tested that he uses different tasks some more motor some more perceptual different sensory modalities signal from sensory modalities and it founds out basically this study found out that the scallop property varies indeed if you change the properties also of the stimuli so I imagine that say if if you have a if you look at longer time scales if it fails because your distribution has more features let's say then then then it is because that when you have a longer time duration you use more information or more bits you are less limited in the capacity and you engage a different system as well Mateo because if you have to under 20 seconds you know the mechanism that you'll probably use is different so you engage a lot of memory there is a huge memory load for you compared to to half a second right or 200 milliseconds that's totally from the cognitive point of view you probably engage different resources less attention so the smaller range is more into the automatic you probably do it more automatically without really devoting resources like attention that it's limited this is has been proved also memory capacity are limited so I think this is what we are going to see in the next lectures yeah exactly yeah in the next lectures so other questions for Dominica you can write to me if you have as yesterday summer the question is in the in the chat is what is the take-home message is its color property of time perception yeah well the take-home message is in there in most of the cases yes yes there is color properties is a property of time perception but we should bear in mind that there are cases where this color property is not always respected exactly so and this depends we will see tomorrow from the sensory modality and the task at hand can change this but in general yeah it's for most of the cases it works so yes so if there are no other questions I have a question professor yeah you were saying in the two AFC two intervals and then the two AFC single interval and you are trying to avoid the use of working memory right yeah yeah sure but at the same time you have a template you have to build so that is based on memory as well so the role of memory in time perception I think is like of fundamental use and what are the studies on this if you have any reference yeah there are I mean there are of course memory is very important for time perception in that case you in the single case in the single interval you reduce a lot the working memory but but not but you have this longer memory on the other hand no but the load of the income so of you don't have to handle all this first second compare so it's reduced but you cannot avoid it right also because it's intrinsic in the time right you can't if you are interested in reading a classic book of nearest cognitive about cognition and human cognition and William James which is the brother of Henry James by the way brought a seminal book on the cognitive neuroscience and even in the last century so he basically was able to say that you don't without memory we don't have time no so because of course working memory so if you have to integrate information over time there is somehow a form of memory like and even if it's not exactly working memory it's an iconic memory it's a sensory memory it's a very low level memory that you have to engage so this is true it's and the role of memory depends on the range as we were saying with Mattel a few minutes ago that the longer the range the more the engagement of of of memory um it's very difficult to dissociate memory from and so when you encode the stimulus it's very difficult to dissociate the moment where you extract from the moment where you just hold where integrates over time this information so it's not clear so there are a lot of studies that for example so one way to study would be to look at the at the time that is between the two stimuli and see what's going on for example while you are holding while there is nothing on the screen you're just holding the previous information and waiting for the second one I did some studies on that anybody if you want I can if you write me on the chat I can give you some some references but it's very mind that it's not so obvious to dissociate time from memory especially at this short range if we talk about you know episodes like mental time travel and stuff that are more related to putting in sequence events right if you watch a movie no there are some studies that you they make you watch a movie and then they scramble the the temporal sequence of the scenes that you saw and then what do your task is to put things in order in that case there is a lot of episodic memory and it's still time because you have to build a time sequence you have to remember what came first and what came later and in that case the role of the the the medial court this is the pocampus so all the the system that deals with memory it's more important but what I want to and I think this is a message that you will hear from me multiple times what is emerging with the research in this field is that it's really a dream to find an area that does just time the absolute modularity of cognitive function is a dream it's very you know convenient for scientists to think oh this bits of the brain does just that that bits of the brain does just that it's often it's never the case and especially with time because you use time to act in the world so for your motor action you use for perception so and what it's emerging is that depending on the the task that you have to perform then you engage a circuit that can tell time so if I have to do attention to time I use attention on circuits if I have to I need memory and a precise temporal aspect in the memory then I use the memory circuits so it's really very not so modular time in the brain okay but according to the function you can you can engage that network you can use that for for telling time but this is this lack of modularity is something that it's also more and more popular in general in cognition so memory affects the perception right so how do you define memory so what is memory or how the brain actually stores memory so if so say if I want to store something in the physical world like I can store money in my wallet so money so how brain stores memories what's the concept wow so you treat me as as if I was an handbook of neuroscience yeah I'm glad I'm laughing because it's an important question of course it's but it's there is a huge field of research about how the brain deals with memory we had a Nobel Prize that Edward Moser who uses studied a lot for campus so we know a lot we know that there are different types of memory that some as I said some it's a memory that you use for really slow levels you just for it's an iconic memory that it's very sensory but there are you know this working memory with temporary storage there is a long-term memory it's a semantic memory where you store your concepts so this is there is an entire field of research on on that it's not an easy answer to give to you but it has been extensively studied so we know more or less we we learned this to sort of dissect so to sort of partitioning out the problem so we know that there are these different functions and for each of these type of memory that we have we know that more or less there are parts of the brain that are interested in each of these memory functions yes thanks so professor do you mind if I ask one question yeah yeah so in yeah so in the figure on the bottom right of the slide the red dots and I don't know at the last page yes yeah yeah so as you can see on the blue dots which is the trials with higher amounts of time as you can see the the x-axis you wrote trial and I assume that those numbers are the numbers of trials that you showed some stimulus right yeah it's the monkey had that's the whole session it's 800 it's a huge amount of trials yes so I assumed that if we increase the number of trials our brain tend to learn the stimuli and the actually the data points gets near your nearer and nearer to the mean value but your data points shows here that no matter how many times we show the trial there's always a misinterpretation of time that our brains cannot perceive and we always underestimate or overestimate if the duration of showing a stimuli is longer than a particular amount of time so we're not learning if so our brain doesn't adapt itself to predict the correct time no matter how many trials we show yeah well but it's yeah it's okay this is just 800 trial but you can learn so this is uh it's just um this is a measure of of variability but if you if you let's say look at how uh if if for example rather than than um if I use a different task and I measure because this I can I can so here I ask the monkey just to do always 800 milliseconds right but if I imagine that I I manage to I ask a totally perceptual task so I ask to discriminate between 800 and 800 and 900 milliseconds and if I train humans do this in monkeys I'm not aware that there are but all studies are about learning but it's a learning in different they look at different aspects anyway so if I train you for five hours on this task your ability to discriminate so this this 100 milliseconds for you become too big so not to see it too big so your performance will reach uh will become higher and higher so whereas at the beginning maybe your performance is around 70 percent 75 then your performance increases or if I'm able to use to decrease this gap between the two durations over time you will manage to reach the same 80 accuracy but the the the distance between the two stimuli becomes smaller so indeed you can learn time now so if I look at this so if I'm so if your question was whether we can learn time or not because we do we have research on that in this particular figure there is no learning that we could if I mean so I think figure the feedback is whether the stimulus was longer or shorter so there is no need for the animal to to learn more precisely than this no exactly see because they have to yeah yeah sure they don't have to discriminate even they have to just hold the response for a certain amount of time exactly this is a correct and they get reward if enough of the trial if they are able to hold the response at least for a hundred for 800 or 1.5 seconds so meaning that basically uh it's the precision they are they're required is not huge but if you require to uh more precision as I said in my example so that your task is really to discriminate between the duration between two stimuli and you get feedback and you are trained for a certain amount of time you learn so that your your performance becomes better and you need less difference between the stimuli to have a certain level of accuracy and your brain changes so you suggest for just let's just say we have one stimuli and it's just asking a person to estimate 1.5 millisecond and hold the button and if we provide a feedback for just one for just that simplest stimuli we would see after many trials that the dots actually get nearer to the mean value yeah yeah this could be in the reproduction context I don't know a lot of works I know a lot of work they studied learning in the more perceptual context and for sure in perceptual context you learned and you are able to learn and your brain so change changes as a consequence of this learning as well thank you so I think we went over over now it's okay it's actually very stimulating it's very refreshing to give talks in this context because it brings a lot of questions you just it baffles you how things happen that you just for me also for me it's very very interesting yeah thank you guys okay thank you very much Dominica thank you to you see you tomorrow thank you very much thank you and so have a nice day evening or night you too guys thank you tomorrow thank you


Hello MPS people or anybody else who's watching these videos. My name is Peter Denon And I'm a multimedia student first year and I'm it's my week to do my turn to do the vlog How exciting I know I've left it really late in the week and I haven't really got much content So I'm just gonna show you some stuff that I was doing earlier on in the semester So this next piece of footage is from week two And she's locked up So the lads are doing interviews Voice interviews and this is pretty much it So we're talking about where you're from Sligo. Yeah, I'm from Sligo. It's really beautiful there Really close to the sea so I spend lots of time By the sea walking my dog spending time with my family that kind of thing What other hobbies do you have so I love to play sport in particular GA Soccer is a great love of mine as well G is sport that I'm focusing on the name is James Murphy James kill and where you from James? I'm from Dunboy County me cool and any hobbies James. Yeah, I'm adding to photography Photography what you like what you like taking pictures of lots of different things. I like sports photography I like landscape. Can you tell us about the last holiday or anything any events that may have took place take place holiday? The last holiday was actually in Ireland I went I went traveling around a few different places and I went my cousin. No, we're about yeah prevent south Down around Kerry. Cool. Did you go to the ring and Kerry? I Haven't actually been to the ring Kerry. No. No, I'll kill cool stardew. You can see that you can see the whole galaxy Yeah, anyway, James. I think we're done here. Yeah, thanks very much. See you know Yes, it was interviews were for a Sound production module that we're doing because I've left it so late in the week I just I'm now going to I guess show you a couple of things that I'm gonna do today have a website to do for Information design and I have to go to the shop and buy milk. So here we are at the milk section And They don't have the milk I need so we're gonna have to make another stop to another little So cue the next little joy So it's making a video now say what's up? Hey deuces me and fear a little security man. What do we what do we used to do usually McDonald's? You should work in McDonald's security inside. Yeah. Yeah, those were the days. Hey. Yeah, those were not the days So to go in that last clip I used to actually work with him and it was just a coincidence that he actually asked me What was I doing and I was like, yeah making a video and he's like can I see your camera? I was like, yeah, no problem. So that's the reason for that I didn't just pull out my camera and start making a video with him. That would have been awkward. Oh milk Oh milk, where are you? Where are you? Where are you? Holy moly? There it is 385 are you having a laugh? Not a hope 385 for milk. I'm gonna try something new maybe I'm gonna try this whatever this is Royce milk Sounds disgusting, but we'll give it a go. Thank you guys for joining me on my little mission to try and find milk I just had a bowl of cereal with the rice milk and Tastes like piss Definitely won't be having that stuff again.  I feel sorry for them But this is not one of those videos it obviously isn't one of those videos But just poor little cows between seeing the guy used to work with some random clips I hope this vlog was kind of half entertaining. I'm gonna finish it with a little photosuck thing We did a light drawing painting thing with sparklers. Oh And one more thing I did an ice bath today. The only reason why I did it was for the video Here it is Really though, thanks for watching and Have a good semester have have a solid finish to you guys semester. All right, and look after yourselves. See you later


Hello and welcome to the session. In this session we will discuss measures of dispersion. The dispersion or scatter in the data is measured on the basis of the observations and the types of the measure of central tenancy used there. Measures of central tenancy is not sufficient to give complete information about a given data. For this purpose we use a factor which is called variability and the number that is the single number which describes variability is called measure of dispersion. Here we will discuss measure of dispersions like range and mean deviation. First we have range. Range of a series is equal to the maximum value minus the minimum value. The range of data gives us a lot of idea of variability or scatter but it does not tell about the dispersion of the data from a measure of central tenancy. Now we shall discuss mean deviation which is very important measure of dispersion. Mean deviation is basically the mean of the absolute values of the deviations from the central value. Now we shall discuss mean deviation for ungrouped data. Mean deviation about the mean denoted by this is given by 1 upon n summation i goes from 1 to n modulus xi minus x bar. Here we have xi are the observations. X bar is the mean. N is the total number of observations. Then mean deviation about the median denoted by this is given by 1 upon n summation i goes from 1 to n modulus xi minus m where this m is the median. xi are the observations and n is the total number of observations. Consider this data given to us. Here we have total number of observations that is n is equal to 10. Now the mean x bar is given by summation xi upon n that is sum of all these observations which comes out to be equal to 120 upon n that is 10 is equal to 12. So we get the mean for this data is 12. Now the values xi minus x bar are given by 3 5 minus 2 1 minus 5 6 minus 3 minus 6 2 minus 1. Then the values modulus xi minus x bar are given as 3 5 2 1 5 6 3 6 2 1. Now we have mean deviation about the mean is equal to summation modulus xi minus x bar that is sum of these values which comes out to be equal to 34 upon n that is 10 and this is equal to 3.4. So we get mean deviation about the mean for this data is 3.4. Then we need to find the mean deviation about the median for that purpose we will not calculate the mean x bar but we will calculate the median m. Next we discuss mean deviation for group data. We know that the data can be grouped as discrete frequency distribution and continuous frequency distribution. First we shall discuss mean deviation for discrete frequency distribution. The distribution in which we are given different observations with the corresponding frequencies is the discrete frequency distribution. In this case mean deviation about the mean is given by 1 upon n summation i goes from 1 to n f i into modulus xi minus x bar. Here we have the mean x bar is given by 1 upon n summation i goes from 1 to n x i into f i. x i are the observations f i are the corresponding frequencies then n is the total number of observations and this n is equal to summation f i i goes from 1 to n that is sum of the given frequencies. Next the mean deviation about the median m for discrete frequency distribution is given by 1 upon n summation i goes from 1 to n f i into modulus xi minus m. Here we have the median is m. Consider this data given to us in which we are given the observations xi and the corresponding frequencies f i. Now here we have n is equal to summation f i that is sum of these frequencies which is equal to 66. Now let's calculate the mean x bar which is equal to summation xi f i upon n this is equal to 528 upon 66 and this is equal to 8. So we get x bar that is the mean is equal to 8. Now the values for modulus xi minus x bar is given by 5 3 1 1 3 5 and then f i into modulus xi minus x bar is given by 30, 24, 15, 25, 24, 20. Now summation f i into modulus xi minus x bar that is sum of these values is equal to 138. Now mean deviation about the mean is equal to 1 upon n that is 1 upon 66 multiplied by summation f i into modulus xi minus x bar that is 138 and this is equal to 2.09. Hence we get this is the mean deviation about the mean for this given data. Likewise to calculate the mean deviation about the median we need to find the median for the given data. Now let's discuss how we find mean deviation for continuous frequency distribution. A continuous frequency distribution is a series in which the data are classified into different class intervals without gaps along with the respective frequencies. Mean deviation about the mean for continuous frequency distribution is given by the same formula as for discrete frequency distribution that is equal to 1 upon n summation i goes from 1 to n f i into modulus xi minus x bar but in this case we compute x bar that is the mean by standard deviation method that is x bar is given by a plus summation i goes from 1 to n f i into d i upon n multiplied by h. Here this a is the assumed mean h is the common factor n is equal to summation f i that is sum of all the frequencies then d i is given by xi minus a upon h. So in this way we calculate the mean that is x bar for continuous frequency distribution. Mean deviation about the median is given by the same formula as for discrete frequency distribution that is 1 upon n summation i goes from 1 to n f i into modulus xi minus m. Here the median m is given by the formula l plus n upon 2 minus c upon f multiplied by h. Here l is the lower limit of the median class h is the width of the median class f is the frequency of the median class and c is the cumulative frequency of the class just preceding the median class. And we know that the median class is the class interval whose cumulative frequency is just greater than or equal to n upon 2. Consider this continuous frequency distribution given to us in which we have given the class intervals and the corresponding frequencies xi is the midpoints of the class intervals given by 100, 110, 120, 130, 140, 150. Now see if that is the cumulative frequencies are given by 9, 22, 47, 77, 90, 100. Now here we have n is equal to summation f i that is sum of these frequencies which is equal to 100 then n upon 2 is equal to 50. Now median class is the class interval whose cumulative frequency is just greater than or equal to 50. So as you can see cumulative frequency for the class interval 125 to 135 is 77 which is greater than 50. So we say the interval 125 to 135 is the median class and so from here we have l that is the lower limit of the median class is equal to 125 h width of the median class is 10 f that is the frequency of the median class which is 30 then c which is the cumulative frequency of the class just preceding the median class that is for this class the cumulative frequency would be 47 so c is equal to 47. So now the median m is equal to l that is 125 plus n upon 2 that is 50 minus c that is 47 upon f that is 30 multiplied by h which is 10 this comes out to be equal to 126. Now the values for modulus xi minus m are given by 26, 16, 6, 4, 14, 24 and values for f i into modulus xi minus m by 234, 208, 150, 120, 182 and 240. Now mean deviation about the median m is equal to 1 upon n that is 1 upon 100 multiplied by submission f i into modulus xi minus m that is sum of these values which comes out to be 1134 so this is equal to 11.34 so this is the mean deviation about the median for the given continuous frequency distribution. This completes the session hope you understood the concept of mean deviation and how we find the mean deviation for ungrouped data and group data.


Here we are in the next tutorial, we're going to look at the scatter plot. First of all, my cascading style sheet, let's run that, and we have this notebook that looks a bit better. Scatter Plots, let's set up our Plotly Library. As per usual, we're going to import iPots so that we can plot right inside of the notebook and we've got to initialize this notebook mode, so we're going to import it and then we're going to execute that function with these parentheses there. I should say we're also going to import the high-level chart objects, so plotly.graph objects as go, go there. We go, indeed. We're going to import the numerical Python library, so numpy, and we're going to use the abbreviation np, and then we're going to seed this seeder number generator. So let's go numpy.random.seed. Let's create a bit of data, some data point values for us to work with. We're going to have one, two, three, four, and then five, six, seven, eight computer variables here, female age, male age, so we're going to stick to just for the sake of ease of explanation, just to this binary way of looking at gender, so only female and male, and we are going to have female. So let's create these data points. We're going to have female age and male age, so just for the sake of ease of explanation here, stick to this binary view of gender, so only female and male. We have the age there, we have salary, and we have debt. So female age is going to be from a random integer with a load of 20, a high of 65, and 100 values, and then the same for males. The salary, we're just going to play a bit. So we're going to take female age, and we're going to add to that random uniform value from negative 10 to 10, and add another thousand. So this is going to be element wise, so for each element in the list of 100 values that we have here in this numpy array, we're going to add the corresponding value in this uniform value of 100 and add another thousand, and we're going to do the same to male salary there, and then we're going to have female debt equals male debt, so that's the way to make two computer variables and make them exactly the same as each other, and that's going to be a random integer from 15 to 30 with 100 values, so instead of using the keyword name saying low equals high equals, because these are normal keywords, you don't actually have to use the names, and so it's 15, 30, 100, and then the tax, we're going to create some of those and again just add 10 to each of those values. So let's run that, let's do a bare bone scatter plot, that's what it's all about, so we're going to go go dot scatter, scatter being this high level plot that we can use, what is created on top of our figure, and we're going to use x equals female age, y equals female salary, so when you see here with a scatter plot, it's numerical variable against numerical variable, and each one of them will be each dot that we create in the scatter plot will be part of a pair, and the mode that we're going to use is just markers, and data equals trace, so just this trace part of a list, and we're going to use this key value pair of a Python dictionary to pass it to the i plot, and let's run that, and there we can see the way that we created it by adding those values, that there's some sort of correlation between what we have at the bottom edge and the salary on the left inside the y-axis that we can see here, so those are quite small dots, we can really do something about that, so let's change these markers, so I'm going to have mode still being markers, but then for marker we're going to pass a dictionary of values, so the dict function here in Python, so the size being 12, and the marker being this orange color with a bit of opacity there, only 90% of the opacity, and let's change the layout, so the way that I'm going to use layout here is again as a Python dictionary, so we're going to have title being correlation between female, age, and salary, the x-axis is the key, the value is another dictionary with a couple of key value pairs, title being age, and zero line being false, and with a y-axis title being salary, and the zero line being false as well, and the i plot, the data is data, and the layout is layout, as per usual, there we go, so now we have an x-axis title here, a y-axis title, we have a title here at the top, correlation between female, age, and salary, and we see these much larger orange dots, and if I just hover on one you can see that the value for that one was 1039, and the age was 34 that we can see at the bottom, we can change that, and now we can see them plotted, the hover there being 31, the age, and 1021 being the salary, 0.161, so let's do more than one dataset, so for that I'm going to create two separate traces, and one being the female, one being male, and again it's age against salary, I think you know what's going on here now, data will be the list of the two traces, and the data I'm going to just pass the data that I've created here, this list of the two traces, to the data key value in my dictionary here, and we can i plot that, so there we go, we've got female and orange, and the male in this blue, and we can see all the values as we go up, we can see this beautiful correlation between age and salary there, so let's add a third variable in this 2d space, and that's what scatter plots are all about, and I can do that in a few ways, one is by marker size, and the other one is by marker color, so let's start with this marker color, and that's to introduce a color scale, and you can see all the color scales that are available, grays, and this and that, and that, and that, and that, etc, we can use Portland, there's Portland there, so we're going to create a trace, and it's x equals female age, y equals female salary, mode being markers, the marker being a dict of the size of 10, the color is, color is going to be the female debt, and the color scale is Portland, so we have age, salary, and debt, all in the same 2d plot, and that's going to create a scale on the right hand side, a color scale, and we want that scale to be true, look at the layout, what we've done there, let's do the i plot, there we go, and now we've added this third variable, because we've got age and salary, but this color is also going to be this color that we introduced here as the debt level, so down from 16 up here, 28, so these red ones have more debt, say, than these blue markers here, so that's one way to introduce a third variable, the other one is just by way of what we would know as a bubble chart actually, but that's just the marker size, so what we're going to do here is just change from female to male, and the marker is going to be the size of the marker as passed as a part of a dictionary here, and we give it a color, let's have a look at this, so now we see that this debt is now the size of these, so the larger the size, the larger the debt, so that's one extra way of bringing in this third variable, so that means we can actually have four variables that we plot in 2D space, because we can just combine the color scale and the size, so here I've made the size, the debt, and the color, the tax, so that I have four variables actually drawn right here in my two-dimensional scatter plot, and that's actually quite fantastic to do, so we've added this four variables just in this flat file by just looking at this bubble size, the marker size, and then the color scale, and you can see there the size was the debt and the scale here was the tax, so higher the tax value here the more brown these values are, and we've again used earth, this time we've used earth just as the color scale that we have on the right-hand side, so have a lot of fun with your scatter plots, you can nearly convey a lot of interesting information just using scatter plots, I'll see you in the next, in the next tutorial, please remember to subscribe and hit the bell so that you can receive notification of all the tutorials that I do upload to YouTube.