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Dialogue: 0,0:00:21.11,0:00:26.95,Default,,0000,0000,0000,,Due to technical difficulties, only a portion of lecture 1 is available for viewing
Dialogue: 0,0:00:26.95,0:00:31.09,Default,,0000,0000,0000,,Welcome to Teaching College-Level Science and Engineering.
Dialogue: 0,0:00:31.09,0:00:36.32,Default,,0000,0000,0000,,Now, the title contains the word "teaching," which may spark some questions in your mind.
Dialogue: 0,0:00:36.32,0:00:43.91,Default,,0000,0000,0000,,For example, is teaching just an art? Or is it something that's just - something you're born with.
Dialogue: 0,0:00:43.91,0:00:49.46,Default,,0000,0000,0000,,In which case, either you have it or you don't have it. Well, obviously I don't believe that
Dialogue: 0,0:00:49.46,0:00:51.98,Default,,0000,0000,0000,,or I wouldn't be teaching a course on it.
Dialogue: 0,0:00:51.98,0:00:52.85,Default,,0000,0000,0000,,What would be the point?
Dialogue: 0,0:00:52.85,0:00:59.01,Default,,0000,0000,0000,,Or is it purely a science, where there's a set of equations and procedures to learn,
Dialogue: 0,0:00:59.01,0:01:02.07,Default,,0000,0000,0000,,and then all of a sudden you'll be an excellent teacher?
Dialogue: 0,0:01:02.07,0:01:08.84,Default,,0000,0000,0000,,Well, actually, it's neither and it's both. It's things that we're all born with,
Dialogue: 0,0:01:08.84,0:01:13.75,Default,,0000,0000,0000,,on the one hand, and they're also procedures and techniques, and ways of thinking
Dialogue: 0,0:01:13.75,0:01:17.01,Default,,0000,0000,0000,,that will improve how you teach, and that we can all learn.
Dialogue: 0,0:01:17.01,0:01:20.06,Default,,0000,0000,0000,,So it's a happy mix, my favorite mix,
Dialogue: 0,0:01:20.06,0:01:29.27,Default,,0000,0000,0000,,an art and a science. So, for example, another example that's an art and a science is book design.
Dialogue: 0,0:01:29.27,0:01:36.32,Default,,0000,0000,0000,,So compared for example to just pure art, painting, say modern painting, very unconstrained
Dialogue: 0,0:01:36.32,0:01:40.54,Default,,0000,0000,0000,,vs. say, biology procedures in the laboratory
Dialogue: 0,0:01:40.54,0:01:48.77,Default,,0000,0000,0000,,you know, very very closely specified. It's somewhere in between there is an art but there is, of all
Dialogue: 0,0:01:48.77,0:01:54.21,Default,,0000,0000,0000,,of the arts, of colors, of space, but they all have to
Dialogue: 0,0:01:54.21,0:02:01.96,Default,,0000,0000,0000,,be used together to achieve a particular purpose. So, again, there are some beautifully designed books and
Dialogue: 0,0:02:01.96,0:02:05.86,Default,,0000,0000,0000,,some not so beautifully designed books. And there are principles behind that that we can use to design good books.
Dialogue: 0,0:02:07.66,0:02:11.92,Default,,0000,0000,0000,,Simiilarly, there are principles we can use to design good teaching.
Dialogue: 0,0:02:11.93,0:02:15.82,Default,,0000,0000,0000,,So this is the whole point of this semester is to design good teaching and how you do that.
Dialogue: 0,0:02:17.16,0:02:20.14,Default,,0000,0000,0000,,And rather than give you a big long theory about it,
Dialogue: 0,0:02:20.14,0:02:22.50,Default,,0000,0000,0000,,because actually there isn't really theory
Dialogue: 0,0:02:22.50,0:02:26.42,Default,,0000,0000,0000,,so much in the equivalent to say Einstein's theory of relativity,
Dialogue: 0,0:02:26.42,0:02:29.14,Default,,0000,0000,0000,,but there's principles to learn.
Dialogue: 0,0:02:29.25,0:02:31.65,Default,,0000,0000,0000,,The best way to learn those principles is
Dialogue: 0,0:02:32.36,0:02:34.04,Default,,0000,0000,0000,,with an example.
Dialogue: 0,0:02:34.04,0:02:35.99,Default,,0000,0000,0000,,So what we're gonna do today is
Dialogue: 0,0:02:35.99,0:02:40.64,Default,,0000,0000,0000,,I'm going to do an example of teaching with you.
Dialogue: 0,0:02:40.64,0:02:46.44,Default,,0000,0000,0000,,We're gonna do it slightly sped-up version of what we'd normally do
Dialogue: 0,0:02:46.44,0:02:49.26,Default,,0000,0000,0000,,say if we were actually using this example in a class.
Dialogue: 0,0:02:49.26,0:02:52.18,Default,,0000,0000,0000,,Then we're gonna analyze why it was done that way.
Dialogue: 0,0:02:52.18,0:02:56.01,Default,,0000,0000,0000,,and from an analysis, general principles of teaching will come out
Dialogue: 0,0:02:56.01,0:02:59.04,Default,,0000,0000,0000,,that will be address throughout the semester
Dialogue: 0,0:02:59.04,0:03:03.65,Default,,0000,0000,0000,,and they'll be addressed in the context of particular tasks,
Dialogue: 0,0:03:03.65,0:03:08.12,Default,,0000,0000,0000,,for example, how to make slides that are useful for teaching.
Dialogue: 0,0:03:08.12,0:03:10.82,Default,,0000,0000,0000,,How to use a blackboard.
Dialogue: 0,0:03:10.82,0:03:12.61,Default,,0000,0000,0000,,How to teach equations.
Dialogue: 0,0:03:12.66,0:03:14.70,Default,,0000,0000,0000,,How to design a whole course.
Dialogue: 0,0:03:14.70,0:03:16.06,Default,,0000,0000,0000,,How to make problems.
Dialogue: 0,0:03:16.06,0:03:20.48,Default,,0000,0000,0000,,So all of those tasks will be the week-by-week subjects
Dialogue: 0,0:03:20.48,0:03:23.91,Default,,0000,0000,0000,,and in each task, all the principles that we're gonna talk about now
Dialogue: 0,0:03:23.91,0:03:30.98,Default,,0000,0000,0000,,will show up in those tasks and you'll see the principles illustrated repeatedly.
Dialogue: 0,0:03:30.98,0:03:35.20,Default,,0000,0000,0000,,So, the problem. One of my favorites,
Dialogue: 0,0:03:36.74,0:03:38.75,Default,,0000,0000,0000,,so these are two cones
Dialogue: 0,0:03:39.87,0:03:42.69,Default,,0000,0000,0000,,one is -- has twice the dimensions of the other cones.
Dialogue: 0,0:03:42.69,0:03:46.63,Default,,0000,0000,0000,,So let me show you how I made the cones.
Dialogue: 0,0:03:50.39,0:03:55.18,Default,,0000,0000,0000,,So I printed out a circle and just cut out
Dialogue: 0,0:03:55.18,0:03:57.57,Default,,0000,0000,0000,,one quarter of the circle
Dialogue: 0,0:03:58.19,0:04:00.63,Default,,0000,0000,0000,,and then I taped this edge to that edge.
Dialogue: 0,0:04:05.81,0:04:10.28,Default,,0000,0000,0000,,Or in mathematician speak, I identified the edges
Dialogue: 0,0:04:10.98,0:04:14.01,Default,,0000,0000,0000,,which I now know means I taped the edges together.
Dialogue: 0,0:04:14.14,0:04:16.30,Default,,0000,0000,0000,,and then you get a cone like that.
Dialogue: 0,0:04:17.03,0:04:20.76,Default,,0000,0000,0000,,So this cone and the other cone were cut out of the same sheet of paper
Dialogue: 0,0:04:20.76,0:04:25.40,Default,,0000,0000,0000,,except this one has twice the linear dimensions in its circle.
Dialogue: 0,0:04:25.40,0:04:32.35,Default,,0000,0000,0000,,This circle was seven centimeters in radius and this is three and a half centimeters in radius.
Dialogue: 0,0:04:33.84,0:04:36.03,Default,,0000,0000,0000,,Other than that, they're the same.
Dialogue: 0,0:04:36.03,0:04:42.30,Default,,0000,0000,0000,,The question is which one has the higher terminal of velocity or are they more comparable.
Dialogue: 0,0:04:42.78,0:04:43.65,Default,,0000,0000,0000,,So the question is this.
Dialogue: 0,0:04:44.80,0:04:47.56,Default,,0000,0000,0000,,I'm gonna drop them and the question is
Dialogue: 0,0:04:47.56,0:04:50.87,Default,,0000,0000,0000,,what is the ratio of their terminal velocities?
Dialogue: 0,0:05:01.62,0:05:06.47,Default,,0000,0000,0000,,So the ratio of the big cone's terminal velocity to the small cone's terminal velocity
Dialogue: 0,0:05:06.47,0:05:13.95,Default,,0000,0000,0000,,is equals to what and you get choices along this axis
Dialogue: 0,0:05:13.95,0:05:38.37,Default,,0000,0000,0000,,So here is...
Dialogue: 0,0:05:38.37,0:05:42.27,Default,,0000,0000,0000,,Okay, so those are the five regions to choose from.
Dialogue: 0,0:05:46.91,0:05:49.14,Default,,0000,0000,0000,,So you have five choices for the ratio
Dialogue: 0,0:05:49.14,0:05:51.41,Default,,0000,0000,0000,,roughly one quarter
Dialogue: 0,0:05:51.41,0:05:53.82,Default,,0000,0000,0000,,some range here, because nothing's exact
Dialogue: 0,0:05:53.82,0:05:55.97,Default,,0000,0000,0000,,and we're definitely not gonna do an exact experiment.
Dialogue: 0,0:05:56.91,0:06:01.60,Default,,0000,0000,0000,,Roughly one half, roughly one, roughly two, or roughly four.
Dialogue: 0,0:06:01.60,0:06:04.68,Default,,0000,0000,0000,,So does everyone understand the question?
Dialogue: 0,0:06:04.68,0:06:06.23,Default,,0000,0000,0000,,You're gonna get to try it yourself.
Dialogue: 0,0:06:08.54,0:06:10.24,Default,,0000,0000,0000,,Question about the question
Dialogue: 0,0:06:10.50,0:06:13.94,Default,,0000,0000,0000,,I don't know if you could restate the question... actually there was a signing sheet going around... and I sorta lost it.
Dialogue: 0,0:06:16.80,0:06:20.05,Default,,0000,0000,0000,,So, uh, yeah, can I restate the question, no problem.
Dialogue: 0,0:06:20.05,0:06:22.28,Default,,0000,0000,0000,,So I'm gonna drop them
Dialogue: 0,0:06:22.57,0:06:24.20,Default,,0000,0000,0000,,just like this no tricks,
Dialogue: 0,0:06:24.20,0:06:27.53,Default,,0000,0000,0000,,I'm not gonna flip this one around or anything.
Dialogue: 0,0:06:27.53,0:06:30.86,Default,,0000,0000,0000,,And the question is, what's the ratio of their terminal speeds.
Dialogue: 0,0:06:30.86,0:06:33.44,Default,,0000,0000,0000,,So right away, as soon as you let go of them,
Dialogue: 0,0:06:33.44,0:06:36.05,Default,,0000,0000,0000,,they come to a steady speed,
Dialogue: 0,0:06:36.05,0:06:37.81,Default,,0000,0000,0000,,which is their terminal velocity.
Dialogue: 0,0:06:37.81,0:06:42.20,Default,,0000,0000,0000,,And the question is how do the terminal speeds of the big one and the small one differ.
Dialogue: 0,0:06:42.83,0:06:46.14,Default,,0000,0000,0000,,So in particular, the question is what's the ratio?
Dialogue: 0,0:06:46.14,0:06:47.98,Default,,0000,0000,0000,,And there's five choices for them.
Dialogue: 0,0:06:49.07,0:06:49.92,Default,,0000,0000,0000,,Okay.
Dialogue: 0,0:06:49.92,0:06:51.27,Default,,0000,0000,0000,,That help?
Dialogue: 0,0:06:51.27,0:06:53.98,Default,,0000,0000,0000,,-Yes, and what were the dimensions of them again.
Dialogue: 0,0:06:53.98,0:07:00.33,Default,,0000,0000,0000,,-So this guy is -- he was cut out of a circle who was 7 centimeters in radius.
Dialogue: 0,0:07:00.33,0:07:05.80,Default,,0000,0000,0000,,And this guy was cut out of a circle who was 3.5 centimeters in radius.
Dialogue: 0,0:07:05.80,0:07:09.100,Default,,0000,0000,0000,,And then I was also very careful to use-- do this right?--
Dialogue: 0,0:07:09.100,0:07:15.25,Default,,0000,0000,0000,,I used half the width of tape on the small guy as I did on the big guy
Dialogue: 0,0:07:15.25,0:07:21.09,Default,,0000,0000,0000,,just to get it really very perfect scale.
Dialogue: 0,0:07:21.09,0:07:27.16,Default,,0000,0000,0000,,Any questions about the question?
Dialogue: 0,0:07:27.18,0:07:31.18,Default,,0000,0000,0000,,Okay, so think for yourself for about 30 seconds or so
Dialogue: 0,0:07:31.18,0:07:34.52,Default,,0000,0000,0000,,just to induct yourself into the problem
Dialogue: 0,0:07:34.52,0:07:36.29,Default,,0000,0000,0000,,and then we'll take a vote.
Dialogue: 0,0:07:36.29,0:08:13.75,Default,,0000,0000,0000,,And then you'll have a chance to discuss it with each other.
Dialogue: 0,0:08:18.74,0:08:20.40,Default,,0000,0000,0000,,Okay, let's just take a vote
Dialogue: 0,0:08:20.40,0:08:29.29,Default,,0000,0000,0000,,so I understand I haven't given all of you enough time to come up with an exact answer or calculate anything.
Dialogue: 0,0:08:29.32,0:08:34.79,Default,,0000,0000,0000,,So let's just get a straw poll and then you'll have a chance to argue about it with your neighbor.
Dialogue: 0,0:08:34.79,0:08:38.44,Default,,0000,0000,0000,,So who votes for 1/4 which is--
Dialogue: 0,0:08:38.44,0:08:42.12,Default,,0000,0000,0000,,so let's see-- 1, 2, 3, 4, 5, 6.
Dialogue: 0,0:08:44.14,0:08:47.96,Default,,0000,0000,0000,,Who votes for 1/2?
Dialogue: 0,0:08:47.96,0:08:54.47,Default,,0000,0000,0000,,[counts] 12
Dialogue: 0,0:08:54.47,0:08:57.80,Default,,0000,0000,0000,,Who votes for C?
Dialogue: 0,0:08:57.80,0:09:01.49,Default,,0000,0000,0000,,About 22.
Dialogue: 0,0:09:01.49,0:09:04.28,Default,,0000,0000,0000,,Who votes for D?
Dialogue: 0,0:09:04.28,0:09:05.62,Default,,0000,0000,0000,,No takers.
Dialogue: 0,0:09:05.62,0:09:06.91,Default,,0000,0000,0000,,No takers for D.
Dialogue: 0,0:09:06.91,0:09:11.13,Default,,0000,0000,0000,,How about E?
Dialogue: 0,0:09:11.13,0:09:13.36,Default,,0000,0000,0000,,Okay, so
Dialogue: 0,0:09:13.36,0:09:15.38,Default,,0000,0000,0000,,now find a neighbor or two,
Dialogue: 0,0:09:15.38,0:09:16.72,Default,,0000,0000,0000,,one or two neighbors,
Dialogue: 0,0:09:16.72,0:09:18.52,Default,,0000,0000,0000,,introduce yourself to your neighbor,
Dialogue: 0,0:09:18.52,0:09:21.53,Default,,0000,0000,0000,,and also by the way, unless you're taking notes on your laptop,
Dialogue: 0,0:09:21.53,0:09:27.30,Default,,0000,0000,0000,,if you could close your laptop, that would be very helpful for the purpose of discussion in this whole
Dialogue: 0,0:09:27.30,0:09:28.04,Default,,0000,0000,0000,,course.
Dialogue: 0,0:09:28.70,0:09:31.95,Default,,0000,0000,0000,,So find a neighbor or two, introduce yourself,
Dialogue: 0,0:09:31.95,0:09:37.65,Default,,0000,0000,0000,,you'll be given a chance to meet graduate students from across te institute,
Dialogue: 0,0:09:37.65,0:09:39.75,Default,,0000,0000,0000,,and try to convince them about your answer.
Dialogue: 0,0:09:39.75,0:09:40.91,Default,,0000,0000,0000,,Especially if you have a different answer.
Dialogue: 0,0:09:40.91,0:09:45.07,Default,,0000,0000,0000,,Or if you happen to share an answer, try to figure out why you're sure of it
Dialogue: 0,0:09:45.07,0:09:48.16,Default,,0000,0000,0000,,or if you're not sure of it, settle...
Dialogue: 0,0:09:48.16,0:09:50.69,Default,,0000,0000,0000,,So, discussion time.
Dialogue: 0,0:09:50.69,0:09:54.36,Default,,0000,0000,0000,,And if you have any questions that come up as you're discussing,
Dialogue: 0,0:09:54.36,0:09:56.47,Default,,0000,0000,0000,,raise your hand and I'll come and wonder over.
Dialogue: 0,0:09:58.52,0:10:01.46,Default,,0000,0000,0000,,Okay, so meanwhile I also handed out
Dialogue: 0,0:10:01.46,0:10:04.32,Default,,0000,0000,0000,,feedback sheets for the end of the session
Dialogue: 0,0:10:04.32,0:10:07.40,Default,,0000,0000,0000,,which I'll ask you to spend a minute on at the end.
Dialogue: 0,0:10:07.40,0:10:11.48,Default,,0000,0000,0000,,You'll notice one of the question is what's the most confusing thing?
Dialogue: 0,0:10:11.48,0:10:14.52,Default,,0000,0000,0000,,So if anything really confusing comes up during the whole session,
Dialogue: 0,0:10:14.52,0:10:17.32,Default,,0000,0000,0000,,you can just put it right there, you don't have to wait until the end,
Dialogue: 0,0:10:17.32,0:10:19.65,Default,,0000,0000,0000,,or if there's something you really liked or hated,
Dialogue: 0,0:10:19.65,0:10:22.46,Default,,0000,0000,0000,,that's question 2, you can put whenever to come up.
Dialogue: 0,0:10:22.73,0:10:26.76,Default,,0000,0000,0000,,But, vote #2 and then we'll take some reasons...
Dialogue: 0,0:10:26.76,0:10:29.44,Default,,0000,0000,0000,,so...
Dialogue: 0,0:10:29.44,0:10:32.50,Default,,0000,0000,0000,,One quarter.
Dialogue: 0,0:10:32.50,0:10:36.37,Default,,0000,0000,0000,,One, two, three.
Dialogue: 0,0:10:36.37,0:10:39.36,Default,,0000,0000,0000,,Okay, four.
Dialogue: 0,0:10:39.36,0:10:41.94,Default,,0000,0000,0000,,One half.
Dialogue: 0,0:10:41.94,0:10:44.23,Default,,0000,0000,0000,,Halves don't have it.
Dialogue: 0,0:10:44.23,0:10:48.37,Default,,0000,0000,0000,,There's one... okay great. 4, 5, 6.
Dialogue: 0,0:10:49.25,0:10:50.90,Default,,0000,0000,0000,,Equall.
Dialogue: 0,0:10:51.76,0:10:54.15,Default,,0000,0000,0000,,Let's call it 30.
Dialogue: 0,0:10:54.15,0:10:58.18,Default,,0000,0000,0000,,Two
Dialogue: 0,0:10:58.18,0:11:00.83,Default,,0000,0000,0000,,and four.
Dialogue: 0,0:11:00.83,0:11:03.26,Default,,0000,0000,0000,,Okay, so
Dialogue: 0,0:11:03.26,0:11:04.94,Default,,0000,0000,0000,,thanks for the votes.
Dialogue: 0,0:11:04.94,0:11:07.04,Default,,0000,0000,0000,,Let's take reasons for any of them.
Dialogue: 0,0:11:07.04,0:11:09.74,Default,,0000,0000,0000,,I'll take reasons for any of them, I'll put them up here.
Dialogue: 0,0:11:09.74,0:11:11.50,Default,,0000,0000,0000,,You don't even have to agree with the reasons,
Dialogue: 0,0:11:11.50,0:11:14.48,Default,,0000,0000,0000,,just something you guys discussed and something that was plausible.
Dialogue: 0,0:11:14.48,0:11:17.47,Default,,0000,0000,0000,,-C...
Dialogue: 0,0:11:17.47,0:11:20.04,Default,,0000,0000,0000,,-Oh....
Dialogue: 0,0:11:21.29,0:11:23.85,Default,,0000,0000,0000,,-When you do these activities,
Dialogue: 0,0:11:23.85,0:11:27.65,Default,,0000,0000,0000,,there's always some... [indistinct]
Dialogue: 0,0:11:27.65,0:11:30.28,Default,,0000,0000,0000,,I want to know what you would do in that kind of situation.
Dialogue: 0,0:11:30.28,0:11:33.58,Default,,0000,0000,0000,,-So, you're hmm...
Dialogue: 0,0:11:33.58,0:11:35.39,Default,,0000,0000,0000,,[laughter] I'm not sure how to phrase this.
Dialogue: 0,0:11:35.39,0:11:37.76,Default,,0000,0000,0000,,Uh...
Dialogue: 0,0:11:37.76,0:11:39.59,Default,,0000,0000,0000,,Let me just take other comments.
Dialogue: 0,0:11:39.59,0:11:41.80,Default,,0000,0000,0000,,[laughter]
Dialogue: 0,0:11:41.80,0:11:43.61,Default,,0000,0000,0000,,I'll come to it afterwards.
Dialogue: 0,0:11:43.61,0:11:45.26,Default,,0000,0000,0000,,Other comments
Dialogue: 0,0:11:45.26,0:11:46.96,Default,,0000,0000,0000,,for any of the reasons.
Dialogue: 0,0:11:46.96,0:11:48.48,Default,,0000,0000,0000,,So again, it doesn't have to be anything you necessarily believe
Dialogue: 0,0:11:48.48,0:11:50.28,Default,,0000,0000,0000,,but things that are plausible
Dialogue: 0,0:11:50.28,0:11:54.13,Default,,0000,0000,0000,,and that's actually more instructive than what you think is for sure right,
Dialogue: 0,0:11:54.13,0:11:58.12,Default,,0000,0000,0000,,because you're trying to figure out what might be true and you're expanding
Dialogue: 0,0:11:58.12,0:11:59.69,Default,,0000,0000,0000,,the ways you're thinking.
Dialogue: 0,0:11:59.69,0:12:06.16,Default,,0000,0000,0000,,-C, because they have identical mass to certain...
Dialogue: 0,0:12:06.16,0:12:11.77,Default,,0000,0000,0000,,-C, so mass-to-area ratio is the same.
Dialogue: 0,0:12:13.71,0:12:19.03,Default,,0000,0000,0000,,Okay, can people think of plausible reasons against that argument?
Dialogue: 0,0:12:20.74,0:12:21.69,Default,,0000,0000,0000,,Yes.
Dialogue: 0,0:12:21.69,0:12:23.85,Default,,0000,0000,0000,,-I have no idea what the actual formula is.
Dialogue: 0,0:12:23.85,0:12:24.64,Default,,0000,0000,0000,,-Right.
Dialogue: 0,0:12:24.64,0:12:29.64,Default,,0000,0000,0000,,-There was a square there...
Dialogue: 0,0:12:29.64,0:12:32.62,Default,,0000,0000,0000,,-Right, so I'll call this not C.
Dialogue: 0,0:12:32.62,0:12:36.89,Default,,0000,0000,0000,,So supposedly, formual actually depended on the square root of A
Dialogue: 0,0:12:36.89,0:12:39.56,Default,,0000,0000,0000,,or something like that.
Dialogue: 0,0:12:39.56,0:12:44.20,Default,,0000,0000,0000,,You know maybe---- say, one chance out of three that it has A to the first power here.
Dialogue: 0,0:12:44.20,0:12:48.06,Default,,0000,0000,0000,,It could have A to the 1/2 or 8 to the 2.
Dialogue: 0,0:12:48.63,0:12:50.90,Default,,0000,0000,0000,,So, could be...
Dialogue: 0,0:12:57.41,0:12:58.79,Default,,0000,0000,0000,,A to the k
Dialogue: 0,0:12:58.79,0:13:03.01,Default,,0000,0000,0000,,M over A to the K for K not equal to one.
Dialogue: 0,0:13:03.01,0:13:05.02,Default,,0000,0000,0000,,Okay, others.
Dialogue: 0,0:13:05.02,0:13:12.07,Default,,0000,0000,0000,,4 against C, intuitive reasons, or for any of the others.
Dialogue: 0,0:13:17.77,0:13:20.64,Default,,0000,0000,0000,,Okay, so hopefully that's...
Dialogue: 0,0:13:20.69,0:13:23.60,Default,,0000,0000,0000,,-[indistinct]
Dialogue: 0,0:13:23.60,0:13:27.68,Default,,0000,0000,0000,,...that air resistance goes with the area
Dialogue: 0,0:13:27.68,0:13:31.28,Default,,0000,0000,0000,,and the gravitational force...
Dialogue: 0,0:13:31.28,0:13:33.100,Default,,0000,0000,0000,,-Okay, so let's see.
Dialogue: 0,0:13:33.100,0:13:42.40,Default,,0000,0000,0000,,F drag partial to area and weight.
Dialogue: 0,0:13:42.40,0:13:44.07,Default,,0000,0000,0000,,So that's the argument for which choice?
Dialogue: 0,0:13:44.07,0:13:46.68,Default,,0000,0000,0000,,For C, okay.
Dialogue: 0,0:13:47.96,0:13:51.13,Default,,0000,0000,0000,,How do you know that the drab scales are the area.
Dialogue: 0,0:13:51.13,0:13:54.94,Default,,0000,0000,0000,,Maybe the scales with the square root of area.
Dialogue: 0,0:13:57.82,0:14:02.67,Default,,0000,0000,0000,,Any argument pro or con?
Dialogue: 0,0:14:05.12,0:14:07.68,Default,,0000,0000,0000,,Okay, yeah.
Dialogue: 0,0:14:07.68,0:14:14.66,Default,,0000,0000,0000,,-scales with the area...you can just break it up...
Dialogue: 0,0:14:14.66,0:14:18.52,Default,,0000,0000,0000,,-Okay, so there's a ....
Dialogue: 0,0:14:18.52,0:14:22.99,Default,,0000,0000,0000,,So for this, let's say there's a ... for subdividing
Dialogue: 0,0:14:22.99,0:14:26.29,Default,,0000,0000,0000,,I'll just know that is subdividing.
Dialogue: 0,0:14:31.55,0:14:34.43,Default,,0000,0000,0000,,Okay, yeah.
Dialogue: 0,0:14:34.43,0:14:38.40,Default,,0000,0000,0000,,-Some weird shape... and then go to the rest of the pieces so...
Dialogue: 0,0:14:38.40,0:14:42.95,Default,,0000,0000,0000,,-So it may depend on the division--I mean, the geometry,
Dialogue: 0,0:14:42.95,0:14:45.72,Default,,0000,0000,0000,,so I'll put that here as geometry.
Dialogue: 0,0:14:52.13,0:14:54.51,Default,,0000,0000,0000,,What else might it depend on?
Dialogue: 0,0:14:54.52,0:15:00.11,Default,,0000,0000,0000,,For example, is air resistance say always proportional to area?
Dialogue: 0,0:15:02.11,0:15:03.29,Default,,0000,0000,0000,,Hmm.
Dialogue: 0,0:15:04.67,0:15:05.71,Default,,0000,0000,0000,,Yeah?
Dialogue: 0,0:15:07.04,0:15:09.04,Default,,0000,0000,0000,,-...Depend on the material of the surface.
Dialogue: 0,0:15:09.04,0:15:12.34,Default,,0000,0000,0000,,-Okay, so it might depend on the material
Dialogue: 0,0:15:12.34,0:15:16.83,Default,,0000,0000,0000,,and it certainly does, which is actually why I was careful
Dialogue: 0,0:15:16.83,0:15:18.88,Default,,0000,0000,0000,,to construct them out of the same piece of paper,
Dialogue: 0,0:15:18.88,0:15:21.74,Default,,0000,0000,0000,,so let me put this.
Dialogue: 0,0:15:21.74,0:15:24.84,Default,,0000,0000,0000,,Material...
Dialogue: 0,0:15:24.84,0:15:28.08,Default,,0000,0000,0000,,So the surface roughness.
Dialogue: 0,0:15:28.08,0:15:30.96,Default,,0000,0000,0000,,[indisctinct question]
Dialogue: 0,0:15:33.56,0:15:36.00,Default,,0000,0000,0000,,-Okay, so whether they fall vertically or downward.
Dialogue: 0,0:15:36.00,0:15:37.37,Default,,0000,0000,0000,,Yeah, that's true.
Dialogue: 0,0:15:37.37,0:15:40.04,Default,,0000,0000,0000,,So it might depend on the way I drop them.
Dialogue: 0,0:15:40.04,0:15:42.23,Default,,0000,0000,0000,,So to make us not have to worry about that,
Dialogue: 0,0:15:42.23,0:15:46.81,Default,,0000,0000,0000,,I'll just drop them simultaniously, pointing downward.
Dialogue: 0,0:15:46.83,0:15:52.54,Default,,0000,0000,0000,,So the fall configuration.
Dialogue: 0,0:15:52.60,0:15:57.02,Default,,0000,0000,0000,,So there's all these other variables.
Dialogue: 0,0:15:57.02,0:15:59.36,Default,,0000,0000,0000,,Okay, so let's do the experiment and then I'll come back to your question.
Dialogue: 0,0:15:59.36,0:16:05.95,Default,,0000,0000,0000,,Okay, so let's do the experiement this way
Dialogue: 0,0:16:09.97,0:16:14.41,Default,,0000,0000,0000,,so I'll stand on the table
Dialogue: 0,0:16:14.41,0:16:23.10,Default,,0000,0000,0000,,and pray that I have matching socks on with is sort of 80% these days.
Dialogue: 0,0:16:23.10,0:16:26.36,Default,,0000,0000,0000,,It's increased.
Dialogue: 0,0:16:26.36,0:16:28.16,Default,,0000,0000,0000,,And I will drop them on the count of 3.
Dialogue: 0,0:16:28.16,0:16:29.34,Default,,0000,0000,0000,,1--
Dialogue: 0,0:16:29.34,0:16:33.86,Default,,0000,0000,0000,,Are they both, the points, about the same level?
Dialogue: 0,0:16:33.86,0:16:35.78,Default,,0000,0000,0000,,They look sort of to me but
Dialogue: 0,0:16:35.78,0:16:40.91,Default,,0000,0000,0000,,my depth perception is actually quite bad
Dialogue: 0,0:16:40.91,0:16:43.31,Default,,0000,0000,0000,,so is that about equal?
Dialogue: 0,0:16:43.31,0:16:46.98,Default,,0000,0000,0000,,Okay, so 1, 2, 3.
Dialogue: 0,0:16:46.98,0:16:48.71,Default,,0000,0000,0000,,Simulateous.
Dialogue: 0,0:16:48.71,0:16:52.90,Default,,0000,0000,0000,,Okay, so there you have choice C.
Dialogue: 0,0:16:52.96,0:16:55.25,Default,,0000,0000,0000,,Interesting consequence of that.
Dialogue: 0,0:16:55.25,0:16:58.30,Default,,0000,0000,0000,,So what that shows is that
Dialogue: 0,0:16:58.30,0:17:01.84,Default,,0000,0000,0000,,drag in this case is proportional to area.
Dialogue: 0,0:17:01.84,0:17:05.51,Default,,0000,0000,0000,,It turns out, that that's not always the case.
Dialogue: 0,0:17:05.51,0:17:08.42,Default,,0000,0000,0000,,So drag very often,
Dialogue: 0,0:17:08.42,0:17:10.26,Default,,0000,0000,0000,,well, not very often in everyday life,
Dialogue: 0,0:17:10.26,0:17:16.18,Default,,0000,0000,0000,,but very easily can be proportional to...
Dialogue: 0,0:17:20.84,0:17:23.12,Default,,0000,0000,0000,,proportional to size.
Dialogue: 0,0:17:23.12,0:17:26.64,Default,,0000,0000,0000,,And you don't know ahead of time which one it's gonna be.
Dialogue: 0,0:17:26.64,0:17:30.85,Default,,0000,0000,0000,,So it vari--- so it turns out at slow speeds,
Dialogue: 0,0:17:30.85,0:17:31.69,Default,,0000,0000,0000,,low Reynold's number
Dialogue: 0,0:17:31.69,0:17:32.68,Default,,0000,0000,0000,,this is true.
Dialogue: 0,0:17:32.68,0:17:34.95,Default,,0000,0000,0000,,Turns out at high Reynold's number, this is true.
Dialogue: 0,0:17:34.97,0:17:37.41,Default,,0000,0000,0000,,And this is the simplest experiment to show that.
Dialogue: 0,0:17:37.41,0:17:40.53,Default,,0000,0000,0000,,So what this shows is that drag is proportional to area
Dialogue: 0,0:17:40.53,0:17:42.90,Default,,0000,0000,0000,,so with the same velocity,
Dialogue: 0,0:17:42.90,0:17:50.06,Default,,0000,0000,0000,,the extra weight is balanced by the extra drag force.
Dialogue: 0,0:17:50.06,0:17:52.44,Default,,0000,0000,0000,,Exactly, four to one.
Dialogue: 0,0:17:52.44,0:18:00.35,Default,,0000,0000,0000,,And what that shows now--the consequence--is that
Dialogue: 0,0:18:02.92,0:18:07.66,Default,,0000,0000,0000,,I'm gonna replace the proportional with a twittle.
Dialogue: 0,0:18:07.66,0:18:09.29,Default,,0000,0000,0000,,So it has an area in it,
Dialogue: 0,0:18:09.29,0:18:12.06,Default,,0000,0000,0000,,so I'm gonna get something with the correct units in it.
Dialogue: 0,0:18:12.06,0:18:13.99,Default,,0000,0000,0000,,So it has an area in it
Dialogue: 0,0:18:13.99,0:18:16.44,Default,,0000,0000,0000,,and now you have left the play with
Dialogue: 0,0:18:16.44,0:18:20.16,Default,,0000,0000,0000,,density, speed, and viscosity.
Dialogue: 0,0:18:20.16,0:18:23.81,Default,,0000,0000,0000,,So now let's actually construct the drag force as a result of that.
Dialogue: 0,0:18:23.81,0:18:27.50,Default,,0000,0000,0000,,So we know from the experiment, it's proportional to area.
Dialogue: 0,0:18:28.39,0:18:29.76,Default,,0000,0000,0000,,And now among these,
Dialogue: 0,0:18:29.76,0:18:34.15,Default,,0000,0000,0000,,so this here is the kinematic viscosity,
Dialogue: 0,0:18:34.15,0:18:39.89,Default,,0000,0000,0000,,which is the one you may be more familiar with divided by row, the density.
Dialogue: 0,0:18:39.89,0:18:44.21,Default,,0000,0000,0000,,So, we got to put some of these guys in, some of these guys in,
Dialogue: 0,0:18:44.21,0:18:46.02,Default,,0000,0000,0000,,and some of these guys in.
Dialogue: 0,0:18:46.02,0:18:49.09,Default,,0000,0000,0000,,And let the units come in as a force.
Dialogue: 0,0:18:49.09,0:18:51.84,Default,,0000,0000,0000,,Well, one of them we can do right away.
Dialogue: 0,0:18:51.84,0:18:57.00,Default,,0000,0000,0000,,There's how many powers of mass over on this side?
Dialogue: 0,0:18:57.00,0:18:58.84,Default,,0000,0000,0000,,In a force, just one.
Dialogue: 0,0:18:58.84,0:19:00.14,Default,,0000,0000,0000,,Right, and there's one here.
Dialogue: 0,0:19:00.14,0:19:02.69,Default,,0000,0000,0000,,So we need to get one over on this side.
Dialogue: 0,0:19:02.69,0:19:04.92,Default,,0000,0000,0000,,Now, among all these guys, which of them have mass in them?
Dialogue: 0,0:19:05.02,0:19:07.60,Default,,0000,0000,0000,,Not this one, 'cause you divided them all out.
Dialogue: 0,0:19:07.60,0:19:09.28,Default,,0000,0000,0000,,Not velocity,
Dialogue: 0,0:19:09.28,0:19:10.98,Default,,0000,0000,0000,,only density.
Dialogue: 0,0:19:10.98,0:19:12.10,Default,,0000,0000,0000,,And density is one power of mass,
Dialogue: 0,0:19:12.10,0:19:15.56,Default,,0000,0000,0000,,so you have to put one density.
Dialogue: 0,0:19:15.56,0:19:17.76,Default,,0000,0000,0000,,Question?
Dialogue: 0,0:19:17.76,0:19:19.24,Default,,0000,0000,0000,,[indistinct question]
Dialogue: 0,0:19:19.24,0:19:21.56,Default,,0000,0000,0000,,So this is a force.
Dialogue: 0,0:19:21.56,0:19:22.60,Default,,0000,0000,0000,,Good question.
Dialogue: 0,0:19:22.60,0:19:24.47,Default,,0000,0000,0000,,So drag is a force.
Dialogue: 0,0:19:24.47,0:19:32.58,Default,,0000,0000,0000,,So this is just newtons or uh, mass legth per time square.
Dialogue: 0,0:19:32.58,0:19:34.70,Default,,0000,0000,0000,,Does it help?
Dialogue: 0,0:19:34.70,0:19:38.25,Default,,0000,0000,0000,,So it's just newtons.
Dialogue: 0,0:19:38.25,0:19:41.72,Default,,0000,0000,0000,,In SI Newtons or in general, mass length per time squared.
Dialogue: 0,0:19:41.72,0:19:46.22,Default,,0000,0000,0000,,So mass times an acceleration.
Dialogue: 0,0:19:46.22,0:19:50.44,Default,,0000,0000,0000,,Okay, so now, we've matched the units of mass
Dialogue: 0,0:19:50.44,0:19:54.43,Default,,0000,0000,0000,,and there's-- but we haven't matched the units of time yet.
Dialogue: 0,0:19:54.43,0:19:56.16,Default,,0000,0000,0000,,So let's sort out the time.
Dialogue: 0,0:19:56.16,0:19:58.52,Default,,0000,0000,0000,,There's no time here, there's not time there.
Dialogue: 0,0:20:00.19,0:20:01.86,Default,,0000,0000,0000,,There's T to the minus 2 there.
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well -- what can we do about that?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,We have to match -- We have to throw in some v and some nu (viscosity)
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And the problem is we don't know how much
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So the time doesn't helps us enough
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Turns out, to make the time and the length work
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The simultaneous constraint
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,The only way we can do it is that
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, making the same argument
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Just to get the masses to match, the legths to match and the times to match
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is the only way to do it
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So you don't have any viscosity
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So actually that's the simplest experiment I know
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,To show that the drag at high speed, most flows are actually high speed,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,High Reynolds number
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Is independent from viscosity
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So it's ro, A, v squared
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And that is a great result because it tells you a lot of stuff
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,About everyday flows and everyday life
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Like for example, why did people reduced speed
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Speed limit on the highway back in the 70's,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,To conserve gas
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well, on the highway
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You're burning gasoline to fight drag
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So if you reduce the speed
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You reduce the drag,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You reduce the amount of gasoline
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,In particular, if reduce speed by 20%,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You reduce v squared by 40%
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Which reduces drag by 40%
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Decreased gas consumption by 40%
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So you can these things right way, just by a simple formula
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Which is a imediate consequence of this experiment
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Now, turns out, this -- how do you get that to work?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is the low Reynolds number limit
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You can't deduce it from this experiment, but, if you know that this is true, you can make the same argument
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And figure out, how the drag force varies for low Reynolds number
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, now let's just check wheter this formula here
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,That we deduced, works at all
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So the folow up question is the following
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Which is that I have -- 1, 2, 3, 4
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Here on this side, I have 4 small cones
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,They're all identical to this small cone
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So 1 small cone, 2 small cones, 3 small cones, 4 small cones
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So I'm gonna stack all 4 small cones, into a thick small cone
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And I'm gonna race it against one small cone
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So the question is: what is the ratio of these guys' terminal speeds?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So let's call v4 and v1
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, 4...
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, so, what is the ratio of their terminal speeds?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,1/4, 1/2, 1, 2 or 4?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, talk to your neighboor for just a minute, we'll take a quick vote and we'll do the experiment
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, so let's take a vote and then we'll do the experiment
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,1/4?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Who votes for 1/4 ratio?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Who votes for 1/2?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,1?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,2?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It's about 35...
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,4?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Oh, 10
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay, so, let's do the experiment
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,1, 2, 3, 4 of them
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay so now let me drop them like --- that
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well it's kinda of hard to tell isn't it?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So that was actually not well designed experiment, right?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Because you actually have to get it out of timer and decide wich one is going faster
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,And measure how long it took
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,It would be nice if had a way that was just like the other experiment
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,What was nice about the other experiment is when I drop them,
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,You got the answer, by the fact that they hit simultaneously
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So if we can make them hit simultaneously
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Then that would be nice, now what do I have to do to do that?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Well I either have to -- Yeah -- I either have to switch their heights
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,4 to 1 or 2 to 1
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So, let's try 4 to 1
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Okay -- [laughter] -- Is that sort of 4 to 1?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,No? What do I have to do?
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This guy got go down
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,This is where my depth perception really fails me
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So I only have a monocular vision. I can see with both eyes, but I don't binocular fuse
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,So I can't tell depth
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,[Indistinguishable suggestion from aluminum]
Dialogue: 0,9:59:59.99,9:59:59.99,Default,,0000,0000,0000,,Oh that's true