Difference between revisions of "Alan Kay: Big Ideas are Sometimes Powerful Ideas"
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+ | |||
+ | <subtitle id="0:0:24">so we</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:27"> actually are dealing with an academic hour here</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:30"> and be fitting with our school setting</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:33"> marvin minsky once said school was the greatest</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:36"> invention anybody ever came up with to keep</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:39"> you from staying interested on anything for any reasonable</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:42"> length of time because of course</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:45"> it has all these schedules in assembly line movements</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:48"> and we have one of those today and</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:51"> I also wanted to leave time for</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:54"> questions but one of the ways I want to leave time</subtitle> | ||
+ | |||
+ | <subtitle id="0:0:57"> for questions is to encourage you to ask questions as I</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:0"> talk so I have no idea how long this</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:3"> talk is and I am going to stop after</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:6"> 50 minutes and regardless of what what</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:9"> happened so please don't be</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:12"> shy ask questions as we go if</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:15"> you like and because this talk is</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:18"> not for me but for you</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:21"> so it's</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:24"> in a series of ideas which are</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:27"> somewhat connected I hope so</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:30"> one contrast</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:33"> I'd like you to think about is the notion beach of</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:36"> common sense that</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:39"> most people take</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:42"> the world around them as reality I</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:45"> once came up with</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:48">at said technology is anything that happened after</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:51"> you were born because</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:54"> the technology that you're born into is</subtitle> | ||
+ | |||
+ | <subtitle id="0:1:57">part of your world and it's taken to be normal there and most</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:0">internet Prince the Internet is one of the great inventions</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:3"> of all time not the web but the internet itself</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:6"> one of the great maybe one of the greatest engineering</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:9"> feats of all time and</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:12"> it worked so well that hardly</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:15"> anybody appreciates it particularly</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:18"> in computing where they should pay more attention to why</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:21"> it works so well so here's a</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:24"> common-sense deduction that</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:27"> has been made by most</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:30"> people on the planet for the slightly less</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:33"> than 200,000 years modern humans have been here</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:36"> and that is something like a king</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:39"> natural and normal</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:42"> extension of the head of the family</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:45"> hunted leaders</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:48"> of hunting groups and etc etcetera so</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:51"> this is just regarded as common sense</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:54"> and in fact was not regarded as it as an idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:2:57"> it was just part of the part of the world that people</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:0"> lived in then in</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:3"> January 1776 Thomas Paine</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:6"> wrote a book which he ironically titled common</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:9"> sense everybody here has heard of Tom Paine's Common Sense</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:12"></subtitle> | ||
+ | |||
+ | <subtitle id="0:3:15"> but he had a big idea in it which</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:18"> was instead of having the King be</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:21"> the law we can have the law be the king and</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:24">what he meant was we can design a much better society</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:27"> than the what the natural</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:30"> seeming hereditary monarchy as we can take our</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:33"> future into our own hands we can come up with a better plan</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:36"> this is an idea that surfaced</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:39"> a couple of times in Greece but not</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:42"> not before not after and</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:45"> this book</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:48"> which pain published at his own expense initially</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:51"> just gave it away had a press run</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:54">between six hundred thousand and nine hundred thousand</subtitle> | ||
+ | |||
+ | <subtitle id="0:3:57"> in six months so</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:0"> that's a lot by today's standards and</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:3"> there were 1.5 million non</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:6"> slaves in the thirteen colonies</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:9"> back then and so this press run</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:12"> encompassed somewhere between almost a half</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:15"> to more than a half of all men women and children in</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:18"> all 13 colonies so imagine just trying</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:21"> to reach that number of people today</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:24"> there is no medium that you could do it with except</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:27"> with the internet I try</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:30"> to get sixty percent of</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:33"> 300 million people no</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:36"> newspaper could do it so</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:39"> so this is a big idea but</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:42"> the powerful idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:45"> and this is the distinction I want to make was the</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:48"> Constitution as a</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:51"> big idea is kind of an insight and</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:54"> often insights insights</subtitle> | ||
+ | |||
+ | <subtitle id="0:4:57"> are wonderful but they're</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:0"> lightweight they're relatively easy to have compared</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:3"> to doing something about it so the</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:6"> Constitution said</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:9"> we should shape society into a self-organizing</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:12"> self-correcting shared idea and resource system</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:15"> and that is a very radical</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:18"> idea even for today for instance most Americans</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:21"> have no idea what the design of the</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:24"> United States was or is it's</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:27">imply not taught in schools it's not the way American</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:30"> history is is taught and</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:33"> so</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:36"> most societies on earth haven't</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:39"> gotten this idea even at the societal level</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:42"> most human beings on earth don't have this</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:45"> idea but this is one of these powerful ideas</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:48"> that makes qualitative</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:51"> differences in almost every</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:54"> area of life and it's related to an even</subtitle> | ||
+ | |||
+ | <subtitle id="0:5:57"> bigger set of ideas so</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:0"> another common sense</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:3"> whoops</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:6"> another another</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:9"> common sense notion which is</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:12"> actually with most Americans today according to the surveys</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:15"> I've seen which is the world is pretty much as it seems</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:18"> so we this</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:21"> is what our nervous systems are set up to do we're</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:24"> basically weren't set up by nature to think</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:27"> we're set up by nature to cope and so</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:30">primary mechanism is whatever environment we</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:33"> find ourselves in so the answer anthropologists</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:36"> know that you can take a child at</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:39"> birth from any culture on the planet and take</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:42">on the planet that child will grow up as</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:45"> a member of that culture you took it too that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:48"> because humans are rather more similar</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:51"> than they are different we have about 300</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:54"> traits that anthropologists have identified</subtitle> | ||
+ | |||
+ | <subtitle id="0:6:57"> that seem to be quite genetic including</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:0"> things like language having culture telling stories</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:3"> and those mechanisms</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:6"> get embodied with the</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:9"> local varieties of those and so the</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:12"> reality you grow up within the language you</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:15"> grew up with is the language and</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:18"> the reality of the culture you you're born in Q</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:21"> so</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:27">now this big ideas</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:30"> have been had a number of times in history I happen to like the</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:33"> Talmud version of it</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:36"> we see things not as they are but as we are</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:39"> so this is a bit I'd love to know</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:42"> what actually</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:45"> happened to the person who came up with this</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:48"> idea did they take it to its logical conclusion</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:51"> considering and</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:54">was interesting that was published in this Talmud is part</subtitle> | ||
+ | |||
+ | <subtitle id="0:7:57"> of the commentary</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:0"> but this is one</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:3"> of the great big ideas of all time this</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:6"> is a really hard one because it</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:9"> completely relative izes what's</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:12"> going on however it's not a powerful idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:15"> but had numerous</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:18"> times and</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:21">powerful idea came in</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:24"> the 17th century and you</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:27"> could point to a number of people and you could point to various</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:30"> societies but</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:33"> 17th century has a has a perfect</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:36"> atomic</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:39"> bomb place where science started</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:42"> because we had Galileo</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:45"> and Kepler and maybe Copernicus</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:48"> beforehand and a few other people but in fact</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:51"> when Newton did</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:54"> the Principia he actually revolutionized</subtitle> | ||
+ | |||
+ | <subtitle id="0:8:57"> human thought and it's probably the largest leap in human</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:0"> thought of this kind that we know of historically</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:3"> this is why most scientists</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:6">think of Newton as being the greatest scientist</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:9"> and he was almost the first scientist and</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:12"> not just in</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:15"> relative terms but in absolute terms the amount</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:18"> of distance he was able to cover not just</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:21">in terms of knowledge but in terms of about look and</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:24"> the powerful idea of science</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:27"> is not so easy to state everything</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:30"> else comes out pretty nicely as slogans and</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:33"> there's more to science than just</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:36"> this but this is one half of it which</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:39"> is science is not about knowledge as</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:42"> niels bohr said science is not there to tell</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:45"> us about the universe is what most people think</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:48"> most non-scientists most kids in school</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:51"> are taught what is called science</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:54"> as in roughly the same way they learn religion in</subtitle> | ||
+ | |||
+ | <subtitle id="0:9:57"> when they go to church or</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:0"> synagogue or mosque but</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:3">in what science is at all it's not about knowledge</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:6"> it's about relating the</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:9"> stuff we can do and can't do in here</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:12"> all the things that we can do with</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:15"> our representational systems to stuff</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:18"> out there that we can't get to directly because</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:21"> everything we do is filtered through our nervous</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:24"> systems as filtered through our culture's is</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:27"> filtered for through the the difficulties</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:30"> we have with making relationships</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:33"> about things and this was not an</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:36"> easy idea to have we'll</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:39"> see in a bit but</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:42"> what's happened in the last 400 years in</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:45"> many many dimensions</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:48"> has been more than has happened</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:51"> in the rest of the 200,000 years and you</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:54"> know the cliche that</subtitle> | ||
+ | |||
+ | <subtitle id="0:10:57"> most scientists 90 more</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:0">of all the scientists who ever lived you're alive today</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:3"> and most of the things that</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:6"> are happening today and some</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:9">of the problems and some of the solutions to those problems</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:12"> are all caused this by different way</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:21">and much is made</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:24"> particularly in the pop culture of</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:27"> bringing bright</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:30"> this is because pop</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:33"> culture's or cultures without a lot</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:36"> of developed knowledge basically</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:39"> live by their wits and so you out</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:42"> with each other and you</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:45"> compete at the level of width but</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:48"> imagine being born with an IQ</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:51"> of 500 who knows how</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:54"> smart leonardo was let's</subtitle> | ||
+ | |||
+ | <subtitle id="0:11:57"> just no 203 who because</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:0"> those figures don't what does IQ me in any</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:3"> way but let's just say hey suppose</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:6"> you're just a hell of a lot smarter than anybody who ever lived</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:9"> but you were born in 10,000 BC</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:12"> how far you going to get so</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:15"> you can probably out wit everybody around you before</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:18"> they burn you at the stake</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:21"> but in fact Leonardo</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:24"> who we know is very very bright could</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:27"> not invent a single engine</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:30"> for any of the vehicles that he designed so</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:33"> he's famous for designing things that look</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:36">like planes and things that maybe look like helicopters</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:39"> and I'll and they're wonderful and he did a lot</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:42">hings but he couldn't make a single goddamn one of</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:45"> them work that is and that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:48"> because he wasn't smart enough to think himself out</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:51"> of the era he had been born into as</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:54"> far as we know if nobody has the closest person who's ever</subtitle> | ||
+ | |||
+ | <subtitle id="0:12:57">thought himself out of the era he was born into his</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:0"> Newton so</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:3"> you have this odd paradox</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:6"> that whoops sorry that</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:12">Henry Ford who is not nearly as smart as</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:15">Leonardo just happened to be born in the right time and</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:18"> so he did revolutionize one</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:21"> of the areas that Leonardo wanted to revolutionize</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:24"> by being able</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:27"> to do adaptive engineering and a little</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:30">invention to the stuff that was already around</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:33"> so his knowledge was</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:36"> processed knowledge and this was very powerful and what</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:39"> was the difference between these two these</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:42"> two guys was this</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:45"> change of outlook that Newton</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:48"> was one of the promulgate errs of</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:51"> so one of the ways I</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:54"> when I talked to grabs grad students</subtitle> | ||
+ | |||
+ | <subtitle id="0:13:57"> or children I say well knowledge</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:0"> is silver but outlook is</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:3"> gold our</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:6"> world is built on changes of outlook that was what the</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:9"> Constitution was that was what Tom Paine did</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:12"> and that's what science did and</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:15"> IQ is led</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:18"> because there is no</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:21"> we know of no developed field knowledge in</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:24"> which you can get by with just talent there's</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:27"> no developed sport in which you can get by with</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:30"> just talent and some of the most</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:33"> difficult sports have been</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:36"> excelled in by people who are not as athletic</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:39"> so for instance Chris effort</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:42"> as an example who is not a particularly athletic</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:45"> tennis player but man that you know</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:48"> how to work and so she got very very</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:51"> good at it and most things have</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:54"> this thing an Outlook also</subtitle> | ||
+ | |||
+ | <subtitle id="0:14:57"> tells you what kind of knowledge to</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:0"> go after because of course every group</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:3">in history had a zillion amount of not you going to the</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:6"> Australian outback without a</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:9"> native Australian there</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:12"> to help you you're going to die whereas for</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:15"> them is just a walk in the park because</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:18"> everything is food they know how to get water and</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:21"> it's there just they know where the dangers are they</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:24">it's no big deal so every group</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:27"> has lots of knowledge the real thing to think about is</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:30"> what kind of knowledge is that what's the quality</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:33">level what's the level of flexibility what can you</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:36"> you do with it and these outlook</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:39"> changes are more pine Steiners another</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:42"> one so about a hundred years ago</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:45">something</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:48"> that Newton in a</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:51"> slightly different Einstein was quite sure that</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:54"> Newton if he lived longer and had not</subtitle> | ||
+ | |||
+ | <subtitle id="0:15:57"> been put in had a head</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:0"> of the Treasury in England that Newton would have actually</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:3"> come up with a theory of relativity I don't</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:6"> know whether he could have could have actually</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:9"> done that because but Newton</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:12"> didn't know that</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:15"> he thought it was ridiculous that his equations</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:18"> had action at a distance</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:21"> so he said so in letters as just</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:24"> that nobody could measure well enough</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:27"> and what they did measure the</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:30"> gravitational forces seem to</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:33"> transmit instantly but</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:36"> from Newton standpoint that was ridiculous</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:45">okay so that was</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:48"> the first section so the second section is to look at</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:51">children can actually do under ideal conditions and</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:54"> this is not easy to find so</subtitle> | ||
+ | |||
+ | <subtitle id="0:16:57"> a couple of these things are results of</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:0"> just dealing with hundreds</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:3"> and hundreds of teachers over more than 40</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:6"> years and in this case this was an</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:9"> accident because we were working in the fourth</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:12"> and fifth grades in the school and of course I started</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:15"> wandering around the school and I happen to poke my</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:18"> nose into first grade and</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:21"> what I saw was quite shocking</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:24"> to me i should mention I have a</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:27"> degree in mathematics and another one in molecular biology</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:30"> as well as the computer science degrees</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:33"> so when I walked into this math this first grade classroom</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:36"> and SAT there for a few minutes</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:39"> I gradually realize</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:42"> that this teacher was doing real math with</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:45"> first graders not school</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:48"> math but real math the real deal and</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:51"> as I got to know her Julia nishijima was her name</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:54"> I found she was that</subtitle> | ||
+ | |||
+ | <subtitle id="0:17:57"> she have not taken any math in college but</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:0"> she was like one of these musician friends you</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:3"> might have who was just a natural musician she</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:6"> was a net she just saw the world in terms of math and</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:9"> her outlook was in the world of the</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:12"> kindergarten and first grade child so</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:15"> over a couple of years I saw some</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:18">most amazing things I've ever seen in any classroom at any age</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:21"> this one was done after the kids have been there for</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:24"> about three months and the school</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:27"> is a busing school in LA and what</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:30"> that means is that the children in order</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:33"> to induce the parents</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:36"> to get on the that have</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:39">their children but if you think about bus driving</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:42"> a car in LA as ridiculous so</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:45"> let's put our children on buses twice</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:48"> twice a day to</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:51"> try and deal with some of the racial imbalance</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:54"> problems and but</subtitle> | ||
+ | |||
+ | <subtitle id="0:18:57"> they did and there was</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:0">interesting inducements to get the parents to do that but</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:3"> the law was that for each of the busing</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:6"> schools had to have the same demographic</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:9"> as the city as a whole so</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:12"> these busing schools were the perfect place for doing</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:15"> educational experiments because the city</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:18">forty-five percent Hispanic until you have forty-five</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:21"> percent Hispanic kids in there and</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:24"> just down the line in these schools so</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:27"> here's the thing she</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:30"> had and this is not unlike a lot of the things</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:33"> that she did with the kids so this one</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:36"> was fine to shape you like a square diamond</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:39"> a triangle a trapezoid and</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:42"> make a progression</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:45"> of shapes just using these shapes</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:48"> so next</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:51"> larger size next larger size next larger size and trapezoids</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:54"> are coarser are a tricky but</subtitle> | ||
+ | |||
+ | <subtitle id="0:19:57"> so 30 kids in the class and</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:0"> they all pick</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:3"> the ones that they like they all did did something and</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:6"> then she did something</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:9"> that seems a little strange to me which was to have</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:12"> him now go from these easy to handle wouldn't</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:15"> manipulatives to cutting</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:18"> out the same shapes out of cardboard so I asked</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:21"> her afterwards why she did this and she said well little</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:24"> kids are always jumping to conclusions and this</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:27"> part now that they've done the thing I want them to think about</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:30"> it so this part slows them down so the idea here</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:33"> is make a we're going to make a little thing to free to take</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:36"> home to your parents to show what what</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:39"> you're doing and so here's one of them and</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:42"> Laura in here</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:45"> on this sheet she wrote down what she</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:48"> noticed that the first diamond</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:51"> here took one diamond the total number of diamonds</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:54"> was one and then she had to add three</subtitle> | ||
+ | |||
+ | <subtitle id="0:20:57"> more diamonds to get the next</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:0"> diamond shape and the total was four and then she had to add</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:3"> five to get the next one the total number of tiles</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:6"> was nine and she could see</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:9"> that she was adding to each time</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:12"> it's get the first column and then</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:15"> up you can see</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:18"> she wasn't quite sure what six times six was</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:21"> but she knew the square numbers</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:24"> up to five times five</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:27"> then she worked this all out so this is her sheet</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:30"> then the teacher</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:33"> julia had</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:36">kids all bringing their projects up to the front of the room</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:39"> there it is</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:42">kids</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:45"> look to each other's projects and they looked at the little</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:48"> tables and they went holy shit</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:51"> technical term</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:54"> because everybody had filled</subtitle> | ||
+ | |||
+ | <subtitle id="0:21:57">same table regardless of what the shapes were the</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:0"> growth laws were the same so</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:3"> this was hugely exciting I was there</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:6"> I just happened to be there that day and</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:9">I'm looking at this stuff with tears running down my because</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:12"> this is one of the best mathematical</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:15"> things I've ever seen done in any classroom at any age and</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:18"> some of you</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:21"> are we'll</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:24"> have some mathematical background and</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:27">realize what the kids were doing is actually</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:30"> deriving to</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:33"> differential laws one</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:36"> is the differential law for smooth progressions</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:39"> sometimes called linear progressions</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:42"> that's that first column and</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:45"> of course if they used instead of using two</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:48"> they used one it would have a different growth</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:51"> but it would still be smooth and linear</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:54"> they could use three or they could use 3.5 so</subtitle> | ||
+ | |||
+ | <subtitle id="0:22:57"> basic ideas are just adding the same</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:0"> thing in there and in math that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:3"> called the first order differential equation if it were</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:6"> in a continuous space like we like</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:9"> to teach in school but for the kids this is the screen</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:12"> and there's a math for that its</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:15"> a math we don't teach but it's called a</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:18"> first order differential discreet relationship</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:21"> and the second one is</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:24"> all the square numbers</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:27"> it's a quadratic one so this is</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:30"> called the second order differential discreet</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:33"> relationship and it's built on the first an important</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:36"> thing here is that virtually everything</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:39">in high school physics and most things in your first physics</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:42"> course in college can be handled with no more</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:45"> mathematics than this this is</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:48"> actually the real basis of the calculus</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:51">wind using in high school and college his</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:54"> calculus has nothing to do with algebra even</subtitle> | ||
+ | |||
+ | <subtitle id="0:23:57"> though it's cloaked in algebra for historical</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:0"> reasons most Mountain mathematicians did not realize this</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:3"> what calculus is is actually an idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:6"> quite separate from the symbology that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:9"> used on so</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:12"> and of course the kids could calculate with this</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:15"> so the</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:18"> little rule they had was you start with</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:21"> one piece and then you add to the new new pieces column</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:24"> add to each time and then you</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:27"> add from that column to</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:30"> the total column to get the next one and</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:33"> a few if you act it out you get something like this</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:36"> so you start off with ones and</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:39"> you do a plus two to get</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:42"> the next guy there and then you take that guy and the preceding</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:45"> guy to gets the next guy in okay</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:48"> so that's called a second</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:51"> order differential machine</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:54"> and</subtitle> | ||
+ | |||
+ | <subtitle id="0:24:57"> it just happens to be what</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:0"> Babbage member Babbage what</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:3"> did Babbage do then the invented computer so first</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:6">hing he did was to actually make a machine for computing</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:9"> exactly those numbers and it</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:12"> was just he did it so you could compute seven stages</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:15"> of them because again in mathematical</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:18"> terms this is a way of computing all of the values</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:21"> of all of the polynomials of up to a certain</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:24"> order and Babbage did it because when he was</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:27"> a kid he was 19 or 20 there</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:30"> were so many errors in his mathematical</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:33"> tables booked in the early 1800s he</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:36"> screwed across the room and he said to his friend</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:39"> herschel who became a great astronomer he</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:42"> said I wish to god these calculations have been executed</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:45"> by steam meaning</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:48"> gee whiz people make</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:51"> so many mistakes we can build a machine to just</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:54"> compute all its math we can</subtitle> | ||
+ | |||
+ | <subtitle id="0:25:57">machine to compute all this duck so</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:0"> that's what this teacher intuited from</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:3"> these kids and now let's take a look at</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:6"> relationship</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:9"> to the world that you're more familiar with and</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:12">going to do is go through this thing again and just watch</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:15"> where the points</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:18"> are and I've drawn a line through</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:21"> the curves are so start</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:24"> off again so there's the ones</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:27"> okay there's</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:30"> a3 and a4</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:33"> so you can see the quadratic one is growing very quickly now</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:36"> it's next one will be out of sight there</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:39"></subtitle> | ||
+ | |||
+ | <subtitle id="0:26:42"> the difference here is pretty interesting because</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:45"> this way of looking at</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:48"> it is simply not what you do in first grade because</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:51"> the looking at</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:54">all the values at once which is the way classical mathematics</subtitle> | ||
+ | |||
+ | <subtitle id="0:26:57"> likes to look at them</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:0"> in this case requires multiplication</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:3"> so even in the simple</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:6"> guy you have to multiply the slope</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:9"> times X</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:12"> to get each succeeding y as you go through</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:15"> there and you have to square you</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:18">have a squared term to get the quadratic so so this</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:21"> way takes it completely out of the child's world and yet the</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:24"> idea and the capturing</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:27"> of what change is actually is more fundamental</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:30"> than the algebraic way of looking at it</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:33"> because we've made a machine we</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:36"> don't have to solve in equations we can generate the answers</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:39"> so</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:42"> in other words we can mechanically in calculus terms</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:45"> we can mechanically integrate these things</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:48">instead of symbolically having to integrate them and it just changes</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:51"> everything round this was see more paper</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:54"> it's great insight not this particular example but</subtitle> | ||
+ | |||
+ | <subtitle id="0:27:57"> another one this this is an example I did</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:0"> but the basic idea is if you have a machine that</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:3"> can help you do the integration then all</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:6"> of a sudden you can chop ten years and change</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:9"> outlook to teaching</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:12"> real math in terms that are built into human beings</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:15"> so one of the reasons and it happened science</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:18"> thinks of math this way</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:21"> because</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:24"> scientists are lazy mathematicians that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:27"> because it takes so much energy to deal with the real world that</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:30"> you don't want to spend a lot of time messing around with</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:33"> mathematics so everything in science is</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:36">done by just adding things together and these additions</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:39"> are quantities that are called vectors you've heard</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:42"> of those but there are fairly simple generalizations</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:45"> of what numbers are so this</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:48"> whole area is incredibly fruitful for</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:51"> dealing even with very young children</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:54"> and of course we have computers</subtitle> | ||
+ | |||
+ | <subtitle id="0:28:57"> so we can do things</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:0"> with them based on these ideas</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:3"> and we're used to using computers</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:6"> in school not for this stuff we're</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:9"> used to using it to imitate paper</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:12">in fact</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:15"> it's expensive paper with a little bit of magic</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:18"> in their pay a little extra money and we can run a movie</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:21"> in our book and we</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:24"> can go look at something in a library that spread</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:27"> out over the entire world rather than going down the</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:30"> hall to do it but by and large pretty</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:33"> much every use of computing in most schools particularly</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:36"> in elementary schools is to do what business</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:39"> people do with their computers which is not to use them for</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:42"> anything interesting it's basically automating the past</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:45"> but if</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:48">take a look at what computers actually are so</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:51"> we can get our selves a little</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:54"> paint palette here</subtitle> | ||
+ | |||
+ | <subtitle id="0:29:57"> and I'll</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:0"> make a little car</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:3"> and obviously</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:6"> i'm not using powerpoint here but</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:9"> you can think about this as a teacher as to whether</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:12"> you would</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:15"> when you're trying to help</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:18"> children with examples and stuff you</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:21"> kind of would like to just be able to</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:24"> make things on</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:27"> the fly because you do have a dynamic medium</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:30"> this has been one of the hardest idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:33"> is to make happen because people</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:36"> okay I've got my little car and</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:39"> the thing that's understandable it's sort of a graphical</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:42"> object and I'll just call it a car here</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:45"> and but I can also look inside it and here's</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:48"> something that's a little less usual for</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:51"> instance here's cars heading it's</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:54"> where the car is pointing and if I click</subtitle> | ||
+ | |||
+ | <subtitle id="0:30:57"> over here and start changing the angle you</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:0"> can see it's changing the car and conversely if</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:3"> you look over where it says heading and notice</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:6"> what happens when I change it</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:9">so here I have a visual representation where</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:12"> the car is pointing and here i have a symbolic 1 and</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:15"> similarly I have little behaviors car</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:18"> turn by five car 4 by 15 and</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:21"> those of you tried logo you recognize these are standard</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:24"> logo ones if I want to make a little script</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:27"> to take advantage</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:30"> of these I can just pull out some tiles and</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:33"> now I've got my car going and maybe</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:36"> I'll get it to go 10 at a pop</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:39"></subtitle> | ||
+ | |||
+ | <subtitle id="0:31:42"> okay so</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:45"> in fact that I can steer</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:48"> my car so for instance if i</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:51"> want to make the car go straight i can take it down to</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:54"> zero that's a big one for kids go</subtitle> | ||
+ | |||
+ | <subtitle id="0:31:57"> the other direction turned it in the negative direction</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:0"> so very young children just</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:3"> get a sense of concrete</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:6"> magnitudes and numbers but</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:9">driving a car this way is a little bit like kissing your sister</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:12"> so what you really want to do is make a steering</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:15"> wheel so we'll paint another</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:18"> little drawing</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:21"> and these drawings were all the same entities and</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:24"> when I look inside this wheel I</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:27"></subtitle> | ||
+ | |||
+ | <subtitle id="0:32:30"> see the same thing and</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:33"> if I turn this wheel</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:36"> can see the number going up and</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:39"> negative and stuff and if you remember the number</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:42"> i put in here determine</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:45"> which way the car was going which direction</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:48"> to turn and how much so it's kind of a invitation</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:51"> to take the name of those</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:54"> the turn numbers coming out of the wheel</subtitle> | ||
+ | |||
+ | <subtitle id="0:32:57"> and just dropping it into the script here and</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:0"> now as I change the wheel</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:3"> we can see that</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:6"> the car is turning by whatever the wheels heading</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:9"> is so here's an interesting thing to think about</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:12"> if you've ever had trouble with teaching children about variables</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:15"> a child who learns variables this</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:18"> way learns it the first time and forever</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:21"> it's not the variables are hard for</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:24">children it's just that the way they're taught is completely</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:27"> unseated yes</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:30"> oh this so this is called squeaky</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:33"> toys if you go to squeak LAN</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:36"> org runs on every it's</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:39"> free</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:42"> yes that was so both of these the</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:45"> scratch was not the media lab</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:48"> and was also done on top of squeak so</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:51"> scratch and e toys or to scratch</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:54"> was done kind of four teenage</subtitle> | ||
+ | |||
+ | <subtitle id="0:33:57"> after school kids as</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:0"> a media thing they're both relatively similar</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:3"> and you can both do a lot of the same things here</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:6"> so the basic idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:9"> here is that you're trying</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:12"> to situate a</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:15"> motivation if I want to I</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:18">to drive this car with a steering wheel and</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:21"> the fact that the number is coming</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:24">out of the steering wheel are going to be different and so it makes sense to have</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:27"> them name and this script</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:30">icking over and over again so this could hardly be simpler</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:33"> and one other little</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:36"> thing is the car is a little difficult to control</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:39"> here and so</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:42">to the kids will want it why don't you just put a gear and a</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:45"> gear here being for example dividing</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:48"> the number coming out by three</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:54">now you have to turn</subtitle> | ||
+ | |||
+ | <subtitle id="0:34:57"> the way the wheel much further in order to get the same influence</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:0"> on the car so most 5th graders</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:3">have no idea why they should ever learn how to multiply or divide</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:6"> because in the world that they're taught in school</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:9"> math they're taught it's not about scaling</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:12"> it's about solving other kinds of problems but</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:15"> in the world of science and</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:18"> engineering it's not about scaling</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:21"> not about</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:24"> multiplying as we as</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:27">we generally do but it's about scaling things okay</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:30"> so let</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:33"> me try another little idea on you i'm going</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:36"> to make a little script here so</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:39"> i'm going to set cars speed to 30 and</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:42"> i'm</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:45"> going to</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:48"></subtitle> | ||
+ | |||
+ | <subtitle id="0:35:51"> set say</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:54"> increase the cars</subtitle> | ||
+ | |||
+ | <subtitle id="0:35:57"> horizontal position by cars speed each time</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:0"> so if I just do this</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:3"> or if I just let it go</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:6"> stop</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:9"> so does does everybody see that</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:12"> this is that</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:15"> first column that the six-year-olds did</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:18"> what I'm</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:21"> increasing is the position</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:24">where they are so the</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:27"> car is doing a uniform</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:30"> speed and these little dots i'm</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:33">dropping help us see the uniformity of it but</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:36"> what if i say okay instead</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:39"> of instead of doing that what</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:42"> if I okay</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:45">look at this one really carefully now what if I increase this by 30</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:48"> each time alright so the speed is going to start off</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:51"> 0 36 d all</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:54"> right so now the speed is growing and</subtitle> | ||
+ | |||
+ | <subtitle id="0:36:57"> then I'm going to whatever</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:0">that has grown to i'm going to then bump the car ahead</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:3"> right so you see this is the two columns</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:6"> so the car is going to go exponentially</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:9"> so if i go do</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:12"> it cow</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:15">and this gives us a visual way of</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:18"> thinking about acceleration because the</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:21"> distance between those two dots is the distance</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:24"> travel per unit time and the distance travel</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:27"> per unit time is the speed</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:30"> right so many so much distance</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:33"> per tick 30 miles per hour</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:36"> and so what's happening here is we can see</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:39">accelerating and the fifth graders love to</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:42"> know that the term for this is acceleration</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:45"></subtitle> | ||
+ | |||
+ | <subtitle id="0:37:48"> okay we have a question yes I</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:51"> know</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:54"> your your commentary is focusing on math</subtitle> | ||
+ | |||
+ | <subtitle id="0:37:57"> but my question has</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:0"> to do with the kids response to reading</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:3"> and writing or reading and typing in this case do</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:6"> you find that the kids</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:9"> are more do they get the transference from being able</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:12"> to use this high place and I try that after</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:15"> yeah</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:18"> that's a good question though</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:24">reason I'm hurrying along here is I'm</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:27">going to be cut out regardless of how interesting this talk is</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:30"> it's going to end at 10 minutes to</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:33"> the hour okay let's move</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:36"> so I want the only comment here</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:39"> is does everybody</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:42"> see that what you're doing on the</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:45"> computer can't be science but</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:48"> is only math that you can't do</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:51"> science on a computer</subtitle> | ||
+ | |||
+ | <subtitle id="0:38:54"> why</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:0">eah</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:3"> I can simulate any goddamn thing I</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:6"> want on a computer I can live up one side</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:9"> and down the other so it's just all math is is</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:12"> a story that's consistent but</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:15">he problem is the degrees of freedom in in any reasonable</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:18"> human language are larger than those the universe has</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:21"> and so this is this is why the Greeks</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:24">quite invent science except maybe Archimedes</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:27"> and the reason is they thought God was a mathematician and</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:30">thought if they started off with self-evident</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:33"> first principles that they could just</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:36"> deduce the universe the same way God did</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:39"> could be true because that this is a</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:42"> lot of physicists think this might</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:45"> be true I doubt it so</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:48"> let's take a look let's look at the kids in the world now</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:51"> so you're a bunch of objects objects that</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:54"> you think will fall to the earth at the same</subtitle> | ||
+ | |||
+ | <subtitle id="0:39:57"></subtitle> | ||
+ | |||
+ | <subtitle id="0:40:0"> okay</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:3"> oh do not pay any attention to</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:6"> what anybody else the grapefruit now</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:9"> you two levels of shot put sponge balls</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:12"> are a couple</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:15"> sleep janet</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:18"> is up on the roof because</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:21"> stopwatches by</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:24"> the way to do it but</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:27"> when do you really not go</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:30"></subtitle> | ||
+ | |||
+ | <subtitle id="0:40:33"></subtitle> | ||
+ | |||
+ | <subtitle id="0:40:36"> together so put a sponge ball</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:39"> okay I think we should do the shot</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:42"> right and the sub ball because</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:45"> they're two totally different ways and if</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:48"> you drop them at the same time but they'll drop</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:51"> at the same speed drop</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:54"> okay so</subtitle> | ||
+ | |||
+ | <subtitle id="0:40:57"> if you do this so Aristotle</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:0"> did not ask any children when</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:3"> he came up with the wrong theory of this he</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:6"> just deduced it using</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:9"> a using a wrong a common-sense way of thinking about</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:12"> what's actually going on but we found that one</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:15"> child in 30 roughly so if you if</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:18"> you have a class of 30 kids</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:21">you've got an excellent chance that one child will do what that little girl</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:24"> did which is to pull the Galileo and just</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:27"> cut to the chase and say hey wait</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:30"> a minute that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:33"> the I'm already in the</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:36">place</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:39"> where all I have to do is just listen and of course the</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:42"> scaffolding in the Leaning Tower of Pisa was</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:45"> what Galileo listen to it was under repair at</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:48"> that time so</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:51"> but that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:54"> quality could call that a big idea</subtitle> | ||
+ | |||
+ | <subtitle id="0:41:57"> however</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:0"> can also do something</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:3"> a little bit more here so we</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:6"> take a video these</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:9"> might look like funny video frames but video is just</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:12"> part of the objects that these this language deals</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:15"> with so we can make the frames convenient to take every fifth frame</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:18"> you can stack them sideways or</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:21"> you can stack them like this if</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:24"> you look at this what do you think the kids say</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:27"> when they see that pattern</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:30">acceleration four months later</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:33"> so four months previously they did the horizontal</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:36"> thing with the car four months later remember the</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:39"> visual path what kind of acceleration</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:42"> so well</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:45"> let's measure</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:48"> so we measure from the bottom of one</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:51"> guy and so we can just use these little</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:54"> translucent rectangles to do it</subtitle> | ||
+ | |||
+ | <subtitle id="0:42:57">pre-measured these so</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:0"> i don't have to fiddle while I'm rushed</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:3"> for time as it is but then the cool thing</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:6"> is i can just stack these up</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:9"> like</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:18">okay what do you think these</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:21"> things mean what are these</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:24"> these are the differences</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:27"> between the speed at each time tick</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:30"> right each rectangle is the speed at</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:33"> each time tick in i'm doing a visual subtraction</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:36"> there and what i'm showing is their progressive if I just subtract</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:39">hem off they're all the same what kind of acceleration is</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:42"> that acceleration</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:45"> so the kids immediately write this</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:48"> little script right here</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:51"> let's listen to Tyrone here</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:54"> and to make sure that I was</subtitle> | ||
+ | |||
+ | <subtitle id="0:43:57"> doing it just right I got</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:0"> a magnifier which would help me</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:3"> so I figure out if the size was just</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:6"> right after I'd done that I would</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:9"> go and click on the little basic</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:12"> category button and then a little mini</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:15"> would pop up and one</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:18"> of the categories would be geometry so I click on that and</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:21"> here it has many things have</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:24"> to do with the size and shape of</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:27"> the rectangle so</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:30"> I would see with the Heidi I kept</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:33"> going along the process until I</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:36"> had them all lined up with their height i subtracted</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:39">the smaller ones height from the big one to see</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:42"> if there was a kind of pattern anywhere there</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:45"> could help me I'm not as this worked so</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:48"> in order to show that it was working</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:51"> i decided to leave a doc copy so that it</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:54"> would show if the ball was really the exact right speed Henry</subtitle> | ||
+ | |||
+ | <subtitle id="0:44:57"> simulated ball is tracking the movie</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:0"> this is how he's showing that his model</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:3"> is in accord with the real world at</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:6">least two within a pixel so what you got here so</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:9"> here's something to think about lily and mcdermott of</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:12">Washington is a physicist who looks at college kids seventy</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:15"> percent of all college kids including science majors</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:18"> in this country fail to understand Galilean</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:21"> gravity that's what this is ninety</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:24"> percent of the children going doing it</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:27"> this way actually derive the equations</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:30">themselves actually make the simulations from scratch</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:33"> themselves and show within</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:36"> the limits of the accuracy hear</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:39"> that their model is an</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:42"> accord with physical reality and in fact the difference</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:45"> between Galilean gravity 14</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:48"> feet above the ground and Newtonian gravity is only one part</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:51"> in a million and so we can think of get</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:54"> Galileo is very lucky that</subtitle> | ||
+ | |||
+ | <subtitle id="0:45:57"> he couldn't measure that one part</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:0"> in a million or he would have been very confused right</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:3"> this way had to be done first before the</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:6"> Newtonian way hat okay so let me I think I'm</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:9"> getting to the point where I have to finish up</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:12"> so</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:18"> let's think about serious stuff now</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:21">e</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:24"> live inside of systems and we are systems so</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:27"> it's a nice unification through all of the</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:30"> sciences engineering and art</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:33"> so if you're going to make up a middle school science</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:36"> curriculum for say the eighth grade I would</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:38"> not pick a science like biology but I pick</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:41"> a uniform unifying rubric</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:45"> like systems and I teach all of different Sciences</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:47"> the systems aspect of those and</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:50"> use mathematics to deal with those</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:53"> things and my romantic ideal</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:56"> would be the planet is in trouble and we need to learn</subtitle> | ||
+ | |||
+ | <subtitle id="0:46:59"> how to save it</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:2"> and</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:5"> what we've got going in general is</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:8"> something like this if you hit</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:11"> this mystery object with a hammer it</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:14"> returns to equilibrium but if</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:17"> I raise it up far enough it</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:20"> doesn't come back</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:23">so</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:26"> what we got here</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:29"> the most systems</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:32"> are like this the equilibrium</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:35"> they have is actually dynamically</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:38"> stable but not statically stable so</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:41"> if you just tap this thing</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:44"> it won't do anything but if</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:47">tap it enough to get it passed its center of mass bunk</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:50"> and</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:53"> thing to understand here is that's</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:56"> that's what we're doing so what we're doing is stressing</subtitle> | ||
+ | |||
+ | <subtitle id="0:47:59"> the earth and</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:2"> little bits of stress like</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:5"> burning the river in Cleveland can</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:8"> be fixed up in large amounts of stress</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:17">can topple the system and think</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:20"> about systems is when they get toppled they</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:23"> don't stop but it's in a new state</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:26"> now and it's going to resist</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:29"> getting it back it could so</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:32"> for instance when the climate has toppled in the past</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:35">aken between ten thousand a hundred thousand</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:38"> and five hundred thousand years to restore all</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:41"> of those numbers are a lot larger than our lifetime</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:44"></subtitle> | ||
+ | |||
+ | <subtitle id="0:48:47"> okay</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:50"> let me just try it</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:56">so</subtitle> | ||
+ | |||
+ | <subtitle id="0:48:59"> what we've seen here is a Jerry</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:2"> Bruner idea but I've tried to show you</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:5"> is that the</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:8"> most important idea here is that you have to heed the level of</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:11">development of the person you're trying to teach and</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:14"> if you know yourself like it doesn't</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:17"> make sense for a non mathematician to try and teach math to</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:20"> a six-year-old it just doesn't</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:23"> because the six the</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:26"> six-year-old doesn't think in the same way as a teenager or an</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:29">doesn't if you want to teach real math you</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:32"> have to be a mathematician or have a mathematician</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:35"> in the loop because the mathematicians job is to figure out what</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:38"> kind of real math is within the wheelhouse</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:41"> of the six-year-old</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:44"> that's really the job</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:47"> so discovery learning so</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:50">here's the thing we have two poles in the United States back to</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:53"> basics and discovery learning</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:56"> both of this both these are absolute</subtitle> | ||
+ | |||
+ | <subtitle id="0:49:59"> vs it</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:2"> so it's very complicated going into a meeting with</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:5">educators because they tend to polarize long those and you</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:8"> know any scientist and mathematician guys think Oh No</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:11"> and the</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:14"> the joke here is about discovery learning is is</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:17"> whoops is the teacher</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:20">saying oh no they're discovering the wrong things why</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:23"> are they discovering the wrong things well consider</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:26"> our 200,000 years on the planet</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:29"> we had to go almost all the</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:32"> way to the present to just do agriculture Greece was</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:35"> only 2,500 years ago that was modern math and</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:38"> real science was just 400 years ago</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:41"> think about that the</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:44"> u.s. know a stable</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:47"> dynamically stable democratic government</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:50">is only a few hundred years old these ideas are</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:53"> not easy so what you need is a guide</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:56"> so</subtitle> | ||
+ | |||
+ | <subtitle id="0:50:59"> it's not Hillary climbing Everest it's Tenzing</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:2"> and Hillary and</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:5"> sure we'd love to have Socrates and Fineman</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:8"> as guides but these guys don't</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:11">scale this is one of the problems with school</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:14"> books are great because you can get some</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:17"> of Fineman and Socrates but</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:20"> I used books a lot but I needed to have</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:23">real teacher that teacher had something libraries didn't</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:26"> have which is a table full of junk you could make things and learn things with</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:29"> libraries should have</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:32">these but they don't know that they should and I have</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:35"> my dad who is a physiologist to ask questions of</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:38"> so what we're thinking about</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:41"> today is what</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:44"> kind of use could we make</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:47"> out of the computer since it has booked like properties</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:50"> but it also is active enough to</subtitle> | ||
+ | |||
+ | <subtitle id="0:51:53"> be able to sense what the user is doing</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:2">so here's a simple</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:5"> thing that's very popular guitar hero</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:8"> so the interesting thing</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:11"> about guitar hero is that people</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:14">don't have to go to school to learn how to play it like</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:17"> most video games</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:20"> now the bug with this is that</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:23"> real guitar I used to be a professional guitar</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:26"> player jazz guitar it's just</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:29"> like a thousand times harder than guitar hero guitar hero</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:32"> is it like simple drumming if</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:35"> you ever tried drumming is very like</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:38"> just having a snare and a high hat</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:41"> and that's tricky enough if</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:44"> you've ever tried it you have to get a couple of things going it's tricky</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:47"> you can think it's the entire world because</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:50"> this trick Ian of itself and there's all these great sounds</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:53">coming out but it's absolutely a snare and a delusion and</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:56"> most here's the prediction most schools</subtitle> | ||
+ | |||
+ | <subtitle id="0:52:59">States are going to wind up using computers in</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:2"> classrooms to do a form of guitar hero</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:5"> for most of the important subjects</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:8"> because most teachers in</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:11"> the united states are not guitar players</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:14">alright so this is a huge</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:17"> problem and yet</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:20"> without</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:23"> replacing humans it's</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:26"> absolutely possible to make some</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:29"> a fantastic tutoring system for learning any level</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:32"> of guitar playing at any level</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:35">without having to have a human in the loop that's what's interesting</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:38"> you don't get everything you get with</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:41"> a human but you get about ninety-five</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:44">stuff that you need to be able to do anyway you</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:47"> can do it and that's what</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:50"> I want you to think about is not replacing teachers</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:53"> here but to listen</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:56"> to our smarter than the average President as</subtitle> | ||
+ | |||
+ | <subtitle id="0:53:59">talked to the National Academy last spring he</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:2"> gets it the</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:5"> only way we're ever going to get enough science</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:8"> savvy knowledge into schools is to help</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:11">existing teacher with media that understand</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:14"> the science as children can practice it</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:17"> this is going to be a revolution</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:20">going to happen over the next year and it is a grand challenge it's</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:23"> as difficult as the challenge that we faced</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:26"> 40 years ago where the challenge was everybody</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:29"> should have a personal computer pervasively network worldwide</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:32"> and</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:35"> we have the funding for it and</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:38"> we were able to invent it now several billion</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:41"> people have it and it's time to use the computers</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:44"> for what they're really good for what</subtitle> | ||
+ | |||
+ | <subtitle id="0:54:47"> do you think thank you very much</subtitle> |
Latest revision as of 21:57, 6 December 2017
so we
actually are dealing with an academic hour here
and be fitting with our school setting
marvin minsky once said school was the greatest
invention anybody ever came up with to keep
you from staying interested on anything for any reasonable
length of time because of course
it has all these schedules in assembly line movements
and we have one of those today and
I also wanted to leave time for
questions but one of the ways I want to leave time
for questions is to encourage you to ask questions as I
talk so I have no idea how long this
talk is and I am going to stop after
50 minutes and regardless of what what
happened so please don't be
shy ask questions as we go if
you like and because this talk is
not for me but for you
so it's
in a series of ideas which are
somewhat connected I hope so
one contrast
I'd like you to think about is the notion beach of
common sense that
most people take
the world around them as reality I
once came up with
at said technology is anything that happened after
you were born because
the technology that you're born into is
part of your world and it's taken to be normal there and most
internet Prince the Internet is one of the great inventions
of all time not the web but the internet itself
one of the great maybe one of the greatest engineering
feats of all time and
it worked so well that hardly
anybody appreciates it particularly
in computing where they should pay more attention to why
it works so well so here's a
common-sense deduction that
has been made by most
people on the planet for the slightly less
than 200,000 years modern humans have been here
and that is something like a king
natural and normal
extension of the head of the family
hunted leaders
of hunting groups and etc etcetera so
this is just regarded as common sense
and in fact was not regarded as it as an idea
it was just part of the part of the world that people
lived in then in
January 1776 Thomas Paine
wrote a book which he ironically titled common
sense everybody here has heard of Tom Paine's Common Sense
but he had a big idea in it which
was instead of having the King be
the law we can have the law be the king and
what he meant was we can design a much better society
than the what the natural
seeming hereditary monarchy as we can take our
future into our own hands we can come up with a better plan
this is an idea that surfaced
a couple of times in Greece but not
not before not after and
this book
which pain published at his own expense initially
just gave it away had a press run
between six hundred thousand and nine hundred thousand
in six months so
that's a lot by today's standards and
there were 1.5 million non
slaves in the thirteen colonies
back then and so this press run
encompassed somewhere between almost a half
to more than a half of all men women and children in
all 13 colonies so imagine just trying
to reach that number of people today
there is no medium that you could do it with except
with the internet I try
to get sixty percent of
300 million people no
newspaper could do it so
so this is a big idea but
the powerful idea
and this is the distinction I want to make was the
Constitution as a
big idea is kind of an insight and
often insights insights
are wonderful but they're
lightweight they're relatively easy to have compared
to doing something about it so the
Constitution said
we should shape society into a self-organizing
self-correcting shared idea and resource system
and that is a very radical
idea even for today for instance most Americans
have no idea what the design of the
United States was or is it's
imply not taught in schools it's not the way American
history is is taught and
so
most societies on earth haven't
gotten this idea even at the societal level
most human beings on earth don't have this
idea but this is one of these powerful ideas
that makes qualitative
differences in almost every
area of life and it's related to an even
bigger set of ideas so
another common sense
whoops
another another
common sense notion which is
actually with most Americans today according to the surveys
I've seen which is the world is pretty much as it seems
so we this
is what our nervous systems are set up to do we're
basically weren't set up by nature to think
we're set up by nature to cope and so
primary mechanism is whatever environment we
find ourselves in so the answer anthropologists
know that you can take a child at
birth from any culture on the planet and take
on the planet that child will grow up as
a member of that culture you took it too that's
because humans are rather more similar
than they are different we have about 300
traits that anthropologists have identified
that seem to be quite genetic including
things like language having culture telling stories
and those mechanisms
get embodied with the
local varieties of those and so the
reality you grow up within the language you
grew up with is the language and
the reality of the culture you you're born in Q
so
now this big ideas
have been had a number of times in history I happen to like the
Talmud version of it
we see things not as they are but as we are
so this is a bit I'd love to know
what actually
happened to the person who came up with this
idea did they take it to its logical conclusion
considering and
was interesting that was published in this Talmud is part
of the commentary
but this is one
of the great big ideas of all time this
is a really hard one because it
completely relative izes what's
going on however it's not a powerful idea
but had numerous
times and
powerful idea came in
the 17th century and you
could point to a number of people and you could point to various
societies but
17th century has a has a perfect
atomic
bomb place where science started
because we had Galileo
and Kepler and maybe Copernicus
beforehand and a few other people but in fact
when Newton did
the Principia he actually revolutionized
human thought and it's probably the largest leap in human
thought of this kind that we know of historically
this is why most scientists
think of Newton as being the greatest scientist
and he was almost the first scientist and
not just in
relative terms but in absolute terms the amount
of distance he was able to cover not just
in terms of knowledge but in terms of about look and
the powerful idea of science
is not so easy to state everything
else comes out pretty nicely as slogans and
there's more to science than just
this but this is one half of it which
is science is not about knowledge as
niels bohr said science is not there to tell
us about the universe is what most people think
most non-scientists most kids in school
are taught what is called science
as in roughly the same way they learn religion in
when they go to church or
synagogue or mosque but
in what science is at all it's not about knowledge
it's about relating the
stuff we can do and can't do in here
all the things that we can do with
our representational systems to stuff
out there that we can't get to directly because
everything we do is filtered through our nervous
systems as filtered through our culture's is
filtered for through the the difficulties
we have with making relationships
about things and this was not an
easy idea to have we'll
see in a bit but
what's happened in the last 400 years in
many many dimensions
has been more than has happened
in the rest of the 200,000 years and you
know the cliche that
most scientists 90 more
of all the scientists who ever lived you're alive today
and most of the things that
are happening today and some
of the problems and some of the solutions to those problems
are all caused this by different way
and much is made
particularly in the pop culture of
bringing bright
this is because pop
culture's or cultures without a lot
of developed knowledge basically
live by their wits and so you out
with each other and you
compete at the level of width but
imagine being born with an IQ
of 500 who knows how
smart leonardo was let's
just no 203 who because
those figures don't what does IQ me in any
way but let's just say hey suppose
you're just a hell of a lot smarter than anybody who ever lived
but you were born in 10,000 BC
how far you going to get so
you can probably out wit everybody around you before
they burn you at the stake
but in fact Leonardo
who we know is very very bright could
not invent a single engine
for any of the vehicles that he designed so
he's famous for designing things that look
like planes and things that maybe look like helicopters
and I'll and they're wonderful and he did a lot
hings but he couldn't make a single goddamn one of
them work that is and that's
because he wasn't smart enough to think himself out
of the era he had been born into as
far as we know if nobody has the closest person who's ever
thought himself out of the era he was born into his
Newton so
you have this odd paradox
that whoops sorry that
Henry Ford who is not nearly as smart as
Leonardo just happened to be born in the right time and
so he did revolutionize one
of the areas that Leonardo wanted to revolutionize
by being able
to do adaptive engineering and a little
invention to the stuff that was already around
so his knowledge was
processed knowledge and this was very powerful and what
was the difference between these two these
two guys was this
change of outlook that Newton
was one of the promulgate errs of
so one of the ways I
when I talked to grabs grad students
or children I say well knowledge
is silver but outlook is
gold our
world is built on changes of outlook that was what the
Constitution was that was what Tom Paine did
and that's what science did and
IQ is led
because there is no
we know of no developed field knowledge in
which you can get by with just talent there's
no developed sport in which you can get by with
just talent and some of the most
difficult sports have been
excelled in by people who are not as athletic
so for instance Chris effort
as an example who is not a particularly athletic
tennis player but man that you know
how to work and so she got very very
good at it and most things have
this thing an Outlook also
tells you what kind of knowledge to
go after because of course every group
in history had a zillion amount of not you going to the
Australian outback without a
native Australian there
to help you you're going to die whereas for
them is just a walk in the park because
everything is food they know how to get water and
it's there just they know where the dangers are they
it's no big deal so every group
has lots of knowledge the real thing to think about is
what kind of knowledge is that what's the quality
level what's the level of flexibility what can you
you do with it and these outlook
changes are more pine Steiners another
one so about a hundred years ago
something
that Newton in a
slightly different Einstein was quite sure that
Newton if he lived longer and had not
been put in had a head
of the Treasury in England that Newton would have actually
come up with a theory of relativity I don't
know whether he could have could have actually
done that because but Newton
didn't know that
he thought it was ridiculous that his equations
had action at a distance
so he said so in letters as just
that nobody could measure well enough
and what they did measure the
gravitational forces seem to
transmit instantly but
from Newton standpoint that was ridiculous
okay so that was
the first section so the second section is to look at
children can actually do under ideal conditions and
this is not easy to find so
a couple of these things are results of
just dealing with hundreds
and hundreds of teachers over more than 40
years and in this case this was an
accident because we were working in the fourth
and fifth grades in the school and of course I started
wandering around the school and I happen to poke my
nose into first grade and
what I saw was quite shocking
to me i should mention I have a
degree in mathematics and another one in molecular biology
as well as the computer science degrees
so when I walked into this math this first grade classroom
and SAT there for a few minutes
I gradually realize
that this teacher was doing real math with
first graders not school
math but real math the real deal and
as I got to know her Julia nishijima was her name
I found she was that
she have not taken any math in college but
she was like one of these musician friends you
might have who was just a natural musician she
was a net she just saw the world in terms of math and
her outlook was in the world of the
kindergarten and first grade child so
over a couple of years I saw some
most amazing things I've ever seen in any classroom at any age
this one was done after the kids have been there for
about three months and the school
is a busing school in LA and what
that means is that the children in order
to induce the parents
to get on the that have
their children but if you think about bus driving
a car in LA as ridiculous so
let's put our children on buses twice
twice a day to
try and deal with some of the racial imbalance
problems and but
they did and there was
interesting inducements to get the parents to do that but
the law was that for each of the busing
schools had to have the same demographic
as the city as a whole so
these busing schools were the perfect place for doing
educational experiments because the city
forty-five percent Hispanic until you have forty-five
percent Hispanic kids in there and
just down the line in these schools so
here's the thing she
had and this is not unlike a lot of the things
that she did with the kids so this one
was fine to shape you like a square diamond
a triangle a trapezoid and
make a progression
of shapes just using these shapes
so next
larger size next larger size next larger size and trapezoids
are coarser are a tricky but
so 30 kids in the class and
they all pick
the ones that they like they all did did something and
then she did something
that seems a little strange to me which was to have
him now go from these easy to handle wouldn't
manipulatives to cutting
out the same shapes out of cardboard so I asked
her afterwards why she did this and she said well little
kids are always jumping to conclusions and this
part now that they've done the thing I want them to think about
it so this part slows them down so the idea here
is make a we're going to make a little thing to free to take
home to your parents to show what what
you're doing and so here's one of them and
Laura in here
on this sheet she wrote down what she
noticed that the first diamond
here took one diamond the total number of diamonds
was one and then she had to add three
more diamonds to get the next
diamond shape and the total was four and then she had to add
five to get the next one the total number of tiles
was nine and she could see
that she was adding to each time
it's get the first column and then
up you can see
she wasn't quite sure what six times six was
but she knew the square numbers
up to five times five
then she worked this all out so this is her sheet
then the teacher
julia had
kids all bringing their projects up to the front of the room
there it is
kids
look to each other's projects and they looked at the little
tables and they went holy shit
technical term
because everybody had filled
same table regardless of what the shapes were the
growth laws were the same so
this was hugely exciting I was there
I just happened to be there that day and
I'm looking at this stuff with tears running down my because
this is one of the best mathematical
things I've ever seen done in any classroom at any age and
some of you
are we'll
have some mathematical background and
realize what the kids were doing is actually
deriving to
differential laws one
is the differential law for smooth progressions
sometimes called linear progressions
that's that first column and
of course if they used instead of using two
they used one it would have a different growth
but it would still be smooth and linear
they could use three or they could use 3.5 so
basic ideas are just adding the same
thing in there and in math that's
called the first order differential equation if it were
in a continuous space like we like
to teach in school but for the kids this is the screen
and there's a math for that its
a math we don't teach but it's called a
first order differential discreet relationship
and the second one is
all the square numbers
it's a quadratic one so this is
called the second order differential discreet
relationship and it's built on the first an important
thing here is that virtually everything
in high school physics and most things in your first physics
course in college can be handled with no more
mathematics than this this is
actually the real basis of the calculus
wind using in high school and college his
calculus has nothing to do with algebra even
though it's cloaked in algebra for historical
reasons most Mountain mathematicians did not realize this
what calculus is is actually an idea
quite separate from the symbology that's
used on so
and of course the kids could calculate with this
so the
little rule they had was you start with
one piece and then you add to the new new pieces column
add to each time and then you
add from that column to
the total column to get the next one and
a few if you act it out you get something like this
so you start off with ones and
you do a plus two to get
the next guy there and then you take that guy and the preceding
guy to gets the next guy in okay
so that's called a second
order differential machine
and
it just happens to be what
Babbage member Babbage what
did Babbage do then the invented computer so first
hing he did was to actually make a machine for computing
exactly those numbers and it
was just he did it so you could compute seven stages
of them because again in mathematical
terms this is a way of computing all of the values
of all of the polynomials of up to a certain
order and Babbage did it because when he was
a kid he was 19 or 20 there
were so many errors in his mathematical
tables booked in the early 1800s he
screwed across the room and he said to his friend
herschel who became a great astronomer he
said I wish to god these calculations have been executed
by steam meaning
gee whiz people make
so many mistakes we can build a machine to just
compute all its math we can
machine to compute all this duck so
that's what this teacher intuited from
these kids and now let's take a look at
relationship
to the world that you're more familiar with and
going to do is go through this thing again and just watch
where the points
are and I've drawn a line through
the curves are so start
off again so there's the ones
okay there's
a3 and a4
so you can see the quadratic one is growing very quickly now
it's next one will be out of sight there
the difference here is pretty interesting because
this way of looking at
it is simply not what you do in first grade because
the looking at
all the values at once which is the way classical mathematics
likes to look at them
in this case requires multiplication
so even in the simple
guy you have to multiply the slope
times X
to get each succeeding y as you go through
there and you have to square you
have a squared term to get the quadratic so so this
way takes it completely out of the child's world and yet the
idea and the capturing
of what change is actually is more fundamental
than the algebraic way of looking at it
because we've made a machine we
don't have to solve in equations we can generate the answers
so
in other words we can mechanically in calculus terms
we can mechanically integrate these things
instead of symbolically having to integrate them and it just changes
everything round this was see more paper
it's great insight not this particular example but
another one this this is an example I did
but the basic idea is if you have a machine that
can help you do the integration then all
of a sudden you can chop ten years and change
outlook to teaching
real math in terms that are built into human beings
so one of the reasons and it happened science
thinks of math this way
because
scientists are lazy mathematicians that's
because it takes so much energy to deal with the real world that
you don't want to spend a lot of time messing around with
mathematics so everything in science is
done by just adding things together and these additions
are quantities that are called vectors you've heard
of those but there are fairly simple generalizations
of what numbers are so this
whole area is incredibly fruitful for
dealing even with very young children
and of course we have computers
so we can do things
with them based on these ideas
and we're used to using computers
in school not for this stuff we're
used to using it to imitate paper
in fact
it's expensive paper with a little bit of magic
in their pay a little extra money and we can run a movie
in our book and we
can go look at something in a library that spread
out over the entire world rather than going down the
hall to do it but by and large pretty
much every use of computing in most schools particularly
in elementary schools is to do what business
people do with their computers which is not to use them for
anything interesting it's basically automating the past
but if
take a look at what computers actually are so
we can get our selves a little
paint palette here
and I'll
make a little car
and obviously
i'm not using powerpoint here but
you can think about this as a teacher as to whether
you would
when you're trying to help
children with examples and stuff you
kind of would like to just be able to
make things on
the fly because you do have a dynamic medium
this has been one of the hardest idea
is to make happen because people
okay I've got my little car and
the thing that's understandable it's sort of a graphical
object and I'll just call it a car here
and but I can also look inside it and here's
something that's a little less usual for
instance here's cars heading it's
where the car is pointing and if I click
over here and start changing the angle you
can see it's changing the car and conversely if
you look over where it says heading and notice
what happens when I change it
so here I have a visual representation where
the car is pointing and here i have a symbolic 1 and
similarly I have little behaviors car
turn by five car 4 by 15 and
those of you tried logo you recognize these are standard
logo ones if I want to make a little script
to take advantage
of these I can just pull out some tiles and
now I've got my car going and maybe
I'll get it to go 10 at a pop
okay so
in fact that I can steer
my car so for instance if i
want to make the car go straight i can take it down to
zero that's a big one for kids go
the other direction turned it in the negative direction
so very young children just
get a sense of concrete
magnitudes and numbers but
driving a car this way is a little bit like kissing your sister
so what you really want to do is make a steering
wheel so we'll paint another
little drawing
and these drawings were all the same entities and
when I look inside this wheel I
see the same thing and
if I turn this wheel
can see the number going up and
negative and stuff and if you remember the number
i put in here determine
which way the car was going which direction
to turn and how much so it's kind of a invitation
to take the name of those
the turn numbers coming out of the wheel
and just dropping it into the script here and
now as I change the wheel
we can see that
the car is turning by whatever the wheels heading
is so here's an interesting thing to think about
if you've ever had trouble with teaching children about variables
a child who learns variables this
way learns it the first time and forever
it's not the variables are hard for
children it's just that the way they're taught is completely
unseated yes
oh this so this is called squeaky
toys if you go to squeak LAN
org runs on every it's
free
yes that was so both of these the
scratch was not the media lab
and was also done on top of squeak so
scratch and e toys or to scratch
was done kind of four teenage
after school kids as
a media thing they're both relatively similar
and you can both do a lot of the same things here
so the basic idea
here is that you're trying
to situate a
motivation if I want to I
to drive this car with a steering wheel and
the fact that the number is coming
out of the steering wheel are going to be different and so it makes sense to have
them name and this script
icking over and over again so this could hardly be simpler
and one other little
thing is the car is a little difficult to control
here and so
to the kids will want it why don't you just put a gear and a
gear here being for example dividing
the number coming out by three
now you have to turn
the way the wheel much further in order to get the same influence
on the car so most 5th graders
have no idea why they should ever learn how to multiply or divide
because in the world that they're taught in school
math they're taught it's not about scaling
it's about solving other kinds of problems but
in the world of science and
engineering it's not about scaling
not about
multiplying as we as
we generally do but it's about scaling things okay
so let
me try another little idea on you i'm going
to make a little script here so
i'm going to set cars speed to 30 and
i'm
going to
set say
increase the cars
horizontal position by cars speed each time
so if I just do this
or if I just let it go
stop
so does does everybody see that
this is that
first column that the six-year-olds did
what I'm
increasing is the position
where they are so the
car is doing a uniform
speed and these little dots i'm
dropping help us see the uniformity of it but
what if i say okay instead
of instead of doing that what
if I okay
look at this one really carefully now what if I increase this by 30
each time alright so the speed is going to start off
0 36 d all
right so now the speed is growing and
then I'm going to whatever
that has grown to i'm going to then bump the car ahead
right so you see this is the two columns
so the car is going to go exponentially
so if i go do
it cow
and this gives us a visual way of
thinking about acceleration because the
distance between those two dots is the distance
travel per unit time and the distance travel
per unit time is the speed
right so many so much distance
per tick 30 miles per hour
and so what's happening here is we can see
accelerating and the fifth graders love to
know that the term for this is acceleration
okay we have a question yes I
know
your your commentary is focusing on math
but my question has
to do with the kids response to reading
and writing or reading and typing in this case do
you find that the kids
are more do they get the transference from being able
to use this high place and I try that after
yeah
that's a good question though
reason I'm hurrying along here is I'm
going to be cut out regardless of how interesting this talk is
it's going to end at 10 minutes to
the hour okay let's move
so I want the only comment here
is does everybody
see that what you're doing on the
computer can't be science but
is only math that you can't do
science on a computer
why
eah
I can simulate any goddamn thing I
want on a computer I can live up one side
and down the other so it's just all math is is
a story that's consistent but
he problem is the degrees of freedom in in any reasonable
human language are larger than those the universe has
and so this is this is why the Greeks
quite invent science except maybe Archimedes
and the reason is they thought God was a mathematician and
thought if they started off with self-evident
first principles that they could just
deduce the universe the same way God did
could be true because that this is a
lot of physicists think this might
be true I doubt it so
let's take a look let's look at the kids in the world now
so you're a bunch of objects objects that
you think will fall to the earth at the same
okay
oh do not pay any attention to
what anybody else the grapefruit now
you two levels of shot put sponge balls
are a couple
sleep janet
is up on the roof because
stopwatches by
the way to do it but
when do you really not go
together so put a sponge ball
okay I think we should do the shot
right and the sub ball because
they're two totally different ways and if
you drop them at the same time but they'll drop
at the same speed drop
okay so
if you do this so Aristotle
did not ask any children when
he came up with the wrong theory of this he
just deduced it using
a using a wrong a common-sense way of thinking about
what's actually going on but we found that one
child in 30 roughly so if you if
you have a class of 30 kids
you've got an excellent chance that one child will do what that little girl
did which is to pull the Galileo and just
cut to the chase and say hey wait
a minute that's
the I'm already in the
place
where all I have to do is just listen and of course the
scaffolding in the Leaning Tower of Pisa was
what Galileo listen to it was under repair at
that time so
but that's
quality could call that a big idea
however
can also do something
a little bit more here so we
take a video these
might look like funny video frames but video is just
part of the objects that these this language deals
with so we can make the frames convenient to take every fifth frame
you can stack them sideways or
you can stack them like this if
you look at this what do you think the kids say
when they see that pattern
acceleration four months later
so four months previously they did the horizontal
thing with the car four months later remember the
visual path what kind of acceleration
so well
let's measure
so we measure from the bottom of one
guy and so we can just use these little
translucent rectangles to do it
pre-measured these so
i don't have to fiddle while I'm rushed
for time as it is but then the cool thing
is i can just stack these up
like
okay what do you think these
things mean what are these
these are the differences
between the speed at each time tick
right each rectangle is the speed at
each time tick in i'm doing a visual subtraction
there and what i'm showing is their progressive if I just subtract
hem off they're all the same what kind of acceleration is
that acceleration
so the kids immediately write this
little script right here
let's listen to Tyrone here
and to make sure that I was
doing it just right I got
a magnifier which would help me
so I figure out if the size was just
right after I'd done that I would
go and click on the little basic
category button and then a little mini
would pop up and one
of the categories would be geometry so I click on that and
here it has many things have
to do with the size and shape of
the rectangle so
I would see with the Heidi I kept
going along the process until I
had them all lined up with their height i subtracted
the smaller ones height from the big one to see
if there was a kind of pattern anywhere there
could help me I'm not as this worked so
in order to show that it was working
i decided to leave a doc copy so that it
would show if the ball was really the exact right speed Henry
simulated ball is tracking the movie
this is how he's showing that his model
is in accord with the real world at
least two within a pixel so what you got here so
here's something to think about lily and mcdermott of
Washington is a physicist who looks at college kids seventy
percent of all college kids including science majors
in this country fail to understand Galilean
gravity that's what this is ninety
percent of the children going doing it
this way actually derive the equations
themselves actually make the simulations from scratch
themselves and show within
the limits of the accuracy hear
that their model is an
accord with physical reality and in fact the difference
between Galilean gravity 14
feet above the ground and Newtonian gravity is only one part
in a million and so we can think of get
Galileo is very lucky that
he couldn't measure that one part
in a million or he would have been very confused right
this way had to be done first before the
Newtonian way hat okay so let me I think I'm
getting to the point where I have to finish up
so
let's think about serious stuff now
e
live inside of systems and we are systems so
it's a nice unification through all of the
sciences engineering and art
so if you're going to make up a middle school science
curriculum for say the eighth grade I would
not pick a science like biology but I pick
a uniform unifying rubric
like systems and I teach all of different Sciences
the systems aspect of those and
use mathematics to deal with those
things and my romantic ideal
would be the planet is in trouble and we need to learn
how to save it
and
what we've got going in general is
something like this if you hit
this mystery object with a hammer it
returns to equilibrium but if
I raise it up far enough it
doesn't come back
so
what we got here
the most systems
are like this the equilibrium
they have is actually dynamically
stable but not statically stable so
if you just tap this thing
it won't do anything but if
tap it enough to get it passed its center of mass bunk
and
thing to understand here is that's
that's what we're doing so what we're doing is stressing
the earth and
little bits of stress like
burning the river in Cleveland can
be fixed up in large amounts of stress
can topple the system and think
about systems is when they get toppled they
don't stop but it's in a new state
now and it's going to resist
getting it back it could so
for instance when the climate has toppled in the past
aken between ten thousand a hundred thousand
and five hundred thousand years to restore all
of those numbers are a lot larger than our lifetime
okay
let me just try it
so
what we've seen here is a Jerry
Bruner idea but I've tried to show you
is that the
most important idea here is that you have to heed the level of
development of the person you're trying to teach and
if you know yourself like it doesn't
make sense for a non mathematician to try and teach math to
a six-year-old it just doesn't
because the six the
six-year-old doesn't think in the same way as a teenager or an
doesn't if you want to teach real math you
have to be a mathematician or have a mathematician
in the loop because the mathematicians job is to figure out what
kind of real math is within the wheelhouse
of the six-year-old
that's really the job
so discovery learning so
here's the thing we have two poles in the United States back to
basics and discovery learning
both of this both these are absolute
vs it
so it's very complicated going into a meeting with
educators because they tend to polarize long those and you
know any scientist and mathematician guys think Oh No
and the
the joke here is about discovery learning is is
whoops is the teacher
saying oh no they're discovering the wrong things why
are they discovering the wrong things well consider
our 200,000 years on the planet
we had to go almost all the
way to the present to just do agriculture Greece was
only 2,500 years ago that was modern math and
real science was just 400 years ago
think about that the
u.s. know a stable
dynamically stable democratic government
is only a few hundred years old these ideas are
not easy so what you need is a guide
so
it's not Hillary climbing Everest it's Tenzing
and Hillary and
sure we'd love to have Socrates and Fineman
as guides but these guys don't
scale this is one of the problems with school
books are great because you can get some
of Fineman and Socrates but
I used books a lot but I needed to have
real teacher that teacher had something libraries didn't
have which is a table full of junk you could make things and learn things with
libraries should have
these but they don't know that they should and I have
my dad who is a physiologist to ask questions of
so what we're thinking about
today is what
kind of use could we make
out of the computer since it has booked like properties
but it also is active enough to
be able to sense what the user is doing
so here's a simple
thing that's very popular guitar hero
so the interesting thing
about guitar hero is that people
don't have to go to school to learn how to play it like
most video games
now the bug with this is that
real guitar I used to be a professional guitar
player jazz guitar it's just
like a thousand times harder than guitar hero guitar hero
is it like simple drumming if
you ever tried drumming is very like
just having a snare and a high hat
and that's tricky enough if
you've ever tried it you have to get a couple of things going it's tricky
you can think it's the entire world because
this trick Ian of itself and there's all these great sounds
coming out but it's absolutely a snare and a delusion and
most here's the prediction most schools
States are going to wind up using computers in
classrooms to do a form of guitar hero
for most of the important subjects
because most teachers in
the united states are not guitar players
alright so this is a huge
problem and yet
without
replacing humans it's
absolutely possible to make some
a fantastic tutoring system for learning any level
of guitar playing at any level
without having to have a human in the loop that's what's interesting
you don't get everything you get with
a human but you get about ninety-five
stuff that you need to be able to do anyway you
can do it and that's what
I want you to think about is not replacing teachers
here but to listen
to our smarter than the average President as
talked to the National Academy last spring he
gets it the
only way we're ever going to get enough science
savvy knowledge into schools is to help
existing teacher with media that understand
the science as children can practice it
this is going to be a revolution
going to happen over the next year and it is a grand challenge it's
as difficult as the challenge that we faced
40 years ago where the challenge was everybody
should have a personal computer pervasively network worldwide
and
we have the funding for it and
we were able to invent it now several billion
people have it and it's time to use the computers
for what they're really good for what
do you think thank you very much