 Thank you, Kevin. Yes, precisely, one of the things I want to do is share some of the things I'm thinking with you. I visited here in February because I was giving a seminar in Stanford, and I just popped over to meet some of you guys. And I noticed that this is a very interdisciplinary crowd, and some of the things I've been thinking about are veered dangerously into other disciplines, and I want to explore the possibility of developing these ideas further when I'm here in the spring. So one of my goals would be to gauge the crowd and see who might be interested in these reflections. And I'm going to skip introductions about who I am, or what, you know, the About Me page, and invite you to visit our website, where there's a splattering of samples of things that we do in teaching and research, mixed with some tweets and little view and far between blog articles, and get right to it. This conversation today is an extension of what I already started talking about at my keynote last year at SciPy. The title of the talk was, If There's Computational Thinking, There's Computational Learning. It was a keynote at SciPy. Last year, the conference had a specialized track on education, and I was able to take advantage of that, focus on that topic, because I had just finished an interesting experience teaching a course on aerodynamics using iPython, now Jupyter, notebooks, and more about that later. And for some reason, I connected with the buzz over the idea of computational thinking, and then I started developing this idea that computing generates new knowledge. I'm a computational scientist, and you know that you use computing through simulations or data analysis to create new claims to scientific knowledge, and this is why we care about reproducibility, another of the topics that is a focus area in here at BIDS. And so this got me thinking that indeed we could translate that idea from our research activity to teaching and learning, and perhaps develop some narrative about what the role of computing can be in pedagogy in teaching. And so let me trace you back through this sort of path that I took and tell you a little bit about this idea of computational thinking. In 2006, as you can see here, Janet Wing, then a computer science professor at Carnegie Mellon, now she's VP of research at Microsoft, and she had a stint as division director at NSF, she published a short viewpoint paper on the communications of the ACM titled Computational Thinking. And this kind of brought to the forefront of the computer science community these serious conversations about computational thinking. Janet Wing between the years of 2001 and 2007 was at NSF, and she led huge investments in cyber infrastructure, and she used this narrative of computational thinking to get a lot of people interested and extend the investments of the NSF in computational science. She went on a speaking tour and did lots of talks all over the United States with this topic of computational thinking in which she talked about an attitude, a skill set that everyone can use, not only computational scientists. She also says that computation can be added to reading, writing, and arithmetic as a fundamental skill that we could even start early to try to get children involved in developing. But then she proposes that computational thinking involves solving problems, decomposing problems in a certain way, trying to approach problems in all sorts of applications with fundamental ideas from computer science like decomposition, abstraction, recursion, and things like that. So ideas that are basic to computer science can be applied to solving problems in any other field. And in her speaking tour she often used the example of computational biology as one subject where computing has had a big impact and another example that she often uses the subject of machine learning as one area of computing that has impacted our lives in many applications e-commerce and all sorts of things that are part of our daily life where machine learning has now basically changed the way we interact with entertainment and reading and shopping and so on. So that's the story behind this publication. And as you can see here, a few days ago I searched on Google Scholar and this little two, three-page viewpoint paper with no references and no really real scholarly content has 1,654 or probably has more now citations according to Google Scholar in nine years. Now I don't know about you, but I'll be thrilled if one of my papers got this amount of citations even in a decade. And so in engineering the number of citations, perhaps in biology or computational biology, the number of citations are in those numbers, but in engineering it's not for that often. I don't know about computer science, but it seems like a pretty respectable number of citations. Now the first computational thinking nevertheless goes back all the way to 1980. It was first used by Seymour Papert and I've taken a screenshot there from Google Books of the page, page 182 of the book Mindstorms by Seymour Papert in 1980 where he uses that phrase for the first time. And it also appears more, you know, treated a little bit more extensively in this paper and exploration in the space of mathematics education and X-rays I think there. In 1996, Wing doesn't mention Seymour Papert and I guess a viewpoint article or essay doesn't really need to have citations, but I find it important to go back to the source and understand all, you know, I found it very useful to go back to the source and read those original mentions of the idea because it turns out that it's a lot richer than how the idea of computational thinking has been popularized since the viewpoint article in 2006. And we'll get to that. All right, now we even have a Google MOOC, massive open online course for those that have been under rock, that is being offered of course free of charge through the new course platform of Google. And this is aimed at educators with the idea that they could adopt computational thinking as something that can be used in the classroom. And in Google's version of the idea of computational thinking, I'm going to give you what this course describes as the key of computational thinking. These are the key features according to this course in Google and you can also draw, these terms are also used by Jeanette Wing in her viewpoint, the idea of using decomposition, breaking down a problem into simpler parts, pattern recognition, absorbing patterns from irregularities in your data, abstraction, identifying the general principles that unify the patterns you noticed, and algorithm design, devising a process for solving your problem. Now you notice that the focus now is completely on problem solving and that's how it is viewed more in the popular version of computational thinking, the idea that you can have a skill set to approach problems. Now Seymour Papert, here's a picture of Seymour Papert, how many of you guys know or have heard of Seymour Papert? All right, maybe half the room or less, one third of the room. He was one of the pioneers in artificial intelligence, a professor at MIT way back when, and also the inventor of the logo programming language. So many of you have perhaps interacted with logo or remember about the turtles? How many of you guys know about logo and the turtles? More? Okay, well that's a turtle. That thing that you see in that picture is a turtle, the original turtles. Now perhaps some of you computer science students or those who were exposed to computer science in school may have seen a little blip on a green screen and called that a turtle, but the original turtles were physical little toys, robots that were used by children to draw pictures from big pieces of papers on the floor. And Seymour Papert's meaning of the idea of computational thinking was deeper than the now popular version, the buzzword. He said, my interest is in universal issues of how people think and how they learn to think. So it's not just problem solving. There's a little bit more subtlety there and that's what got me really interested because of the experience that I had in the classroom using ipython notebooks. They were called ipython notebooks. Then I'll switch to Jupiter when we move to the future in my story. And you know when I had experience in the classroom using this approach to teaching aerodynamics I was really moved by this deeper meaning of computational thinking that we find in the original writing of Seymour Papert. And I had a little two minute video, 1972 video that was an optional. The technology doesn't let me show you the video right now because I don't have audio but I can show it to you at the end once they finish the recording of the official part of the talk. I think you will enjoy that. And here is another little bit from the book Mindstorms. He's talking about the visions that people have about using computers previously in this passage and saying all of the ways that people talk about using computers and then at the end of the previous paragraph he says a few talked about the computer as a teaching machine. A few like really nobody's thinking about that was the tone of that passage. This book poses the question of what will be done with personal computers in a very different way. I shall be talking about how computers may affect the way people think and learn. I begin to characterize my perspective by noting a distinction between two ways computers might enhance thinking and change patterns of access to knowledge. If you think about this it really is he's thinking deeper than just the idea of using computational thinking for problem solving. And I'll switch gears now and tell you a little bit about my path using Python in teaching and then connect back with this. In my type I talked last year I simply said these Jupyter notebooks are a killer app for education and I really think that if they are incorporated in the teaching of technical subjects and mathematics we can really do something transformative. And I want to tell you a little bit how I got to that conviction. I will share some of my experiences. The background for this was that back in 2011 I was preparing to write my NSF career proposal and my teaching methods at the time were pretty much standard. I would lecture as I am right now making the best effort to keep people awake but nevertheless it was a one way transfer of information type of model for teaching. And so I knew that there was a need for looking to increase the level of interaction with my students and I started just researching online for ideas on how to do that. And I bumped into this concept of the flipped classroom. And this is 2011 and I want to show you this trends notebook, this trends plot on Google of the term flipped classroom. And I think that I probably was one of those five people that searched for the term in May 2011 as I was preparing for my NSF career proposal because I submitted in July 2011. Now of course the term now takes off and becomes a buzz word and now you know January 2015 at the beginning of this year like everybody had to flip classroom and it becomes this thing that you're starting to feel a little bit suspicious about because it's all over the higher ed media, right? Unfortunate but you know because that produces a backlash but it was for me really transformative to think about the flipped classroom or this basic idea whereby you understand that just being exposed for some new information for the first time is really the easy part of learning. The harder part of learning is when you have to assimilate that new concept or idea and apply it on something new and the idea of the flipped classroom is of course you move that easy part of being exposed to a new concept or content for the first time to outside the classroom when the student can read not necessarily watch videos and read or in any way prepare to come to a very active classroom where you apply inquiry based learning or any form of active learning to assimilate and apply knowledge in a group setting collaboratively with other, with peer or something instructor. That's the general idea. Unfortunately in this flat line where it becomes a buzzword the general opinion of flipped classroom has been that you record video lectures so it's a very shallow sort of view of that. The important part of flipped classroom of course is what you do in the classroom about how you manage to transfer information content is the easy part in this digital age how you deliver content there's a million ways there's an internet you don't even have to package it very much. Okay so this is the background and I was teaching at Boston University a class in computational fluid dynamics at the time and I decided to flip the classroom and I had a track record of using technology in my classroom and I was recording my lectures through screencasts that is I would do annotations on a graphic tablet while I was presenting and then record that and put it online so that the students would be able to replay, revisit the material because I knew that half the people were falling asleep in lectures because lectures are passive. Now I don't do that anymore. Anyway I had some videos to remove that initial friction of not having to record videos because I already had them and I used the videos from that previous year and decided just in 2012 to develop something active to do in the classroom and we used for the first time Python and not in that version of the on campus class but afterwards I had to teach a summer school and I just grabbed this exercise that I had developed for the classroom that's called the 12 steps to Navier-Stokes and it's literally 12 steps for coming at the end of it to write your own version of a Navier-Stokes solver in two dimensions with Python. The first step is the easiest possible PDE solver that you can imagine is to find a different solution of a one dimensional linear convection equation so it's the easiest partial differential equation that you can write down and from then slowly adding elements at the end of 12 steps you actually have a Navier-Stokes solver and that had worked well in the classroom but my students in the classroom took normally about five weeks to complete that and then with the help of my Able PhD student we developed this as a set of notebooks and published this of course available for everyone to use and there an open license on GitHub and I used it on an intensive summer school in Argentina when I had two days to teach a numerical CFD to teach a numerical fluid mechanics and I found I had 20 students quite a diverse group, some physicists some students that were programmers some others that didn't really know the program very much and it's quite a variety so one of my objectives was if I have this scaffolding, this material that students can use actively in the class in the lab then the difference in levels won't matter because they will just go at their own pace and I would simply go desk to desk helping them through and they will reach whatever level they can reach at the two intense days and at the end of those two days of the 20 students about four or five had actually completed the whole assignment the whole set of 12 lessons there were about eight of them that were somewhere between lessons seven, eight or nine in the middle and of course a few stragglers that really didn't have any programming experience and they luckily got through step five say but I thought that was pretty good because a bunch of students actually had written a solution to Navier Stokes in two days and I don't know if you're aware but Navier Stokes is pretty you know, it's a pretty scary thought for many engineering students that you have to write a Navier Stokes solver so that's when I thought wow, this is actually really cool there's some onto something here I've prepared a set of notebooks I've actually coached a group of students through a process of going through these lessons and some of them really succeeded and some other ones really went away with some that could possibly finish on their own time because now they have this material that they can follow and after this experience I didn't want to go back I'm addicted to this stuff I was tasked to teach an aerodynamics class next at GW and the aerodynamics class are classical aerodynamics and I don't know how many of you have a background in physics but it's really potential theory any of you, how many of you know what I'm talking about potential theory maybe in the context of electricity okay, quite a few of you potential theory, if you go back I think the classic book on potential theory was written in like 1920 or something, Kellogg the classic book and a potential flow or aerodynamics course has been taught in either aeronautics or mechanical engineering context since the early times of aeronautics and probably in the 50s or 60s the same time as it is today it's all theoretical, it's on the blackboard and it's potential flow solutions and a lot of algebra take away homework where you do a lot of algebra and so on all chalkboard and pen and paper and here I am in front of a teaching task that is a purely theoretical course and I want to do notebooks because I'm right I like them so much so what do I do? I ask myself well what is the one thing that I want students that I think students should learn in a modern version of an aerodynamics class and after reflecting for a while I decided well the one thing that I want them to know is how you can build a potential flow numerical solution of flow around an airfoil and then set myself to follow that same pattern of decomposition I suppose the process of computational thinking of taking the problem and decomposing into steps and came up with this now it's only 11 unfortunately because the lesson zero is just an introduction to Python I wish it could have come up with 12 but it's only 11 in this case steps to a solver of the source vortex panel method is the way that you can solve numerical potential flow around an airfoil so I prepared this with the help of my PhD student as a set of interactive computational lecture notes basically so you have the lecture notes the equations, the material and the coding and there was no lecturing in classroom the students had to read the material the theoretical part and work things out and I basically checked there that they were doing their mathematical derivations but we didn't do any of that in class in class we interacted with the computational part of these notebooks and so I would be walking desk to desk in the classroom asking questions using the computational parts of these notebooks as the medium that allow me to ask questions and have the students inquire the system of potential flow solutions now one of these lessons you'll see it there number six right in the middle is the first time that the students see the concept of lift in potential flow you start constructing the idea of being able to numerically solve for flow around an air flow producing lift by adding fundamental solutions of potential flow so for example if you have an electricity background there's a source it's one fundamental solution and a sink is another fundamental solution if you bring them infinitely close together you have a doublet that's another fundamental solution and in this field if you have a doublet and you add a free stream you get flow around the cylinder something like in that picture if you add a vortex in the middle you get lift that's just hand waving my way through the whole half of an aerodynamics class so we have lift on a cylinder lesson six and here's just a screenshot of the lesson how the beginning of the lesson looks for the students when they encounter this is the original version in February 2014 and there's a parameter that's available for the students to play with which is that little cappa there well no actually that's the doublet but further down there's another parameter which is the strength of the vortex and I ask the students to play with that parameter and they have the code there available to do that and well let me go back to this one you see this picture there's some green dots those green dots are called stagnation points and if you think about this there's a flow going around the cylinder these are streamlines that go up and around and these streamlines go under the cylinder and lift is produced upwards in that direction it's kind of the idea of the spinning baseball right when you have spin you can create a force opposite the direction of motion and these two green dots are the stagnation points so that's the picture of my original presentation of the problem in the notebook and as the students change the parameter that is the strength of the vortex inside the cylinder they got one student got a picture like that he raised his hand and he said professor professor the stagnation points have disappeared I said what do you mean the stagnation points have disappeared I walk away and I say oh yeah if I go back that's how it looked at first and that's how it looks afterwards no stagnation points I said well what value of the vortex strength do you use well I use 10 suppose I'm reproducing here with some parameters what I may have experienced in the classroom with a student then I said well try a different value try something smaller he tried maybe seven well try smaller he tried two they were back with two suppose we were back to that picture okay try bigger and he suddenly suppose that he tried five and then there's two stagnation points are right there and he tried another value like in front of me he started trying different values and then suddenly he said oh this stagnation puts move away move away from the body like yeah that's what happens that's exactly what happens now think about the way that normally a student is exposed to this idea the teacher would probably write draw a picture on the board where the two stagnation points are right underneath the cylinder and he writes gamma bigger than that he'll write draw another picture where the stagnation points are right like here in this picture and the gamma is less than equal to that and then draw another picture where one stagnation moved away from the body and gamma is less whatever and the student will dutifully write the same sketches on their notebooks and write gamma bigger than that gamma equal to that and then it's done and he'll probably never remember again except before the exam of course he'll look at the picture and say oh yes of course go into the exam probably be able to reproduce those figures in the exam and then forget two days later I think I'm very very convinced that the student that went through that process of actually interacting with the code and seeing that happen in front of him and came to this realization and said to me ah this is what happens I'm pretty sure he's going to remember much better than this other students that just simply take notes from the boy so this is why I think the opportunity of Jupiter notebooks of giving interactive computing within an environment of content that we with the most basic thing that we do as teachers is to share content near content with our students has a really big opportunity this idea of interactivity through computing and this was my experience and then I started of course going back and trying to read and trying to understand what I have seen after this course that I taught in spring 2014 I decided to I was tasked to teach another course Numerical Methods for Engineers and I decided to again base it on a set of notebooks and to go a little further put this all online and invite people from across the world to join us using a MOOC platform and teach it as a MOOC so I announced this at SciPy on the end of my talk in July last year and then said about to install a platform to invite students to join us we used the Open edX platform it's an open source online learning software that was developed by MIT and Harvard and Berkeley and then Stanford as well contributed code and it was made open source in July 2013 at the time though when I announced this really no one was using this open source software and people went about their MOOC business by joining either course or our edX that was the trend that was the way to do it and I decided no I I'm just going to do it myself code is open source we'll just download install it of course it was much harder than that but we got some help and managed to get it done here's a screenshot of our own customized version of the Open edX platform that we deployed for this course with just three courses actually that's just my courses the whole platform just had my courses and some little experiment in doing teaching modules and that is the experience that has motivated me to go back and reflect a little bit more about our thinking and computational learning so let me take a detour now and since at BIDS one of the focus areas is reproducibility ask you why do you think we are concerned about reproducibility and computation what is it that we care about why is it that we care about reproducibility and computational science or data science because it's science okay correct correct what do you mean but it's science this is a proposal what do you think computer simulations create scientific knowledge do you think that's a fair statement let me see if you agree let's see if this works let's see I'm going to do something this is a okay okay let me go back I'm sure most of you are online with a device of some sort so go to this website c.socrates.com enter room number gwc if you have any device any phone and you answer true or false computer simulations create scientific knowledge I'm going to go back to there let's try it let's see what you guys think let's get let's get a quick poll c.socrates.com enter the room number gwc so you should see a true or false question and the true or false is computer simulations create scientific knowledge of course true means yes and false means no do you get it do you see it yeah this is I use this in classrooms in my class so that's why this is my my little code to enter this is a cheap free student response system that allows me to ask questions in class co-opting devices for my purposes alright and the question is computer simulations create scientific knowledge yes or no let me see I got live a live feed now or 82% say yes so you agree many of you except well how many 80% do not agree of the 15 people in the room that's fair there's always dissenters but this is interesting many of you do agree that computer simulations create scientific knowledge cool I'll take a screenshot of that oh some dissenters more dissenters now cool 25% alright still took a screenshot of that 14 people some of you left the room so many of you do agree that computer simulations create scientific knowledge and so if we're creating knowledge we're actually developing knowledge together through simulation or data analysis then it's a form of learning and this was kind of the process I followed as I came with this idea for the sci-fi lecture last year it's a form of learning we can use computing to learn and this was I thought what I was seeing in the classroom students actually using computing to learn to discover something we use it in engineering sorry in computational science all the time in research and so we understand that from the point of view of research and what what I want to propose is that we move that same perspective to teaching to teaching and learning that it's a form of learning and I found myself reading a lot about learning theory because of course if we're talking about a form of learning then I guess we have to sort of know what learning means and I found myself going back to some some of these learning science publications and I thought that the that this idea of computing as a form of learning was aligned interestingly aligned with the more modern theory of learning that's called connectivism and this is a thesis that knowledge is distributed across a network of connections I'll tell you a bit more about what that means and therefore learning consists of the ability to construct and traverse those networks that's the most modern version of a theory of learning that we have one of the seminal papers was this connectivism a learning theory for the digital age published in 2005 by George Siemens previous learning theories are known as behaviorism cognitivism and constructivism connectivism comes right after and the idea of this being a theory for the digital age is that well over the last few decades technology has really rearranged how we live how we communicate communicate and how we learn and everything we do in our daily lives now is through through technology so the idea behind this movement is that learning theories have also to now reflect on how technology is used in this social process of learning and the previous versions of the previous learning theories of connectivism are all at all view learning as something that happens in the person just inside a person right something happens in your brain you learn and they did not address what occurs outside of the person the possibility that learning could be stored or manipulated by technology happens outside a person and so this point of view learning can be manipulated by technology and how to include technology in our sensemaking of the world and also even describe how learning happens in organizations so in communities beyond the single the person alone and this is very interesting starts getting interesting from the point of view of what we know in open source communities and the idea of connectivism is that learning actually can reside in non-humor appliances the internet or our network of people which involves communities and these are the basic basic hard to grasp ideas Steven Downs is the other connectivist early proposers together with George Siemens learn knowledge is distributed knowledge is created by conversation and interactions the idea that knowledge can be created and shared by the community of individuals the interesting thing about this is that now the role of the learners to participate in a community and this is why open education is so important because to participate you have to be able to create learning objects share learning objects remix and make derivative works and from the point of view of open source communities we can't understand those concepts the idea that open education has to involve sharing and in connectivism the starting point for learning occurs when knowledge is created in this process of learners connecting through a community so what is this idea of a community George Siemens defines a community as a clustering of similar areas of interest that allows for interaction sharing dialoguing and thinking together now some of you are coders right so does this ring a bell community the idea that we are you know interacting dialoguing thinking together this is how we function when we develop projects in a community and if you think about it no not one person can actually produce any of those large projects in open source communities we do them together and this this is how this is sort of the digital age version of knowledge creation in community so in the context of all of this learning theory of connectivism sciences understood as well a conversation among scientists a conversation between the scientist and the experimental apparatus you interrogate your experiment to get answers to your questions and and the social process of science there science is a social process a conversation a constant stream of conversations whereby you are making sense of things and science becomes this act of connecting things that's the whole framework of connectivism and going back to this experience of using computing as the process of learning then my connection here is that computing becomes gives you this ability computing through something like the Jupiter notebooks where you can mix all forms of content with the interactive use of computing to interrogate a system this interactivity a fundamental aspect of using computing as a conversation with the new content that you're learning we're used to hearing about computing in the context of skills and capacities but this is more in the line of thinking about as a literacy as a material intelligence something that makes us more intelligence because we have it and I'm going to skip a couple of slides on the interest of time let's get to the examples of this that I have and tell you about a couple of historical examples that explain this or help us understand this idea a little bit better here's a very interesting book Changing Minds by one of your own Berkeley professor Andrea DiCessa and he is of the same school of thinking as Seymour Papert I would think and there's this passage in this book that says computers can be the foundation of a new and dramatically enhanced literacy now this is using the word literacy not skills or problem solving and here's a passage if a true computational literacy comes to exist it will be infrastructural okay what does that mean infrastructural let me give you a couple of examples okay here is a little picture of the publications of Isaac Newton where he introduces calculus to the world I won't get into the arguments of who was the invariant of calculus whether it was Leibniz or Newton let's just use this for our imagination what is calculus well calculus a way of writing down and drawing inferences from various aspects of physical quantities that change in time rates basic thing Newton wanted to reason about the instantaneous properties of motions and he had no proper representation for it so he had to invent calculus now today we find this pretty normal but at the time you know he just had no language or representation to develop those theories the process of calculus becoming infrastructural as it is now in the universities for all technical and mathematical training happened 200 years later in the beginning of the 20th century when a couple universities actually Caltech was one of the universities with the influence of the European trained professors that came in decided to introduce calculus across the board to all of the students and early on you know freshman year or something at the time that was not the way engineers were trained after this was somehow redeemed a success university starting started adopting this idea and nowadays we find it pretty natural that all incoming students learn calculus the first year it's become infrastructural and the proposal of Andrade says in this book is that the true literacy of computation will happen when it's infrastructural when actually we can take for granted in later courses for example that students so that we don't need to worry about them using computing for their for their exploration of physics biology or whatever it may where it may be okay so here's another passage that I found really interesting 2000 we may now have sufficiently learnable and powerful computational inscription systems to have dramatic literacy implications now 15 years later perhaps the dream of Andrade has not yet been realized but potentially we have an opportunity now with all of the exciting things happening in Jupiter project and similar things now how does this work how does this using a tool like that and I was born to use the word tool very carefully but this bridge that takes you to everywhere to nowhere to everywhere that's the idea of a tool how does it work here's another example also from the book of Andrade Cessa he talks about in this example how Galileo developed these theorems of uniform motion so here are his six theorems and I I'm going to read the first two okay and see how many of you have had basic physics like almost all of you okay theorem one if a moving particle carried uniformly at constant speed traverses two distances then the time intervals required are to each other and the ratio of distances okay I'm saying okay theorem two if a moving particle traverses two distances in equal intervals of time these distances will bear to each other the same ratio as their speed and conversely if the distances are at the speed then the times are equal well yeah that's starting to read a little bit like same thing and if you read the rest of the theorems there's too much out of about nothing here why did they have to so painfully describe the motion of particles we even today and ninth grader can probably explain this and you can't imagine how difficult the proofs were because each one of these theorems carries a proof I need these two pages for each one painfully draws out the proof okay simple variation of distance equals rate times time so let's get two particles two distances two rates and two times use the subscripts one and two for each one of those and we divide the two equations to get started then we can express theorems one through six in very simple terms the first theorem just assumes that r1 equals r2 the two distances are equal and therefore immediately the r terms cancel out leaving our backs very very easily now described in a way that even any high school student absolutely will be able to follow it we can't really blame Galileo for such a convoluted presentation of his theorem because Galileo didn't know algebra in fact there's not a single equal sign in all of his writings so how could he give us the simple version of his theorems I think it was a great feat of his imagination to be able to explain those theorems of motion and prove them mathematically without having any knowledge of algebra it was the cart that 50 years later just started getting a little bit of a handle on algebra and it wasn't until the 20th century before it really became infrastructural to the way we teach and learn so this is the idea of a system that can make us smarter we have algebra now so we really cannot we don't have to go through pages and pages of explanations to understand the simple theorems of motion of Galileo and in this sense when computation becomes infrastructural and easily accessible to all students then that Andrea talks about this way of representing something like calculus is a way of representing the motions of the instantaneous motions of things that change the instantaneous quantities then when sort of we become smarter as individuals and also society and this is the proposal I guess I have for this idea of computable content the idea that we can use notebooks to embed code and visualization together with explanations and mathematics to use it and throughout the educational system even for students that are quite young as Seymour Papert visualized the idea that rich interactive content can become now material intelligence that will make it smarter and there are some even publishers that are catching on to this and I really am very eager and enthusiastic to see how how this moves to this potential ground transformational technology which is educational content that is interactive fully interactive and has a compute engine ideally with no installation friction in the cloud and in all learning platforms and I want to leave you with this last site a citation of Seymour Papert 1980 don't forget 35 years ago I believe that certain uses of very powerful computational technology and computational ideas can provide children with new possibilities for learning thinking and growing emotionally as well as cognitively and 35 years later maybe we finally do have that technology and we just need to sort of agree on deploying making it infrastructural and understanding how to manage our communities so that we can actually create more knowledge together there was my I brought some of it today