To launch the new year, I've renamed the show from Hawaii Reimagine to Work Reimagine to be more aligned with the show's focus on the future of work and workforce innovation. So yes, you are in the right place. And as we're facing massive work disruptions due to automation and the pandemic, our challenge is to create solutions that address the future of work and the demands of a new labor market. In Work Reimagine, I feature innovators and entrepreneurs who are addressing these workforce issues with innovative solutions that will make a positive social impact for people in our communities and economy. I'm Ruby Menon, and I'm your host today. And my guest today is Sean Hinton. He is a CEO of Skyhive, which is an artificial intelligence or AI based platform that matches workers to jobs and identifies the skills workers need to stay marketable. Workers entering the workforce now face an unprecedented and continuous need for reskilling and upskilling as newer capabilities become requirements for the next job promotion or career change. Skyhive's technology reads an individual's work and educational history and translates it into skills. And then it finds the correlations between those skills and the skills extracted from jobs to identify career pathways through learning solutions. And this is all done automatically using millions of real time labor market data points. Skyhive also has a mission that's near and dear to my heart. They're committed to fulfilling their mission to reducing global unemployment and underemployment with a focus on doing social good. So Sean, I'm so happy you're able to join me today. And I'm so excited to learn about you and the amazing work that Skyhive is doing in the workforce innovation space. So welcome. Thank you for having me. Thanks for having me in Aloha, Hawaii. Yes, Aloha. And you're actually in Vancouver. We were talking about how you're also looking at mountains and ocean but just a little bit colder over there. So I wanted to start off with learning a little bit more about you and your career pathway and what led you to get into this work with Skyhive. Sure. So I would say that Skyhive is chapter three of my career journey. And so very much consistent with an ever-evolving career pathway. So I started my career in the early 2000s. So I was a labor economist. And so I did private consulting with the government of Canada. And I was part of a program where we rolled out a multi-billion dollar multi-year initiative of the government of Canada called the Sectoral Council Program. What this was was we were looking at Canadian demographics and noting that by 2016 we were going to be experiencing net population decline. And so without the influx of newcomers or immigrants to the country, Canada would begin to suffer net population decline and therefore decline in economic growth. And so we began to formulate policy around looking at the recognition of foreign credentials of newcomers and making it a more fluid process because we were aware of the socioeconomic barriers that existed to newcomers coming to Canada. So for example, if we brought a cardiologist from India, he or she would end up as a mid-level manufacturing manager or something like that. So we were really trying to solve the issue of right leveling out capability and the recognition of credentials. The program then evolved into working with the private sector across Canada, so 55 or 60 different sectors, and linking human resource professionals with training and vocational institutions to talk about the requirements of geographic specific upskilling and re-skilling of learners and workers. And that worked then evolved into a national context where we looked at the development of national occupational classifications or basically the job classifications that we write for new roles and new occupations in the Canadian economy. From there I transitioned into the private sector, and so I started working with the world's largest water park companies. So we did all of the attractions engineering, attractions manufacturing, construction project management for the largest theme park and water park projects around the world. So think Disney, Six Flags, Carnival Cruise Lines. I started my time at that company by building out the markets in EMEA, Europe, the Middle East and Indian Africa. I then transitioned to Shanghai, building out the Asian Pacific markets and then eventually took over as CEO of that company. And so that company had 500 employees across 23 global offices. So my hive gets established in 2016, where I'm in Dubai, and I attend a conference of the young presidents organization. And in the morning a group of Syrian women get on stage. They speak to us about the atrocities of the treatment of women during the Syrian Civil War. When I have a stream of consciousness I think about time in Damascus that I had spent the Syrian capital prior to the Civil War, and you know seeing women and children and families in the squares and restaurants etc people that I had worked with them business with etc. And I came out of that session in Dubai with a new vision that I wanted to take my energy experience and enthusiasm and apply it to solving a world problem to help build a company that can be hugely successful from a traditional profit perspective, but drive true positive social impact in tandem with that growth. And that was really the genesis of Skyhide. I mean that that story is really remarkable because I think you know oftentimes we'll get those types of streams of consciousness and then we'll think about what we've got to do something about it but very few act on it. And so I'm just very curious about what was that journey like for you to go from the stream of consciousness to this you know memory of Damascus and then actually like going forth and creating this company like how what was that like for you. Yeah, I often you know I'm a big believer that the universe conspires right to bring things together when people try to go forth with good intention and so the universe definitely began to conspire I had no idea what I wanted to do, I just knew I wanted to do something. I began to think about what my background was in my my passions, and I knew a lot about learning I knew a lot about skills I knew a lot about labor market data. I knew a lot about technology and sort of sophisticated engineering because building attractions that need to keep people safe is actually a very engineering intensive situation and so I started to bring those two pieces together and there were several things that you know we don't have time for on this on this interview but several moments over the next three or four months after that, that really reinforced to me. Yes Sean the universe is tapping you on the shoulder saying, you need to go and do this. And so it just gave me the energy that I needed to keep going at that point. And I think that's something that probably a lot of us who are in the midst of career change could certainly learn a lot about so that's a great story. And let's let's dive into sky high because I really want to unpack a little bit about, you know, what the technology really is all about and we've thrown some terminologies around like AI based reskilling technology. So, how does this actually work I mean in terms of the user experience. What can we unpack this so that we have a better understanding of beyond the terminology what what the technology does and how does it help the job seekers find employers find job seekers. Yeah, absolutely so I began to think about why at that time in 2016 we were blessed with the most advanced computing power we had ever had in the world's history with the lowest cost to access it. Yet if I asked somebody a basic question which is what are your skills. And by skills I mean technical skills soft skills capabilities tools technologies and methodologies. And at that time, even answering that question if I asked you Ruby, tell me all your skills, you'd really have to put your mind together to think about what what that would mean. And when I ask the follow up question, which would be, what are the skills that you've acquired through your work experience life experience and educational experience. And how do we inform the changing nature of work and desired career pathways in other words, all of us have a unique skill DNA that we bring to the world based on those three areas education work experience and life experience. How does that DNA apply to how the world of work is changing and different types of jobs and career pathways. On the workforce side, we've typically seen the lens of the labor market or a workforce through the lens of what we call classical labor analysis, which is job title level and credential level. And so, if we look at any job title in the workforce project manager. This is a job title that's been the same for decades, but the actual requirements to do that job the technical skills the soft skills the tools the technologies the methodologies are constantly changing. And so I began to think about how do I apply advanced technology that I didn't have when I was a labor economist and this all had to be done manually. Every single time I wanted to see the new changes in the labor market. Every single time I wanted to analyze a person or a group of people skills. I had to go through this manual process. And so I invented a methodology called quantum labor analysis, which is the application of artificial intelligence to analyze a workforce at its most granular level. What this means is, I'll keep it sort of high level we have three layers of machines. The first machine is going out and capturing anything to do with labor market supply and demand movements. So, it's capturing job descriptions course outline see these labor market information from governments, but even forward thinking things like patent applications subject matter expertise annual reports and companies. Anything that's helping us understand what what is going on in the in the job market. So the second layer of machines that does all the work of extracting technical skills soft skills tools technologies and methodologies from that larger, more aggregate data set. And then those machines take it and put it into the third machine which is a deep learning technology, a modern AI technology that brings all of that together and says okay. How are jobs changing, how are skills changing, what set of skills relate to what jobs and it starts to look at this data, but this is all done in an automated way. So effectively what we're doing is we're a human optimization technology so we're helping utilize AI to optimize human potential, where I can very quickly see the skills that I have. The skills that I'm missing in relation to any job, and I can see right away the career pathways and the type of training and re skilling I need to go and get in order to better prepare me for the jobs that are emerging. So our clients, we serve companies and communities through large corporations and governments. And so we support on four continents now the rapid re skilling of global 2000 organizations and governments at a communities at a government level. So if we, if I was a job seeker. My understanding is that the enterprise or the government has to purchase the technology and then the job seeker gets to use it or how does it work for the end user like a job seeker do they go to a site like indeed and then they put all their stuff in there and then the AI does its magic and comes out with a skills match or how does that work from the end user standpoint. Yeah, so skyhive was built and designed with the inherent focus on ensuring that we get the entirety of the labor market so what I mean by this is linked in is a good resource for, you know, white collar professionals executives for social networking and doing things like that. But we built our technology to serve low income communities, youth veterans people with learning disabilities etc and so we want to make it very very simple so today, or prior to skyhive. If I needed to find a job, and I would go on to individual job boards, and I would fill out and register my information, and then I would begin to search by, you know, titles of jobs, etc. Then if I needed training, which I would have no idea what skills I have or what skills I don't have for these job vacancies on these job boards, then I would have to go search for training separately. What we've built is called a skill passport, and it can be very analogous to the Expedia for work and jobs and training. And so we want you to go to one place, the technology aggregates all the jobs on all the other job platforms, all the training that's available, and it brings all of that down using the process I mentioned previously. So for a skill passport, all that needs to happen is a job seeker needs to spend five or six minutes filling out and registering for their profile they do that once. They get to go through the process of discovering their skills because the AI is taking their work experience and automatically extracting skills they get to choose what level of skill they have them I beginner intermediate or advanced. So if I was in place then the AI does all the work for you so it goes out and takes that skill set, and it will identify any job that that is a high match to that skill set, and it will also identify the career pathways that are a high match to that skill set If, for example, as a result of COVID I lost my job in tourism and hospitality, and I need to understand how my skills that I've developed which are valuable everybody has valuable skills in their skill DNA. How those skills relate to other types of jobs, for example digital marketing or customer service or other types of jobs. The system is doing that automatically and it's helping me, it's helping me and job seekers find their way to that next job as quickly as possible, using artificial intelligence. The access though to the technology it's how how would let's say if I was a person that lost I was in the hospitality industry lost my job, how would I be able to access the technology does our government have to have access to it or how does somebody like a regular Joshua job seeker, you know right now you can go on the web and you can go on indeed linked in and all of these other job boards but how do you get access to skyhive. Yeah, so our technology is built for what we call enterprise grade rollout so we're not a consumer technology we're not like an app you have on your phone. What we are is a technology where for most people who have lost the job they'll visit some one of their states or local governments websites to to register for you know unemployment insurance or something like this. From there, we're working with the state and local governments to implement skyhive, because what's important is it's not just about the job seeker experience but it's also about the data that can help governments in terms of mobilizing. They can see what's happening in their real time labor market, and they can help mobilize economic development initiatives very rapidly to support that re skilling retraining that needs to happen. In order for those new jobs to, you know, to come into these communities and so. So we're working mainly with governments as it relates to the application this application of our technology. Well, I guess we're going to have to get Hawaii to purchase this technology for the rest of us to use it. I was kind of curious. I know that your company is growing so how is the technology helping you to source out the right candidates for the job openings that you have. So for every single person in our company everybody has a skill passport and everybody's matched with training as they would on on our technology. But we also use our technology to help formulate the right role that we need to hire for and so I think a lot of mistakes that employers make and obviously they don't have they don't have access to the information that we have but they'll utilize a job you know software engineer or transportation manager and not really understand the nuances that are coming with the future of work in terms of functional skills. And so we're able to do proper role what we call role architecture in terms of defining unique jobs that that specify to a function that's required in our company at that time. And then our technology goes out and finds those people right because we're able to access all the candidates in the world that have this skill set. And so we're able to go and find talent without having to post jobs or to you know post on a job order Oh how interesting. Wow. You know it's something that I'm a next HR professional and it was something that I used to grapple with all the time whenever managers would give me these job titles and then I'd have to try and dig into the weeds and finding out you know one project manager like I said, across departments might have different types of skill sets that they need or a different role. And it was something that was very difficult to manage oftentimes because that nuance of the details was never really a part of the lexicon of how people do their whole recruiting process just find me a project manager, you know, but it was so generic that it was trying to find a needle in a haystack so it sounds like this technology is really crack the code on being able to get into the very details of that position. And from you as an employer it sounds like you're also able to do a much better job of architecting the roles for your company so that's that's a huge, huge win. One of the things I wanted to find out from you, especially because you crunch so much data around labor analysis. What skills are you finding are the most in demand. You know what we've got automation nipping at our heels and of course now pandemic. So as humans, what skills are we going to need for the future of work to be to be and stay marketable. This is a very common question as you can imagine that that I get. And so, you know, I think first I'll speak to the misconception.  The reality what's happening is the near term future is going to be what we call low code or no code type technology and if you're familiar for example with wix.com where you can make a website simply by dragging and dropping things. This can be analogous to what we call low code or no code and so a lot of the sort of standard software engineering jobs are going to be going away. So we're going to include data science because we're going to start to see more data science as a service and less of the requirement to have to sort of like custom develop algorithms and things like this and so that's happening over like literally the next call it three to five years. So I see a lot of skills that are going to be required as first of every single person should be focused on the whole notion of lifelong learning. So the, the skills of learning in general, critical thinking communication teamwork. That will be core to any any role moving forward, but I think more specifically, there's also a misconception that the future is nothing but soft skills. That is also completely false. And the example that I give here is when I need somebody to weld something a bridge a hospital and a highway. It's great that they're a team player and it's great that they are a good communicator, but they need the functional skill of welding right. So even if we look for example at robotic surgery, you're still going to require doctors to monitor those those those machines to ensure that they're doing their job properly which will take medical background, coupled with technology background right. So, overall, as we see increases in automation and digital transformation, what where we're going to get zeroed in is on on what we call the cognitive skills design thinking agile thinking strategy. These are all skills that machines will not be easily able to replicate right from machine to replicate something it requires huge amounts of standardized data in order to do that. And in the absence of standardized data. These are skills that are going to be around for a long long time. So, yeah. So one of the things that I've been also seeing in the research is that the days of the specialist are coming to an end, and that it's better for people to have more generalized or generalist skills. Is that something that you're finding to be true as well. I think it goes back to that welding example I think, you know that the data that was collected to make some of the assumptions prior to skyhive and quantum labor analysis. The data was at that classical labor level. Right. And so for example we've done a lot of work with governments in the analysis of quantum computing skills, cybersecurity skills, AI skills. The reason why governments come to us is because that data is not available anywhere else because it's so new that the labor market is only showing clusters of skills that have not yet formed into roles for appropriate role architecture. So, from my perspective, there will still be the nuance of strong technical skills, coupled with that general skill set of, you know, willingness to learn lifelong learning, you know, absolutely that will be important, but the functional technical skills are not going away anytime soon. In certain areas they will, but in the majority of the labor market they will not. I know that one of the things that you talked about was the ability to help the underserved communities with some of this labor market data and helping them to elevate into, you know, better jobs. It, and it seems to me that in order for this technology to have a really good grasp of those skill sets, those workers would need to have some type of a digital profile. But we know that in underserved communities that there might be some pockets of people having them and probably a lot that don't.  So how does that work like, is there a best practice to try to integrate that that information, or is there a best place like should they go to LinkedIn or should you know where should they go to start to put together the digital profile. That's a great question so I think overall there there's, there's, there needs to be an understanding first and foremost that the lower skilled populations will not the problem of re skilling will not be solved by self directed learning, or digital for example if we go into low income communities or we go into reserve, you know communities in Canada we have our northern Canadian, you know reserves that don't have access to huge amounts of technology, do not have a strong level of digital literacy. You know having having online courses and data science that's not going to, it's not going to help them.  So that will be very important to the future economy don't don't get me wrong, however, I think a lot of the the approach is being oh let's just flip the switch and assume that, you know, low income or frontline workers are going to be able to reskill based on taking courses online it doesn't it doesn't work that way. We've done some work for example with Indigenous communities where participants had come off reserve. They had left their their home. They had ended up in an urban center. They would left school left work. So I had no formal trail of skills. But what happens in a situation like this which would be, you know, the very most disparate end of digital profile is you go through a process of what we call experiential learning assessment. So for a person on reserve, they have cared for the elderly, they've cooked food, maybe they've done music, art, culture, understand things about natural resources etc. Doing the experiential learning assessment and then feeding that into the standard labor market in terms of how does that skill DNA fit what's going on in the training and workspace in the overall labor market is how we begin to solve the issues of recognizing the skills of people without digital profiles. Oh, that is fascinating. Oh my goodness. I'm, I could have another, like three hours of conversation with you. Unfortunately, we've come to the end of our show. And so we're out of time and we'll have to wrap it up. I want to thank you so much. This has just been so enlightening and the technology is really, really fascinating. So I'm hoping that maybe I can have you back so we can dig into it a little bit more. So I want to thank you so much for being here and I'm Ruby Menon and this is work we imagined on Think Tech Hawaii. Thank you all for being here and please check back for our next show on Wednesday, January 27 at 3pm, Hawaii time. I'll be talking to Sue Ronnie, the CEO of dollar ride, which is a start of the provides employment opportunities for drivers to deliver alternative transportation options in marginalized communities in New York City. So until next time, be safe and take care of one another.


So, say you've been doing some searching in a library database and you've found a few articles that are exactly perfect for the kind of research that you're doing. You might be wondering, how can I find other articles that are along the same lines of research? Well, you can use the articles that you've initially found in the library database search as a jumping off point to find additional information that might be helpful for your research. This video will show you how. Here, we're looking at an example of an article's record landing page in the database Eric. We've run a search in the Eric database using the following keywords, science education and language or vocabulary, and we're looking for it in the elementary school context. We've found an article, The Role of Language and Literacy in K5 Science and Social Study Standards, and after reading the descriptors here and reading the abstract or summary of the article, we've determined that this is a pretty good one for our research. And we're wondering, how can we find more like these? A great research tip is to use the reference list or work cited page from this article as a means to find more information that will help you on your way to research. So let's go ahead and open up the PDF full text of this particular article. To do that, we need to click on the full text finder link, and then when you get to a page that looks like this, usually you want to click on the link that has a little piece of paper next to it. Now we're looking at the full text of this particular article. And a great first step when you found an article that you really like for your research is to go straight to their reference list or work cited page all the way at the end of the article and start scanning it for ideas for other articles or books or other types of information that you can actually use for your research. So let's take a look at one. Say after scanning the reference list, you found this particular article from the Journal of Educational Psychology to be one of interest. This is the citation of the article that we're looking at. And the citation provides all the pieces of information we need for actually locating this article at Jang. The first thing that you need is the title of the journal. In this case, Journal of Educational Psychology. So we're going to go ahead and copy that and then go over to our library homepage where we'll use the third tab over in the search the library section, the journals tab. For the purposes of this search, since we know the name of a specific journal that we're looking for, we're going to use this top search option looking for specific journals, magazine or newspaper, search journal finder. So go ahead and click on the search journal finder link and then paste in the title of that journal that we're looking for. And what we're doing here is we're searching across Gordon's resources to ask ourselves, does Jang's library have access to this particular article? And if it does, the title of the journal will appear with access options listed below it. In this case, we only have one. This database of psych articles contains all issues back to 1910 of this particular journal. So we're going to go ahead and click into psych articles. Now we're looking at the landing page for the journal itself. The next piece of information that we need from our citation is to know exactly what year and what volume and issue number it was actually published in. So in this case, our article was published in 2017 in volume 109. So we're going to go back to our results records and journal finder and click into 2017. And then we have a bunch of issues for 109. So this particular phase, notice that that's all the location information I am given for this particular article. So I'm actually going to use the page numbers here, 301 to 320 to guess which issue I think that this might be in. Since my page numbers are early on in this particular citation, I'm guessing that my article is going to be located in somewhere in one of these beginning issues. So we're going to try issue number three to begin with. But please note, there's also this search within this publication link right here that you could use to do some fast searching within the journal as well. Let's click into issue number three because we're in 300 page range here. I'm just going to do another double check on my citation to get the title of the article that we're looking for, acquiring science and social studies knowledge. And then I'm going to scroll down through this list of 10 issues published within this journal in your 2017. The very first article is the one that we want. And since we are searching in Journal Finder, you'll have links to the full text right below the record information about this particular article. So we could click on the PDF and here is another potential Scarley article for our research. So hopefully that you can see that searching by someone's reference list and trying to find some of these articles can be a really powerful and quick way to help build your own bibliography. If you have any questions, don't forget you can ask Jakes.


This is going to be about one semester course on electromagnetic theory. The essential content of the course will be to take you through electrostatic and the magnetostatic phenomena and leading to both the integral and the differential form of the Maxwell's equations. At the end of this course, you will have an appreciation of what are the important phenomena and problems connected with electromagnetism and later on, we will go over to electromagnetic waves and if time permits some discussions on antenna and radiation. However, this course requires a good knowledge of vector calculus and so we will be spending a bit of time in revising or giving an introduction to essential vector calculus. It will not be rigorous in the way the mathematicians would like it to be, but should be good enough for our purposes. So, the first module which will consist of approximately four to five lectures, we will be talking about the vector calculus and its basic applications. The first lecture will concentrate on scalar field and its gradient. We will start with or rather recalling the concept of ordinary derivatives and define the gradient of a scalar function.  So, let me begin with the concept of a field. Field is basically something associated with a region of space. So, to understand what I mean by that, for instance this room in which we are can be considered to be a region in which let us say a temperature field which happens to be a scalar field exists. So, when you are in a room depending upon where you are in the room, for instance in a room where windows are open, if you are near the window, you might find the temperature there to be higher than the temperature in the remaining parts of the room. Similarly, if you are in the kitchen, you are close to a stove or an oven, you will find those areas are hotter than the remaining parts of the room. So, in other words, even though we normally talk about the temperature of a room, it is meant only in an average sense. In practice, what happens is that every point of the room or the region of space can have a different temperature. So, we talked about temperature which happens to be a scalar quantity. So, essentially our definition of a field is a scalar or a vector quantity which can be defined at every point in a region of space. So, as I said, the room is a seat of temperature field and temperature being a scalar which can be defined at every point in the room. Now, let us talk about a vector field. Just like a scalar, as you know the difference between a scalar and a vector is that a vector not only has a magnitude, but it also has a direction associated with it. So, for instance, if I again talk about this room, we normally say the gravitational field in this room is this much, which means what is the force that a unit mass which is located in this room experiences. This is connected with the fact that the acceleration due to gravity in this room is generally taken to be constant. However, we know in reality the gravity or the force of the earth on a mass at any point on the earth depends upon the location of that mass on the earth. So, therefore, if I am talking about associating a force with every point in space in a particular region of space, I am in what is known as a force field which is a vector field. So, typically supposing I am in two dimension, then vector f which is a function of x and y in two dimension and similarly in three dimension, I would write the vector f as being dependent on the positions x, y and z. For our purposes, other than gravitational field, the electric field and the magnetic field are examples of a vector field. So, as we said a scalar field is a number associated with every point. It is very easy, what we could do is for example, take a graph paper and wherever we want, we can associate a number, we can write down. But, since a vector field has both magnitude and direction, it can be very nicely and graphically sketched. I am giving you an example of a field written as f of x, y. This is a two dimensional vector field which is y i minus 2 x j. Now, let me illustrate how does one represent the two dimensional field on a graph paper for instance. So, let me try to draw a graph. I will take some arbitrary units. This is the origin, this is 1, this is 2, this is 3 etcetera and similarly on this side, I have minus 1, minus 2, minus 3. Repeat that on the y axis. Now, let us look at some specific points. Now, notice that at the origin, my value of x is 0 and y is 0. So, as a result the field is 0 there. So, since 0 does not have a vector direction associated with it. So, we just put a point there. Now, let us look at what happens for example, at the point 0 1. So, notice 0 1 is this point. Now, if it is 0 1, since x is 0, y is 1, the value of the vector field at this point is simply y. Now, which means it is in the x direction, in the x direction having a magnitude of 1. Now, what I do is, I take an arbitrary scale. So, let us suppose I decide that this is my 1 unit vector from here to here. Since it is an i direction, I just write it here and I can scale it like that. Now, let us come for example, to the point 1 0. Since y, x is 1, y is 0, you notice this is minus 2, but in the j direction. Minus means in the negative y direction and since its length is twice as much, I will have represented by a vector twice the length of this. Similarly, let us take the point 1 2, which is the point here. So, let us look at what is 1 2. Since y is equal to 2, this is 2 i and x is equal to 1, it is minus 2 j. So, what is 2 i minus 2 j? It is a vector, which I must first take 2 units along the x direction and another 2 units along the y direction and take complete the perpendicular and find the resultant. So, therefore, the field at this point is represented by a vector along this. So, what I have done is this, that you could go on. You could take various representative points on a graph paper and sort of try to draw your own grid. Some of the values on a graph paper are given here, but you could do it yourself. Now, so if you take a large number of points and draw this, according to this you will find the vector field has a pictorial representation of this type. It is pictorially represented like this. Of course, if you are doing it yourself manually, there are just so many vectors you can draw, but if you want to get an idea of what it looks like, you could take some computer package like for example, Mathematica. So, this is what the field would look like if you are going to draw it over a very large number of points. I am not going to be able to draw it in three dimension, but on the other hand it is possible to get a computer simulation of vector fields in three dimensions as well. Well, since we will be primarily concerned with electric and magnetic field, let me illustrate the vector field concept with something that you already have learned in your schools. Here what we have done, I have a positive charge which is represented with this and a negative charge which is represented in this red color. Now, supposing I have to draw the vector fields, these are incidentally called sources. As you know that if you put a, if you have a positive charge and you put another small positive charge near it, that charge is repelled. In other words, the direction of the force supposing you put it here, the direction of the force on that charge will be from this charge to that charge and it will be repelled and if the charge happens to be attractive, positive negative then it will be attracted. So, this is what the vector fields would look like for a region which has a positive charge and a negative charge. Now, these lines are so close, the lines along a particular direction are so close that we normally connect them by a continuous curve and these are generally known as lines of force. So, in other words that if you have drawn the lines of force, if you want to know what is the direction of the vector field at this point. So, you have to take draw a tangent to the field at that point and that will give you the direction of the vector field. Well, the next picture simply shows what happens if both the charges are similar. So, in this case both the charges are positive. So, therefore, you know that it is repelled from both the charges. We will of course, come back to discussion of lines of forces later when we take, we look at the electrostatic field. .. So, let me now begin the discussion of calculus that we talked about, but before I do that let me remind you of the definition of an ordinary derivative of a function. Let us look at how you define ordinary derivative in your school. The if you recall that if a f is the function of a single variable x, then we define d f by d x at the point x as limit of the following quantity. I take the value of f, the function f at the point x plus h, where h is a small quantity. Subtract from it the value of the function at x and divide it by the increment h and when you take the limit of h going to 0, this is my definition of a derivative. Now, what I have done here is to actually rewrite. So, the if this is the definition, this means that the value of f at x plus h is simply equal to its value at x plus h times the value of the derivative of the function at the point x. Here I talked about h, because that is the way we normally talk about in school and here I have used instead of h at delta x. So, it tells me that the value of the function at x plus delta x is equal to d f by d x times delta x. Now, the question is this, suppose I want this happens in one dimension, what happens if I want to extend it to 2 or 3 dimension. Now, we have a problem, when we want to. So, let me first tell you how does it interpret. Supposing this is a graph of function with x, so I can draw an arbitrary graph. You notice that if I am at a given point and I draw a tangent to it, that is the definition of the slope at that point, geometrical interpretation. In other words at this point, the slope is positive, which means the value of the function is increasing. On the other hand, if you are here for instance, then you notice that the slope is negative. So, slope essentially gives us an idea about the rate of increase or decrease of the function. Now, if I want to now extend this concept to higher dimension. So, let me try to extend it to 2 dimension first. So, now I cannot obviously draw the function in 2 dimension. The reason is I need x and y and if at all I am going to draw the function, it has to be along the z axis, which I do not have, but let us not worry about it right now. So, supposing I am at this point, some value of x y and I want to find out some value of f at this point x y and let me say I want to find out the value of the same function. So, this is my point x y and this is the point x, let us say plus well if you like h 1 and y plus h 2. Now, the point is the following that if I want to go from this point to that point. This of course, since I have 2 points the direction is clear, but you notice that if I tell you that what happens to the value of the function, what happens to the value of the function as I go away from this point x y by an amount delta s for instance. In 1 dimension delta s could be in either of the 2 directions just positive or negative, but here once I am told that I am I have to move by an amount delta s, I can move in any direction. In other words, it would depend upon the direction in which I move and we introduce what is known as the directional derivative. . So, what happens is this that I am then asking that suppose you move by an amount delta s, move by an amount delta s along a specific direction along a specific direction which we will represent by delta x delta y delta z, this is my directional derivative. So, look at what does the directional derivative imply, see I have d 5 by d s. Now, when going along this direction I could actually go off. So, suppose I am going from this point to let us say this point. So, this is point number 1 to point number 2, well I need to go like this. This I can calculate in many ways, what I could do is to say that well I will go like this and then like this along this y is constant along that x is constant. So, what we do is to say that look d 5 by d s d 5 by d s I take a special type of derivative which is not written as d 5 by d s, but it is written as del phi by del s del x, this is some people call it partial phi with respect to x. So, this is partial phi with respect to x meaning move along the x direction keeping y and z constant. So, d 5 by d s is partial with respect to x and of course, then I need to multiply with d x by d s partial with respect to y d y by d s partial with respect to z t z by d s. Now, so that is my definition of a directional derivative. Now, what I am going to do is I am going to illustrate the calculation of directional derivative by taking a specific function phi this is I will take it in two dimension for convenience you could repeat it in three dimension. So, phi x y equal to x s square plus y square and I will calculate the directional derivative at the point 1 2, but along three different directions, but let me first illustrate the first one that I want to calculate directional derivative along i plus 2 j. Let us do that let us look at what does this function look like. So, this is a picture which is which comes from certain computer plot. So, here I have x y plane these are the coordinates and the function is plotted along the z axis. Now, if you plot phi x y which is equal to x square plus y square in such a three dimensional plot what you find is a cup like structure a cup like structure. So, this is what it is and so what we are trying to say is this suppose I have I know the value of the function at let us say this point this is x y plane and this I know is this much.  So, I have to climb up put a perpendicular here and know what is the value. So, let us come back to the formula that we wrote down we said d phi by d s I will cut out the third direction is partial phi with respect to x d x by d s plus partial phi with respect to y d y by d s I do not have a z component. So, I told you that partial derivative means treat the other variable as constant. So, y is constant.   So, if I am calculating d x by d s I will actually calculate d s by d x and take the inverted. So, d s by d x is square root 1 plus d y by d x whole square and this is this quantity is what we are interested in. Now, notice that I have a particular direction I plus 2 j. Now, along that direction if you look at I plus 2 j direction the relationship between y and x is y is equal to 2 x. Now, if y is equal to 2 x then d y by d x is just equal to 2. So, this is simply 1 plus 4 which is equal to square root of 5. In an identical way I can compute what is d s by d y and of course, I need d x by d s which is then 1 over square root of 5 and this of course, is 2 by square root of 5. So, plug these things in there and compute what is d 5 by d s which will work out to 2 root 5. The second part of the problem I will not do, but I would expect you to do it as an exercise, but I want you to look at the third problem a little carefully. Here what we have asked we ask that we want it along the direction I plus alpha j where alpha is a constant. Now, along this line y is equal to alpha x. Now, you can essentially repeat the same calculation that I did for the first part of the problem and you can show that the directional derivative of the function phi d phi by d s is along this direction is given by 1 plus 2 alpha divided by root of 1 plus alpha square. Now, if you examine this function you will find that the directional derivative takes a maximum value when alpha happens to be equal to 2. You of course, know how to do it you know that I want maximum of this. So, I differentiate this one put it equal to 0 evaluate what is alpha. Now, if you take alpha equal to 2 I am saying that the directional derivative is maximum in the direction I plus 2 j, but notice I was calculating this directional derivative was calculated at the point 1 2. Now, if you look at if you look at the graph the. So, the point 1 2 is this point at the direction I plus 2 j the direction I plus 2 j at this point is a radial direction. So, therefore, the directional derivative for this function takes the maximum value along the radial direction. Now, let me now define what is meant by gradient of a function. Now, this gradient is written using a symbol which is called a grad it is an inverted triangle like thing. You also write is we call it del phi we also write it sometimes in word as grad phi. So, we define grad phi we will come back to what it means a little later as unit vector I partial of phi with respect to x plus unit vector j partial with respect to y plus unit vector k partial with respect to z. So, let us suppose I have a unit vector u which has components a i plus b j plus c k. Remember I have said u is a unit vector in other word a square plus b square plus c square square root must be equal to 1. So, let us just represented by a vector like this. Now, we are at this point this is the direction of the unit vector as shown here this tells me that if I am at the point x 0 y 0 and I want to go to a point let us say x y then my x is equal to x 0 plus a s s is the total length by which I am moving in this direction y equal to y 0 plus b s z equal to z 0 plus c s trivial to see it in two dimension. Because supposing this is s supposing this is this is s then this is the direction of the unit vector this is the direction of i this is the direction of j. So, clearly this is nothing but the cos theta which is the angle between the unit vector and the x direction and. So, therefore, this follows now with this d phi by d s which if you recall we had written partial with respect to x d x by d s etcetera this is the gradient phi this is the gradient phi definition this is the gradient phi definition and u is a unit vector like this. So, this is nothing but so what is this quantity since we have seen what is x is x 0 plus a s y is y 0 plus b s etcetera etcetera this tells me that this d d x by d s which is what I need here x 0 is a constant is nothing but a. Similarly, d y by d s is b z by d s is c. So, therefore, I write this as d phi by d x a plus d phi by d y b plus d phi by d z c, but a b c are components of a unit vector along the three direction d phi by d x d phi by d y and d phi by d z are component of the vector grad phi. So, this is nothing but the scalar or the dot product of grad phi with the unit vector u. Now, once we have derived this let us look at what does gradient mean u is a unit vector as a result grad phi dotted with u is magnitude of grad phi magnitude of u is 1 times cosine of the angle between the gradient direction and the unit vector direction unit vector is the direction in which you want to move. So, since the maximum value of cos theta is 1 it tells me that and the cos theta becomes 1 when theta is 0 which means the direction in which you are moving is along the gradient direction. So, therefore, the magnitude of gradient is maximum magnitude of the directional derivative and the direction of the gradient is the direction in which the directional derivative is maximum.  Now, there are many ways of coming down the slope, but let us suppose you want to move by a given distance if you want to move by a given distance the fastest you will go is if you move along the direction of the steepest slope the steepest slope and that is the direction of the gradient that is the direction of the gradient. So, let us return back to that function phi x y well we do not really have a z there. So, equal to x square plus y square notice that the gradient we just approved is in the direction in which the slope or the amount of change the rate of change is maximum. Therefore, it follows that that if I have a surface phi x y z the gradient must be perpendicular to the a surface along which the value of the function does not change. So, let us the same picture let us look at it slightly differently. Now, this is the picture that we drew of the function x square plus y square the axis etcetera are removed there. Now, if I have to look at the intersection of this surface with a plane. So, this is a plane now obviously, a plane on which the value of the function will remain constant will cut this surface in a circle. So, that is my level surface in physics we are familiar more with what is known as an equipotential surface that is a surface on which the potential is constant. So, what we have proved is this the magnitude of the gradient is directed along the normal to the level surface or in our case the equipotential surface. So, this is the surface on which phi is constant now we know that for the curve that we have been talking about the for for the curve that we are talking about phi x y x square plus y square x square plus y square equal to constant will give me the level surface, but what is x square plus y square equal to constant this is nothing but family of circles. And these are the circles in which they flat plane cuts that picture that I showed you sometime back. Now, so gradient of phi of this function remember i times d phi by d x partial phi by partial x is 2 x plus j times 2 y which is nothing but 2 times the radial vector radius vector radial vector. So, this is nothing but along the radial direction and which is normal to the level curve. So, this is what is shown here that I have chosen 3 circles as representative circles and you notice as the radius of the circle increases the gradient increases and as a result what I have done here in this picture is to show these as the radial vectors, but when the circle is smaller my vector magnitudes are smaller their radial as the circle becomes bigger and bigger the arrow lengths become bigger and bigger. So, in other words gradient itself is a vector field. So, please understand this gradient of a scalar function is a vector gradient of a scalar function is a vector it is a vector because its direction its direction is normal to the level surface. So, this is a quantity which is both magnitude and direction and as a result it is a vector field. I want to prove this formally. So, we have talked about a level curve well in the example that I gave you the level curve was a circle, but supposing I am looking at a level curve for which phi is equal to c which is a constant and let us say that this curve is parameterized by a variable t. So, therefore, on the curve I write down r of t equal to x t i plus y t j plus z t k and my function phi which is a function of x y and z can then be written as phi x t y t z t equal to the constant c. Now, let us write down the tangent vector to the curve let us write down the tangent which is written as let us say r prime of t. So, this is because it is parameterized by t the tangent is nothing, but the derivative of this quantity with respect to t. So, this is d x by d t i plus d y by d t j plus d z by d t k. Now, I want when is d phi by d t 0 because I am looking at a level surface the value of the function is constant. So, d phi by d t 0, but d phi by d t is according to our earlier discussion partial with respect to x d x by d t plus partial with respect to y d y by d t plus partial with respect to z d z by d t which is if you look at what is r prime and the definition of the gradient is nothing, but is nothing, but the dot product of grad phi with the r prime vector and this must be equal to 0 this must be equal to 0. So, this tells me that the gradient of phi the gradient of phi is normal to the tangent vector is in other words it is normal to that curve. One could try to do some of these things from first principle. Now, for example, I am going to illustrate a partial do a problem that let me take a very simple function 3 x square y and I want to find out the directional derivative of this at a point c which is minus 2 1 along the direction 3 i plus 4 j. Now, notice this is my this is not a unit vector this is what I represented earlier as d s the direction s. In order to make it a unit vector and call it u according to our previous notation I must divide it by the magnitude of this vector namely square root of 3 square plus 4 square. So, which will be 3 i plus 4 j divided by 5. Now, what is the directional derivative of f at this point c this is this is a notation which mathematicians use directional derivative along the direction u of the function at the point c. Now, from first principle this is limit h going to 0 value of the function at c plus h u minus the value of the function at c divided by h. Now, this is a vector. So, I could rewrite this as limit h going to 0 of f at minus 2 plus x direction is 3 by 5. So, it is h times 3 by 5 comma 1 plus h times 4 by 5 minus f of c which is f of minus 2 1 and divided by h and you can now of course, plug in these and you all this is a very simple derivative to calculate. So, let us look at what have we done today. We started with a review of elementary derivatives as we have learnt in school and extended it to 2 and 3 dimensions. In doing so, we also introduced the concept of a field we found that we can have either a field could be a scalar or a vector. A scalar field for instance a temperature field is one where the region of space at every point in a region of space and every point you have a scalar quantity associated with it. In case of a vector field we in a region of space at every point we associate a vector. Now, having defined the scalar and the vector functions, we concentrated primarily on scalar field today and defined what is meant by a gradient and we found that gradient of a scalar is a vector which is directed along the normal to the level curve or level surface and it is the direction along which the change in the value of the function is maximum. In the next lecture, we will be talking about quantities associated with a vector field and go ahead from there. Thank you.


What's up developers and problem solvers why checking anyone to bring you guys another video today and today? We're gonna talk about why you should never become a word press developer. And yes, I mean Never let me explain first of all guys in the early Early on when web development was pretty young and there wasn't any of these Web page designers and all this gooey stuff that allowed people to actually go in and actually drag and drop Actually elements on a page where you can visually see it. That's relatively new guys That used to be done painstakingly manual by manual CSS Tables images and just meticulous just dropping stuff on there either be cold It was not a easy experience It was actually a painful experience and Anybody who had the balls to do it or the patients got paid a lot of money This is where web developers came in and made a killing early on and they was paid just like Standard back-end developer today because it was so technical and time-consuming to get a website to look professional That most people didn't want to deal with it. So They just paid them to do it and life was good well as technology start to advance and people start to want to use the web more and more and These software companies got wind of this and start to create software these drag and drops the wicks the word press to Shopify the standard page builders so that the average person didn't need to hire a dedicated developer just for the visual of a website and That's where you start to bring in platforms like wordpress and all these other sites that allows you to do content management blogging all this now this start to hit the same so Early on people Wordpress was a foreign concept people didn't understand it. I'm gonna be honest I wasn't real big on it myself because I was just one of those pure developers who's on a Container right there code and create their website with a code because I'm a coder That's what I do I'm not gonna use a platform to do that when I know how to build it myself At least that's my set I had at the beginning but obviously that change all my website or wordpress websites And I stand by that product but back to the original story Everybody wanted to get wordpress site and these developers came along first of all to help set up the site They help add plug-ins if there wasn't any plug-ins They can make a killing on adding plug-ins and functionality that they didn't currently have With social media platforms and all that stuff and they made a killing throughout the two thousands with the wordpress Platform when it came in new and it really start to take shape or take over the website I think it's like 25 percent of all websites or wordpress website So there's billions of at least millions of websites that are out there and 25 percent of them in wordpress That's a lot of websites so it was a lot of money to be made guys but as I said before technology keep advancing to the point where the lower-end task are being automated or Drag-and-drop or even push of a button somebody could actually up I was up low in the wordpress site the other day for a client and Go daddy and I think blue hosts can do that too. It's a click of a button.  This is easy and I was thinking about it's like if I was a web developer and this is what I did to make money I would be afraid especially for the wordpress developers and They always had the argument that hey, I can still build custom templates or a plug-in stuff, which is good but Even that now, you know, it used to be a pain in the butt to actually Implement a plug-in now they can just go shop it like that store a fine one and say yes And all apps are being commoditized So you really can't make a killing off of that unless you have a really specific niche Which again the higher-end web developers are making bank the high-end web developers or wordpress developers are making bank I'm talking about the low-end average ones who don't have the skill set of the higher-end rock star Wordpress developers those are the ones who's who who's making the bank but the other ones on the bottom no because of these tools that I'm explaining to you guys but Yes, I was going through and then anything you want as far as just a plug-in or template is already pre-built for you So it's not a lot of code. You have to write it's actually Almost allow building now to have a one-off Where prep wordpress developer create a plug-in and put it on your site and then life is good Well, what happens, you know three years from now when you upgrade to a new version of wordpress and it breaks That developer long gone or was an intern or something That's why I always recommend people to go with a reputable software development company or platform or plug-in That's gonna be around for a while.  Okay, right. What should I do if I don't become a wordpress developer? The key thing is Don't market yourself. It's just a wordpress developer only word market yourself as a Problem-solver that just happen to use wordpress as a platform that you fix and That's what's gonna really put you in a position To make the most money to always have a job a lot of the higher-end web developers are WordPress developers are just basically full stack developers. They do all this technical stuff They limit themselves for the low pay of just being a low-end WordPress developer when they have all these skills to go into any company and be a top tier full stack developer That's how you should market yourself guys You shouldn't market yourself as something that make less money Market yourself of somebody who have higher skills who's more rare that can solve more problem and this is how you do it So let's take a step back guys. So now, you know, okay, we're not gonna be a wordpress developer We're gonna really start to focus on the problem Specifically and we're just not gonna do just the basic drag and drop stuff We're gonna focus on problem solving What problems should I solve first ride? Tell me how to do it. Well guys again wordpress is a content management system it use most people use it for websites now that's why I use it for and People want to get data from their websites. They want to see who come who actually came to the website Statistics integration with social media. They want to know Google analytics on the PPC campaigns all this stuff You can integrate into that WordPress site that people don't talk about marketing automation That's a huge niche that you guys need to get in if your wordpress developers or full stack developer Or a front-end developer that you can make a ton of money in Marketing automation your CRM automation Just to name a few projects that's gonna really put you in a position to win guys So again a lot of that basic wordpress development Stuff has dried up The bar has been raised guys You guys have to put yourself in a position to be more valuable to command that six-figure salary So that you can live the lifestyle you want to live Being a basic wordpress developer. You can still do that.   That's how I do I don't do anything else, which is not the right mindset AI machine learning All that stuff is gonna replace your job real soon. Most of you guys can't get a job So that should let you know Automatically like the bar is being raised, you know I is the unemployment rate right now is like 3% you got people out here want software development jobs It's got tons of jobs and people don't want to get hired. They won't hire them. Why is that your skills is not on par? Get your skills up Get ready to win now guys now now now so Let's take action 7 step guide below Sign up for it really put you in a position so that you can take your wordpress development skills To the next level and get you that job also give you access to our community also so that you can deal You can work with like-minded software developers work with myself really put you in a position to win So like subscribe to the content if you have additional questions comment below I'll see you guys in the next video. Well, hold on. Hold on before you leave I Little red button down there subscribe click that thing for me click it now click it now click it Click it. You didn't click it yet. Click it. Okay. You clicked it.  Let's click that bail guys Click it click it.  Let's start a conversation if you agree Great if you disagree, tell me why description box. I'll see you guys in the next video. Peace


Let's talk about time. We experience it as a steady stream, always moving forward at roughly the same pace, quantum physics aside. We count down the days, anticipate an event or anniversaries, staring at the clock as if to will it to move forward faster and faster. But the second hand defies our extrasensory projection and ticks away now, and now, and now, and now. This is the human experience, aware of the pace of our existence and unable to do anything about it.


If you have strange men or women pursuing you on Instagram or Facebook, they look beautiful or handsome and they want to add you as a friend or they're following you on Instagram or they message you or something like that. And just know that and if you can't see from their profile that they're actually active and engaging with their followers and like putting real content out and then adding comments and things. It's it's almost certainly a bot. BOT bot.    And, and then they're usually, you know, posing, posing at you know, here's my fancy lifestyle, but but I know that they're not a real influencer because I've seen this stuff so much that I can tell instantly I have a very good intuition about it. And then, and it's like, and they do post pictures of their, of their them at lunch beautiful pictures of them at lunch or at the pool or something like that. But I'm like, yeah, even though you look like you're engaging with your people I know it's not, it's not a real profile, and not a real person. And anyway, so just, just know that, you know, when it comes to Instagram and Facebook you have to add friends or follow people very, very, in a stingy way, I guess, to be very, very choosy about whom you follow and it's really has to be, which I talked about in the separate segment, certain types of people like your attention referral sources people actually, you can see from their content that they're, they're really engaging with their people. So anyway, hope, hope that helps. And I want to appreciate somebody who just added a comment here, I'm live with with some people. And she mentioned that for women, it can feel creepy and gross and maybe a little bit violating when you receive those kinds of requests or followers. And I just, I, I, of course I can't relate because I'm a man, and it's different. But if it's, if it helps, I'll say that you can picture the person on the other end, and almost certainly being a teenage or young man from some probably third world country, who is trying to trying very hard to make a living. And that's the only way they know how.  And literally, they get trained in this stuff, they have a whole script and literally it's because I saw a thread. I saw a thread somewhere where someone lightheartedly wrote back and started following that thread down to see what they what they would try to get them to do. And they got the person to say, I'm sorry, I'm just trying to get something to eat. It's very hard in my country. And this is the only thing I know how to do. I was trained to do this. And hopefully this will make me some money so I can feed my family that kind of thing. It's that kind of situation, oftentimes like more and more often than we realize, it's not the military handsome man who's, you know, or or some creepy whatever. It's it's this sad young person in a third world country that was taught to do this, and they that's all they know and of course, I when I saw that thread of that conversation this person had that person, you know this person was like, you clearly can can write English. Okay, and you can do more than this, you know, but that's all they know. So I hope this helps and, you know, you can you can you can simply block them. I mean the practical way is just to block them knowing that oh it's it's it's not necessarily a young boy it could be a young girl to you know or or somebody who is desperately trying to to make a living by by using these scams. If you had followed the thread all the way through if you if you actually message them back or whatever, they'll try to get you to sign up to get more followers on Instagram or to invest in some opportunity or to like, you know, they'll trick you into signing up on a website that looks like Facebook or Instagram and putting your information in there because suddenly you thought you were logged out. No, why am I logged out, you know, and then you put your information in there and now they've got your username and password now they can hack and send the same messages to your friends that kind of thing. This is, there's a whole script for all this stuff. And anyway, I hope this provides some perspective that helps to to feel a little bit. Yeah, calmer about it and you just blocked it.