Welcome everyone to this session brought to you by learn.wordpress.org. This is the intro to WordPress accessible color presented by Joey Simpson, Jr. And I am your host, Courtney PK. I am a contributor to the WordPress training team. We bring you the educational resources at learn.wordpress.org. And we do, we try to do sessions like these daily on a variety of subjects. So if you're just joining us, a learn.wordpress.org workshop for the first time, welcome. All right, so our agenda today. We'll have some introductions and a welcome, which we're in the process of doing right now. And then Joe will present his presentation intro to WordPress accessible color. We'll have some time for questions and discussion at the end and of course wrap it up at the end of the conclusion. Note that I will be monitoring the chat for questions and we'll be saving questions till the end. So if you have any questions for Joe, as he's presenting, just make sure you throw them in the chat and I'll make sure to get back to those at the end. So again about online workshops, like the one you're sitting in right now, this is a space where we learn together so you can ask questions in the chat at any time. If you happen to know the answer to someone else's question or have anything to add to the conversation, please feel free to contribute live in the chat. This and other online workshops are recorded and uploaded to WordPress.tv. So this session will be posted on WordPress.tv within about 24 hours of this workshop. So here's that link if you'd like to keep that handy. And lastly, online workshops like these are hosted by a variety of folks that enjoy WordPress and giving back to the community. So if you have a WordPress related topic that you're excited about, you too can host an online workshop like this. And I'm happy to help you make those ideas happen. The training team is here to help you with that journey. It's about us. As I said, my name is Courtney Piquet. I'm a contributor to the Make WordPress training team. I've also contributed to the community team and TV team. Community team is where I met Joe. Joe has been a contributor to the community team, the accessibility team. And you can tell us a lot more about it in a moment. But yeah, Joe is the organizer of the Santa Clarita Valley Meetup Group. He's an accessibility advocate. He's a designer and developer. He's a Joe of all trades. I am very, very happy to have him here today. And I will hand it over to you, Joe. I will stop sharing my screen. Sounds good. All right. Good afternoon, everyone. My name's Joe. As mentioned, we're going to talk about color today. We're all visual creatures. We often see the world through the prism of color. Color is closely tied to our identities. It's how we express our personalities. It's how we want to be perceived. It's who we are. Welcome to Intro to WordPress Accessible Color. Today we're going to talk about the basics of color, accessibility, and WordPress. So let's get after it. There's an old saying, we eat with our eyes first. I've seen so many times where I'll sit something in front of my daughter and if it doesn't look right, she won't eat it. Color also has the same effect as music. It has an emotional connection that we often make. Music touches us in a certain way. It sort of identifies us with a point in time in our lives. But can you imagine a world without color? This picture here, would you imagine that this person really looks like this? Color is a form of expression. It's how we want to be seen. Again, welcome to Intro to Color. One of the things I generally start many of my presentations with is this photo. Way back, maybe five, six, seven years ago, I could just imagine this scenario. At the NFL offices in New York, a hot young intern came in with full of ideas that was going to change the NFL for the better. It was going to cause more sales in jerseys. They said, hey, we're going to do the color rush. NFL color rush jerseys. How many folks remember that are sport fans? These uniforms that were all one color in the beginning, it was no stripes or anything. It was just splashes of color. And in this particular game, this was the first game between the Jets and the Bills. A green team and a red team played. And it was very controversial because someone that had color blindness saw this. The reds and greens for people with color blindness were seen as gray. So on the screen, when they were watching TV, the grass was green. The strip around the padding around the stadium was green. It was gray. Everything was gray. And it was such a disaster from a PR standpoint that they made changes eventually. A lot of times designers don't take into consideration their entire audience. And that's what I generally talk about when I talk about accessibility. It's like, how many of us set out a product and don't want as many people as possible to buy it? Do you want less money? Do you want less eyeballs on your webpage? Do you want less impact? Of course not. So why would you do things like the NFL and limit your audience potential? So I have a confession to make. These books on the wall are from a distant part of my past. I was a graphic designer for the first 14 years of my career out of college. And I learned about things like color theory, how color makes an impact. And as a graphic designer, I would think of the witch and how Darren would pitch a concept and he would make an emotional connection with his client. And they would say, oh, this yellow looks great. And they would buy it. And a lot of times as a graphic designer, that's what we do. But we don't think about how color affects our audience. And especially in the web space, color is a critical part of getting your message across. Because again, we often see things first. My path was as follows. I started as an intern in high school at Henry Ford Medical Center. It was the largest hospital brand in Michigan. When I was in college, I worked at UNISIS, which was, at that time, it was going through a merger between Burrow and Sperry. They became the largest computer company where I was in their brand identity group. And my first job out of college, I worked up the street. I lived in Highland Park, Michigan, which was a home of Model T. I worked at the Chrysler Corporation, which was also going through a merger at the time at the Pina Group, which was their brand. So I've always been associated with big brands. And I currently work at Metro here in Los Angeles, which is the third largest transportation agency in the country in their brand group. And I've gotten the foundation of thinking about things holistically and as a strategy and as a process in terms of communicating to the public. Back in college, as I mentioned, I learned about the psychology of color. Back then, we learned that hospital walls are a certain color to keep people calm. Our elementary schools are the same way. Fast forward, think of Tiger Woods on Sunday, he would wear all red and tribute to his mom was of Thai descent. And I guess red is a power color in that culture. So color means different things in different countries and different cultures. It communicates in different ways. And again, as a designer, I mentioned how we try to make that connection with our client emotionally by what we want to sell to them or the ideas that we want to pitch or how we want to communicate their concepts. So today, we're going to talk about Intro to Accessible Color. We're going to first talk about color contrast, which is what's really going to impact you in terms of how you're going to build your WordPress sites. We're going to look at some tools on how to help you make better color decisions by looking at WordPress accessibility ready color themes, accessibility ready themes. We're also going to talk about how to make color choices inside the WordPress admin when you're working with 2023, as well as look at some browser based tools and some web pages that can also help in this endeavor as well. And then I'm also going to talk about, before we get started, the story I love to share also is when I was on the design side, I had someone in our marketing department at Metro and she was very insistent on always using PMS 314, which was Magenta in everything, whether it's maps, brochures, et cetera. It didn't matter what the client was, even if we had a gold line event, she would want to put Magenta in it. So what I'm trying to communicate to you today is that we all have these blind spots when we're working on things. We have a friend that works out in the gym and he likes to work on his upper body and his legs are skinny. So what I want you to do when we're thinking about accessibility and color, don't get set in your ways. Be open to new ideas and also really try to design with your clients in mind. A lot of times we design what we like, what makes us happy, and we don't really think about the client. All right, so I'm going to give you a few definition slides before we jump off into some demos and more discussion, but this is the definition of contrast. Contrast and color are vital to accessibility. Users, including users with visual disabilities, must be able to perceive content on the page. And WCAG 2, contrast is a measure of the difference between the perceived luminance or brightness between two colors. And the phrase color contrast is never used in WCAG, just an FYI. And here's more WCAG 2.0AA, it requires a certain type size. It also talks about the color crunch contrast ratio and level three is a little more stringent and it's a little higher. So these are what you can design to and these are sort of basic guidelines in terms of the color of your fonts and how they work in terms of color contrast. Large text in this, what I'm going to show you in terms of demonstration is considered 14-point or larger, bold or larger, 18 to 24 pixels. All right, let's jump out and do some demo again. Put your questions in the chat, we'll get to them at the end. And again, I'm focusing on a small sliver of accessibility. We're going to talk about color contrast because again, what I always try to do when I do presentations is try to, you know, a lot of times when you think of accessibility, people think it's overwhelming, it's daunting. But if you look at, if you take care of little things, it can really improve the quality of the work that you do. There was a report on the web aim. They do it each year, it's called the million websites report. They look at a million websites and I think over 90% fail. So many, it's like six or seven basic things, including color, alt text, et cetera. And if you take care of those small things, it'll make your site more accessible. And that's all I want you to get from today, is make these little changes to your process. It'll improve your skill set. It'll also add to your arsenal so that you can charge more. And, you know, adding to your services as a company, it creates a niche also. How many developers do you know that develop with accessibility first? How many designers? So again, it's a ready-made niche. It's something that always needs improvement. Like I said, just take a look at the million pages report that comes out each year. And again, there's little things that you can do to get to put yourself on the path to success. All right. So I'm going to jump off to web pages. All right. So what we have here is I spun up a site locally here for demo today. We're in the dashboard. Let's go ahead and take a look at a page. Oh, let me show you one other thing too. On the .org site, this is the definition of accessibility ready. We're going to jump in and take a look in a second. I'm going to share these links also. This is the definition of accessibility ready. The great thing about using WordPress themes that are approved in the repository, and I always, if you've been to a presentation line, I always say start with the repository because themes that have the accessibility ready tag have gone through an audit process. They have to meet certain conditions to even be listed in that way. So if you find a theme outside of the repository that claims to be accessible and they're not in here, they haven't met these guidelines. So I would be a little wary of that. All right. So let's get back into the dashboard. This is the sample post. All right. So let's take a pattern. We're going to drop this pattern onto the page and let me know if everyone can still see the screen. Let me know if you can. All right. So I've dropped in this pattern. Let's take a look at the settings here. You're going to look at the background. All right. So in terms of color contrast, WordPress has something that's neat, that's in the back end, that you may not have even noticed. Like say for instance, we're going to let's make the background black. What you see, you can't see the text, but over here on the right, if you notice, this pop up occurred. It says the color combination may be hard for people to read. Try using a brighter background color or a darker text color. So built into automatic accessibility-ready themes is this feature. So as you're trying to decide on what to use in this part of your block, if you dynamically update it. So for example, when we went to this line green, now that warning disappeared. So you have a dynamic tool within the admin that allows you to check color. So that's one thing that I'm sharing. And if you already know, kudos if not, this is a great tool that you can use. So when you're creating your text, the color of your text, the color of your links, these things are important. And it's an easy step. It's something you see right away and you can change right away. Another thing that I always recommend is, when you're developing things for a client, do these tests early. Don't wait till the end until you design it. It's harder to work backwards rather than doing it along the way. So inside the admin, you can do this. Again, it's a dynamic way for you to check color contrast. If you don't get anything on the right, that means the light blue and the black is good to go. All right. So inside appearance, if you want to find a theme, so how do you find an accessibility-ready theme? All right. So when you come into the admin in the back end and you see the themes, you can see that 2023 is installed and that's what we're demoing right now. Let's go over here to feature filter. And what I recommend also is, under features, you can select accessibility-ready. It shows you the one filter that you selected and let's go ahead and hit apply filter. What this does, it shows you all the themes in the repository that it says 87 up here in the upper left-hand corner here. 87 themes are considered accessibility-ready. All right. So you can go through here, take a look and again, you can see there's a number of different visual approaches that you could take and these themes give you at least a foundation or a basis to build on. So again, start with an accessibility-ready theme. I love the automatic themes just as a starting point, especially if you're using full site editing or the block concept, and then you could build out your site from there. All right. I talked a little bit about accessibility-ready. There's a definition here that I'll share with you. Now there's another way that I recommend you get into checking color in your projects. All right. It's through the browser. One of the great things about Chrome and Firefox and such browsers is that you can find extensions that do some of this work for you. So a couple that I recommend, in terms of color contrast, you can just come in and search for color contrast and it gives you a list of color contrast browser tools that when you install it, it'll put it in your browser and let's just do a little quick demo here. All right. This is my local city, the city, local city government, city of Santa Carita. We look at their website and I see a few things right away, just from my keen eye, but let's go ahead and run one of these browser tools. I installed the WCAG contrast checker and once you click on it, you can see right away, it says you have about half of the features that it checked that we failed. And as you click on it, you can see on the right hand here, it highlights the area that failed and it tells you why. So it looks like there's some issues here. We can see here in the menu, the light blue background with white text is another no-no. And so this is a great way to quickly see what the issue is on your site. Another tool that I appreciate also, and this one is one that I go to a lot. I'm currently on, we're looking at the National Cherry Blossom Festival website and the reason that I did it, I'm on the lead team for WordCamp US and it's going to be in National Harbor, Maryland, which is right across from DC and in that area blossoms happen. When I grew up in Michigan, they were the cherry tree in my backyard, so I have an affinity for it, but this is a beautiful site. There's pinks and whites, it's very festive, but let's take a look at it from color contrast, a color contrast perspective. All right, I'm using this time, I'm using the accessibility insights for the web. Let's go here and just do a fast pass. The cool thing about this tool is that it has a couple of different options for you to check your site. But a fast pass gives it a quick pass through and it tells you right away. This is our site here, the National Cherry Blossom Festival. It says there's 31 instances that failed right off of that that it caught. So let's go ahead and expand that. The cool thing about this tool is that you can export this report, you can present it to your client, you can say, hey, this is what failed on your site that we need to work on immediately to make sure that it's accessible for more people, because again, a lot of folks are facing lawsuits because their sites aren't accessible. So especially for one of your clients, it's important that they consider this too, because as a designer, you're liable as well. I'm not going to get into the legal thing, I'm just trying to show you some basics here. So I've opened, I've toggled this down and the cool thing about this is it goes through each item and it tells you why it failed. It also gives you a how to fix. So the cool thing, it'll tell you exactly where it's at in the code you can go in and you can fix that issue. Here for color contrast, it tells you, the thing that I appreciate about this tool is that it tells you how to fix it. It says, hey, this color isn't accessible enough and sometimes it also makes suggestions in terms of changing it, which can help you as well. So this is a great tool to sort of go through, look at specific items, especially color and make your changes there. All right. So those are two browser-based tools and also once you run it and you come back to the page, it also flags the area. So you can see the button, which is white text on pink. And that was that. And actually, this is a very current design trend. You'll see on, especially in commercials, there's white text on a really, it's a beautiful, you know, nice light, beautiful color, but for someone with color contrast issues, I can't see it and someone that's colorblind really can't see your product. So again, it tells you where you fail and how you can work on it. So you could see just about on every part of this page, there's some issues in terms of accessibility or color contrast. All right. The next tool I want to show you is another go-to for me. These folks at Idaho State University started the Web AIM site. This is a place again, where you can see the million web pages reported, comes out every spring. They look at the top traffic websites and they break it down. They tell you why the homepage just fell. They also break down the areas because again, there's six or seven areas that we all can address on our page to make it more accessible. I like the color contrast tool here because it gives you a breakdown of colors. So for example, okay, so say you had it like a lighter color. Let's do the pink that we just saw. All right. So say we had pink here. You can copy paste your hexadecimal color into the two boxes here. If it's background or foreground, you can do it either way. You can flip them around. It dynamically updates here, but it tells you that it fails. It also says in terms of graphic components, like your text boxes and things like that, which we all love to design. The other cool thing is that below your dynamic area where you can enter your colors, it has explanations. It also has an API that you can actually build into your process. It also points out that ColorZilla is another excellent tool for those of us that don't have Photoshop. I work in the Adobe Cloud, so I have it, but if you want to find a tool that can do color picking for you, ColorZilla is the browser-based tool that allows you to do that too. I'm totally into free tools. If you're a member in the audience of one of my presentations or if you come to WordPress Santa Carita, we always stress open source, free, especially for a beginner or someone that's willing to learn a topic or wanting to learn a topic, it's important that you get up and running faster than investing in a premium tool that you may not even like. So again, start with open source free tools and go from there. They also have a contrast tech, a link contrast checker, which also tells you about your links. How many of us have fallen into the design trend of gray hyperlinks, which are incredibly bad in terms of contrast? You would have to go with a very dark gray. So why not just use a black and underline your links also, which is another pet peeve of mine. All right. So again, it's great because it allows you to dynamically check your colors. So as you're building, hey, I love this blue, drop it into this box and see how it works. And then the other cool thing is again, you can go ahead and slide the dynamic slider until you pass three, four, and you get a passing grade in terms of color contract. All right. So let me see what else I have here. Again, this is the link color contrast checker, which does the same thing, which is another thing that I recommend. And this is a whole section on contrast and color accessibility. So with those basic tools, you get a great start on making your websites accessible. Let's just jump back in and finish up here. I have a couple of resources I want to share with you as well. Go ahead and, all right. Again, the stuff that I talked about today is here, the color picker, the accessibility insights for the web. So make sure you grab those links and what I'll do as we start doing questions and answers. I'll paste these links in the chat as well. And that's it. All right. Before we get to the questions, and I'll turn it back over to Courtney so that we can handle that. Thanks again for your time today. Again, what I like to do is break down these concepts into small, more digestible chunks. I hope you enjoyed it. I'm glad to see so many familiar faces in the audience because our journey and accessibility is connected. We all, especially in the WordPress community, we always try to help each other. So I'm here for you. I'm here for your questions. And thanks again for your time today. Thank you, Jo. Yeah, I'm scrolling back to look at some questions. So we have a few. Let's scroll back a little too far. So a question from Ron. As a designer, did you ever take one of those online color tests? And should we all, in parentheses meant in particular, always utilize color analyzer tools when making websites, designer building websites? In terms of color tests, I'm not sure what you mean. I'm not sure if you mean to determine whether I'm colorblind or not. I don't think I've done that. But again, back in school, I learned color one way. And then again, as I became more in tune with how I worked in the web space, it was a different thing. User experience and the user experience for accessibility is sort of first and foremost for me. So color is always important. I always design. And I think I've done it from the beginning. Unfortunately, at certain companies, it's not a priority. But it's your job to sort of advocate for it. It's again, it's up to your client. But now that we're faced with the threat of a lawsuit or the threat of legal action, if our sites aren't accessible, that should bring it more to the forefront. And just think about the last three years, what's happened in the world. In terms of the pandemic, most companies shut down. They were forced to move their business to their websites. How many restaurants didn't have online ordering? How many restaurants didn't have a cart that you could drop your order in and have them deliver it or have it picked up curbside? So so many, so much business happened that first couple of years and people trying to get their sites up and running. So it's a niche. It's actually still a need. And it's always, if you go by the web aim report, there's a lot of work that we need to do. So again, I would always stress bookmark these color contrast analyzers. Again, I would love, Ron, if you could share a little bit more about that, what that color test was. But I think I have, I'm not colorblind. So I I'd love to hear more about that. Yeah, the tool that you were, one of the tools you were just using was talking about the blue and white contrast. I think and I'm noticing my slide here is blue and white. So yes, that is something that I can improve upon. It's like the branding for for Learn WordPress. That's something that we need to look at. Got another question from Ron. Favorite color checker or analyzer? Well, I generally show the web aim color contrast analyzer. That's the one I like. There's so many now. I know Adobe in the Adobe cloud, they have one. It's really a way to drive traffic to their site. But to me, I love the simple ones. There's also a couple of color contrast analyzers or colorblind testers that I recommend. There's a desktop one that's called dims. So I forgot the name, but it it it allows you to drag it's sort of a box over your part of your page. And it shows it as if someone that was colorblind. And there's three forms of colorblind that allows you to test for. And it allows you to see it dynamically. There's also one where you get pasted in the URL of your website. And it checks your website. And it pulls out a report on the side. It's by Ben Gage. And although it's a little buggy, that's one that I've used. In terms of the company I work for, one item that I found during this research, we do a lot of maps. And I'm always fighting folks in the agency who want more bills and whistles. Maps, they want to see things popping out and popping over and sliding left and right. But maps are generally not accessible. So there's an ArcGIS color contrast tool that I'm going to share with my colleagues in our map group. So there's a number of them out there. So part of what I love to do during these presentations also is have people drop their recommendations in the chat as well. Yes, Ron just shared color contrast analyzer TGPI. And there's a link there in the chat. There's a recommendation. Cool. And I'll paste mine in the chat also. Great, thank you. That we just took a look at. All right, next question. What else you got for me? Is the built-in color contrast checker that you demoed available in all WordPress themes or just in automatic slash WordPress themes such as 2022? Well, I'll have to confirm because I generally use the core automatic themes for a lot of what I do. I'll check. It could be... And I don't want to speak out of turn again. What I'll do is I'll put it in our meetup notes on the page, but I'm assuming that it's part of core. So if you're using full site editor in the blocks, I'm assuming that it's going to be part of that. So, but again, let me check to make sure. Patrick in the chat says it's built into the block editor, but yeah, I'm not... I'm also not sure if it's built into core. Cool, thank you. Scrolling through again. There's quite a bit of chatter here. Question from Lynn. You have mentioned browser extensions for checking color. Do all or most browsers give the same result or should a developer check many different browsers? Well, the browser based extensions, these are for Chrome. So I'm assuming that if you're in Firefox, they'll have their extensions. It just depends on whether... It's sort of like your iPhone versus your Android. Some apps go cross phone, but some of them don't. I'm assuming that if you have a similar tool in Firefox, it may work differently. The one thing that you love to test between browsers is really to see, like for the longest time, IE worked different than Chrome. So your pages would display differently. So all browsers will probably represent your pages differently in terms of structure and things like that. But make sure that you have the tools to check independent of your browser in terms of color contrast. And I think you should be fine. Great. Thank you. Peter also shared a link for testing a number of colors at once. So contrast-grid.hshapes.com. Thank you. Yeah, I can check that out. Question from Steve. As this is an Elementor meta, is the Hallow Elementor theme one of those accessible themes? It's not specifically an Elementor meetup, but that is a good question. I'm not familiar with the Hallow Elementor theme. Oh, that's fine. And the reason is that I have another. I do a different meetup in it. So the thing about page builders and it's a fact. Most page builders allow you a different kind of freedom, which the full-site editor and the block experiences is going after. And that gives you drag-and-drop capabilities, the ability to use a whole bunch of different widgets exactly in the way you want. But unfortunately, the big drawback is that most page builders aren't accessible and you have to do a lot of retrofitting to make it happen. So I would say these are not. Hello is probably not fully accessible. So the thing that I always recommend is that as you build, you need to test. One test that I would always recommend doing.   That'll say your site is accessible to this point with nothing in it. And then as you add widgets or different features to your site, each time you do that, test it. And that's the way you should really go about it. Because again, these page builders aren't really accessible and they give you a lot of freedom, but at the cost of accessibility. If you look at a lot of what they market or a lot of the, you know, if you look at their sites, they're really pushing your ability to create and design anything. So again, that is also, that's kind of counter to making sure everything's accessible. Because again, we see with our eyes, we're more visual creatures, the more bells and whistles we see the more that we think it's more effective. But really just think about the most effective sites.  The service that it provides, it just allows you to get to that sell button quickly. Now they have accessibility problems on that website. But again, really think about what your client needs in the simplest way to provide them that. Because again, we want more people seeing our information, not just a very specific sliver of an audience. Lisa shared a link to the Hello Elementor theme in the chat and says that this theme seems to have the accessibility ready tag. But she has never used the theme. So yeah, a question that did come up was about the, if the themes that are submitted to the repository, how are those, how are those, how do those come to be tagged, accessibility ready? As far as I know, the themes team reviews them for accessibility. As was mentioned on that handbook page that you shared, is that correct? That is correct. Like when, so say for instance, you want to build a theme. As you get that theme ready, you submit it to the repository and then they go through a process of evaluating whether the site, I mean, whether the theme is one ready to go up. There may be a little give and take on making sure that your site meets certain criteria. But then they also run that accessibility tag check, accessibility ready check to see if it meets a different set of guidelines, but more specific to accessibility. And what do we do if we find a theme that actually isn't accessibility ready and it's in the repo? How do we submit that feedback? Well, you can reach out to the developer to see if they're willing to do that. But I would say start with an accessibility ready theme. Because again, just think about a lot of times we're drawn to a theme because of the way it looks. And again, in the accessibility ready realm, there's, I think there were 83 or 87 themes that had different looks and feel that you can start with. And again, you can build to anything using your blocks or your patterns and things of that nature. So I would say it makes a little more work if, I mean, if you choose not to do that, that's sort of your choice. But again, it'll make it more difficult for you to, you'll have to do more work to bring it into compliance. Thank you. Looks like we don't have any more questions related to the, to your presentation. Lots of good information in there. Thank you. I see, let's see, there's a question from Ron for me. Good captions on this session. Are we using a live caption or is this the auto-captioning from Zoom? This is actually the auto-captioning on Zoom. I'm guessing that that has improved a lot in the last few months or so because I often found it not 100% accurate. I would always manually go over the captions after these sessions and edit them, make sure and review them for accuracy. So before I upload them to WordPress.tv. So yeah, it's good to know that the captions for this session have been great. So thank you. Let's see, I don't see any more questions here. If I missed your question, please feel free to paste it in there again. I did scroll through and just really quick to find anything that people preface with the word question. But yeah, we just have folks just chiming in here. Yeah, I'm taking a look also. Yeah. Yeah, it's so awesome too. I see Sumner out there. Hey Sumner. Sumner is someone that's really important in our community. We have a whole bunch of meetups that sort of spawned out of a presentation that she did in terms of accessibility. So she's very impactful on what we're doing in the community. So it's always good to see her here. Yes, a couple more questions here. Any future enhancements coming in WordPress that are specifically accessibility related? Ah, that's a great question. I'm part of my journey this year, and it started about six months ago, was I wanted to do some behind the scenes stuff. I wanted to see how themes were made and how accessibility is being folded into WordPress. So each time there's a release, how do they make improvements in terms of accessibility? So I joined the Make Accessible team for WordPress. And each Friday, there's a bug scrub that goes through a list of issues that are reported. So if you find an issue with, and it goes back to your question, or the item that you pulled earlier, if there's an issue with a theme, you can submit it and they'll take a look at it in the GitHub repository. And they'll address it if they have the opportunity to. And then also we have a meeting every other Friday, where we talk about what's coming in the next release. How do we fold in accessibility? Another key component, and again, that's why I'm sort of wearing all white today, is I want to make sure that we get more people involved in that part. We need people to test. So even though I'm not a developer, I tested the last round, and you get to, for me, I'm always interested in how people use it. So there's a script that I go through in terms of accessibility, how does someone use part of the full site editor? So that way they make improvements. We report those, people address them. And so each iteration of the full site editor, they're building more in. And the one thing that I'm kind of happy about, and again, I haven't been with the team long, is that a lot of these, each time we go through one of these updates, or version, as we move up in terms of versions, there's more accessibility that's being built in because of the suggestions made by the team and through the process. So it's always a working process. I don't have specifics, but I know, again, it's related to how the editor is functioning. I know at the beginning, and it's still a cause for hesitancy. For some people, they felt like the backend isn't usable in terms of someone that has to use it if they're accessible. So a lot of those things are being worked on. But again, it's a slow process, but it's awesome to see behind the scenes how they're trying to make it work. Thank you. Question from Summer. What do you do when a client protests your color selections? Oh, that's a great question. There's a story that Sumner shared with us. It's a great story, and I hope she's okay with me sharing it, but she had a client, they insisted on a certain color scheme. And at Metro, I do the same thing now based on the story. They were insistent on a certain color scheme. So she said, at least let me show it to your partner. So she took it to the partner, and they found out that he was colorblind, and he couldn't see the color. So that made the point that we assume that because of our brilliance or because of our eye for color that we know what's better for the customer. So you really need to test it, show it to someone. And what I've done at Metro back in the day, I did some user tests. So it's really good to record people doing. I think Hot Jar allows you to record user sessions to see how people use your site. It's also would be great if you can get people in, and you could just do some tests to see if they can find something on your site, just to see how people use it. So I would say if you have an example or someone showing them that these colors aren't accessible or the reasons why, I mean, you really need an example to show them if you can't persuade them just through logic. Thanks for that question, Summer. Question from Steve. What are your thoughts on the one click accessibility plugin which was developed in part by the Hello Bean folks? And there's a link here. Ojo Python accessibility. I haven't used it, Steve. I'll have to test it. I know there's a couple of things from this meeting that I need to check on in the Elementor space. Like the one click, I'm always a little hesitant because, again, if it sounds too good to be true, a lot of times it's not. But I'll promise you this, I'll take a look at it. And again, I can't really respond because I haven't used it yet. Summer mentions in the chat that Ojo is an overlay. How overlays do you not work? Yes. And overlays track more than a hill. Yeah, and I was going to say the thing that really happened during that time in a lot of businesses had to close and go to online format. These overlay companies popped up because they gained in popularity because they promised, hey, we can take care of all of this with just popping this little accessible guy icon in the lower left-hand part of your screen when it actually impedes the ability for someone with an accessibility challenge to use your site. So part of what we always do is we always try to dissuade people from using overlays at any cost. And one of the success stories that I'm proud of, and again, Sumner was really critical in this, meet up about four or five months ago, they popped up one of those accessibility overlays. And the WordPress community went nuts. And I was part of the team that met with Meetup and Sumner as well to say, hey, you really should pull this down, and this is why. And it actually worked. So one of the things that we always try to do, and there's another success story, someone in our community, Alicia Rose, when we were doing this project for the air competition, we were using Generate Press and she would find things and she would reach out to the theme developers and they would make adjustments. So just ask. You never know if it'll work or not. And these are just two examples that did work. Unfortunately, there's a couple that I've tried to do the same that haven't, but all you can do is ask. And again, if they're willing to improve their product and make it more open to more people, they should. Thank you. Yeah, we have folks talking more about overlays in the chat. Yes, it's not as Sally says. Maybe that'll be my second topic here. Sally mentions accessibility is not a thing you can do in one place. Yeah. And as Ron says, got to do the work. Yeah. Yeah. Peter also shared a link to overlay fact sheet dot com. Oh, that's a great one. That's a great one. Yeah, there was a petition that went around as part of that because again, during the pandemic, it became such an annoyance that there was a response from people on our side that really wanted to inform people. Because again, a lot of times it'll be a sales call to somebody at the company and they think it's a great idea and they go ahead and just do it without researching it. Because again, it sounds too good to be true. Hey, I can pay this much money a year to take care of this problem that really a developer should work on. Let me buy that. So it's something that you really want to avoid at all costs. Yeah. Yeah, I would say, Ron, I wouldn't have put that link in there. We don't have any further questions on accessibility. Yes, lots of talking about overlays that yes, maybe this is like a future topic for the workshop. Yeah, but what my hope was, and again, we started with a really basic topic and I generally talk to a beginner's audience is because you're the people that will carry this message out and you'll be able to talk to your client, at least talk to them, make them aware of it. And again, you're informing them on something that they could easily do and it really benefits their bottom line. Again, who wants fewer people to buy their product? Who wants fewer eyeballs on their site? So if you're driving people away by not creating accessible content or content that's easier to read with a screen reader or other assist device, I mean, you're limiting your audience. There's a whole segment of the population that they want to give you their money. So build sites that welcome everybody. Great. Yeah, thank you for sharing your knowledge with us, Joe. I agree with you as like we have to start somewhere, starting with these introductory topics and help a lot of folks get started. And accessibility is a huge topic. We have an entire main WordPress team dedicated to it. So we are all doing our best to make our sites accessible and this is a great start. So thank you, Joe. Oh, thank you. And again, this is a full circle moment for me. Again, I remember way back when you helped me start our meetup here. So it's just my pleasure to talk with you again and share with the Learn Community. Yeah, same here. So again, learn.wordpress.org is where you can find more workshops like these. We also have tutorial videos for learning about specific subjects. They're usually like five to 10 minutes long. And there are also lesson plans if you're an educator or a meetup organizer. If you're looking for a topic to teach at your meetup, you can find lesson plans there. And yeah, if you'd like to join some conversations about WordPress, we have a Slack where all the contributors to the WordPress open source project chat about the work that we're doing. So you can join that at chat.wordpress.org. If you want to save the chat from Zoom, you can click the readout icon on the chat window and save the chat. So all the links that were shared in the chat you can have saved locally. I think we'll also be providing a link to the recording with captioning within the next 24 hours or so on wordpress.tv. I don't think that is it from me. And yes, we're right in under an hour. So thank you, everyone, for joining us today. I'll see you next time. See you, folks.


My name is Lisa Min and my role is clinical social worker at Social Services at the Tang Center. I think oftentimes the mainstream definition of rape is a stranger jumping out of the bushes. That's what people think of first. When you work on a university campus, a much more common profile is someone goes to a party, there are a lot of people around, you're meeting new people, there may be alcohol involved, and people connect. And sometimes intimate behaviors begin and they start out consensually, but then sometimes things can move too fast, people can feel pressured, and a sexual assault occurs. And sometimes people aren't even able to name it in the moment, they just know, okay, this was uncomfortable, I feel a line was crossed. Our Cal students are so smart, they're so accomplished, they're so in control that when something like sexual assault happens where your control is taken away, it's very confounding for people. And oftentimes their guilt, blame, and confusion go inward and they blame themselves for what has happened. Something I will often say to students as we're trying to properly assign responsibility for what has happened is by telling students the person who was responsible for your sexual assault is not in this room. And that can often be a pretty impactful statement that people find helpful.


The narcissist is struggling without you. When you stop living your life for the narcissist and put the focus back on yourself, they will get mad. They will feel as though you are taking something away from them. They need you to focus all of your time and energy on their interests or needs. It is essential for their emotional survival. So when you stop doing that and start attending to yourself, they begin to panic. They experience sudden, uncontrollable fear or anxiety. They engage in wildly unthinkable behaviour because in their minds, it feels like life or death. Narcissists constantly feel like they are drowning. As their primary source of supply, you are their life jacket. You are meant to keep them afloat. But when you start to take care of yourself again, in their minds, you are taking something away from them. They feel entitled to your time and energy. Whenever they want it, they have to operate in this way because it is essential to their survival. If you don't wait on them hand and foot and provide everything they need or want, if you don't act as a servant to them, it will feel as though their life jacket is no longer functioning properly. So they will begin to panic. They will begin to lash out. And in their minds, they believe it is justified because they feel like they are drowning. They feel like their lives are at risk even though you may be the one who is at risk of danger or harm. They can't see it that way because the problem exists in their minds. And when you finally get fed up of serving them and you begin to focus on yourself again, the narcissist is likely to leave. They are likely to move on and find someone else to provide to them. But it's not so easy for them to find another grade A source to supply. It's not so easy for them to find someone who is going to wait on them hand and foot and attend to their every need. They will often end up with people who aren't willing to do that, people who refuse to assume responsibility over another person, which then leaves the narcissist drowning without a functioning life jacket in a condition where they are just trying to survive. They have no one to regulate their emotions. No one to provide for them financially. Their bills are mounting up and they have no one around to blame. No one around to project their feelings of self-hatred onto. They might get online and start stalking your social media. They might see that you are starting to move on. They might see that you are finally beginning to live the life that you always wanted to live. They might see that you are happy now.  It just reminds them that they made the wrong decision. And while they wish they could go back to you, while they wish that you could comfort them and support them financially, they know that you're not going to take them back. They know that you're not going to trade your happiness to put up with their BS all over again. So they suffer in silence. They endure their pain, distress and hardship without saying a word. And they may even put a few pictures of their own on social media. It might appear as though they are doing something fun. It might appear as though they are with someone. But it's all an act. It's all designed to make you feel as though you are missing out. As though you made the wrong decision by letting them walk away. They are very good at deceiving people. Just remember when you first met them, they tricked you. And once they knew they had trapped you, they showed you who they really are. When they leave, they do the same thing again with someone else. And they will use that to make you believe that they are happy. As though they have everything they want. When it's just not true, they just know that you finally got to move on and be happy without them. And it's killing them inside. Misery loves company. And these people are always miserable. They are always unhappy. And they are always struggling. Which is why whenever they come around you, it's only because they need your help or support. Because they're constantly struggling. They're constantly just trying to survive. But it is not your responsibility to help a grown adult who should be able to take care of themselves. You didn't come to this world to be a narcissist life jacket. You didn't come to this world to be their life support. You came here to be the best version of yourself. And you can't do that while someone is constantly clinging on to you in an attempt to survive.  You came here to be so much more. Thank you for watching. I hope this video is it with you. Please like, comment, share and subscribe. Click the bell icon to receive notifications for my future videos. If you like to donate, my PayPal link is in the video description. Coaching inquiries, you can email me at narcosfathercoaching at gmail.com. Thank you for watching and I'll talk to you soon.


In the last lecture, we had talked about the curl of a vector field. Before that, we introduced the ideas about a divergence of a vector field as well as the gradient of a scalar field. Today, what we want to do is to introduce another operator which goes by the name Laplacian or del square operator. The grad, curl and divergences, they are essentially first order differential operator. For instance, the gradient which is given by i d by d x plus j d by d y plus k d by d z. As we talked said earlier, acts on a scalar function f of x y z and gradient of f is a vector given by unit vector i times the partial f with respect to x plus unit vector j times partial f with respect to y and unit vector k times partial f with respect to z. Divergence or del dot on the other hand is an operator which acts on a vector function giving a scalar. The expression for divergence is almost similar to that of the gradient accepting that after i d by d x plus j d by d y plus k d by d z, there is a dot. So, that on the right hand side of the dot, I expect to see a vector function and if vector f has components f x f y f z, then del dot of f or the divergence of f gives me partial f x with respect to x plus partial f y with respect to y plus partial f z with respect to z. The curl is again a vector operator acting on a vector, it gives me yet another vector. So, what we have seen that how one can get a Cartesian expression for the curl last time and for example, the x component of the curl of f is d by d y of f z minus d by d z of f y etcetera. Now, this del square which is also called nabla square sometime, but is also it has a name Laplacian operator which is basically a del dot del del. Now, what is del dot del? Now, del dot del means the second del is essentially a gradient. So, in other words I am expecting a scalar function to appear to the extreme right. So, therefore, del dot del let me sort of work it out. So, del dot del means divergence of the gradient of the function f.  Now, the way to look at this is that the vectors on this side is to be dotted with the vectors on that side.  So, I get d square f by d x square.  So, in other words the del square operating on a scalar function f is same as d square by d x square plus d square by d y square plus d square by d z square operating on f. So, this is the expression for the Laplacian operator or del square operator. Now, there is a class of function known as harmonic function and they are characterized by the fact that the Laplacian of such functions is equal to 0. In fact, this equation is known as Laplace's equation. This equation is known as Laplace's equation and we will see that in electrostatics this equation is of great importance. So, we have seen what is del square of a scalar function. Now, is it meaningful to write del square of a vector function? Is it meaningful? This is really a some sort of a notation if you like. Say del square is del dot del. So, therefore, obviously a gradient of a scalar makes sense, but when we write del square of f this is f as a vector this is a shorthand notation for three quantities. These are basically three terms there.   So, del square of each one of them is defined as per our previous discussion. In this I have listed a few vector identities. I will not be deriving them, but we will expect you to try to work out some of them, but notice some of them are rather interesting. The first equation says curl of a gradient is equal to 0. We have discussed it earlier. We have said that if a force field can be written as a gradient of something then that is a conservative field. There is a conservative field curl of such a force field is 0. This is actually a test of conservative force field. So, del cross del f is equal to 0. Now, I know that del cross a is a vector, but it can be shown that the divergence of the curl of a vector function is equal to 0. You remember we had said earlier that if the curl of a vector field is 0, the field is said to be irrotational. If the divergence of a vector field is 0, it is said to be solenoid. So, what we are trying to say if I have a field del cross a, then such a field vector field has to be a solenoidal field. The third equation that I have written down, this is an identity you must have seen in case of ordinary vectors, vector triple products like a cross b cross c. For instance, we are aware of this that a cross b cross c. Now, you have to put in a bracket because otherwise we cannot be sure whether you are first taking a cross b and then cross taking a cross product with c or the way I have written down. And this turns out to be given by the famous occasionally called the back minus cap formula b a dot c minus c a dot b. Now, when we write del cross del cross of a, again the brackets are important. The difference between this expression and this is the fact that these are differential operator. So, one has to write them, when you write them they act to the quantities that appear to their right. So, you cannot simply reproduce this, you have to rework it out. Now, it turns out to be the grade del cross del cross of a which has to be a vector because this is a vector and this is a curl of a vector. It is gradient of del dot of a. So, it looks very similar to the first term excepting that you have to know that this is my b, but this is the differential operator. This is a differential operator del of del dot of b a minus del square of a. The next equation that I have written down is what is gradient of f g.  What is divergence of a scalar times a vector function? Very interesting. So, it also works like a chain rule, but you have scalar times divergence of the vector function. Then, the dot product of this vector with the gradient of the scalar function. So, these are some of the identities which you will have to work out and we will be probably using them as we go along. We have been talking about a vector field and we have introduced, we have introduced two properties or two types of operators which can act on a vector field and they are the divergence of a vector field and the curl of a vector field. The question is what makes a vector field unique? Given what quantity you can say this uniquely describes a vector function. Now, it turns out that if you are you provide the curl and the divergence of the vector of a vector and the normal to the surface in which this field is defined, then these three properties uniquely determine a vector field. This is a very important property what makes vector field unique. So, let me let me try to establish this. In trying to establish this, we use an identity which is known as green's identity. There are two of them the first green's identity and the second green's identity. The second one is also known as green's theorem. They are rather straight forward, but let us look at what they imply. Supposing a is a single valued and continuously differentiable vector function inside a volume v which is bounded by a region s. So, I know the vector a in that. Now, we had seen earlier that if a vector a is defined in a region which has a volume v and is bounded by the surface s, then the divergence of the vector del dot a its volume integral is given by the surface integral of the vector a taken over the surface which binds this volume. This was known as the divergence theorem. Now, what you are going to do is this. Let me take the vector a to be given by a scalar function phi times the gradient of a second scalar function phi psi. Substitute this into this equation. So, let us see what we get. We get del dot of a we have just now said what is del dot of a scalar times a vector. We had shown an identity. So, remember what we said is that del dot of a scalar times a vector is the scalar times del dot the vector which is del dot del psi. So, scalar is phi times del square psi plus dot product of the gradient of this with the second vector which is gradient phi dot with gradient psi and this whole thing volume integral being taken and that is equal to the surface integral of phi is a scalar. So, I just like write like this times gradient of psi which is a vector dotted with n d s. This is known as the green's first identity. So, phi del square psi plus del phi dot del psi d v is phi del psi dot n d s. Now, phi and psi are arbitrary scalar function. So, what I do is I simply interchange them. Now, if I interchange them I would get wherever there is a phi I write a psi wherever there is a psi I write a phi I will get as psi del square phi plus del psi dot del phi which is the same as del phi dot del psi integrated over the volume is equal to integral over psi del phi dot m d s. Now, when you subtract 2 from 1 you notice this del phi dot del psi term cancels out and I will be left with them integral of phi del square psi minus psi del square phi d v that is equal to the closed surface defining the volume phi del psi minus psi del phi dot n d s. This is known as the green's theorem. Let me come back to the theorem that we talked about. We said that a vector field is uniquely specified in a region v which is bounded by the surface s provided its divergence is known at every point its curl is known at every point and the normal component of the field is specified at all points on the surface which encloses the volume. The three conditions which are necessary to make a vector field unique. Let us say how does one work? Now, what we do is this? We will prove it by what is known as the reduxio ad absurdum namely let us assume that these three things are given and a vector field a satisfies it and a second vector field b also satisfies the same three conditions. In other words what we are saying is del dot of a is the same as del dot of b curl of a is the same as curl of b and the normal component of a on the surface is same as the normal component of b on the surface. Now, what we do is this? Now, if this is true that a and b are different then if I define a vector c equal to a minus b then c should be a non zero vector but let us see whether that can be satisfied or not. So, I have defined c is equal to a minus b that c is equal to a minus b and if del cross of a is equal to del cross of b it tells me that del cross of c must be zero in other words c must be a conservative field. So, I can write c as I take a traditional minus sign times the gradient of phi a scalar function phi. Secondly, we know that divergence of a is the same as the divergence of b so that tells me that c is such that del dot of c must be equal to zero but we have just now seen that c is gradient of a scalar function. So, what it tells me is c is such that del dot del phi so del square phi must be equal to zero everywhere in that volume. The third thing that we have given is a dot n is the same as b dot n at every point on the surface. So, that tells me that c dot m d s which because c is gradient of phi which is del phi dot n d s must be equal to zero because c is a minus b. Now, let us do the following. We had worked out an identity known as the greens first identity. If you recall greens first identity was let us go back a little bit. The greens first identity was phi del square psi plus del phi dot del psi integrated over a volume is the same as the surface integral of phi del psi dot m d s. Let us suppose phi and psi are arbitrary scalar functions. Let me take phi to be equal to psi in the greens first identity then this equation becomes phi del square phi plus del phi square absolute square integrated over a volume is equal to integral of phi del phi dotted with n d s. Now, notice right hand side of this should be equal to zero. We had further seen that del square phi is also equal to zero. That tells me that the integral of del phi absolute square d v equal to zero. Now, del phi absolute square is an integral over positive terms. Now, it cannot be zero unless gradient of phi is zero. This implies that gradient of phi must be zero, but what is gradient of phi? It is nothing but minus c. So, therefore, c is equal to zero. So, that proves that c defined as a minus b cannot be a distinct vector function. .So, what we have said so far is that if in a given region I need to specify a vector field uniquely I must know three things about it. Its divergence must be known at every point, its curl must be known at every point and at each point on the surface which is which provides a boundary for the volume. The value of the normal component of the vector field must be known at every point on the surface. Given three conditions the vector field is uniquely determined. This essentially brings us to an end of discussion on various vector operators which are useful in electromagnetism or electromagnetic theory that we will be doing in the rest of the course. However, in the remaining time that we have I would like to bring in two more mathematical notes which are also useful. The first one is called Dirac's delta function. Dirac as you probably know was a very well known physicist who had actually shared a Nobel prize with Schrodinger for his contribution to quantum mechanics. Now, Dirac's delta function is a funny function. In fact in strict sense it is not a function at all. It is either called a generalized function or a distribution but will not go into the mathematical final points of a delta function. But let us look at how does one define delta function. So, the definition of delta function is interesting. It says it is a function which is 0 everywhere accepting at a point. So, delta of x is equal to 0 delta of x is equal to 0 if the argument is not equal to 0 if x is not equal to 0. Now, what happens at x equal to 0? Well we do not quite define it by giving a value but you can already see. So, what we do is this we say that suppose you take an integral of a test function f x multiplied with this delta of x and if this interval includes the point which provides the argument of the delta function. In this case the argument of the delta function 0 of the delta function is at x equal to 0 not 0 but the argument of the delta function is x. And so therefore, the integration has to be done over a region which includes the point x equal to 0. So, let me let me just take it from some minus epsilon to plus epsilon. This is guaranteed to include the point x equal to 0. You could take it from minus a to plus a minus infinity to plus infinity as you desire. What is required is that wherever the 0 the argument of the delta function has a 0 the integral limits must include that point and this is equal to function value of the function at the point x equal to 0. In fact, if you wrote integral f x delta x minus a d x then it will be f of a. So, this is at f at 0. Now, this is of course, f x has to continuous function. Now, notice already why delta function is not a function. We are all familiar with Riemann integration. Now, if I have a function which is 0 everywhere accepting at a point no matter what could may be the value of the might be the value of the function at that point. The integral of f x is essentially the area of the curve below that point. Now, since the width is 0 the area of such a curve is 0. So, the Riemann integration should give you 0. Now, we are saying that the Riemann integral gives you f 0. So, obviously this is not strictly a function. So, how do you understand this? Direct delta function is best understood in terms of a limit of a sequence of functions. For instance, this is a sequence delta n x which is 0 if x is less than minus 1 by n n in a small interval from minus 1 by 2 n to plus 1 by 2 n and is again 0. In other words it is a rectangle it is a rectangle which has a spread only from minus 1 by 2 n to plus 1 by 2 n. Now, notice let me draw this function. I have plotted this function here for various values of n. You can check that the green one for instance is for a smaller value of n. This next one is red I increase n further increase n. Now, as I go on increasing n you notice what is happening is that the width of this function is going on decreasing. But the height keeps on increasing in such a way that the width times the height which is nothing but the area remains constant. Now, as n goes to infinity then this represents a delta function because as n goes to infinity its width will essentially become 0. But the area under the curve namely the area of the rectangle is finite because it remains finite because it is height times the width. Other examples would be as a limit of a Gaussian limit sigma going to 0 1 over root 2 pi sigma e to the power minus x square by 2 sigma square this is a Gaussian function as the limit of sigma going to 0. So, this is again a plot of that go on changing the parameter and you find that the width goes on becoming smaller and smaller and the height keeps on rising such that the area under the curve remains the same. Well, there are other options as well for instance as a sequence of a sinc function sinc function is basically sin x by x function. But there are some normalize factor we have done. Now, notice if you again I am not showing you but if you again plot this function sin n x by pi x as limit n goes to infinity is oscillating function. But because of that 1 over x as distance increases the amplitude of oscillation decreases with distance and the height of the central peak increases. This is a function which is familiar to you while you did you discuss diffraction phenomenon optics. Now, notice one interesting thing that let us look at and what is known as an integral representation of a delta function. So, for instance look at a simple function like e to the power i k x integrated over k and the value of k is from minus infinity to plus infinity. Now, you would not be able to directly evaluate it. The reason is e to the power i k x integrated over k gives you e to the power i k x divided by i x and if you evaluate it at x equal to plus or minus infinity I mean you do not know how to find the values. But let us look at it this way instead of integrating it from minus infinity to plus infinity. Let us integrate it from some minus n to plus n and make this n as large as possible. Then of course, I know how to integrate this because this is limit n going to infinity e to the power i k x divided by i x n is equal to from minus n to plus n. Substitute you get e to the power i n x minus e to the power minus i n x by i. If I had another i 2 on the denominator I would get this as a sin n x. But because my definition of sin x is e to the power i x minus e to the power minus i x by 2 i. So, I need to multiply to the 2 and divide it by x. But this is precisely was our definition of the delta function. So, this is nothing but 2 pi times the delta function. So, notice 1 over 2 pi integral from minus infinity to plus infinity e to the power i k x d k. This is what is known as an integral representation of the delta function. Well we could go on for instance a delta function can also be viewed as a sequence of a Lorentzian function. This function is called a Lorentzian function epsilon by x square plus epsilon square. Let this epsilon go to 0. You can again find another representation integral representation of the delta function here. Delta function has some interesting properties delta of minus x equal to delta of x which should be obvious. Because if delta of x equal to 0 at x not equal to 0 if x is not equal to 0 minus x is also not equal to 0 x times delta x is 0 and some of the other properties that we have written down which you can yourself prove fairly trivially. Having discussed the delta function what remains in building up a mathematical machinery for the discussion of electrostatics, magnetostatics etcetera that we are going to be doing is to discuss some different coordinate system. So far accepting occasionally we have been mostly confining ourselves to Cartesian coordinate system. However in some problems it is more natural to have a different coordinate system. One of them is known as a cylindrical coordinate system. Now, cylindrical coordinate system as the name suggests is useful if the system that you are discussing has what is known as a cylindrical symmetry. The cylindrical symmetry means that the object has a symmetry axis which you will call as the z axis and if you go around the z axis the object looks exactly the same. Now, cylindrical coordinate system is extremely easy to understand because its z axis is identical to the z axis or the z direction of the Cartesian coordinate system. So, I am only left to describe the x y coordinates and in the x y coordinate system. So, supposing I am in the x y plane. So, this is x this is y and the z direction is the same as that of the Cartesian system. It is as if on this circle there is a cylinder. Now, we parametrize in the following way. The instead of taking x and y supposing I am looking at a point p. If I am looking at a point p the direction from the origin to the point p that is origin of the axis this base to the point p this I call as the radial direction. I will represent it by rho so that you do not get confused with the radial direction of the spherical polar system that we will be talking about. This angle is theta. So, therefore, the x coordinate is given by rho cos theta rho is the distance from origin and y coordinate is rho sin theta. This is the radial direction actually polar two dimensional polar radial direction and if you take a perpendicular to this in the direction of increasing theta that is my angular direction transverse direction. Now, look at what happens how does one describe a volume element in a cylindrical system. The length elements are rho unit vector rho d rho along the theta direction rho theta because theta if you remember does not have any dimension. So, I need since I am talking about a length I need a length and it is an arc. So, arc is nothing but r theta rho in this case rho theta. So, rho theta along theta direction and of course, z direction the same k d z. So, a volume element there is given by rho d theta d rho d z. The more interesting and slightly more complicated coordinate system is what is known as a spherical polar coordinate system. In fact, this is a very natural coordinate system to us because our earth itself is a spherical polar coordinate system. So, the way you do it is this. Imagine a sphere imagine a sphere and take the center origin at the center of the sphere. Now, notice there is an equatorial plane this equatorial plane is what I call as the x y plane. I identify the equatorial plane with the x y plane and the axis of the if you like the rotation of the earth. Suppose, the earth is rotating about an axis joining the center of the earth with the pole. So, that is perpendicular to the x y plane. I am of course, assuming earth is a perfect sphere which as you know it is not. So, what happens is this. Now, how do I describe a point p what are the coordinates. So, the point p the first coordinate is very simple. Now, remember I do not have to be on the surface of the earth it is anywhere in that sphere. So, first coordinate is simply join the point p with the origin and the distance r is the radial distance this is called the radial coordinate and the direction from the origin to the point p along the radial direction along that will be my unit vector r r cap. Now, other point p now what I do is this this radial vector o p is making an angle theta here is the picture which describes what I am doing making an angle theta with the z axis. Now, what I do is this now this angle theta is another coordinate of my spherical polar coordinate system from p drop a perpendicular on to the x y plane. Now, notice that and then join the origin to the foot of the perpendicular. So, this is the p drop a perpendicular on to the x y plane join o with this. So, whatever angle this makes with the x axis that is called an azimuthal angle. So, I have got r theta and phi notice that this distance here that is the distance from the origin to the foot of the perpendicular is r sin theta and the perpendicular distance from p on to the x y plane is r cos theta where theta is the angle which o p makes with z. Now, you can immediately see what are the relationship between the x y and z coordinates of the Cartesian system with my spherical polar coordinates. So, one of them is obvious which is z is equal to r cos theta now let us look at what is x now. So, I have a foot of the perpendicular here. So, x is nothing but this distance parallel to x axis and since this distance is r sin theta the x is nothing but r sin theta cos phi and y is r sin theta sin phi. So, this is what we have written down there elementary trigonometry tells me r is nothing but square root of x square plus y square plus z square which obviously is the distance of the point o to the point p. And from those relation you can find out what is theta what is theta and what is phi. So, these are. So, you can see immediately that cos theta is z by r. So, cos theta is z by r I know what is sin theta x square plus y square plus z square is r square and all these relationship become clear. The other thing that I want to point out in this is that what is the volume element in this spherical polar coordinate system. Now, look at this picture now here I had a point p and I am sort of looking at how much is the length element in various directions length element in the radial direction is clearly d r. Now, in the theta direction it is r d theta very much like what happens in a polar case. And from the picture it becomes clear that in the azimuthal direction a length element is given by r sin theta d phi. So, therefore, the volume element which I have written here as d tau is r square sin theta d r d theta d phi. The last algebra that I want to do is to find out what is del square of 1 over r this is very important because 1 over r happens to be the potential the Coulomb potential with which will be very much you know involved in the next few lectures. Now, in order to understand what is it I need the expressions of the divergence and Laplacian del square operator acting on. So, what does divergence of a vector v in spherical polar system is a involved algebra, but on the other hand straight forward because we have already given the relationship between the Cartesian coordinates and the spherical coordinates. And you can sort of see that these are the type of expressions that you get. However, since I am dealing with 1 over r this function does not have any dependence on theta or phi. So, therefore, if my function v vector function v here or scalar function v does not have any theta or phi dependence then only point that I am involved with is the radial component there is the radial component there. So, let us look at what is it.  Now, I am interested in finding out what is del square of 1 over r. Now, I have told you earlier that del square is nothing, but del dot gradient of 1 over r. Now, gradient of 1 over r you can easily calculate because there is nothing. So, v r is just 1 over r. So, there is r square there. So, I get just d by d r of r. So, which is nothing, but 1. So, I get del of 1 over r is given by a. So, this is a vector which is 1 over r square, but along the unit vector r. So, which can be written as vector r by r cube. Now, you know that this is divergence of a vector by a times a scalar. So, this is equal to del dot r by r cube plus vector r dotted with gradient of 1 over r cube. Del dot of r we have seen is 3. So, this is 3 by r cube. This is r dot del of 1 over r cube and you can easily see that this is also 3 by r cube, but with a minus sign and hence it is equal to 0. However, this is true only if r is not equal to 0. What happens if r is equal to 0? So, let us look at what happens to the integral of del square of 1 over r over the volume. I know del square is del dot del of 1 over r d cube r and by using divergence theorem, this is simply the gradient of 1 over r dotted with the unit vector n d s. I know that the gradient of 1 over r is minus 1 over r square times the unit vector r. So, as a result this gives me this 1 over r square and there is a d s there. So, this is minus 1 over r square r square sin theta d theta d phi. Now, notice that there is no integral over r that is because it is on a surface where r is fixed. So, this is equal to minus the integral. Now, azimuthal angle gives me 2 pi and sin theta d theta that gives me a factor of 2. So, I am left with minus 4 pi. Now, this is the definition of a delta function that r not equal to 0 the function vanishes, but at r equal to 0 the integral does not vanish. So, therefore, I can what we have shown is del square of 1 over r d cube r is equal to minus 4 pi delta function. Since, it is a 3 dimensional delta function I occasionally write delta cube of r. With this we have completed the mathematical introduction to the electromagnetic theory and from the next module onwards we will start discussion of electrostatic phenomena.


Hi everyone, I'm a dumb. I forgot to do the break credit So here's a separate video for the break credit as it says here If you bought at least two or more teams two teams purchase equals one entry four teams two entries Six teams three entries top five get $50 a break credit each So big thanks to all of these folks for getting into the action Let's see who got those multiple teams sort by your your team name Or by your first names right there So Adam you got four teams including two that you won. So that's two entries John same as when you bought two. That's an entry EA bought to that's an entry Gabe bought to that's an entry Greg bought to that's an entry John bought to that's an entry Michael bought to that's an entry Nick Stober bought to that's an entry Rhea ended up with five four count. That's still two entries. I Think that's it. Yeah, so Rhea Nick Michael John Greg be Gabe P. E a CJS and a K All right, so There it is so five out of the 11 we're gonna get it's gonna get break credit. That's pretty nice So let's put you into a blank list right here Let's roll it and randomize it seven times. So top five after seven fifty bucks of break credit each. Good luck one two three four five six and Seventh and final time after seven there you go top five right there Greg Nick Gabe John Samuelsson and EA fifty bucks of break credit each going your way. Thanks for joining. Thanks for breaking with us I'm Joe from Jasper's case breaks calm. I'll see you next time for the next one. Bye. Bye


The Rocky Port incident, an event that birthed legendary figures and furthered the status of others. But in doing so, mark the end of the reign of Legends Pass, an incident perpetrated by Trafalgar Law, resulting in Kobe being recognized as a marine hero and Blackbeard becoming the new ruler of Hachinosu, displacing other notable figures. Because yes, this involves infamous Rocks Pirates member Wang Zi, so make sure to watch until the end. Chapter 1063 set up what might be a dive into finding out what really happened at this mysterious incident. An apologies that Potato Setup continues, but I am at the latter part of my holidays, so you shouldn't have to put up with this quality for much longer. But the prospect of finding out the truth behind what really happened at this event means I just have to talk about it. The first half of this recent chapter contains your standard new arc outfit change for the main characters, with Luffy, Chapo, Jinbei and Bonnie all getting arc-appropriate attire, which means new merchandise. Seriously though, this is one of the most fun things about One Piece. Getting to see characters dressed up according to the theme of the arc, this time wearing futuristic clothing, and I really can't wait to see what the costumes will be for the rest of the Straw Hat crew. Something even greater that I can't wait to see happening, however, is you subscribing to this channel. Gotcha! But perhaps the most impactful part of the first half of 1063 is Bonnie's reaction to seeing a familiar face. And is Oda still improving as a mangaka? Because Bonnie's crying reaction, asking Luffy not to hurt Robo Kumar, probably has a claim to be one of the best the detailed reaction drawings that Oda has ever put to page. I mean, just look at that. I love the details and the dark shading that really feels like Bonnie's backstory promises a heart-wrenching tale. I am really loving the Bonnie characterization that we're getting. We did get a brief glimpse of her in action, and this has me really wanting to see more of her in actual combat. Oh, and the reveal that Bonnie's last family member was Kumar. This gives me a strong feeling that we may have a future Nakama in mind, because Bonnie is in need of a new family. Or is this just another joy-girl wishful thinking we never learned? Seeing that the pacifista is serving like a cop, like Oda's rendition of Robocop, this has me really excited for all the fun and different types of futuristic sci-fi references that may come in the arc. But after that gut-wrenching sort of reunion, the chapter again made our stomach spin, putting one of our most beloved characters' lore in a really dire situation facing off against Blackbeard and a few improved members of the Blackbeard Pirates. Actually, we were made to feel all sorts of emotions in some fan service given in the form of waifu lore. It seems Oda has heard our jokes about lore being a princess, turning the tsundere into the quite amusing but very attractive lady. And providing this sort of comedy in between two segments with much darker and heavier tones was a really great way to keep the chapter fresh and engaging, so that it really packs a punch when it comes to the prospect of lore having to face a very ominous Blackbeard. Finding out the devil fruits of Blackbeard's crew, we can say for sure he really hasn't been playing around. He now has himself a group of pirates with very formidable or at least tricky abilities fit to be the final opponents for our very own straw hats when that time comes. Blackbeard says that he's after the Ponoglyph robbings, but I'm sure he wouldn't mind taking lore's devil fruit in the process, given his interest in acquiring very strong devil fruit. And to do that, that means death for Trafalgar lore.  And we know that Blackbeard is the type that doesn't make moves unless it leads to certain victory or advancement of his plans, so I really do fear what the future has in store for the Doctor. On another note, seeing two Titans who had a very similar path rising up in the world meet in a monumental clash is nothing short of exciting. Both these men are a part of the worst generation who was later given the title of Warlord and are also already familiar with one another having been centre stage at the Rockyport incident. And the truth of this incident is really what I think will come out out of this encounter. Given the speed at which the story has been developing and the fact that lore isn't a main character, I know a lot of people are expecting the battle to be off-screened with the outcome only being told to us as a form of big news that sweeps the world, which only further adds to Blackbeard's legend and his perceived level of threat. But whether that is the case or not, what this interaction could also result in is shedding some light on the Rockyport incident. Blackbeard already has Kobe, whose fate is still unknown, another character who was also heavily involved in the incident with the Marine captain finding a place to create a legend for himself. And all of these players taking the stage in this new arc leads me to believe that we may be seeing the Rockyport incident's details through a short flashback from the perspective of these men or at the least that it's going to be an event that is referred to, providing us with much needed background and information on what really went down in this very well-known event. An incident that's been mentioned since chapter 700, but details of the incident has come far and few.  Because whilst the entirety of the event is unknown, we do know for sure that it is one hell of an important encounter. It's probably one of the most important things to have taken place in terms of its implications. In fact, even what's happening now and the most recent events of 1.0 can be attributed to have all occurred off the back of what happened during the event. Everything that happened, everything that is happening can all be seen to be the consequence or follow-on events from what happened on that day. Because Law's a character perhaps even more calculative than Blackbeard, an extremely thorough planner who carefully plots his moves. Following Marineford, Law purposely chose not to go into the New World straight away, indicating that he has bigger plans in mind and steps to achieve his goals. We now know that those plans were to raise his status as a Shichibukai, a rank that he obtained in exchange for the hearts of 100 pirates. And this status, in turn, was all part of a larger plan to topple Doflamingo, a feat that he was only able to achieve via an alliance with Luffy and the Straw Hat Pirates, which also resulted in his involvement at Wano against two of the fearsome Yonko. And then following the events of Wano, Law again carefully chose a very special path as the quickest route to take him to this certain place, which has only resulted in him coming face to face with Blackbeard, another mastermind when it comes to planning. So we can really say that the Rocky Port incident may just be what's triggered all that's happened post-timeskip. It seems that Rocky Port may be the location where Law found 100 pirates to remove their hearts from. But this incident didn't just elevate the status of the Surgeon of Death because it also birthed the legendary status of Kobe, owning him the title of Kobe the Hero. And while we previously knew this to be the result of the young Marine saving the lives of innocent citizens during the event, we more recently found out that his actions actually also assisted Blackbeard. Of course, details aren't clear as to this was just incidental and it doesn't necessarily mean that Kobe worked with Blackbeard. But with the incident also somehow involving Wang Zi of the former Rocks Pirates, I also wouldn't be surprised if an alliance was absolutely necessary at the time to avail themselves of such a mysterious and legendary figure such as Wang Zi. We now know that Wang Zi had been previously ruling over Hachinosu, the island known as the Pirates Haven or Pirates Paradise. So maybe he had an extremely large following, making them the perfect target for Law to acquire 100 pirate hearts. I wouldn't be surprised if Law, Kobe and Blackbeard all had to work together to bring Wang Zi down. And it's a somewhat disturbing idea, but also one that could provide a very dark but nice parallel to some other key themes or events in one piece history. Kobe being Garb's protege, also having experienced a similar interaction, having to work with pirates to take down a greater evil and in the process becoming a hero of the Marines and such an alliance being very similar to the number of very unlikely alliances that Luffy has made in the past in order to free countries from an authoritative figure. The parallels between Luffy and Blackbeard as being two sides of the same coin is obviously a significant theme in one piece, and the events of the Rocky Port incident could be another example added to that list. Obviously, this one involving Blackbeard, however, would be a lot darker than the story of liberation that Luffy is usually associated with, an immediate difference being that Luffy doesn't necessarily have any interest in taking over the territories that he's saved for himself, only interested in freeing people from oppressive rule. Whereas in this case, it seems like Blackbeard toppled Wang Zi in order to take Hachinosu for himself, using the Pirate's Paradise as his base, where we've already seen that he has been terrorizing others.  Blackbeard, after potentially liberating Hachinosu from its former authoritative figure, has become another, perhaps even more brutal one. In fact, the dark contrast to Luffy's story could even be that Wang Zi wasn't even an oppressive ruler. It could even simply be a case where each member of the alliance had their own reasons to get rid of him, law to further his own goals of becoming a shichibukai to take down Doflamingo, Blackbeard with his desire to obtain Hachinosu for himself, maybe even getting a formidable devil fruit in the process, who knows. And Kobe only being involved because this was the only way to save the innocent civilians caught up in this mess. Now, this may or may not be what transpired on that fateful day or days, however long the incident was, but with all three characters continuing to be involved in this storyline that's unfolding simultaneously with our current arc, I can't help but feel that a deeper dive and exploration into what happened at Rockiport is at our fingertips. So these are just some of my thoughts. Let me know what you guys think of the Rockiport incident as well as your thoughts on Chapter 1063 by leaving a comment below. Please do subscribe for more One Piece discussions. You can also join the Joyfleet Discord server or even become an executive officer by becoming a Patreon or channel member. And I do want to thank all of our executive officers for help supporting the channel. This is Joygirl and I'll see you again soon.