Hi, Jeff Frick here with theCUBE. We're on the ground in Phoenix, Arizona at the Phoenix Convention Center with 8,000 attendees of the Grace Harper Celebration of Women in Computing. And it's put on by an organization called the Anita Bork Institute, and we're really excited for this next segment to get Telly Whitney on. The president and CEO of the Anita Bork Institute to give us the kind of the background of what's going on. So first, welcome. Thanks for stopping by on, and I'm sure it's been a very busy day. Oh, it's nice to be here. Thank you for having me. It's our pleasure. So why don't you give us for the people that we had never heard of this event until really we were told by some of the Intel social media team that, hey, you guys got to get down there. There's a lot of great things happening. So give us a little history on the Anita Bork Institute, and then a little bit of history on the show. Okay, so close your eyes, and it's 1994, and that is the year that Anita Bork and I, Anita was a close friend, held the first Grace Harper Celebration of Women in Computing conference. She held it in Washington, D.C. There were 500 women. For myself as a computer scientist, it was a life-changing experience because I had never been in a room of so many women. And as I understand it, it was really about being in a room with other women involved in the industry really is more of a peer networking opportunity. Well, from the very beginning, there was two very important aspects. One was the connection, having the chance to meet with other women. I mean, that was what gave you hope for the rest of the year. And there's also inspiration. I mean, hearing from these remarkable women talking about their technical journey was really helped all of the attendees to aspire for more. For the first quite a few years, we held it every three years. Okay. Then Anita Bork founded the Institute for Women in Technology in 1997. And we took over the Grace Harper Celebration as part of that. Okay. I became CEO in 2002 and Anita Bork passed away.  So I really helped out reluctantly for a while and I've been there for 12 years. And talk about the name celebration of women in computing. You know, I love, you're using a lot of great adverbs here. It's a celebration. So why did you pick that number? Really, what does that represent? Well, you've got to understand that for women who often feel very isolated in their roles, the chance to celebrate the achievements of all these remarkable women is really important. And at this point, as you mentioned, we're at 8,000 women. We have 4800 students. We have 2800 students. We have 2800 students. And we have a lot going on. It's become much more of a platform. Universities bring a lot of their students because the data says that it helps them to stay in the discipline. Okay. We have a lot of companies that bring a large number of their employees because they have found that it helps to retain those female employees. Increasingly, we have executives. You saw the CEO of Microsoft speak this morning. We have a number of other CEOs. And they come and they meet with their employees. And it really means a lot to the women who work for them about that they have a commitment to bringing more women into their company. And then we also have well over 200 companies that come here to recruit. Yeah, it's interesting that you've got the education track and you've got the recruiting track. And I think I saw an email thread where I think Google has like 450 people attending the show. That's an amazing turnout. Right. So companies like Google, I mean, they really are very thoughtful about their participation at Hopper. They have quite a few executives. The best known is Alan Eustace, who's been on our board for a long time and was a close friend of Anita Borgs. He was on the male allies panel last night. But they actually have a large number of their executives at the most senior level. They bring a lot of their women. They also support a lot of their students to come. So they really see themselves as organizing across their own pipeline. So let me shift gears a little bit. Let's go back before 1994. And I wonder if you can share a little bit about your story, what it was like in the early days as a woman in computing. Well, I got my, all my degrees are in computer science. I got my degree from the University of Utah in 1978. And I stumbled across computer science. I knew nobody who was an engineer in my family. And I really, but I found that I was really good at it. And so I took a class and I stayed with it. Then I had the opportunity to go to Caltech to graduate school. I was introduced to people who were founding the department at that point. And at that point I learned about VLSI and which is Integrated Circuits, it's building ships. And so I loved it, but there were not many women around. I loved what I did, but I was always the only woman. So tell me, I'm gonna give you the last word for the people that were not familiar with the celebration. Why should they come next year? You said it's gonna be in Houston, it moves around. Give a little plug for the 15th annual celebration of women in computing. The Grace Hopper Celebration is a remarkable place for women in technology and for organizations that have a large technical workforce. You will find that it is life-changing, inspirational, and remarkable, it will change your life. Terrific, well thank you for taking a few moments out of your very busy day. I'm Jeff Frick, we're on the ground at the Grace Hopper Celebration for Women in Computing in Phoenix, Arizona at the Phoenix Convention Center. Thank you.


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We got green rookie wonder Franco AL East No bullshit came off Rookie auto Reese Gnare numbered to 299 for the NL West Reese Gnare, and we've got a blue Mike trout 10 at 25 AL West 25 on the trout Trouble that box right there. All right. What's the biggest trade that happened to you guys outside of Durant? What's there was the craziest one to you Outside of the Durant trade that happened today Cal Raleigh rookie. We got Boba Shet the AL East green and a Rosarina as well AL East silver ink rookie auto case hits NL West Tyler Gilbert 77 of 99 The silver ink is the case hit or golden could be sometimes the silver signings NL West Tyler Gilbert ready to the pads I'm trading some Victor to I don't know where I would trade some Victor green rookie Jackson co are AL central green rookie Josiah Gray and Elise She has them in Bogarts. You got a horizontal RPA AL West. It's Reed deadmers 38 to 50 Untradable sin. Are you going to the national this year? 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Thanks again everybody We are on to basketball for a little bit now


Stand by. My fellow Americans, we are now in our 56th month of economic growth, close to the longest peacetime expansion in our entire history. We've enjoyed low inflation and job creation that has captured the imagination of the world. Over 13 million jobs have come into existence. And contrary to what some critics of our administration have been suggesting, most of the jobs, over 60 percent of them, are in the higher paying occupations. Our country's in the middle of a great jump forward. In these last few years, many American companies have restructured, cut overhead, brought down costs and significantly improved quality. They've computerized their operations and invested in the most up-to-date technology. Last year, this innovation pushed manufacturing productivity in the United States ahead by three and a half percent, a greater increase than in any other major industrialized nation. Like the late 1970s, when our major corporations seemed to be lagging behind, today they're again pulling out in front. In the last decade, our most productive citizens, the ones we depend on to carry our flag in a highly competitive world market, had their investment capital taxed away and were hamstrung by well-meaning yet often intrusive regulation. High taxes and over-regulation were dragging us down. We've done our best in these last six and a half years to turn that situation around, and it's beginning to pay off. Federal tax rates are no longer increasing, draining even more resources out of the private sector into the bureaucracy. We've also kept under control the bureaucratic impulse to issue more and more regulations, mandates and edicts, telling us how to run our lives and businesses. We've done our best to free our economy and get government out of the way. In recent months, I've visited several companies like Harley Davidson in Pennsylvania and Dictophone Corporation in Florida. The confidence of the men and women who worked for these American corporations was inspiring. It reflects a mood in companies across this land. If you could meet them as I did, you'd be confident that American workers, if provided the tools and permitted to compete on a level playing field, can outproduce any rival and keep them made in the USA label something to be proud of. Lean, fast-moving and efficient American corporations are moving into the world market, and the latest figures suggest they are more than holding their own. In the last few months, we've seen an overall surge of American exports. In fact, from the third quarter of 1986 to the first quarter of 1987, exports were increasing at an annual rate of 14 percent, and imports were declining at an annual rate of almost 5 percent. In short, our country turned the corner on our trade deficit last fall, and the situation continues to improve. The increased competitiveness of American business, the positive adjustment that has occurred in the international exchange rates, the improvement of the economies of our trading partners, and our ongoing efforts to pry open any foreign markets closed to American goods, all of this has helped us meet the trade deficit challenge. Ironically, just at a time when we're making great progress, Congress is seriously considering legislation that could set us back. The last thing our economy needs now is congressional action that is behind the curve. In the proposed bill, Congress takes aim at a problem that is correcting itself. It's a little like closing the barn door when the horse is trying to get back in. If the Congress really wants to help solve the trade deficit, the single best thing it could do is cut the federal budget deficit. Now's the time to be talking about opening markets, not closing them, about expanding trade, not putting up roadblocks. What is called for now is hard work at the negotiating tables with our trading partners and innovative thinking. Well, that's just what we've been doing, especially concerning the international market in agriculture. This week, following through on an initiative we set in motion at the Tokyo Economic Summit last year, we proposed dramatic reform of the Free World's Agricultural Trading System. Our idea is to open world markets and, over a ten-year period, to end the costly subsidies and price controls that are a heavy weight tied around the necks of the Western economies. Free from this burden, everyone, including the farmers, will be better off. Trade, commerce, and competition are positive forces carrying mankind to new levels of prosperity. And as usual, Americans are leading the way. Until next week, thanks for listening, and God bless you.


Russians got order to capture Chassiv Yar by May 9th, Ukrainian forces fortified defence. Russian troops have been ordered to capture the town of Chassiv Yar in Denechsk Oblast by May 9th. Ukrainian armed forces are strengthening defence in this direction to contain the enemy's advance, according to the General Staff of the Armed Forces of Ukraine on Facebook. Chief of the General Staff of the Armed Forces of Ukraine, Oleksandr Sirsky, noted that the enemy is attempting to breach the defence west of Bakhmut to reach the Sivesky-Denech Donbas Channel. Capturing Chassiv Yar will create conditions for further enemy advancement towards the Kramatorsk agglomeration. Sirsky emphasised that Ukrainian brigades have dug in effectively. Indeed, the armed forces managed to destroy infantry groups that advanced into the Novii micro-district. Occupiers were eliminated by FPV Kamikaze strikes and artillery fire. However, the threat remains relevant, considering that the Russian military command has tasked its troops with capturing Chassiv Yar by May 9th, Sirsky noted. According to him, measures have been taken to significantly reinforce brigades with ammunition, drones and electronic warfare assets to strengthen our troops' defence in this direction. The main conclusion from the two-day work on the front line is the necessity to enhance the quality of training, including the moral psychological component, increase the number of high-tech unmanned systems of various purposes with trained operators, and improve the quality of conducting asymmetric actions to reduce the enemy's combat potential, added the chief. Overall, following the capture of Abdiivka, Russian forces continue to push further eastward in an attempt to break through the defence. One of the enemy's priorities is Chassiv Yar. The Ministry of Defence emphasised that the village of Bodanivka in the Bakhmut district remains under the control of the Ukrainian armed forces where heavy fighting is ongoing. The modernised Ukrainian uncrewed surface vessels can now deliver nearly a ton of explosives over more than 1,000 kilometres. This means that the Security Service of Ukraine can target practically any point in the Black Sea, Artem Dektyurenko, spokesperson for the Security Service of Ukraine said this. Dektyurenko did not disclose all the technical specifications but noted that these are next-generation drones, on the improvement of which experts from the Security Service of Ukraine, the Ministry of Internal Affairs and other brothers-in-arms are working together. He mentioned that the current sea-baby uncrewed surface vessel differs from the previous model in appearance and technical characteristics. In addition, it is capable of delivering almost a ton of explosives over more than 1,000 kilometres. Dektyurenko said there were no alternatives to the Security Service of Ukraine's attack surface vessels worldwide in 2022. Existing Western drones were large but not manoeuvrable, making them easily detectable by enemy's radar stations. Recall, in October 2022, uncrewed surface vessels of the Security Service of Ukraine attacked the Russian Black Sea fleet ships in Sevastopol Bay, damaging, in particular, the frigate Admiral Makaroviy.In 2023, uncrewed surface vessels of the Security Service of Ukraine struck the Khorvets-Sammem and Pavel Derzhaven, the tanker SIG, the landing ship Olinogorsky Gornjak, and damaged. The tugboat professor Nikolai Muru and the latest reconnaissance and hygrographic ship Vladimir Kozitsky.


Ergonomics has been very good for me. They allowed me to keep my job, stay with the same profession that I went to school for, and without them I would have had to change my whole profession. In my opinion this is a lot of better, a lot of better. Just through sheer repetition we've developed methods that have kept us from becoming injured. You want to come to work and do the job now because it's a lot easier and you don't have to worry about getting hurt. Ergonomics. Ergonomics is the scientific study of how the human body performs tasks in the workplace, fitting the job to the worker. The goal of ergonomics is to create jobs, tools, equipment and workplaces to fit the worker. It has been scientifically proven that ergonomics can actually reduce the risk of some types of injuries. These injuries are called work-related musculoskeletal disorders or WMSDs. There are many things that everyone does on the job and at home that could contribute to WMSD if they are done for long enough periods of time. Risk factors include working in awkward postures, using high hand force, performing repetitive motions, using your hand or knee to make repeated impacts, heavy, frequent or awkward lifting and exposure to moderate to high levels of vibration. Just because your job has risk factors doesn't mean that you're going to have a WMSD though. In fact a little bit of exposure to some risk factors can actually be good for you. Occasionally moving into awkward postures like reaching or bending will help to stretch and exercise your muscles. Whether or not a risk factor will result in a WMSD depends on the vibration, the frequency and the intensity of whatever it is you are doing. How long, how often and how much. The longer you're exposed to risk factors and here we're talking about hours per day, not just minutes, the more likely an injury will occur. You are also more likely to be injured if you have more than one risk factor at the same time. Now let's take a closer look at each risk factor. Awkward postures. To understand what an awkward posture is, it helps to understand the opposite. Good posture. A good posture is one that places the least amount of stress on your joints and muscles. This is referred to as neutral posture. It takes the strain out of your muscles and joints allowing them to work more efficiently. While neutral posture places the least stress on your body, it wouldn't be good for you to stay in that position all day. Your body was designed to move around and is much happier when it is active. Some parts of your job may require you to move into or maintain postures that aren't neutral.  Repeatedly moving in and out of this posture could lead to a shoulder or elbow WMSD. Holding your arms up overhead without bringing them down can also cause problems. Working with your neck bent forward too far can place strain on your neck muscles, especially if you hold this position for a long period of time. Your head can weigh as much as a bowling ball and that's a lot of weight for your neck muscles to hold up. Over time the muscles in your neck and shoulders can tighten up, resulting in chronic muscle soreness. Similarly, working while bent over places a lot of strain on the muscles of your back. The weight of your upper body is a lot for those muscles to hold up, especially since they were intended to hold you in an upright position. Bending over like this also increases the pressure on the discs of your spine. Squatting is a good alternative to bending at the waist, but only for short periods of time. If you squat for too long it builds up the pressure behind the kneecap and it can cause damage to the knee. Kneeling is another way to get down low, but it also causes pressure to build up behind the kneecap. Working with your wrist bent in any of these directions, backward, forward or sideways can also be a problem. However, bent wrists are only really a risk for injury when combined with high hand forces or repetitive motions, but more about that later. Some jobs will always require awkward postures, but many can be done better with a few simple fixes. Some things that might work include changing the height of a workstation or display, tilting or rotating work to a better position, standing on a platform to bring you up closer to the work, or putting your work on a platform to bring it up closer to you at bringing items within easy reach. Remember to pause to stretch once in a while if you do have to work in an awkward posture for any length of time. The amount of force required to grip something depends on a number of factors, but the most important thing is how you grip it. Gripping something with the whole hand, known as a power grip, is five times more powerful than gripping something with your fingertips, known as a pinch grip.   This increases your risk for injury, especially to the wrist and elbow. Other things can increase the amount of force needed to hold an object, such as if it's slippery, or if you're wearing loose-fitting gloves, or if your hands are exposed to the cold, any of which make it difficult to feel what you are gripping. One of the best ways to reduce grip force is to use power grips instead of pinch grips whenever possible. For example, picking up an object from the bottom using your whole hand. Attach handles to things or use lift tools. Another great idea is to build up the handles on small tools to reduce the grip force. There are several things you can do to reduce the force you use when handling objects. Pick up smaller loads. Use power tools instead of hand tools. Keep tools maintained to reduce the force required to operate them. Use lighter tools or tool balancers. Use two hands to cut the force per hand in half. And remember to keep your wrists straight. Grip forces are also a problem if you hold on to an object for a long period of time. You can avoid this by using clamps to hold on to your work, placing items on a cart rather than carrying them, and putting a tool down when you are not actually using it. Motions are considered highly repetitive when you use a part of your body to make the same motion over and over again without pauses. Most repetitive motions involve the hand, wrist, elbow, shoulder and neck. Making the same motion repeatedly can cause a lot of wear and tear on the joints. If you don't rest to allow time to heal, the damage can just keep building up. Repetitive motions may be required for your job. However, a lot of times you have some control over what motions you make and how often you make them. Things you can do to reduce repetitive motions include Arrange work to avoid unnecessary motions. Let power tools and machinery do the work. Spread repetitive work out during the day. Take pauses to stretch. Change hands or motions frequently. If possible, rotate jobs with coworkers. Intensive keying is the specific kind of repetitive motion. It involves highly repetitive movements of the fingers for a long duration. Four or more hours a day. Doing tasks like data entry or transcription. The repetitive movements of your fingers create a risk for hand and wrist injuries. However, intensive keying can be stressful for your whole body. Especially if you work in awkward postures as well. There are several things you can do to reduce risk of injury from intensive keying. Spread keyboard work throughout the day. Take pauses to stretch. Improve your posture and move around as much as possible. Repetitively using your knee as a hammer, such as this carpet layer is doing to stretch carpet using a knee kicker, can damage the soft tissues in the knee. God, that has got to hurt! Similarly, there are many soft tissues in the palm of your hand that are easily damaged when using the palm as a hammer. Fortunately, there are easy solutions to these risk factors. I was glad to find out that there are power stretches available for carpet layers that don't require a knee kicker. Tools like rubber mallets can be used in place of the palm in many cases. Most people are aware that lifting heavy objects increases the risk for injury. Fewer people know that repetitive lifting and lifting even moderate loads while bent over or reaching out can be just as hazardous. When you bend over to pick up something from below your knees, not only does your back have to lift the object, but it also has to lift the weight of your upper body. Something else to keep in mind. The same stresses are there when you lower something as when you lift it. Look for alternatives to lifting, including hand trucks, conveyors, carts, and other mechanical assistance. If these aren't available, get help from a co-worker. Avoid storing things on the floor unless you use a hand truck to move them. Store them on the surface between knee and waist level instead. Power tools can transmit vibration to the hands and arms. Now surprisingly, this has a number of effects on the body. If you're exposed to enough vibration, it can cause damage to the blood vessels and nerves in your hands and arms. Vibration also tends to make the muscles tighten up. The tighter you grip the tool, the more vibration gets transmitted to your hands and arms making injury more likely to occur. It takes quite a bit of vibration to actually cause an injury. But if you use a lot of power tools, you should take all the steps you can to reduce your exposure. Use low vibration tools if they are available. Keep your tools well maintained and keep your hands warm. This increases the blood flow and minimizes the damage that vibration can cause. Ergonomics. Remember, it's a tool you can use to make your job healthier and better. By applying ergonomics, risk factors can be reduced and WMSDs prevented. You are the expert when it comes to your job and you can play an important role in your company's ergonomics efforts. There are a lot of changes that you and your employer can make to the way that you do your job that will make it more enjoyable. And there's nothing wrong with that. Thanks for your time and attention.  Where did you get that cookie? Take me to the cookies. What do you mean that's the last one? Give me a bite. Come back here.


Now, growing up, when I was a lot younger, I was a huge wrestling fan in the WWF and WCW heavy. My favorite, all-time favorite, was the Undertaker. Whenever he would come out, whoever he would wrestle, I would always be cheering for him and rooting for him. But then, when he would be out for a long period of time due to injury or injury, then I would be like, oh man, he's out, he not gonna be at my favorite event, whether it's Royal Rumble, WrestleMania, Raw, whatever. He wasn't gonna be there for a little minute. But then, when he would come back, when you heard that gong, when you heard his music hit, when you heard them pyrotechnics and you saw all the smoke coming out, it was like, oh, let's go, he's back. And that's the same feeling now that it can be with Lamar Jackson. Since now he's been out for a period of time due to injury, but now he's expected to return tomorrow. So I know it's not gonna be all the music and it's not gonna be all the smoking, it's not gonna be all the pyrotechnics, but it's exciting knowing that the Raven starting quarterback is eligible to return tomorrow. Now, of course, he does have to go through the COVID protocol and whatnot. He still has to test negative and whatnot in order to be clear to return, but it's nice knowing that we are on the brink of Lamar being back. Now, hopefully, Hollywood and Miles Boykin, they can follow suit as well. And Sammy Watkins can return too to Friday's practice and they can all be back together. That can be a beautiful thing and I hope that's the case. But for Lamar Jackson to be returning, to just really reestablish himself with this Raven's offense, to really start getting that chemistry going with all of the guys, whether Sammy's there or not, whether Hollywood's there or not, whether Boykin is there or not, but with his rapport with Rashad Bateman, that's big because we know Bateman looks to have a significant role on this team. With him even getting stuff with Deionne Kane, with Benjamin Victor, with Tyler Wallace. See, Nana, I ain't forget. But with everybody who is out there, it's important that Lamar start really building this chemistry up because pre-season, it's gonna be here next week. I know we got the Dallas and Steelers game tonight and I know for me, just to be straight up, I'm probably gonna watch about, and I know we all miss football, but the Hall of Fame game, it's not the same. It ain't no disrespect to anybody playing in it, but it's just not the same. I'll probably watch like five minutes. I'll probably get a little excited hearing the music and whatnot and just seeing football on a TV screen and it's live, not watching an old YouTube video or highlights anything like that. But it'll be live, but I'll probably watch like five minutes of it and then get back to whatever I'm doing. But anyway, next week is the Raven's pre-season game. Now I do not expect the starters to play in there, but especially being a Raven's fan, you get super excited being able to see a lot of the depth guys be out there on the field, be playing and really, because we know a lot of these. We know pretty much all these guys. We know who's on the team and we just really wanna see these guys on the field because we've heard so much in training camp. We hear this and we hear that. We heard all the excitement. We heard some players maybe have not been looking so good, but when you get to actually see them on the field for pre-season, it's a beautiful thing because that means that you're that much closer to the regular season and this time this year, because last year we didn't get a pre-season, but this year we'll have a chance to evaluate guys a lot more, but more so the coaching staff will have a fair chance to evaluate guys a lot more. Now with them adding a 17th game and then removing one of the pre-season games, that has hurt and will hurt a lot of people. So that means during those three pre-season games, you whenever you get your shot, you are really going to have to give it your all.  So they may feel like they gotta press. But anyway, with Lamar Jackson returning, that it's gonna be good. It's gonna be good, but he's not the only guy that's expected to be joining the Ravens again. Well actually not even joining the Ravens again but making his debut with the Ravens. Justin Houston, he is also expected to join the team between Friday and Saturday. So Justin Houston being out there, that'll make the competition. That much better. That'll make everybody on that defense with the pass rush outside linebacker deal. That'll push everybody that much harder. Why? Because Justin Houston is gonna be out there. So he's going to take away reps from some people. Now you gotta split it up even more since you added number 48 there. And even though that's an ugly number, especially for DN, I think he'll probably change it once the roster gets slimmed down. But anyway, Justin Houston being out there is going to be a beautiful thing because he makes the team that much better. He provides that veteran leadership. And like I said in yesterday's video, the Ravens right now, these boys got a squad, man. They really got a squad, man. And they have such a good mix of youth, an injection of youth, but they also have a good veteran presence as well. They sure do. And I'm not one of those people. Oh man, wow. When you think about that, does it remind you of the 2012 Ravens? I'm not getting on all that because we said the same thing last year and then other people said the same thing in 2019. Oh man, do you see the similarities between these 2012 Ravens? No, these are the 2021 Ravens. Hopefully it ends the same way, the season ends the same way that it did in the 2012, 2013 year. Hopefully it does, but I'm not here to compare the two. But I hope that they have the same result. We all do. But anyway, this is a beautiful thing. So be excited. Get excited.  No, be hyped. Be excited. Be happy. I love y'all team keeping clean. I appreciate y'all. Lamar Jackson is gonna be making his return very, very soon. Could be tomorrow, could be Saturday, but it's going down. We out.


So I thought I'd shoot a quick update with the backfiring issue that I posted a video on about two days ago. I replaced the head gasket on this and because of the backfiring issue it actually caused the head gasket to blow. So my last video I posted issues with the throttle cable. So I since replaced the throttle cable, and that's all working properly, and one thing I missed, and that's something important to look at. You can't tell by looking at the car boot, let me show you here, look at the car boot, it all looks pretty decent, well I couldn't figure out why it was still backfiring until I saw this. If I grab this, there is a crack. I don't know if I can get that to focus in, right there. And it's sucking in air. If you get more air in with your fuel, it's going to cause a backfire. So I learned the hard way, because this is my second head gasket now that I replaced the backfiring caused the head gasket to blow. So I resurfaced the head, and I got myself a different car boot. Also while you're at it, check this out, make sure everything functions right, make sure these open and close. This one looks pretty good, and the inside of here looks good, because if that's not functioning right, and say one of these reeds are stuck open, that too is going to suck more air in. This atomizes the fuel, so if it's not atomized right, once again you'll be dumping too much fuel in. Okay, and here we have it, backfiring issues solved. Replaced the car boot, put a carburet build kit in, I've got my new throttle cable, and I'm going to start it up, and show you how it runs. Good to go, thanks for watching.


Okay yesterday we had discussed this result SB linearly independent subset of a vector space V and T be a spanning set also assume that SS finitely many elements as well as T SS U1 U2 etc Um and T is V1 V2 etc Vn then what we had shown yesterday was that m is less than or equal to n okay let us use this result and prove that any two bases for a finite dimensional vector space will have the same number of elements. So let us consider the following I want to prove this theorem that S and T be bases for a vector space V with S equal to U1 U2 etc Um and T equals V1 V2 etc Vn that is I have two finite sets that are bases for a vector space V then they must have the same number of elements that is the conclusion then m is equal to n okay two finite subsets of a vector space V if they satisfy the condition that they are bases for the vector space then they must have the same number of elements okay the proof will use this result that I stated just now. Now S is a basis so S is linearly independent S is a basis so it must be a spanning set as well as a linearly independent set S is linearly independent similarly T I will explore the fact that S is linearly independent and the fact that T is a spanning set by the above result it follows that m is less than or equal to n okay the next part is to reverse the roles of S and T S is a spanning set T is a linearly independent set the number of elements in T must be less than or equal to the number of elements of S. So let me just say similarly n is less than or equal to m and so m is equal to n so the number of elements in any finite basis the number of elements in any two finite bases is the same okay so this leads to the definition of the dimension let V be a vector space with a finite basis the dimension of V is the number of elements in any basis of V. So this is a definition of the dimension of a vector space this number is unique by the previous theorem this number is unique and so this notion is well defined okay if V does not have a finite basis if V does not have a finite basis then V is said to be infinite dimensional if V does not have a finite basis then V is said to be infinite dimensional. Look at the trivial vector space V equal to 0 is 0 dimensional okay the only vector space which is 0 dimensional this is the trivial space single term 0 so remember it cannot be one dimensional because if it is one dimensional then the basis will have precisely one element and this one vector cannot be 0 because it must be linearly independent and so this cannot be one dimension it is 0 dimensional okay. Let us then look at familiar examples of vector spaces that we have seen before and determine their dimensions examples the first one is R n for R n we had written down the standard basis in the last lecture I will call this B, B is E 1, E 2, etc E n where E 1, E 2, etc E n are the vectors that were defined in the last lecture this is a basis this is a basis for R n and it is called the standard basis of R n this is called the standard basis of R n okay. Example 2 let us look at the space of polynomials of degree k for this look at the collection P 0, T 1, etc P k where this was also defined before where P i of T is T to the i 0 less than or equal to i less than or equal to k T is a real variable so this set of polynomials they are k in number this set is a basis and so the dimension of P k is k plus 1 there are k plus 1 vectors in that basis okay. What is the dimension of C 0 1, C 0 1 is a space of all complex valued continuous functions on the interval 0 1 what is the dimension of this space this is infinite dimension what is the argument for that this is infinite dimension see the reason is as follows let us take the polynomials that we have defined earlier define P 0, P 1, etc by P i of T equals T to the i this time T varies in 0 1 define this polynomial that is 1 T, T square, etc now this is an infinite subset consider P 0, P 1, P 2, etc P k, etc this is an infinite subset I am claiming that this infinite subset is linearly independent now we have seen this definition yesterday that an infinite subset is linearly independent if and only if every finite subset of it is linearly independent okay. So we need to show that every finite subset of this is linearly independent but is that something that we have proved before take a finite subset okay let us say I have the polynomials 1 T square T power 100 let us say T power 1000 then can we show that this is linearly independent you look at a linear combination equate that to 0 differentiate as many times as you want show that the coefficients are 0 okay same idea that we used earlier can be used here to show that this is an infinite subset linearly independent subset this is linearly independent this is a linearly independent subset of C 0 1 every polynomial function is continuous so these are first members in C 0 1 now can you get a contradiction if there is a finite basis if there is a finite basis then the previous theorem would be contradicted so this cannot have a finite basis okay the number of if it is finite dimensional then the number of elements in any two basis any two basis will be the same but we have we need to use a lesser known fact which is if you have a linearly independent subset and a spanning set then the number of elements in the spanning set must be greater than or equal to number of number of elements in the spanning set must be greater than or equal to the number of elements in the linearly independent set that is clearly not possible here if it has a finite basis then this is clearly violated okay so there is no finite basis for this vector space okay I have given the reasoning fill up the details here if it has a finite basis then this would violate the inequality m less than or equal to n okay so this is an example of an infinite dimensional vectors let us also prove a few more consequences of the previous result let V be a finite dimensional vector space that is V has a finite basis let S be a subset of V then we have the following if S is linearly independent then the number of elements of S cannot exceed the dimension of V if S is linearly independent then the number of elements in S this is the cardinality of S that cannot exceed the dimension of V this stands for the dimension this notation will be used for denoting the dimension that is one property property 2 if dimension of V is less than the number of elements in any linearly independent subset in any subset S then S is linearly dependent okay you will immediately notice that statement B is a counter positive equivalence of statement A so statement B does not really need to be proved condition C if S is property C rather if S is linearly independent if S equals let us say U 1 U 2 etc U n with n denoting the dimension of V if this S is linearly independent that is I take a subset which is which has n elements where n is the dimension of the vector space then if it is linearly independent then it must be a spanning set then S is a spanning set of the vector space B okay a linearly independent subset having the same number of elements as any basis would have has to be a basis a linearly independent subset having the same number of elements as that of a basis of a finite vector space must be a basis okay that is property C okay proof the first one is something we have already proved okay you have to just put the framework there let us take dimension of V to be n this will be useful in part C also and write S as U 1 U 2 etc let us say V 1 V 2 etc V M then we have seen earlier that if S is linearly independent then the number of elements in S that is M that cannot exceed the number of elements in any basis of V M is less than or equal to the number of elements in any basis of V this we have seen before but what is the number of elements in any basis of V that is precisely n because any basis will have n elements since the dimension of V is n okay so this number is n so M is less than or equal to n that is condition A holds property A holds the number of elements in any linearly independent subset cannot exceed the dimension of the vector space B is the contrapositive equivalence so I will simply say B is equivalent to A no proof for that property C S is given to be U 1 U 2 etc U n where n is a dimension of V we must show that S is a spanning set suppose S is not a spanning set we will get a contradiction okay okay if span of S is not equal to V we want to show that S is a spanning set for the vector space V which means you must show that span of S is equal to V if span of S is not equal to V then there exists a vector let us call it X, X is in V such that X does not belong to span of S I have two sets which are not equal and one is contained in the other span of S is always contained in V that is a subspace in fact we have seen so one is a subset of the other but the two sets are not equal which means the superset has an element which does not belong to that subset there exists an X in V such that X does not belong to span S I will look at this set S union X okay include this X define a new set this has these elements U 1 U 2 etc U n and X now since X does not belong to span of S what it means is that X is not a linear combination of the preceding vector X is not a linear combination of U 1 U 2 etc U n so this is a linearly independent set this is linearly independent okay let us recall the argument if this set S union X were linearly dependent then there is at least one vector which is a linear combination of the preceding vectors now that cannot happen for U 1 U 2 etc U n because they are already linearly independent so the only possibility if this set is linearly independent is that this X is a linear combination of U 1 U 2 etc U n we know that is not possible because X does not belong to span V so this set must be linearly independent now this is linearly independent and the number of elements here is n plus 1 so that cannot exceed n but this is a greater number and so you have a contradiction and so this cannot happen that is X there is no X in V which does not belong to span V the number of elements in the set S union X this is n plus 1 this is greater than n which is the dimension of V this contradicts this is a contradiction to property A that we proved just now the number of elements in any linearly independent subset cannot exceed the dimension of the vector space this is a contradiction and so there exists no X in V such that X does not belong to span of S that is S is a spanning set of V that is S is a basis of the vector space V okay so you can this is what we say the dimension is the number of elements in any maximal linearly independent subset or the number of elements in any minimal spanning set okay let us now look at some examples of subspaces and determine their dimensions okay examples of subspaces their dimensions let us first look at R2 okay let us say I start with R3 consider R3 look at the following subspace the set of all X in R3 such that AX1 plus BX2 plus CX3 equals 0 for given constants ABC look at the collection of all X that satisfy this single condition what we know is that this is this is certain plane passing through the origin the constant term is 0 this is a plane passing through the origin we have verified earlier that this is a subspace okay let us determine its dimension let us determine the dimension of this subset that is a plane in R3 intuitively we know that the dimension must be 2 so let us prove that this as a basis considering of precisely 2 vectors okay okay without loss of generality let us assume that A is not 0 at least one of these constant must be non-zero okay this is a non degenerate plane non-trivial plane so take A to be non-zero then I can write X1 as minus B by AX2 minus C by AX3 remember I started with a single equation AX1 plus BX2 plus CX3 is 0 single equation in 3 unknowns X1, X2, X3 ABC are given constants so I can fix one of them and determine I can fix two of them determine one in terms of the other two so I have fixed X2 and X3 determining X1 in terms of X2 and X3 then any vector X in W can be written as X is X1, X2, X3 that is X1 is minus B by AX2 minus C by AX3, X2, X3 are arbitrary this can be rewritten as minus let us say X2 into minus B by A1, 0 plus X3 into minus C by A0, 1 so all that I have done is to write X as a linear combination of these two vectors let us call this as V1 this as V2 set V1 to be minus B by A1, 0 this time I am writing the vectors as row vectors set V1 to be this and V2 to be minus C by A0, 1 okay then what is the claim? The claim is that these two vectors form a basis for W so this must these two vectors must be linearly independent and they span W okay the fact that these two vectors span W has been demonstrated here any X and W can be written as a linear combination of V1 and V2 is that okay that is in this notation this is equal to X2 V1 plus X3 V2 I have written any X and W as a linear combination of V1 and V2 and so this is a spanning set these two span W is clear linear independence are they linearly independent one is not a multiple of the other so these are obviously linearly independent clearly V1, V2 are linearly independent and so I have a basis V1, V2 is a basis of the subspace W which is a plane passing through the origin so the dimension of any plane passing through the origin is 2, so dimension of W equals 2 okay we also prove the converse the converse is true if the dimension of a subspace is 2 then it must be a certain plane passing through the origin okay so let us prove that that is we are determining subspaces of dimension 2 precisely okay we are saying that in R3 if a subspace has dimension 2 then it must be a plane passing through the origin and what we have just now shown is that if it is a plane passing through the origin then its dimension is 2 okay so this is complete understanding of two dimensional subspaces of R3 okay so the converse is what I want to show next Firstly let us show that if W is a subspace of dimension 2, W is a plane passing through the origin okay so let us look at W and call a basis B of W consisting of elements u this be a basis of W I know that there are two elements because the dimension is 2 I must show that this W is a plane passing through the origin okay let us take X and W I will take an arbitrary point in W I will show that this arbitrary point satisfies the equation of a plane okay I will show that this point satisfies the equation of a plane so it follows that any point in W must lie on the plane and it will then follow that these two are the same okay let us look at okay before that let me write down X as a linear combination X is let us say alpha times u plus beta times v let me use coordinates u equal to u 1 u 2 u 3 v equals v 1 v 2 v 3 and X is equal to X 1 X 2 X 3 okay so I have X 1 X 2 X 3 equal to alpha times u 1 alpha u 2 alpha u 3 plus beta v 1 beta v 2 beta v 3 this is my X that is X 1 equals alpha u 1 plus beta v 1 X 2 equals alpha u 2 plus beta v 2 X 3 is alpha u 3 plus beta v 3 any X in V is a linear combination any X in W is a linear combination of the vectors u and v I have written down the expanded form of the coordinates of X of the components of X. Let me also define a new vector I will call that as a vector z let me define a new vector z to be the cross product of u and v z is a cross product of u and v remember that u and v are basis vectors so none of them is 0 none of them is 0 one is not a multiple of the other and so u cross v must be perpendicular to both u and v okay vector calculus z is perpendicular the vector z that we have defined is perpendicular to u and v then perpendicularity is what a dot b equal to 0 and for three dimensional vectors a dot b is the component wise multiplication and then addition a 1 b 1 plus a 2 b 2 plus a 3 b 3 so what I have is z dot u is 0 as well as z dot v that is z 1 u 1 plus z 2 u 2 plus z 3 u 3 this is 0 as well as the corresponding equation for z dot v equal to 0 z 1 v 1 plus z 2 v 2 plus z 3 v 3 this is 0 okay this z is perpendicular to u and v now u and v are plane vectors z is perpendicular to u and v we are in three dimensions we will show that X belongs to the plane generated by u and v so we will show that X is perpendicular to z we will show that X is perpendicular to z it would then follow that X must lie on the plane generated by u and v I will write down the equation of the plane explicit so the last step is to consider X dot z I will show that this is 0 X dot z is X 1 z 1 plus X 2 z 2 plus X 3 z 3 use the formulas for X 1 X 2 X 3 so let me write z 1 first z 1 into alpha u 1 plus beta v 1 alpha u 2 plus beta v 2 plus z 3 into alpha u 3 plus beta v 3 I have written down the formulas for X 1 X 2 X 3 in terms of the coordinates of components of u and v so this is take alpha outside z 1 u 1 plus alpha outside z 2 u 2 the last term alpha has been taken outside z 3 u 3 plus the other set of terms beta into z 1 v 1 plus z 2 v 2 plus z 3 v 3 but I have just now observed that these two numbers are 0 so this is 0 so X dot z is 0 that is expand the expanded form gives me X 1 z 1 plus X 2 z 2 plus X 3 z 3 equal to 0 where z is a fixed vector z 1 z 2 z 3 are fixed numbers they are fixed numbers because they come z is u cross v u and v are fixed the coordinates components of u and v are fixed so z is fixed that is the coordinates z 1 z 2 z 3 are fixed numbers so this is like A X 1 plus B X 2 plus C X 3 is 0 so X lies on a plane passing through the origin I have taken X as an arbitrary element here so any vector in W must lie on the plane passing through the origin okay so we have determined all subspaces of dimension 2 in R 3 okay so also look at the following result what are the possible the following result is motivated by this question what are the possible dimensions of any subspace of a finite dimensional vector space all integers lying between 0 excluded till the dimension of V okay intuitively that is clear let us prove it quickly a quick proof of this fact let W be a subspace of a finite dimensional vector space V then dimension W cannot exceed dimension of V dimension W cannot exceed dimension of V okay intuitively this is clear a subset cannot have a greater dimension than the superset proof is as follows let us take B to be a basis of W then B is linearly independent in W any basis must be a linearly independent spanning subset so this is linearly independent W but linear independence in W is the same as linear independence in V because it does not depend on anything that has got to do with W the only thing that I know is that the vectors are in W so this means that B is script B is a linearly independent in V but what we know is that any the number of elements in any linearly independent subset cannot exceed the dimension of the space okay so the number of elements in B cannot exceed the number of the cannot exceed the dimension of the space V but this number is the dimension of W that has dimension W is less than or equal to dimension V okay so that is an easy consequence okay let us now look at R3 and then list all the subspaces and their dimensions we will use this result consider the vector space R3 the dimension of R3 is 3 let W be a subspace of R3 then by the previous theorem what we know is that dimension of W equal to 0 1 or 2 it can be 3 also so let us say it is include that and then see what happens if it is equal to 3 dimension W is 0 1 2 or 3 dimension W equal to 0 this means W is singleton 0 0 dimensional 0 is the only vector space look at the other extreme dimension W is 3 okay in this case W equal to span of B where B has 3 elements okay let us say X Y Z if W has dimension 3 then it has 3 elements in any basis but now look at the result that we proved today if I have a linearly independent subset that has the same number of elements as dimension of the vector space then that must be a basis for that vector space if I have a linearly independent subset having the same number of elements as the dimension of the vector space then this must be a basis for that vector space okay using that result it follows that B is a basis for R3 follows that B is a basis for R3 okay but this means W is equal to R3 is that okay in this case W must be the whole of R3 yes 0 1 2 3 these are the four possibilities the dimension of the previous result says the dimension W does not exceed dimension B it can be equal so these are the yes 0 1 2 3 these are the four possibilities B has dimension 3 dimension is a non-negative number dimension is 0 1 2 etc up to dimension B dimension of R3 is 3 so it is from 0 to 3 0 is really trivial because the only vector space which has 0 as its dimension is a 0 space so that is anyway trivial but we must include it here it is a non-negative number it is a number of elements in a basis so it can be 0 so 0 should also be included even though it is trivial okay so these are the two extremes if the dimension is 0 then the subspace is a trivial subspace if the dimension is 3 the dimension of the original space then the subspace must be equal to R3 so we are left with these two possibilities dimension is 1 dimension is 2 dimension 2 we have disposed of dimension W equal to 2 we have disposed this means W is a plane a certain plane passing through the origin this we proved just now if dimension W is 2 then W is a certain plane passing through the origin so we are left with dimension W equal to 1 so what is your guess in that case it must be a certain line passing through the origin okay so let us dispose that off by giving a quick proof so we want to consider the case dimension W equals 1 let us first observe that let us first observe that if let us call something else let us call h let h be the set of all x in R3 such that let me first write down the set of all points lying on a certain line passing through the origin set of all x in R3 such that x1 is a times t x2 is b times t x3 is c times t where abc are given constants t varies in R abc are given constants t varies in R we have seen this before we have shown that this is a subspace okay now if x belongs to h then x1 by a equals x2 by b equals x3 by c that is this is a symmetric form of a line in R3 that is x lies on a certain line passing through passing through the origin that direction ratios are abc okay x lies on a line through the origin what is also clear is that if x is in h then x can be written as x1 x2 x3 that is equal to use these equations I will take t outside t times abc I will call it t times u where u is the vector whose components are abc okay now this is a non-trivial line so there are 3 constants abc at least one of them is not 0 so the vector u is not 0 a single vector non-zero linearly independent and what we have shown is that any x in h is a multiple of this any x is a linear combination of this and so this is a basis for h so dimension of h is 1 what we have shown is that if the collection of all points lying on any straight line passing through the origin that is a subspace of dimension 1 converse maybe I will leave it as an exercise if h is a subspace of R3 of dimension 1 so that h is precisely the set of all points lying on a certain line passing through the origin okay that is going to be an exercise for you it then follows that we have understood all one dimensional subspaces of R3 they are precisely lines passing through the origin okay let me stop here.


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My name's Keith Bannerman. I'm part of the Executive Committee of the Australasian Tunneling Society. We're a committee which is initially founded in 1974 as a joint venture between the Engineers Australia and the OZIMM, which is a mining organisation, which really highlights the, we cover both civil and mining aspects in the work that we do. The members are made up of contractors, clients, suppliers, academics from the entire region, the Australasian region, Australia and New Zealand. So it's not just purely engineers, but there are other professions involved. We're the peak industry for anyone digging a tunnel which is greater than a metre, up to 30 metres. So any hole excavated, someone from the ATS has been involved in some way, shape or form. The ATS also has a strong history of collaborating with regulators, whether it was through the generation of the tunnel encoded practice in New South Wales, or working with SafeWork Australia in the recent revision of the tunnel guide, which was 2013 revision. So we're a group of volunteers. We are a member of EA as a technical society. So last year we had our Triennial Tunneling Conference. I think we had about 1,500 people attend over the three days. Multiple parallel streams running across the three days of the tunneling conference, as well as tunnel visits to the M4 East and NorthConnex projects. As part of that discussion, the ATS initiated this working group. The working group brought together people from all of the major tunneling projects currently underway in Sydney, so Stage 1B, Stage 2, Sydney Metro and NorthConnex. It brought people from the client side, the contractor side, and people from even upstream. So we had RMS representatives in the room who wouldn't necessarily be involved in this sort of a project. So this sort of a working group isn't new for the tunneling industry. Internationally we're also affiliated with the ITA, the International Tunneling Association. They had their World Tunneling Congress last week in Dubai, which I was luckily enough to attend the response ship from the ATS. They have 14 working groups. One of those is a health and safety working group. So as part of that initial workshop, we asked a series of questions of the participants. The first one was how important is it that we address the issue of silicosis in tunneling. Some people were concerned what the results of this question might be. They had no need to be. The industry has a strong history of trying to work together and trying to address issues, whether they're technical or safety. There's always a very pragmatic approach from people who are involved in the tunneling industry. And why was it important? There's some great points that are put up there. So these are all by tunneling contractors and clients, highlighting why they believe it's important to deal with the issue of silicosis. And there were some pretty common themes through there that it's our problem. It's our industry we need to own the issue. And the next question that was asked was about engaging with the regulator. Again, ATS and the tunneling industry more broadly, often leads when it comes to this sort of initiative. Again, the question was asked how important do you think it is to collaborate with the regulator? Again, very strong correlation. So again, one being not important to engage, five being very important. So the makeup of this cohort included senior tunneling managers from all of the major projects and the health and safety representatives from the client organizations as well. And these are some of the reasons why the attendees believed it was important to engage. Mainly one of the key issues and it's been raised a few times is the technical understanding of is something better than something else. Each tunnel is different and I think that's important to highlight. Maybe there isn't a one-stop shop when it comes to solving the silica problem. So unfortunately, each tunnel is bespoke. It's its own machine, the way you build it's different. So you need to address those issues. Unfortunately, it makes it quite hard to unpack for those who aren't involved day-to-day in the tunneling industry. We're hoping that through the consultation of the ATS working group that we've established we can help drive what is best practice and share some of this great knowledge which has been developed in Sydney over the last 30 years. We've had a real uptick in the construction of tunnels in the Sydney basin. So some of the challenges that came out of that initial meeting, training and awareness, can't see silica. It's not always the easiest thing to convince people to wear a dust mask for extended periods of time. Engagement and collaboration across tunneling projects was a key initiative. A lot of the tunneling professionals work on various jobs throughout their working life. They collaborate informally, is often the case, but it was looking to formalise some of that interaction to spread some of that knowledge more broadly within the industry. The other one was to strengthen our standards legally and contractually. That's been talked about already. Improving the process of health surveillance. Everyone does it a little bit differently. So I suppose it was around identifying these, the SEGs so we can compare apples with apples across projects and time and highlighting the leadership of the importance of health in the tunneling industry. Some of the solutions that were also discussed, so leadership from the highest levels across these projects, as discussed it was a key goal for this working group to make sure that it was project team members who were involved in the discussions, not necessarily corporate types. Sometimes it was a disconnect and we wanted to make sure we got to the people who have the knowledge and the power to change things on site. Again, all key NSW projects were involved. And it was about developing practical standards through the development of whether it's the last revision of the Safe Work Australia guide for tunneling. The ATS has been pragmatic in highlighting some controls which haven't been practical or in fact impossible to achieve. So it's important to address and put forward solutions which are practical in nature. As well as developing training and awareness packages with the guys from Safe Work NSW and the other key stakeholders, whether it be Metro or any other major client delivery team. So the key areas of focus for the group going forward, so standardising practices across the industry where we can, understanding what is good practice, raising awareness. It's pretty simple but as we have more and more new entrants into the market putting on orange shirts, they need to know why do we have to wear dust masks. And identifying key work tasks through this process. There's been some activities which you wouldn't necessarily assume would be high risk, but in fact turned out to be. The routine visits by the safety and health professionals has recently started. So actually getting into the nuts and bolts of defining the challenge that we have in the tunneling industry. One of the key ones though as well was sharing lessons learned on dust control between projects has been a really strong area of focus so far for the group without beating around the bush. There's a couple of multiple contractors that work in the Sydney Basin and they operate slightly differently. We're trying to understand what are the best practices for the contractor used to operate. What are the differences from another contractor? It's important to get that sort of collaboration in an open professional environment. So the key points, it's about the effective management of the work, health and safety risks and it relies on a collaborative approach from the entire sector. So throughout these discussions there's been a strong focus on the role that the client plays. It's important. The schedule challenges which we face on these projects have been highlighted multiple times and the impacts that they have in the delivery phase of projects. Engaging with the professional engineering community is also important. Making sure that those people who are doing design work understand how important it is to design something which doesn't create excess dust, minimising cross-sectional excavation, those sort of things. And also the industry groups such as the ATS are a great way to actually bring people together from multiple areas. I'm not sure if this level of engagement would have happened without an industry group like the ATS. It's just the collaborative, pragmatic attitude of tunnelers that we have in the industry. Thank you.