Hi, good afternoon. Welcome. I'm Lynne Brockington, a librarian here at West Vancouver Memorial Library. Welcome to coping in a time of change and uncertainty, moving from coping to growing. So we have with us today Dr. Marilyn Chotum. She is a registered psychologist with a private practice in West Vancouver. Since 1980, she has worked in community mental health, hospital, psychiatry, and addiction treatment programs. Marilyn sees individuals, couples, and families in her private practice, which is located in the professional building between Amica and Capilano care facility on Clyde Avenue near Park Royal. Dr. Chotum will be talking about coping skills for living in a time of uncertainty and how we can use stressful circumstances for a springboard for growth. So I'll just ask Dr. Chotum to come online now if she'd like to start your video. And I just want to mention to everyone that if you do have questions, she will be answering questions at the end and you can write just type them into the Q&A at the bottom of your screen. And we'll see them there. Thank you. Thank you, Marilyn, for coming and I'm I'm going to turn off my video and mute myself and you can start. Okay. Thank you, Lynn. So I'll just start by telling you a little story. When Lynn asked me to speak on this topic, I reflected on my own reaction to COVID-19 in March when everything shut down. Well, actually it started before March. It started in January and February. We were hearing about COVID and the dangers and how life threatening it was and I tend to get sick easily.  I'll get exposed to it.  So I wasn't afraid of dying so much as I was afraid of not having my affairs in order. So I contacted a lawyer and got went through, you know, figuring out a will and and the funny thing is we won't be signing that will until this Thursday. So if I had died, I wouldn't have done any good. Anyways, my next reaction after that initial not panic, but certainty that this is the end was discovering that I was really healthy and it felt good that I was protected. But changing to social distancing, working online and the deluge of new and often contradictory information through my sense of order to the winds. I felt like I had no ground under me and everything felt chaotic and I felt lost. It was very uncomfortable. Thought hard about what would bring back equilibrium. What did I need to feel grounded again? The answer for me was recreating routine. So since then, I started dressing for work and writing my bicycle to work to my office following my regular schedule as I always had. Even though I'm working online and could theoretically be working from home in my pajamas like other people. I continue to ride my bicycle every day, get out in nature, connect with friends and family. I'll be at a two meter distance or online. For the most part, it feels like nothing's really changed, although I'm well aware of my good fortune in the face of the losses and stresses that other people are experiencing. And I worry about our future. We're going to be paying for this for a while, unfortunately. So change and uncertainty are stressors that can cause physical and psychological symptoms. Then in turn, control. Stressors that can cause physical and psychological symptoms. Then in turn, can trigger habitual coping mechanisms that may be adaptive or maladaptive. Stability comes from predictable routines and routine attachments or stable attachments, sorry, as well as stable social networks. What happens when our networks, routines or situations change in profound ways? As in a divorce, loss of a family member or a pet. Or as in our current pandemic. We are living in a time of enormous upheaval with COVID-19 and other world concerns. Such as troubling political systems, elections, systemic racism, global economic concerns, climate change, and please add anything I've forgotten. With COVID-19, there are job losses, financial insecurity, health anxiety, loss of a loved one, or fear of losing a loved one, and potential loneliness from social isolation. If on top of these current global stressors, you are dealing with personal change and uncertainty too, you may be having trouble coping. Too much change and uncertainty all at once can overwhelm our coping capacities and cause symptoms like depression, anxiety, worsening OCD, obsessive compulsive disorder, worsening addictive behaviors, or physical symptoms like headaches and stomach aches, tension, trouble sleeping. So what tools will help us adapt and stabilize in the face of current and future periods of change and uncertainty? Thinking about your own situational stressors and what if any symptoms or reactions you may be having to them? Know that our symptoms are here to inform us. Rather than fighting them, begrudging them, or medicating them, let's reflect on what they're expressing or calling for. If we are hurting physically, is that an expression of emotional pain? Our bodies often feel our emotions, or we feel our emotions through our bodies. If so, labeling the emotion and what is causing it can lead to an understanding of what corrective action could be taken to bring relief. Everyone has different circumstances, a different character, and different needs. And there is no one size that fits all in terms of remedies, but there are recommendations which I'll give you later. So each of you will have your own reactions and needs in the face of your situational stressors. The challenge is to attune to our physical and emotional states, to find what they are communicating to us. This ability to self-attune takes time to develop, but necessity is the mother of invention and pain is the great motivator, if not the best. When we are better able to identify and meet our own needs, we are stronger and more resilient in the face of challenging and changing circumstances. Sometimes our suffering comes from our outlook or beliefs, that is the way we think about things. Can we reflect on the thoughts and assumptions that might be hurting us and change them? For example, if we assume that someone is purposely doing harm to us, we're going to react with hostility, probably, which can harm the relationship when the other person may be having a bad hair day that has nothing to do with us. Rather than making negative assumptions, keep an open mind, be curious, form hypotheses, and gather more information before you make a decision or take action. Another example of an outlook that can cause suffering is believing that you can't do things or that you are helpless. I always liked the children's story, the little engine that could, written in the 1930s. In the case of the little blue engine, she had never been over the mountaintop and knew she had to get the children to the other side. She knew she had the ability to accomplish the task, but wasn't sure she could actually do it until she said, with a smile and determination, I think I can, I think I can, I think I can, and she did. What a great message to anyone at any age. There are many forms of cognitive distortion that can be problematic. Think about some of the self-talk statements that go through your mind that work against you and have really no basis in reality. They're just subjective thoughts, like, I'm not smart enough, I'm not good enough, I'm not pretty enough. Other people have it easier than me. My life is hard. I think I'll go eat worms. In cognitive behavioral therapy, people replace negative self-talk with positive alternatives. Our habitual negative thoughts can harm us, but so can our habitual behaviors. For example, some people have worsening addictive behaviors or compulsions when they are stressed. We all have habitual learned ways of adapting to our circumstances. Whatever the current circumstances are, they offer an opportunity to become more self-aware and to better meet our own needs. When there's a will, there's a way. All change depends on motivation. If we're having an internal battle over doing the things that are good for us, we may not be ready for change. Getting alignment between our healthy selves and our unhealthy habits is key to success when dealing with compulsive, addictive behaviors. It's not about self-will. How do we get to that clarity? It can be through journal writing, mutual support groups, treatment, meditation, reflecting, but I think talking with another person is probably the most helpful. The challenge is to shine a light on the shadow side of ourselves, those parts of ourselves that we may be unaware of. Our defenses protect us from knowing our true feelings and thoughts. Consequently, we don't always know what we need because at some point in the past, it wasn't okay to have that need or to express it. We learn to repress our feelings and thoughts. Through meditation, journal writing, psychotherapy, you can become more self-aware and less ruled by the unconscious. Self-acceptance strengthens our sense of self as agent, you know, empowered to be in charge of our lives in the driver's seat. Curiosity and compassion, as I said before, for ourselves and others allows us to be less reactive, and all of the above processes lead to greater resilience, a reduction in symptoms, both physical and mental. Acceptance of subjective and objective truth can calm visceral and emotional reactivity. When we can identify what we are feeling and trace it to a trigger, we are in a position to change the outcome. Sometimes what needs changing is our way of perceiving or thinking about a circumstance, as I mentioned about earlier. What assumptions are we making? What evidence is there to support? Confirm our assumptions. Sometimes what needs changing is our behavior. What behaviors could we change to make things better? Lastly, can we listen to our own wisdom? What is your gut feeling or intuition telling you? Some people find praying gives them equanimity and insight. Others find meditation can calm their thoughts and allow insights to surface. Others find their meditation through exercise, long distance running, long distance cycling, the mind, quiet and insight surface. To recap, what are our symptoms calling attention to? How are we perceiving our situations? And what are the opportunities in our circumstances? We are creatures of habit because habits are efficient, and we don't need to reinvent the wheel for every new experience. Nevertheless, our habits may be ineffective or even self-defeating or destructive. We have both behavioral and mental habits. For example, people can habitually catastrophize their experiences, creating emotional roller coasters for themselves and those around them.  Other people may habitually withdraw or avoid, and others may rage, others may cry. It's how do we typically respond and is there an opportunity to improve? Coming back to the earlier question, what tools will help us adapt and stabilize in the face of current and future periods of change and uncertainty? Here are some stress management tools that can help. I'm calling them balancing tools. These are not in any order. They're not equally important or equally, you know, vertical. They're just a quantity of tools to put in your toolkit.  Spending time in nature, taking a walk in the woods, force bathing, can calm the nerves and give you a new perspective. Know your limits. If you're overwhelmed, narrow your focus, prioritize and say no to what isn't a priority. For example, ignore non-essential emails, unsubscribe from solicitous emails that come advertising stuff every day that you don't need and they clutter your inbox. Turn the news off if it's overwhelming you. Not everything is equally important and you can decide what is necessary to attend to, what can wait, and what can be deleted or ignored. Listen to your intuition. Create routines to the best of your ability, maintain or create predictable routines that are realistic for you, given your mental and physical capacities. But do keep putting one foot in front of the other, especially if you were having a depressive episode.  It can be like quicksand, so you don't want to go down with it. You want to put one foot in front of the other, do something, don't isolate, and just follow one foot after another. What often happens is as you get engaged in what's going on around you, it pulls you out of the depression to a win-win. Don't make any major life changes that are not essential until you can restore inner stability. Now the exception to this is if you've had a traumatic event in which case you may need to be close to loved ones who do not live nearby. Outlook changes. Change I can't to I can, or this is catastrophic to I have choices. Don't take assumptions as facts. They're feelings. They're subjective and they're often based on distorted perceptions and assumptions. Attitude of gratitude. Gratitude lifts our spirits. It makes us appreciative of what we have. Reflect on what you have rather than what you don't have and be grateful. Coping messages from the Alcoholics Anonymous. This too shall pass one day at a time and keep it simple. Meditation helps calm the mind and body so that you can think more clearly and problem solve more effectively. It is a process of learning to observe, consider and act rather than reacting to surface perceptions. It's taking the time to be still and observe. Thinking that we're all like icebergs. There's a visible part that's very small compared to the mass that's not visible. Which is another reason for being curious and compassionate with yourself and others that often we shoot on ourselves and the more we shoot on ourselves the more we rebel against the shoulds and that can keep addictions flying high. So it's becoming aware of that and saying, no I have choices. I don't have to do anything and I'll do what's important to me. Journal writing can help with self-attunement by writing out feelings and thoughts, dreams, observations or simply free associating on paper. This is different different from keeping a reporting diary of events that doesn't help you get in touch with Molo's feelings thoughts. Journal writing can be a way to gain insight into the elusive shadow. Exercise releases tension, helps reduce anxiety, improves mood and improves sleep quality. It also regulates appetite for people who may eat compulsively. Regular cardiovascular workouts create a natural high from end orphan production in the brain and these become healthy addictions unless you overdo it. It's always keeping things in balance. Regular balanced healthy meals, nurturing yourself nutritionally can improve your mood and energy. There's also a way of showing yourself that you care about yourself and we need that. We often rely too much on do other people care about us but if we don't care about us the caring of others may not we may not receive it too. Sleep routine, restorative sleep improves your mood and outlook. Have a regular nighttime sleep routine to unwind and prepare for surrendering and letting go of worries and responsibilities from the day or about tomorrow or worrying about the past present and future. Connections, if we think of ourselves as trees our attachments are the roots that keep us standing upright. Remember the people who love you and hold them close to your heart. Keep them in mind and reach out as you are able. If you are feeling socially isolated consider joining a group online or in person but do not isolate. Be curious and compassionate with yourself and others if you are hurting make it okay to say I'm hurting but then see what needs to change in order to stop hurting. If someone else is something that you feel hurt by be curious about why they might have done that was it intentional? Are they having a difficult moment? Know that everyone is struggling with something. Moderate your use of substances or commit to abstinence if you are unable to control the quantities you consume. Alcohol is not the only addiction but it's the most common one and alcohol is a depressant. It also worsens anxiety because it becomes like a fall skin when you stop drinking you become more anxious you're more sensitized to danger and any addiction is depressing. So get support if you were suffering from an addiction or addictive behaviors and I have a list of resources at the end for you. Change starts with awareness then choosing to do things consciously differently until the new practices become habits. Every day brings opportunities for growth instead of begrudging what is look for the opportunity in the circumstance. I used to begrudge headaches so painful why can't it stop and then I realized that when it stops I feel so good that I wouldn't know to feel that good if I hadn't been hurting. Now do that with winter which always brought me seasonal affective disorder and now I just distract myself and get through it and then I'm so grateful when the sun returns in the spring. If things were always good we would become desensitized and unappreciative of what we have so maybe think of the bad times as opportunities to enjoy more of the good times. If we are lucky life is more or less predictable but when change and uncertainty overwhelm us it is time to stop and reflect what are we feeling what are we thinking what are we doing and what are we needing and how are we going to meet that need. Sometimes it's asking someone for comfort and reassurance sometimes it's being kind comforting and reassuring to ourselves are we needing to clear the air with someone important to us are we needing to get involved in a group to reduce our sense of isolation would it be in person with social distancing and masks or online if we are unable to work in our normal job or career what are the ways are there to make money maybe it's time to go back to school or to study a new field or learn a new skill do we need to get professional help if so where and again I have a list for you that will be emailed to you I will I will end with two adages and an email message that I recently received and the first adage is the truth will set you free and the second is to thine own self be true listen to your feelings and symptoms what truth are they revealing and what is the opportunity in your circumstance and now this email is an example of how to reframe things into gratitude I am thankful for the wife who says that's hot dogs tonight honey because she's home with me and not out somewhere else for the husband I'm thankful for the husband who's on the sofa being a couch potato because he's home with me and not out at the bars I am thankful for the teenager who is complaining about doing dishes because it means she's at home and not on the streets I am thankful for the taxes I pay because it means I am employed I am thankful for the mess to clean after party because it means I have been surrounded by friends I am thankful for the clothes that fit a little too snug because it means I have enough to eat I am thankful for my shadow that watches me work because it means I am out in the sunshine I'm thankful for a lawn that needs mowing windows that need cleaning and gutters that need fixing because it means I have a home I am thankful for all the complaining I hear about the government because it means we have freedom of speech I am thankful for the parking spot I find at the end of the far far end of the parking lot because it means I am capable of walking and I have been blessed with transportation I am thankful for my huge eating bill because it means I am warm I am thankful for the lady behind me in church who sings off-key because it means I can hear I am thankful for the pile of laundry and ironing because it means I have clothes to wear I am thankful for weariness and aching muscles at the end of the day because it means I've been capable of working hard I'm thankful for the alarm that goes off in the early morning hours because it means I am alive and finally I'm thankful for too much email because it means I have friends who are thinking of me thank you for taking the time to listen to my talk and now I will answer questions great okay thanks thank you so much Marilyn that was great I I love that last email did someone send that to you yeah friend sent it it's come probably everyone will get it and do time yeah you know it's good because um I think of all of the sort of aspects of this last six months it if you do think about it you realize it does make you very appreciative of so many things we took for granted so that was great um I just I had a question just to kind of start you you mentioned as one of the tools for coping as um meditation and I'm just wondering do you have any suggestions for um tapes like um audiobook kind of um guides to meditation or I know there's um John is it John Kabat Zinn is that his name yeah yeah would you recommend him um I would recommend him I I use Headspace which is an app oh okay and I'm going to put that in the chat so Headspace yeah it's all one word all one word it's a the um the logo is a round orange circle okay and started by Andy Petticombe who I believe spent 27 years on an ashram in India um cutting meditation and um then went back to England and started this um it's very good it's excellent I like it um but there are many others there's calm and John Kabat Zinn is very good and I'm going to cover others online yeah I think I think that's the only one I've used is John Kabat Zinn I just read his book you know he wrote but sometimes I think at some point you want to get beyond that and right now it's kind of hard to find a meditation class so it's going to have to be something online or or a tape that you listen to yeah Tara Brock is a psychologist who also does a lot of meditation Ted talks and I'm pretty sure you could get an online okay great YouTube video of meditation with Tara Brock okay good all right I put those all in the chat so people can see that so um if anyone does have a question they can put it in the Q&A um the um tools that I mentioned that uh Marilyn went over I will be emailing to everybody so you'll be able to have a copy of that and you can look that over um yeah so I don't think that we have any questions okay yeah yeah um so thank you so much that was um that was great I really appreciate it I think um it just adds to our our um as you say the toolkit all the things that we need to be thinking about and it's just it's good to have a a check you know things yeah yeah especially right now with smoky skies it's been seems like we have added things to to be concerned about so that was good tips okay thanks very much Marilyn okay thank you then all right bye bye


Strategic Cybersecurity, Module 8, Cyber Conflict and the Law. Once you have completed the readings, lecture, activity, and assessment, you will be able to define use adbellum, articulate why international law has difficulties adjudicating cyber attacks. Welcome to Strategic Cybersecurity, Module 8. In the last module, we introduced some problems that the Internet poses to the concept of sovereignty, as it has been understood since the 400-year-old Treaty of Westphalia was signed. In this module, we cover some problems that cyber technology poses for international law. As you read in the Rosenweig text, two aspects of international law deal with the question of armed conflict, use adbellum, or the right to wage war, and use in bellow, or justice in war. That is, when and how can a country respond to an armed attack? These two concepts have been around for hundreds of years, but were created to be applicable to kinetic, not cyber warfare. Over the last decade, legal experts at the NATO Cooperative Defense Center in Tallinn, Estonia have attempted to codify how these legal concepts should be applied to cyber attacks. This is especially timely, given how common cyber attacks have become in our world. Perhaps the most recent and notorious example is the 2016 U.S. presidential election. Details continue to emerge about Russia's interference in our election, including the purchase of politically and racially polarizing ads on social media to sow discord among the public and possibly create political chaos. How do you think that the United States should respond to these provocations? Should Russian interference be considered a type of armed attack? If so, what should the U.S. response be? Whatever your views, the fact is that international law currently does not provide a cut and dried template on how to respond to such attacks, or even if these actions should be considered an attack. And, as Rosenweil notes, there is actually no international consensus on what constitutes an armed attack in the kinetic world, let alone the cyber world. For our purposes, the principle rule for use adbellum, or when countries may respond to force, is found in the United Nations Charter, Article 2, subparagraph 4, or the 2-4 rule. The 2-4 rule states that countries must refrain from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the purposes of the United Nations. In other words, except for highly specific circumstances, if one country wishes to use force on another for any reason, it must first gain a mandate that is permission from the United Nations Security Council. Barring such a mandate, the country may act in self-defense to stop an incursion by another state, but it may act only to a degree to effectively repel the incursion, nothing more. Additionally, although somewhat controversial, a country may use force to intervene in certain egregious humanitarian situations, but again, the United Nations strictly defines these situations and they are beyond the scope of this module. Not taking into account the United Nations rules regarding the conduct of war, Rosenweig notes that the US policymakers have adopted a view about cyberattacks that considers the amount of damage that they exact. Rosenweig states, for example, that the United States would not categorize another country's theft of sensitive information about a sophisticated fighter jet as a use of force. However, should that country conduct a cyberattack that results in physical damage to our power grid, this would be considered an armed attack. And as far as the United States is concerned, we would be allowed to respond in kind. Keep in mind, however, that unless the United States received a mandate or permission from the UN Security Council to use force, we would be in violation of international law as the rules currently stand. You should be realizing at this point that significant gray area exists with respect to cyber conflict and international law. Rosenweig notes that this situation is highly unsettling, stating that even though cyber war is now a reality, we have no idea what rules, if any, apply. The good news is that many international governmental and non-governmental entities have recognized this fact and have made an active effort to deal with the problem. We have a long way to go, but initiatives by international organizations, such as the initiative by the NATO Cooperative Defense Center mentioned earlier, are certainly a good start. Quiz question one. Which school of thought best describes how the United States views when a cyber attack would be tantamount to an armed attack? A. The U.S. strategy is to compare the damage caused by a cyber attack to that of a kinetic attack. If the former could have been caused by a kinetic attack in the past, then it is considered an armed attack. B. The U.S. strategy focuses on the scope and magnitude of how an attack or how much of an impact it had. According to this view, an attack on Wall Street could be considered an armed attack. C. The U.S. considers any attack on the nation's critical infrastructure, whether successful or unsuccessful, to be an armed attack. The answer is B. The U.S. strategy focuses on the scope and magnitude of an attack or how much of an impact it had. According to this view, an attack on Wall Street could be considered an armed attack. Quiz question two. True or false? Use adbellum may be best described as a set of legal criteria to be consulted to determine if a state is justified in engaging war. The answer is true. Quiz question three. Which of the following best captures why international law has difficulties adjudicating responses to cyber attacks? A. There is no international consensus on what constitutes a cyber attack. B. The United Nations has purposely refused to define the term cyber. C. Each nation has its own definition of the term cyber. D. Both Russia and China refuse to ratify the United Nations Treaty on cyber attacks. The answer is A. There is no international consensus on what constitutes a cyber attack. The activity for this module asks that you write a one-page reflection of your current views regarding how the United States should respond to the Russian interference in the 2016 presidential election. In your reflection, play devil's advocate and argue why your initial suggestion might not be legitimate or effective according to international laws governing conflict.


What I wanted to do next is connect this notion of cross product with normal vectors we had talked about before. It justifies rehearsing a little bit about our discussion of in-flats that we had talked about before. An in-flat or a coset or an affine set, there's a lot of different names for these things. But an in-flat, remember, an in-flat is a set of vectors in our vector space, which here is fn. It's a set of vectors in fn that looks just like fm. It'll just look like an isomorphic congruent copy of fm there. There's two ways of describing flats that we've talked about. There's one approach which we call the bottom-up approach. Excuse me. The bottom-up approach is about using m linearly independent spanning vectors. The key behind the bottom-up approach is we span to make our space right there. Like we saw previously, if we have two vectors, here's v1 and some other vector v2, if these things are independent, then they come together and form a span. These two vectors would form a plane. The plane is just a two-flat, of course, would give us every point you can reach using just these two vectors and it forms a plane. Excuse me again. We can describe that the plane are general flats by a vector equation here, where x on the left-hand side is our variable. A vector x would be formed by some particular vector on the plane or the flat, whatever it is, and then we have our spanners v1, v2, up to vn. We have these spanners. Those are all fixed. Our variables are going to be these parameters c1, c2, cm. These are coefficients and also x on the other side. These parameters are usually, this is what we mean when we talk about parametric equations. Parametric equations. This is one way of describing a flat. We use these parametric equations. That's this bottom-up approach. We just keep on adding. If we want a 12-dimensional flat, what we do is we add one spanning vector, then a second one, then a third one, then a fourth one, fifth one, all the way up to 12, each time making sure we add something that's linearly independent to what we had before. The top-down approach, on the other hand, we can take this situation by taking n minus m. That's the difference between the ambient dimension and the dimension of the flat here. We take the difference of n minus n linearly independent normal vectors, n1, n2, up to nn minus m. The critical thing here is that we are taking not spanners, but we're taking normal vectors this time. We don't define a vector equation. We get a system of scalar equations. Those scalar equations are going to look like this equation ni dot x minus x naught right here. This equals zero vector. I'm sorry, that's just zero scalar. This is what we mean by these scalar equations, which when expanded out will look like this bad boy right here. We can put it in this normal form. This time around, if we have our flat, like so, the idea is, can we describe the flat using normal vectors? Can we take vectors which are orthogonal, which are perpendicular to the space in question? If you're talking about a plane in three-dimensional space, then you need one vector to describe it. On the other hand, if your flat is like a line, then you're going to have to have two independent normal vectors to describe it. So maybe like one like this. Like for example, if you take the white line to be your x-axis, then we're taking the normal vectors, the z-axis and the y-axis to describe that line in terms of normal vectors there. All right, and so you can describe, the space using normal vectors by this linear equation right here. You take the normal vector dot x minus x-naught, and so the dot product, since they're orthogonal should be zero, and then you can derive a scalar equation from that. So that's just a rehearsal of those top, down, bottom, up approach to describing the same flat. And much of linear algebra is the process of transitioning from one representation to another. Like one representation we do all the time is we go from the top to the bottom, and how do we do that? So if you describe a flat using the top, down approach, the idea is it is this matrix equation a x equals b, which of course we can think of that as an augmented matrix, a augment b. And then we go about row reducing that thing, a will then turn into some echelon form u, and then we have some vector y right here, which is whatever the right hand side turned into. And so then from there, it's like, okay, if I wanna write the general solution to this, I look at this matrix u right here, and you're gonna calculate some basis, some basis for the null space of u, which of course is the same thing as the null space of a, since a and u are row equivalent. And then from this vector y, we pull out some particular vector x naught that's on the space right there. And so then you get this combination where x equals some x naught plus, c one times the first spanner, plus c two times the second spanner, and you continue on. This gives you the parametric equations for the solution set there. This one we've done to death. I don't wanna say much more about that right now. Well, what I wanna talk about is actually, how do we do, what happens if we start off with the bottom up approach and we wanna switch it to the top down? Did I never write top down here? Whoops. We wanna switch it to the top down approach. That is, what if we have an answer to the problem but we don't have the problem yet? If we have the parametric equations for some flat, can I come up with a system of linear equations that solves that? So in particular, we start off with this vector equation right here, x equals x naught plus c one, v one plus c two, v two all up to c of v in. So what we want is we wanna find an equation looks like ax equals b. So how do we find a? Well, the thing we know about a is that the null space of a, we know what its span is supposed to be because we have the bottom up approach, we know the spanners of this. So we know the basis, we have the basis for a's null space. Can we build a from that? Well, one thing to notice here is that the null space in the row space are related to each other. If we take the orthogonal complement of the null space, that gives us the row space of a. And so what we wanna do is we wanna look for a matrix b so that the row space of b is equal to the null space of a. And why we care about that is if we take, if we take the orthogonal complements of these things, that then gives us that the orthogonal compliment of the row space of b, which is none other than the null space of b, this would equal the row space of a, which of course is the orthogonal compliment of the null space of a, like so. So we're gonna look for a matrix b so that let me highlight it right here. We wanna find a matrix b so whose row space is equal to the null space of a. So we're gonna set up a matrix whose rows coincide with the spanners right here. And then from that, we can construct the normal vectors. I think this one might be a little bit better to explain via an example because we haven't done a whole lot of this so far. So let's say we are in R2 and we are looking for, we're in R2 and we're gonna construct a two-flat, aka a plane, a plane whose equation is given right here and we can specify those things a little bit. So we're looking for the equation x so that you get the vector one, two, three, four. So that's a vector that is on the flat, it's on the plane. Then you'll have some spanners there, s times the vector one, zero, zero, negative one plus t times the vector two, one, negative three, zero like so. So in a more expanded form, that's what this vector equation looks like right here. All right. And so what we wanna do is we wanna find a linear system of equations whose solution is, whose general solution is this right here. So we wanna find AX equals B so that this right here is your solution. All right. And so what I claim to do is we wanna build a matrix B whose row space is equal to the null space of the matrix A. So what we're gonna do is we're gonna take these two spanning vectors. We're gonna take U whose entries are one, zero, zero, negative one, that becomes the first row of B and then the second row is just the second vector V, two, one, negative three and zero right there. So that part's gonna be basically the exact same. And so you'll notice here, the way that we've set this thing up is that the rows of B span the null space of A. So we have that correspondence. That's what we wanna do. So then row reduce that matrix.  If you row reduce B, you're gonna get pivots in the first column and the second column and then the others are where they are. So you see that you're gonna get these two free variables, free variables showing up in the third and fourth column. So we can build a basis for the, we can build a basis for the null space of B. And if we do that, remember, we're gonna get a one in the three spot since there's gonna be one vector associated to the third variable. And then we're gonna get a one in the fourth spot because there's again, there's gonna be a spanning vector associated to the fourth variable, just free. And then looking at, of course, the first row right here, you take the negations, you're gonna get zero and one and then looking at the second row, you're gonna get three and two. So this gives us a basis for the null space of B. Now the significance of this is that the null space is orthogonal to the row space. And since the row space of B is the null space of A, then when we take the orthogonal complement of the row space of B, which we know how to do, this will give us the orthogonal complement to the null space of A, which is the row space of A. So this right here, this span, these two vectors span the row space of our matrix A right here. And so if that gives us the row space of A, right? We should be thinking of these as row vectors, right? We're gonna get that A is the matrix where we can plug in zero, three, one, zero, one, two, zero, one. That's the matrix one, or the matrix A, excuse me. So that's the first part, right? We're trying to find this matrix AX equals B. How do we figure out the B? Well, we could figure it out from here, but another approach that works really great here is that these vectors right here, you can think of as the normal vectors. So this is N, N1, this is N2. These are the normal vectors to the plane that we're trying to construct. And so what we can do is we're gonna take N1 dot, the vectors we started off with are spanning vectors. So we take U minus X naught, that equals zero. And then we're gonna take N2 dot V minus X naught, which gives us zero right here. And if we expand these things, we take the dot products here. You take N1, you're gonna get zero times. Remember, U, it can't see it on the screen right now, but U was the vector, we'll write it over here, just so we can remember it. U remember was the vector one, what was it again? One, zero, zero, negative one. And V was the vector two, one, negative three, zero. And then X naught was the vector one, two, three, four. That's a fun one to remember. Anyways, so if you use those, if you take the dot product of N1 with these things, you're gonna get zero times one minus one plus you're gonna get the second entry of N1, which is a three times zero minus two. Then we get one times zero minus three.  U was a negative one minus four, like so. And this should all equal zero. That one simplifies dramatically, of course. You're gonna end up with, oh, I'm sorry, what did I do here? I put in specific entries for U and V. We don't wanna do that already, I'm sorry. Ooh, JK everyone, the issue here is we already took care of the U and the V, we don't need that. We want X to be a generic vector, a generic vector for the plane. So we're gonna have an X1 right here, an X2 right here, an X3 right here, and then an X4 right here. And so when you simplify that equation, you're gonna end up with three X2 minus six plus X3 minus three is equal to zero. Setting the right hand side, moving all the constants to the right hand side, you get three X2 plus X3 equals a positive nine. And so this is gonna give us our first equation in our system of equations. You'll notice that the coefficients of the variables are exactly what we said they were gonna be before, zero, three, one, and zero, okay? And then so for the second one, what we wanna do is we wanna take end two dot X minus X naught, this should equal zero. And so end two, remember what it was, end two was one, two, zero, one. So you're gonna get one times X minus one. Plus two, and I should say this was X1, X2 minus two, and then the next entry was a zero, X3 minus three, plus the last entry of end two was a one, X4 minus four, this should all equal zero.  If we move all the constants to the other side, we get X1 plus two, X2 plus X4 equals, when we move everything to the other side, we should get a plus nine, like so. And so if we put all this together, if we take the two observations we made, because this would be our second equation right here, we now have a system of equations, which looks like three X2 plus X3 equals nine. And then we also have X1 plus two X2 plus X4, we'll put the plus right there, and that equals nine as well. So we found a linear system of equations whose solution said will be the plane in R4 that we had talked about before. And so what does this have to do with a cross product right here? Well, this problem itself doesn't. What we did is we know the spanning vectors for the flat and we're trying to find the normal vectors of the flat. And then we could describe the system using those normal vectors instead of the spanning vectors. I want you to be aware that if we're talking about a hyperplane, in the case of a hyperplane, so a hyperplane is when the dimension between the space and the flat is only difference by one. In a hyperplane situation, you only have to find one of these linear equations. Basically the determinant approach we talked about before could be used in particular in R3, we can use the cross product to do this exact same process. So consider we wanna find the equation of a plane in R3 that passes through the following three points. Well, pick one of the points to be your X naught. It really doesn't matter which one you pick. So I'm gonna try to pick the one which I think has easier coefficients. So I'm gonna take negative 101 as my X naught. Once you have X naught, your spanning vectors U will be by taking one of the other points and subtracting the X naught from it. So we take the one negative two, one, subtract X naught from it. So negative 101. That's pretty easy to do. Of course, we end up with two, negative two and zero. And then for V here, we do the same thing, but take the other vector three to zero. And then subtract from your X naught like so. And so we take that difference, we end up with a four, a two and a negative one. And so these give us our spanning vectors. So these vectors right here, these vectors right here give you your spanners. They give you the spanning vectors for the flat. What we wanna do to describe the plane, to find an equation for the plane, we need a scalar equation, we need to know the normal vector. So what normal vector can we use to describe these things? Well, if we're looking for normal vectors, we could do what we did on the previous example, or we could try to use cross products or determinants to find that normal vector. Our normal vector in is gonna be U cross V, like we said before. The cross product is equal to, it'll be orthogonal to the first two vectors. So we can calculate that as E one, E two, E three, one, negative two, one, and then three, two, zero, like so. We can calculate it in that fashion. Now, one little trick I wanna talk about when it comes to three determinants, this one shows up a lot, and I don't think we've talked about in this lecture series here, is we could cofactor, expand across the first column, that gives us the definition. We could try cofactoring across a different column, or row, right? We could do that once, since there is a zero after here, there's a little bit of benefit of doing that. And the fact that we have an E one, E two, E three, doesn't really change the fact that we can do those different rows or columns that we want to. But another way of sort of handling this three by three determinant, one that kind of mimics the two by two case, right? If you have A, B, C, D, we often draw these slashes and things like that. I wanna give you something that works a lot that for three by three determinants. If you take your matrix, and maybe this isn't the best example, maybe I'll do a short video to, I'll just do another video, and show you how to do that in just a second. But if we were to cofactor expand across this row, I mostly just wanna pause because I wanna finish up this lecture, so it doesn't get too long for everyone here. But if we cofactor expand, we're gonna get zero minus two times E one, we're gonna get minus zero minus three times E two, and then you're gonna get plus two plus six times E three. You'll notice when you think of this as determinants, we can get these calculations really quickly. And so you end up with the vector negative two, positive three and eight as our normal vector right there. Let's see, I think I made a miscalculation somewhere. Where did I do it? Negative two, yeah, there is a problem there. Apparently I went too fast. Did I write down my numbers correctly from before? Oh, I think I did, I did. I wrote down the wrong columns and determinant. Whoopsie-daisy, let me fix that. Sorry, I wrote down the points on the plane. I didn't write down the spanning vectors, which were these ones to the right over here. There goes my hope of trying to make this thing short. Two, negative two and zero, four, two and negative one. Let's try these again. So if we do the determinants this time, we end up with two minus zero times E one. And then we're gonna get minus negative two plus zero that time, E two. And then finally, we're gonna end up with four plus eight E three, like so. And so we end up with the vector two, two and 12, like so. All right, so this is our normal vector N. And so once we have the normal vector N, we then will take N dot X minus X naught, this should equal zero. And if we work through this thing, we end up with two times X minus, I guess it should be a plus one, shouldn't it? Because that was our X naught. Then we get two times Y minus X naught has a zero right there. And then finally we get plus 12 times Z minus one is equal zero. And so when you distribute things through, you get two X plus two Y plus 12 Z.  I can't help but notice everything in that and all the coefficients here are even. If you divide everything by two, you get the equation X plus Y plus six Z equals seven. And this then gives us, should I got seven right there? And in my notes, I got a five. Let me double check my arithmetic. Ooh, apparently this lecture's gone on too long since I'm making too many mistakes along the way. So let's see, we had a two. So when you distribute this over here, that's gonna be a negative two. Oh, that's a positive two, which when you switch it to the other side gives you a negative two. I'm good with that. And I'm good with that. There was zero right here. So you times that by two, you get nothing. And so then you get 12 when it goes right here. That should be 12 and one, that's just a 12.  Oh, I guess that's my issue there. I did two plus 12. Sorry about that. Probably people in the watching the video notice this much quicker than I did. But 12 take away two is a 10. And so then the, should have a five right here. All right. And so that gives us the equation for that plane in R three. And we calculate the normal vector using cross products. Do you have to use cross products to find normal vectors? Absolutely not. Can you? Sure, sure, it can be helpful. And so when you can, when you're in R three, feel free to use cross products or use determinants. Although I think the approach in the previous example probably works a little bit better in general here. So thanks for watching this video. It was a little bit of a long one this time. Sorry about that. But thanks for watching it anyways. If you have any questions, please post them in the comments below. I'll be happy to answer them. Feel free to subscribe and like this video if you like to see these things and want to see some more of them in the future. And I will see you next time. Bye everyone.


The Livermore Teen Academy, that's what I'll be talking about. Once again, I'm Nathan Brumley. I'm the supervising librarian for youth services with the Livermore Public Library. And I'll just be going over, well, quite in detail, actually, what it took to put this kind of program together. But let's just jump into what it was. So long story short is that the Livermore Teen Academy is a three-week program that is a combination of local government education and life skills classes, along with an internship at one of our city departments. The program goals were to help teens have a better understanding of local government, inspire them to become more engaged in their community, and help prepare them to become successful adults. This program fit in nicely with the Library Strategic Services Plan, where we had made it a goal to increase our outreach efforts to underserved groups in the communities. And teens in Livermore had been identified as one of these groups. What's more is the Livermore City Council set a goal to, and I quote, strengthen a sense of community and connection. And they specifically called out exploring alternative engagement and outreach approaches, including community academies that target high school students. Wow, it's like we paid attention. So recruiting for the program was pretty intensive. We require all of the applicants to submit a two-page application, which includes an interview if they move on from that point and return additional paperwork by a very strict deadline. To further intensify as teens to participate, because for those of us who work with teens, we know it can be difficult sometimes, we also had a $330 stipend for those who complete the program. And this was to encourage completion of the program as well as applying in all that good stuff. You can see it's pretty large on the flyer. And in later versions, I even moved that to the top. So there are a few limits on who can apply. Teens have to be entering their junior or senior year of high school and turning 16 by the first day of the program. They must also live and go to school in the vermore. The two-page application includes three short answer essay questions and requires teens to furnish a letter of recommendation that is written not by somebody they're related to. For many teens invited to interview, it was their very first interview ever. So nerves were pretty rattled when we got to them, but they did great. To help manage the number of interviews that we were doing, we also invited employees from other city departments to come and help us out because they could potentially influence who were they be getting at their department as well. So that worked pretty well as a carrot. Lastly, after working with our risk management and legal departments, we had two forms for those who were initially selected for the program that they needed to sign. Those were a waiver. And another was a program agreement that they would come to every single class and make up any work that they did miss if they missed something for whatever reason or they would not receive their stipend or any amount. So there's the application. You can tell I was desperate for a slide, so there it is. We begin our advertising for this program. It's a summer program. So we start in February. That's when all the marketing goes to the schools. And we make the application available right at that time. These aren't due until March. So they have plenty of time to get those letters of recommendations, be thoughtful about their essay questions, and research which city council or which city department they would like to intern at. I think you can all guess how much time they put into it and when I received the applications. So our interviews, we do these in April after that. Once we go through all the applications, anyone who submits a completed application and they're eligible will get an interview with us. This last year, we interviewed 2016's. And we were able to accept 15 into the program. It's just how many spaces we were able to do. One thing we really learned from these interviews is that outside of police, fire, and libraries, teens had no idea what we were doing at the local government level. So in the second year, I included a very brief description of all of our city departments along with the application. And that helped a little bit, but it still didn't help enough. So that tells me that the work that we're doing with this program is pretty important. So we finally make our selections of who's invited to the program in May. And everyone who interviews gets a letter letting them know either they're in the program, they're on the waiting list, or they're not accepted this year. And after that, we bury them in paperwork. No, it's just the forms. So the program is, like I said, three weeks long. We found that the best time to do this is the three weeks right after when school starts in June. Each day, the teens are with us for three hours, from 9 a.m. to 12 p.m. That way we don't have to worry about lunches or anything like that. And they're either reporting to the library for one of their class days or their internship site during that time. The format that was most popular with our internship coaches, with our fellow city employees, was the first week of the program is all just a one full class week. Then they're at their internship sites for Monday through Thursday for the second and third week. And then on Fridays, they're back at the library for their classes. Each participant receives a binder. It has information about how a city operates. They get our city's organization chart on there along with a very basic class schedule about what to expect each day and where they need to report. So now I'm going to run through our last activities, our last academies, class schedule, day by day. And so the first day of the program, teens received an overall city department overview by the director of our finance department. And then he really goes into the specifics of how city finance works, where our funding comes from, what's paid with what money, what a general fund is, that kind of thing. And then because we have them cornered, I can't get out, they're forced to take a library tour that includes a library scavenger hunt. And then they're subjected to a presentation on the different databases we offer, which I call that segment speed database thing. The second class day is our city bus tour. And so basically this is something that the city's done for new hires. Typically, they're just given a tour of the city in a bus. The director of community development is with them, and they can answer questions. They talk about the different buildings that are there already in the city. They talk about the different things going into the city. Of course, the teens, they really only cared about what restaurants were coming. And you should have heard the cheers when they heard that potentially a Chick-fil-A was going to be going on in a certain corner. So it's pretty funny. The bus tour also includes a few walking stops. So they stop at a small business incubator downtown. They stop at the water resources department and get a tour of their facilities there. And they also stop at the maintenance yard, where the place where they make the road signs was a real hit. An interesting quote that came out of this, we do feedback surveys at the end of every class day. And my favorite was, it was interesting, had fun, kind of weird touring a city I live in. But they all kind of came away with some interesting stuff. So the third class day brings in our city manager, and he gives a presentation on leadership skills, which is then followed up by a two-hour public speaking skills workshop. So pretty awesome. Let's see. All right. So the next day is a brief presentation on local elections by our city clerk. And then she'll run a mock city council meeting. The idea there is that if they participate in a mock city council meeting, then coming to a real thing and voicing their opinions becomes that much less intimidating, because then they know the format of everything. They know how much time they have to speak, and that anybody can speak. The teens then head over to the city hall for a tour there. And then they are given a day in the life of a firefighter kind of presentation. It was pretty funny to watch them try on the firefighting gear, because then the cameras came out and it was a selfie station all over right there. That brings us to the end of the first week. We closed out with a personal finance workshop, a presentation on information literacy and voting, and a tour of the police department. You can guess which one was the most popular, the policemen. Police just has the coolest stuff. And we also reserved the last portion of this day for them meeting their internship coaches. So following that, they are given a full day of resume and workshops on interview skills. They have a networking class with the Tri Valley One Stop. It's a career center in Livermore. And the final day of the program we spend talking about getting out into the community. So we have organizations present their volunteer opportunities. And then we kind of go around the table and talk about their goals for after the program. And that's typically a really powerful part of it. And they can share their goals if they want to. But it's great. If a teen does miss a class, I'll assign them a certain thing. But it's not going to be any easier than coming to a class day. For instance, one assignment was to read the city manager's budget report to the city council and then get write a report to me about that. So they really don't want to miss any dates. Yep, lots of city departments participated. We had out of nine departments, we had probably let's say eight of them participate. The only one who couldn't do it this year was FIRE. That was one of the things we learned was that there's no good time for all the departments to come and do this program. So sometimes you just got to move on. Other departments have them work on mostly on social media platforms. We're all trying to figure out how to market to teens. And that's what they did. And then we kind of did the same thing. We talked to them about reaching them. But we also had them do things like create flyers and a marketing plan, specifically targeting teens, that kind of thing. Let's see. So we also do a graduation ceremony. This is for anybody who completes the whole program. We try this two different ways. But the way I thought was best was a separate kind of ceremony, not attached to the last day of the program. This way it was in the evening, the following week they could plan to come. And then we found that a lot more of the parents and family members could attend it this way. The mayor was there too, of course. He gives a talk about volunteering and being involved in your community. He gives them their certificates. And I get to hand out the checks. So budget, our first year, we were able to do this with support from a PLP Innovation Grant. Thank you, PLP. We were figuring out a lot this year. So a lot more staff time was used. We offered some things that we thought we would need. But the second year we were able to shrink those costs quite a bit. I think we'll be able to do that again even next year. We decided not to do the bus passes again. We offered bus passes for those getting to the Civic Center. This didn't seem to be a major issue for a lot of them. And the bus routes really weren't very convenient anyway. So it wasn't really being taken full advantage of. So some of our challenges here. It's not a simple or straightforward program to start. We spent a lot of time talking to our HR department and legal for guidance on potential issues surrounding participating teens, mostly because of the stipend. That's what complicated things. We felt it was worth it, though. But that's where we got the requirement of they had to be 16 to start the program. And we had to increase our stipend from $300 to $330, just based on minimum wage, federal minimum wage, and the number of hours that they were in the program. Another challenge was how much face-to-face this program demands with your other city departments. And not to mention all the buy-in that's required to. But it really helped having the city manager totally on board with what we were doing. Shout out to Mark Roberts, yeah. And another challenge would be not every internship coach could spend the same amount of time with their interns or coming up with things for them to do. So the difference between taking on three interns and four, it was significant. I know because I did four the first year. Oh. So what we learned. We learned that teens do not have much knowledge about local government, but teens really did enjoy the experience and they want to know how to get involved. They want to be active in their internships and not just they don't just want to talk to people. They want to get hands-on experiences and feel like they're contributing. And after the program was over, most of them wanted to continue their relationship with the library as well. Thank you.


Now gunmen have killed no fewer than two policemen in Aqaibam on Saturday. It was gathered that the hoodlums who invaded Icono Police, the regional headquarters at Ibiako in Dok O'boe, around 3 a.m. burnt down five police vehicles and also injured the police woman on night duty. Now the police spoke expressing S.P. Odeco-McDonne and the chief press secretary to the chairman of Icono local government area, Nsizong Ntok, confirmed the incident. Ntok in a statement said the hoodlums even hoisted their flag at the police station. He said the council chairman has been making great efforts to ensure that normalcy was returned to the area and other parts of the local government area.


Ladies and gentlemen, the President of the United States. Now please, thank you very much. I hope you're enjoying your visit to the nation's capital, and I appreciate the opportunity to speak with you. Over these last six years, I've defended heavily on the American Legion. James Dean, Evelyn Starr, Dale Reno, they've all been indispensable in the fight for a strong and secure America. I'd just like to express to you and to the legionnaires around the country my deepest appreciation for being there when it counted. It's been an honor to serve with you. Sometimes I think they ought to issue a campaign ribbon for the Battle of the Potomac.  So I suddenly thought I can tell one that's before the war. Back in the 30s when there was a citizen military training program, and then every summer they'd have a couple of weeks of camp and a military maneuver or war game, and usually some brass from Washington would be invited to come out and lend prestige to it, and I was getting a commission in the Cavalry Reserve at Fort Des Moines at that time over at Fort Omaha with the summer affair and the battle and all, and we had horse cavalry then, and the commanding officer at Fort Omaha and the visiting general from Washington were standing there, and someone sent a young reserve lieutenant, horse-mounted, over with a message, and he went over with a splash. He came in there full speed, pulled up the horse. Horse must have had a sore mouth because it put on the brakes on all four feet, and he summer-salted right over the head of the horse, landed on his feet holding the reins and was facing the two generals. So he snapped a salute, and the general from Washington very slowly and deliberately as he returned the salute said to the commanding officer, does he always dismount like that? Well, seriously though, the Legion continues to play a vital role in this democratic system of ours. Six years ago we set out to make up for some of the foreign policy and national security shortcomings of the last decade. We shouldn't permit the memory of American weakness and the consequences of that weakness to fade. During the 1970s the defense budget shrank in real terms as we held back from building new weapons systems. Our Navy lost more ships than it did at Pearl Harbor. New equipment was scarce, spare parts were in short supply, and inflation ravaged the value of our military personnel's take-home pay. It was a weaker America, a safer America. During the latter half of the decade our alliances were strained almost to the breaking point. Soviet expansion was evident throughout the world and in Southeast Asia and Africa and yes in Central America. The Soviets rushed forward to expand their naval and other conventional capabilities and to put online a host of new missiles and other strategic systems. In fact, since 1970 the Soviets have invested $500 billion more than the United States in defense and built nearly three times as many strategic missiles. With that record in mind it's a bit difficult to take seriously those who suggest that we hold back now on the modernization of our forces, strategic or conventional, in order to elicit a positive response from our adversaries. Teddy Roosevelt reminded us long ago that the cry of the weakling counts for little in the move toward peace, but the call of a just man armed is potent. Well to put Teddy in modern terms, speak softly but keep the battleship Iowa close at hand. Since 1980 we've reactivated four battleships, purchased 124 new naval vessels, including two new carriers and 21 top of the line Aegis-class cruisers and destroyers. The Army has two new divisions. We bought over 2,500 tactical fighters and we've made certain there are ample spare parts not just for the planes but for all the weapons and equipment. One of our top priorities was to restore morale to those brave and dedicated citizens serving in our armed forces and to attract top quality individuals to the job of protecting our country.  They've answered the call and today we have the best bunch of young people in our armed forces that we've ever had, the highest percentage of high school graduates in our history, the highest percentage in the top intelligence bracket when they're being tested for various branches of the service or duties within the service. I know you agree with me that those kids will never let us down, so we better darn well see to it that this government, no matter what party is in power, never lets them down. I've gotten some letters sometimes that I just, they turned me inside out. Kid writes he's in a submarine. He writes and he says we may not have the biggest navy, we got the best. And you hear things like that. I was over on the parallel in Korea, the demilitarized zone over there and a young fellow standing up there in the cold and looking out over the no man's land to the other side. And he just turned to me and he said when you get home, he said tell him we're on the frontier of freedom, it happens every place. So often those who oppose defense spending don't think about it in human terms. Those youngsters out in the aircraft carriers and the submarines and destroyers, our army and air force personnel in Korea and Germany, the Marines in Okinawa and with the sixth fleet in the Mediterranean, they depend on us every bit as much as we depend on them. We made a promise that they'd have the first class equipment and weapons they need to do their job and come home safely. And the budget is not going to be balanced at the expense of their safety and America's security. You know back there in that 80 campaign, I campaigned an awful lot not on making speeches like this but on doing question and answer, even crowds that would number thousands. And invariably then, I would get a question that would be well all right, but if it comes to a choice of balancing the budget or rebuilding our defenses, which will come first. And every time I said I have no choice, rebuilding our defenses would come first and every time I said it to an American audience, they did what you were just doing, they applauded. Well, fulfilling that promise in this time of budget restraint means making certain that the maximum benefit is squeezed out of every dollar spent on defense. To accomplish this, we've put in motion one of the most aggressive campaigns against waste and fraud in the history of the Defense Department, aggressively following up on every lead. Many stories early in the administration know how they curdled my blood about procurement waste. You know those outrageously expensive bolts and wrenches and such were actually not stories of faults that were still existing. They were actually stories of our successful efforts to make corrections. We were the ones who found out those $400 hammers and so forth and got them corrected but somehow it never seemed to read that way. Well, we've continued this commitment. The Defense Department, for example, is doing even more to ensure that competitive bidding is brought into the procurement process and this year we're, for the first time, submitting a two-year defense budget. This will, we hope, replace the old year-by-year up-and-down approach, which has proven both wasteful and inefficient. We're also moving forward on changes mandated in last year's Goldwater-Nickels bill and reforms recommended by the Packard Commission. In short, defense management has been and continues to go through a dramatic period of revitalization. We take this job seriously because we know the truth of some other words that Teddy Roosevelt spoke. He said, if we're to be a really great people, we must strive in good faith to play a great part in the world. We cannot avoid meeting great issues. Well, this, of course, is even more true of us today and while such a burden is never easy or cheap, there are many reasons for optimism as we look ahead. A decade ago, freedom was in retreat and now with America's military strength rebuilt, our national confidence restored and our alliance has reinvigorated, there has been a dramatic turn in world affairs. It's significant that during these last six years, not one square inch of territory has been lost to communism, and one small country, Grenada, has been restored to the family of free nations. After that episode there, I made a trip down there to meet with all the Caribbean island nations heads of state. I tell you, after all those things we've heard about signs on the Wall of Yankee Go Home, it was wonderful to be in Grenada, going down the streets and seeing the welcome signs and a great big banner across the street come back and then when I met it was with almost half the population of the entire country gathered at a great outdoor rally and you knew we'd done well there. They like us. So if you're looking for someplace to go on a vacation, I could recommend it. Today clearly history is on the side of the free. In our own hemisphere we've witnessed an historic expansion of democracy. Ninety percent of the people of the Americas now live in democratic countries or countries in transition to democracy. And throughout the third world, the failure of socialism is becoming increasingly evident. Cuba's tyrant has taken to haranguing people for failures that are inherent in the system he's imposed on them. In Ethiopia it's becoming even more apparent that it is Marxism more than drought that brought such misery and the starvation to a runce-proud people. The despotism and atheism of communism have even spurred resistance movements that are threatening Soviet colonial regimes in Afghanistan, Angola, Cambodia and Nicaragua. It's both in our national interest and consistent with our traditions as a free people to assist these brave souls who are struggling for their freedom and national independence. That's especially true when it comes to those fighting Soviet bacteria in Central America. We must not and will not abandon them. You hear anyone any more talking about the danger of Nicaragua becoming a communist totalitarian state? Correct them. It is a communist totalitarian state, and we're helping the people that are trying to change that. General Douglas MacArthur, a leader I deeply respected, is said to have written that no man is entitled to the blessings of freedom unless he be vigilant in its preservation and vigorous in its defense. Well, it's all up to us now. We're the heirs of MacArthur, Pershing, Jefferson and Washington, and of those Americans who put their lives on the line from Bunker Hill to Bellowood, from Normandy to Quezon. We will be vigilant in the preservation of freedom and vigorous in its defense because we will not let down those who came before us or those who will follow. I thank you and your fellow legionnaires for all you're doing to meet this sacred responsibility. For the ladies present having referred to that rough and ready Teddy Roosevelt a couple of times, I think you ought to know that in that era there was no West Wing to the White House, East Wing, all the offices and the cabinet meetings and everything else took place there in the residence. And then one day Mrs. Roosevelt proved to be a match. She said to the President of the United States, if I'm going to raise six kids in this house, you're going to get your people out of here. And they did.  Thank you.