Hi everyone. Welcome again to a live broadcast of the Course in Miracles lessons here in 2023. And these are spontaneous shareings and sessions. Sometimes we have questions written in that we'll deal with and explain the practical application of the lesson as it pertains to a question that's been written in. And sometimes I'll pick a section from the text that will help expand our clarity around the practical application of the lesson of the day. So today's lesson is the 17th lesson of the book and this on the 17th day of 2023 in January here. Today's lesson from Jesus. Wow, we're in for a great release today. In 2017 from the workbook, Course in Miracles says, I see no neutral things. This idea is another step in the direction of identifying cause and effect as it really operates in the world. You see no neutral things because you have no neutral thoughts. It is always the thought that comes first, despite the temptation to believe that it is the other way around. We're going to come back to this. This is like a key to spiritual awakening. If you can just grasp this one idea that I just read in that sentence, you will save yourself thousands of years in the seeming karmic loop. Okay, I'll read it again because it's so good. It is always the thought that comes first, despite the temptation to believe that it is the other way around. This is not the way the world thinks, but you must learn that it is the way you think. If it were not so, perception would have no cause and would itself be the cause of reality. In this view of its highly invariable nature, this is hardly likely. Yes, perception is not the cause of reality. In applying today's idea, say to yourself with eyes open, I see no neutral things because I have no neutral thoughts. Then look about you resting your glance on each thing you note long enough to say, I do not see a neutral table because my thoughts about tables are not neutral. For example, you might say, I do not see a neutral wall because my thoughts about walls are not neutral. I do not see a neutral body because my thoughts about bodies are not neutral. As usual, it is essential to make no distinctions between what you believe to be animate or inanimate, pleasant or unpleasant. Regardless of what you may believe, you do not see anything that is really alive or really joyous. That is because you are unaware as yet of any thought that is really true and therefore really happy. That's a big one. This is where you start to really get humble. I have never seen anything with the five senses that is really happy or really true because I am unaware of any thought that is really true. Okay, it's humbling. This is humbling. This is mind training. Three or four specific practice periods are recommended and no less than three are required for maximum benefit even if you experience resistance. However, if you do, the length of practice period may be reduced to less than the minute or so that is otherwise recommended. Okay, we can just go back to that paragraph 3-2 there. It is essential to make no distinctions between what you believe to be animate or inanimate, pleasant or unpleasant. That's a pretty good reminder there. We may have watched movies and we think we know the difference between what's animated movie cartoons and what is a movie with real persons. Jesus is saying no. There's no difference between Mickey Mouse or Minnie Mouse and the body that you perceive to be yourself, the personality self. We don't have real characters and unreal characters because all of the characters of perception are projections of the mind, projections of the ego. Now you start to see, wow, this is a course in mind training. This isn't a course in just paying lip service to Jesus. I love you, Jesus. I'm going to follow you, Jesus. That's all beautiful when it's sincere and true, but you can't just repeat ritualistic prayers and ritualistic mantras and think that's going to take the place of mind training. What do we mean by mind training is that you have to start to realize, again, that you don't see anything. You don't perceive anything in the world that's neutral because none of the thoughts that are producing the perceptual world are neutral. Opinions are not neutral. Judgments are not neutral. Grievances are not neutral. When we have distinctions, you can say, well, I try to stay free of grievances, but I still believe there's a difference between animation and real life in the world. I still believe there's a difference between what's alive and what's dead. I still believe you can say, wait a minute, I think I can tell the difference between a healthy looking body and a sick looking body, and Jesus is saying, no, you can't. You can't tell the difference because you're reading the meaning into both. That's lesson number two of the workbook. I've given everything I see all the meaning that it has for me. So whatever you try to determine between what's pleasant and unpleasant, that's a judgment. Not in terms of how you feel, when you feel still and peaceful and relaxed, truly, truly, you have let go to the miracle. You're in the miracle, and it's not to say that miracles aren't possible. It's just to say that we need to look closely at this miracle idea because a lot of times there's associations with what a miracle looks like in form. And even Jesus, if you read the Bible and the New Testament, if you watch The Chosen, if you watch Jesus movies, you'll notice that sometimes after there's a raising of the dead or a removal of symptoms where somebody who was blind then could see or someone who was lame could walk. Those are talked about as the miracles of Jesus. And what we're going to go into today is what you think produces what you perceive. And this goes so deep into the mind training that we will start to approach today the idea that what you seem to do as a body comes from what you think. It seems in the human condition, in the sleeping mind, in the deceptive mind, it seems like you can control your body. You can control its weight. You can control its actions. You control what it does, what it doesn't do. And Jesus is going to say, let's start with this one here. I see no neutral things. I don't see any neutral bodies. And I think I can tell the difference between an active body and an inactive body.   And Jesus is really going to invoke the spirit of Albert Einstein and say, no, everything that you perceive in the cosmos is relative. There's nothing absolute. Truth is absolute. God is absolute. Oneness is absolute. Spirit is absolute. But nothing in time and space is absolute. It's all relative. And that's what we're getting at today with lesson number 17 in the workbook. He's pulling in Albert Einstein here right now to say, I see no neutral thoughts. I see no neutral things because I have no neutral thoughts. And Einstein would certainly say that the cosmos is definitely relative. He's actually proven it through his experiments. And Jesus is saying, yeah, let's get into some good cause and effect now. The reason the world is relative is because your consciousness is filled with relative thoughts, and you have no neutral thoughts. They're all, they're all judging positively or negatively because you don't know your real thoughts. You don't know the thoughts you think with God. I am spirit is a workbook lesson. I am as God created me is a workbook lesson. Those are, those are actually real thoughts. There's no perceptual component. I am spirit. There's no body in that. You perceive the flesh or you recognize the spirit. That which is born of the flesh is flesh. That which is born of the spirit of spirit right there from the Bible. And Jesus is saying, as long as you don't recognize that you have no neutral thoughts, every thought you think is either creating the extending the truth or it's multiplying illusions. We went over that yesterday. So what a beautiful lesson we have today. I see no neutral things. And let's go deeper into it. Let's really try to get much deeper into this because like I said, we're going light years ahead today. So let's, let's go back into the text of Course in Miracles. Let's go back to chapter two and section seven. And this section is called cause and effect. And if you want a little background story on how this section seven of chapter two came about, when the Course was being scribed by Helen Shuckman and taken down by and typed out by Bill Thedford, this was taking place in the years between 1965 and 1972. But there did come a point pretty early on where there was a point where Helen was very frightened because Ken Wabnick, her friend Ken was going on a trip and it was, it was going to be a trip in the mountains, I believe, to visit some nuns. And, and while he was gone, she was missing her friend and she was very afraid for his safety on this trip. And so Helen was very afraid and she basically prayed to Jesus and she basically was saying to Jesus, take my fear away. On the surface, that seems like a pretty reasonable prayer for Jesus. Jesus, please take my fear away. And Jesus' response was, I can't take your fear away because if I took your fear away, I would be interfering with the most basic law there is, which is the law of cause and effect. I can't intervene, Jesus told Helen. I can't intervene between your thoughts and their effects. That's why Jesus is saying in the Course, it's a Course in Mind Training. He's saying, I can't take fear away from your mind because you made it up. You believed in the ego and now I can teach you how to let go of the ego. And I can teach you how to choose a miracle in place of ego thoughts. I can teach you how to choose a miracle in a way to be aligned with God even temporarily, even just for a brief time, even for an instant. I can teach you how to use your mind to align with God in the miracle. And that's why he's teaching us to be miracle workers because this is a Course in Mind Training. This isn't a Course in trying to save the planet through doing things in form. This isn't a Course that's saying you can change the world through your actions. Basically, Jesus is saying what you do comes from what you think and what you think is where the problem is. You're thinking with the ego, you see? And therefore, to try to change the form is ridiculous because the form comes from it. We just read that in the lesson that the thought comes first even though it doesn't seem that way in the world. It seems in the world as a human being like things happen to you. And the more you practice the Mind Training, you actually start to see everything that you perceive is coming from your mind, from consciousness. And nothing's happening to you. Then you can start to realize why, oh my gosh, I'm not a victim. I just was thinking thoughts that God didn't create. And then I was perceiving images that God didn't create. And I was perceiving some of those images were doing bad things to some of those other images. Bodies doing things to bodies. They're seemingly physically, psychologically, all that stuff. The whole realm of victimization is based on the idea that there's causation in form. And Jesus is saying, no, no, your mind is causative. And your thoughts are causative. So you got to really watch your thoughts. Because if you don't watch your thoughts carefully enough, you're going to give into temptations of the world to perceive yourself unfairly treated, to perceive an external world that's doing things to your mind. There is no external world doing anything to your mind. The external world is a projection of thoughts in the mind. So this is advanced Mind Training. But we're going to jump now from Lesson 17. I see no neutral things. Let's just hop into chapter two, section seven, cause and effect. This is the section that Helen took down, scribed down from Jesus. Jesus is so practical. After Jesus, she had asked Jesus, can you take my fear away? And he basically said, no, I can't. Because we need to work with your thoughts. I can't intervene between your thoughts and their effects. It's like Jesus is saying, I'm the Christ. And so are you. But if I intervene and try to take away your fear, that would be just showing that you're helpless. But if I showed you were helpless, that wouldn't mean that you're the Christ. Our mind is the same mind. So the mind is powerful. The mind of Christ is our shared mind.  Just keep praying to me and I'll keep scooping your fear away and taking it out. No, he's saying, oh, no, no, we've got to get into some metaphysics. So even people who work with the Course for years don't really work with the Course. They don't understand the metaphysics. They don't understand what's going on with these thoughts. They just read the thought, read the lesson, and they go, oh, I don't know what he's talking about. But that's why we have a text to help make the workbook more understandable, because how are you going to practice something if you don't have a context for it? How are you going to go into a scientific laboratory if you haven't read your textbook and you haven't prepared for the experiment? The workbook lessons of the Course for Miracles are the experiment. But you have to understand what he's talking about in the text to make the workbook lessons more meaningful. It doesn't mean you can't use the lessons. You can always use the lessons. If you're guided to start the lessons first and not read the text, that's okay too. Whatever you feel your internal guidance is, but it's just to remember that the text helps make the lessons more meaningful. Before you get into the laboratory, read your textbook, and that helps you in your experiment. We are a mind transformation experiment that the workbook is all about. Cause and effect section seven of chapter two. You may still complain about fear, but you nevertheless persist in making yourself fearful. I have already indicated that you cannot ask me to release you from fear. I know it does not exist, but you do not. If I intervene between your thoughts and their results, I would be tampering with the basic law of cause and effect. The most fundamental law there is. I would hardly help you if I depreciated the power of your own thinking. This would be in direct opposition to the purpose of this course. I know a lot of you, there's so many spiritual teachers and sometimes spiritual teachers will equate the mind with the ego and dismiss the mind. But you can't dismiss the ego without exposing it and seeing that it's believed in and you have to dispel it by not believing it anymore. The problem is not the mind. The problem is the mind that believes in the ego and the mind is trying to think with the ego, which is trying to think against God and for nothing. Ego is a death wish. It's nothing. But if you think with it, then that's a split mind and some of the spiritual teachers that say, drop your mind, get out of your mind. There is no mind and everything. What they're really saying is ultimately, if you go into the presence of God's love, go into the present moment fully, then you are one with God and you're one with everything. But the ego is the belief in separation. The ego is the one who made up consciousness. So Jesus is the master. We're learning from the master. We don't have to try to mix and match a lot of different spiritualities and philosophies when the master is giving it to a straight. Wouldn't you rather learn from the one who transcended time and space? That's my kind of teacher.  It's a love not of this world. It is much more helpful to remind you that you do not guard your thoughts carefully enough. You may feel that at this point it would take a miracle to enable you to do this, which is perfectly true. It does take a miracle to watch our thoughts that carefully, to guard our mind, to protect our peace of mind by not giving into ego temptations. Yeah, you think that would take a miracle? Jesus is saying, yes, that's exactly right. And this is a course in miracles. You see the good news? This is a course in miracles. We're not here to give lip service to Jesus. We're here to let Jesus instruct us on how to train our minds and purify our hearts. We're not here to give lip service to Jesus. We're here to say, show me through my prayer, my willingness to be shown and show me and instruct me. Guide me in what to say and do. And if our thoughts produce our actions and our words, then what we're really saying when we say guide me, Jesus, guide me as a person, guide my behaviors, is we're really saying guide my mind to be in alignment with you, to be in alignment with the mind that is the mind in Christ Jesus, which is the mind that is inspired and lit up by the Holy Spirit. That's what we're asking for, because what we do comes from what we think and we need help practicing aligning our thoughts with God and not against our last two lessons. You know, I see no neutral things as 17 and 16 was I have no neutral thoughts. Jesus is beginning in the workbook to train us that our thoughts of consciousness that cross our mind throughout the day about people, places, things to pass the future. They're all relative because they're all egoic and we need help. He says, you are not used to miracle-minded thinking, but you can be trained to think that way. All miracle workers need that kind of training. Here we are, chapter 2, chapter 2 out of 31 chapters in the text. Already Jesus is calling us to be miracle workers and he's saying you can be trained to think that way. He wants people to think miracle-minded thoughts. He's going to ask us to be right-minded, not wrong-minded. He's going to teach us the difference between right-minded thoughts and wrong-minded thoughts. Right-minded thoughts, their thoughts in our mind, we're aware of them, and wrong-minded thoughts are thoughts that have the belief in external causation.  Remember when little children, we were saying that? The wrong-minded, we came to this world seemingly with wrong-minded thoughts. That's how you seem to leave heaven is with wrong-minded, egoic thoughts. They say in the Bible, the Satan was a fallen angel. Well, the fall is going from right-minded thinking to believing in wrong-minded thinking, believing in an external world, believing in external causation. That's wrong-minded. If you think you're sick and you're interpreting the way the body looks or how it feels and you're attributing it to something in the world, to germs, to viruses, to weather, to any manner of actions and diseases, to conflict, to war. On and on and on and on. It's all wrong-minded thinking. Jesus is saying, please be a miracle worker for me. Please line up your mind with my mind. He's saying, I'll instruct you on how to do it. All miracle workers need that kind of training. Now, here's the second paragraph. I cannot let you leave your mind unguarded or you will not be able to help me.  You asked any Christian and you said to him, if you gave your heart and your mind over to Satan, do you think that would be helpful for Jesus? They would say, no, that's not helpful. That's not what he wants. He's saying the same thing here. He's saying, I cannot let you leave your mind unguarded or you will not be able to help me. Miracle working entails a full realization of the power of thought in order to avoid miscreation. So you have to understand how powerful the mind is because the ego is the attempt to use the mind in ways that God did not create. Obviously, miscreation would be the misuse of the mind, misuse of the power of the mind. Otherwise, a miracle will be necessary to set the mind itself straight, a circular process that would not foster the time collapse for which the miracle was intended. The miracle worker must have a genuine respect for true cause and effect as a necessary condition for the miracle to occur. So we were looking at earlier and basically Jesus was telling us that it is always the thought that comes first, despite the temptation to believe that it is the other way around. This is not the way the world thinks, but you must learn that it is the way you think. And then he says, if it were not so, perception would have no cause and would itself be the cause of reality. So in the workbook, Jesus is referring back to his teachings in the text on cause and effect. And we're exploring some of those, the early aspects of that here in chapter two. Basically, again, to repeat it because the mind that believes in this world is so caught up in behaviors. What did they do? What did they say? Oh, no, what did they, what? They said that. They said that about me. You see, this is all based on form, form, form, as if somebody can say or do something to hurt somebody else's feeling. No, no, no, no, no. That I know it seems that way. I know you've watched a lot of soap operas, but I know, I know in these dramas, no. Actually, Jesus is saying, no, it's your thoughts alone that we must work with because it's your thoughts that either make you happy when you think with God or make you unhappy or pseudo happy will call it when you're thinking with the ego. And we have to release these wrong minded thoughts. We have to release the thoughts that are telling us that the world is causing us to be a certain way.   No, no, Jesus is saying, no, no, flip it around, flip it around. My wrong minded thoughts is where I experienced the illusion of pain. My right minded thoughts bring me back to God because they're in alignment with the light. The Holy Spirit would never ask you to experience pain. The Holy Spirit is the spirit of joy. The Holy Spirit's teaching is the curriculum of joy. The Holy Spirit is not sponsoring pain. The Holy Spirit does not sponsor suffering. These are all misinterpretations of the Bible, of the teachings of the Bible. God is not asking us to suffer. He's just saying, through Jesus and the Holy Spirit, he's saying, please follow the instructions and learn how to pray truly to purify your heart and to align with God and to think with God and then pain is gone. Never was if you are lined up with God. Doesn't that make common sense? It doesn't that seem logical from a divine logic perspective that you're not at the mercy of the world? Jesus said, be of good cheer. I've overcome the world. He says in the Course, when you line up with the Holy Spirit, there's nothing that can touch you. Nothing can affect your state of mind. Sounds like Victor Frankel, a man's search for meaning. It doesn't matter if your body seems to be in a concentration camp. Where is your mind? If your mind is lined up with God, you can be happy regardless of external circumstances. Your happiness is not circumstance dependent. Your joy is not circumstance dependent. Your joy is alignment with God dependent. That's the kind of dependency I want. There's a song called Addicted to Love. Well, let's say we retranslate addicted to love is I'm dependent on my alignment and thinking like God, thinking like Jesus, thinking like the Holy Spirit. I want to be dependent on that. That's what all the saints and mystics were up to, just becoming God dependent. Well, wait a minute. What about working jobs? It's better to be God dependent. Follow your guidance. What about government handouts? Better to be God dependent. Are you saying that if I change my thinking, the whole world I see will change? Yeah, in your perception, you'll see a different world. That's the way it goes. Okay, third paragraph. We'll just do one more paragraph. This is so juicy, but we're just going to do three paragraphs from the text today. Both miracles and fear come from thoughts. If you are not free to choose one, you would also not be free to choose the other. By choosing the miracle, you have rejected fear, if only temporarily. You have been fearful of everyone and everything. You are afraid of God, of me, and of yourself. You have misperceived or miscreated us and believe in what you have made. You would not have done this if you were not afraid of your own thoughts. Wow. Wow, that is like, he's just laying it on us today. You wouldn't have misperceived God. You wouldn't have misperceived Jesus. You wouldn't have misperceived Mary or the angels if you had not first misperceived with your own thoughts. You would not have done this if you were not afraid of your own thoughts, afraid of the power of the mind. The fearful must miscreate because they misperceive creation. And remember, creation is pure spirit. So when you send your misperceiving creation, your perceiving creation is having something to do with form. God is spirit. God creates in spirit. Christ is a pure idea in the mind of God. So it's a pure idea. And then everything that is perceived in form is part of this misperceiving creation. I created a great painting. No, you didn't. Spirit is the only creation. I created a great song. No, you didn't. You didn't. Wait a minute. What about Lenin McCarthy, George Harrison songwriters? No, only the creations of God are real. Nothing real can be threatened. Nothing unreal exists. Herein lies the peace of God. If this seems like too steep, well, do you want to be happy or not? That's what I'm saying. You've got to really question everything. Creation doesn't have anything to do with with perception. You know, if you really study these teachings that people say, well, there's other spin offs of a course of miracles. Don't even go there. I'm not interested in spin offs. These are the teachings. These are the teachings to be lived. These are the teachings to be applied. You don't need five different versions of the course. You don't need spin offs of the course. And all these different ways to interpret and misinterpret basically this is, he's given us the good stuff. He's given it to us. And he's basically saying, I want you to live this and practice this. Don't just try to make something else up inform. That's not the problem. It's the it's the thinking.  The cause and effect principle now becomes a real expediter, though only temporarily actually cause with a capital C is a term properly belonging to God. And his effect with a capital E is his son. This entails a set of cause and effect relationships totally different from those you introduce into miscreation. I've said it hundreds and hundreds of time, but there is only one prime cause and that is God. That's why we worship God because God is the cause. And Christ, I'm not talking about the man Jesus, which is the reflection, which is the pointer, but I'm saying Christ is the effect and God is the cause. And when Jesus said the father and I are one, he was speaking of a true cause effect relationship. God is the cause. And Christ is the effect. Even in that he will say in the course, even in that statement, I am the father or one, there's two parts because God is greater. Yes, God is spirit, Christ is spirit, but God created Christ and Christ didn't create God. So that's like, let's just have our true cause and effect relationship there that Christ is an effect of God. Okay. And now in this world, cause and effect with the ego is split off and turned around. So it seems like the world causes your mind to be upset. That's why we need workbook lessons. I'm never upset for the reason I think because the cost split off cause and effect is a mesmerism. It's a hypnotism. It's fiction. It's fantasy. It has no reality whatsoever. We've believed in a much ado about nothing that Shakespeare called it. And thankfully, Einstein and some nice quantum physicists started to turn things around and teach us that there was no world apart from our mind and our thoughts. Paul Davis, an Australian quantum physicist, wrote in one of his books years ago, there is no world. What? He said what? And then Jesus says the identical thing, same thing that Paul Davis, the quantum physicist says in his course in lesson 132, there is no world. Period. You know, exclamation point. So this entails a set of cause and effect relationships totally different from those you introduce into miscreation. The fundamental conflict in this world then is between creation and miscreation. All fear is implicit in the second and all love in the first. The conflict is therefore one between love and fear. So there it is. That's it. The fundamental conflict in this world then is between creation and miscreation. For the last 30, 35 years I've been going around and teaching God did not create a meaningless world. God did not create time and space. God did not create the cosmos because if God did create the cosmos, which is part of the old story, then you couldn't forgive it. You can't forgive something that God created. You can only forgive what the ego made up. You can only forgive the illusion. You can't forgive the truth. So when we're talking about truth, we're talking about spirit. We're talking about the eternal nature. Eternal life is truth. That's truth. That has nothing to do with forgiveness. You have to forgive the illusion to remember the truth. You have to forgive the error, the belief in sin. Sin is error. You have to forgive the error. That's what Jesus taught us to do. Overlook the error. See the truth. He saw the Christ in everyone that he met. He carried that light of God with him so that those that had faith in that light, their symptoms disappeared. They either rose up from the dead or the lame could walk, the blind could see. He cast out demons. He showed there was no order of difficulty in miracles. Just when everyone was starting to wonder, really, is there a limit on this miracle working? No. He goes to see his friend Lazarus who's been dead and in the grave in his grave and all he does is he says Lazarus come forth and Lazarus does. No order of difficulty in miracles, even if someone's been dead for days. There's no order of difficulty in miracles because perception is a result and not a cause. So this is how we release the conflict in our split mind. This is how we come back into alignment with God's love. We come back into alignment with our eternal nature by lining up with the Holy Spirit. And there are a lot of people who are practicing the course, students of the course, teachers of the course and so on and on and on. But actually that doesn't really matter either because that's all part of perception. And what Jesus is saying is the faulty perception of perceiving separate people, places, things, separate versions of the course, separate spirituality, separate avatars, separate mystics and saints. That's all part of fragmented perception. And Jesus is saying, let's be real clear, that fragmented perception is coming from these relative wrong-minded thoughts that basically you think you think. They aren't your real thoughts, but you think you think them so you think you see the world that they produce. And then when you go deep inside to what we'll call a revelatory experience is when the world disappears. The world disappears. This is a literal experience because it wasn't really there. It's not like, ooh, it's disappeared. What is it a magic trick? No, there is no world apart from what you think. And when you go into full alignment, full alignment with God, you go into the revelatory experience, which is just light, just abstract light. There's no perception in reality. So when you get a glimpse of reality, that's what we call a revelation in terms of the Course of Miracles or the Bible, revelatory experience. So, wow, we started off with the simple idea, I see no neutral things and I hope that little burst of joy that came through me, whatever was said, I hope it starts to touch your heart. I hope it inspires you to go back and read some of these things in the text. If you're doing these lessons and you go, what did he say? What does he mean? And you're having trouble practicing. Just practice very simply, as he asked us to, very gently, very simply. These are what the early lessons are about. He's now into transfer of training. Now he's saying, let's transfer what I've taught you and what you're beginning to grasp. Let's practice it. Let's put it into practice and then let's go into a direct experience. This is not about theory. This is not a theoretical course. It's not a course into play of ideas. It's a course in giving way and going into a direct experience of God's love, of God's joy, of God's happiness. Okay, thank you. Thank you all. I love you. We'll keep doing these spontaneous workbook lessons as long as the inspiration is there. Okay.


Hey everyone, welcome to this webinar on a greener cost-effective cloud with serverless WebAssembly. My name is Sohan Maheshwar. I'm a dev advocate at Fermion and with me is Kate. Kate. Hi everyone, my name is Kate. I am a software engineer here at Fermion. So today we are going to talk to you about a greener cost-effective cloud with serverless WebAssembly. Now if you're not familiar with the concept of either serverless or WebAssembly, well that's what we're here to talk to you about today. So first things first, let's actually talk about sustainability in tech and essentially the green software foundation has defined this term called software carbon intensity and how they define it is C per R. Now what C is? C is carbon and now this is a rate, right? It is not a finite or an entire value of the carbon intensity of your workload in the cloud but it is a rate of which this actually happens.  Now the carbon in itself, that formula can be expanded to O plus M per R, right? O stands for operational emissions. Now these are based on the emissions caused by the energy consumption of your workload and M is something called the embodied emissions and this essentially is the emissions of the hardware really needed to operate a software system such as the one that your workload is actually running. Now this is an important formula and an important thing because when it comes to sustainability in technology we have to have some metrics to really sort of determine whether your software is sustainable or not or whether over a period of time there is a reduction in the carbon footprint of your software. Why this actually is important? Well there's a recent study that showed that the software industry is responsible for about 3% of carbon emissions in the world which is actually equivalent to that of the airline industry. So it is a fairly large number and in today's terms with things like climate change, sustainability and tech plays such an important role. So today we're here to talk to you about how serverless and WebAssembly and both can help with making your workload a little more greener and cost effective as well. Now the Green Software Foundation actually defines three actions that you and me can take as people who create software to make your software a little bit more sustainable. The first one is energy efficiency which essentially means making your software use less electricity to perform the same function. The second one is hardware efficiency where you make your software use fewer physical resources i.e. hardware to perform the same function and the third one is something called carbon awareness where you're essentially time shifting or region shifting software computation that takes advantage of cleaner more renewable or lower carbon sources of electricity. What this essentially means is when you're choosing a cloud provider for instance if you choose something that's in the US the carbon and the sources of power for the data center in the US might actually differ to the ones in say a part of Asia. So just by shifting the region where your workload is deployed you can be more carbon or less carbon intensive and more carbon aware. Now the reason we are showing you this particular slide is that we want you to take a look at everything else after the slide in the lens of either any energy efficiency or hardware efficiency and we'll talk about how serverless WebAssembly would make you both energy efficient and hardware efficient. Now if you're curious about what WebAssembly actually is few things you need to know. One is then this is the boring answer it is just another bytecode format it's designed as a portable compilation target. Essentially what happened was sometime in the mid 2010s a bunch of companies got together and they came up with this portable format that could run in the browser. The idea was you could write code in any language it would compile to WebAssembly that would run in the browser. The idea also was you could write it and it would compile once and that compile program could run on any number of targets. Now this could be different architectures like ARM, Intel, whatever it could mean different OSs like Windows, Mac, Linux. It could also mean things like Kubernetes and cloud and all of that. So the idea really was to compile it once and then run that code anywhere. And you might hear me refer to this as wasm from time to time. It is just another name for it. So WebAssembly wasm they refer to essentially the same thing. So how does WebAssembly really work? Well you write code like I said in any language this could be in Python Rust TypeScript and there is this compiles to a wasm format. You will get a dot wasm file and this dot wasm file essentially can be run in any place that has a runtime that supports it. So in a sense quote unquote a virtual machine that can support a wasm runtime. And conceptually yes this can be similar to how the idea of a JVM or Java virtual machine ran. The one thing that you do need to know is it is security sandboxed by default unlike unlike the original idea for a JVM. So by default wasm files have a security sandbox which means that nothing can access it unless you give it explicit permissions to do so. Now the thing is all the idea behind WebAssembly was the fact that you could write it in multiple languages. It was a portable compilation target. It was security sandboxed. All of this made it really good for you to run it in the browser. But it also means it's actually great to run outside of the browser potentially on the server side. So in around I think 2018-19 there was this new thing called WASI that was developed which is WebAssembly system interface. For something to run in the browser you need access to things like files, operating system features and sockets and clocks and random number generators. This didn't exist prior to 2019 but once WASI actually was implemented you could actually run WebAssembly on the server side and this opened up a whole new world of possibilities because suddenly WebAssembly was independent of browsers. It didn't need a JavaScript API or a web API and WASI essentially extended WASM's sandboxing to include input-output. What this essentially means is when you run WebAssembly on the server side there are things that actually make it really effective. And these are the four things we think that make WebAssembly ideal for you to run it on the server side. The first one is binary size. And again with the lens of energy, efficiency and sustainability things like binary size make such a big difference when you're doing software at scale, when you're deploying software to like millions of users or to like thousands of applications. Reducing your binary size makes such a huge difference. And just to give you a benchmark a simple Rust Hello World written using WebAssembly is only about two MB. And if you compile it ahead of time to assembly level code, when you know what operating system and you know the details beforehand, you can actually reduce that to around 300 KB, which again is a very small file. If you extend that to SPIN, which is an open source framework for writing WebAssembly, you can do a simple HTTP API app with a 2.3 MB just in time compilation or a 1.1 MB ahead of time compilation. So again, really tiny, tiny binary sizes, which again is more energy efficient. The tradeoff is the startup time where the startup time is comparable with code that is compiled natively. In a recent benchmark, we saw that it's about only two and 2.3 X lower than a startup time for a native code. The other good thing is it's completely portable. So you can build the code once into a wasm file and run that anywhere. And that same build works across different operating systems and different platform architectures as well. And like I mentioned, the default security sandbox applies to any wasm app. So it is only a capability based security model where you explicitly have to give your app permissions for other files or anything to access it. So even if you're writing a HTTP API, you can say that only this particular URL or this particular HTTP API can access your particular Web Assembly component. Just to give you a visual comparison of how a WebAssembly file would look in comparison to say a Docker file, we did a benchmark where we took a simple Python Flask app. And this is what the Docker file looked like in terms of size. And this is what it looked like in terms of a spin app. And it is a fair difference. Essentially, we saw a difference from 23 MB to 550 kilobytes. And that is a significant difference, again, in the lens of being more energy efficient with writing your code. I can maybe just show you a quick demo of how spin would work. So I'm going to open my terminal here. Spin, like I said, is it is a developer tool for building WebAssembly, microservices and applications. It's hosted on GitHub. If you go to GitHub.com slash for me on slash spin, completely open source. So feel free to contribute and join in the discussions. I can show you a quick demo of how spin actually works. The developer experience basically boils down to three main commands. I can do a spin new. And essentially, this gives me a list of preexisting templates that I can use to get started very quickly. I can maybe just choose Rust. And as you can see, there are different languages that you can actually write code in. So I will choose Rust.  You can choose a path that would trigger this particular spin app. In this case, I'm just going to give it slash, which means any request to this app will trigger it. And yeah, let me just webinar demo. And this opens up my VS code. And I can just quickly show you how this looks. So essentially, every spin app has a manifest file, which mentions all the components that are in it. And it has source code. And I can actually say hello, CNCF here. And we can perhaps run the app. All I have to do is a spin build. I did say there were three commands. So this is sorry, I need to CD into the thing and just do spin build. And this essentially builds my app. And I'm going to use my third command, which is spin up, which will actually run it on localhost for me to test the app out. So as soon as this is built, I'm just going to do spin up. And oh, I already have something running on this. I'm just going to do it again. Spin up. And as you can see, I'm just going to open this in a browser window. Yeah, you can see it here. It says hello, CNCF. Right. And that was pretty much how spin works. And we can actually look at this file, which is, yeah, again, fairly small. You can see the source code. The wasm file is in the target folder here. I think it is in this folder right here. There we go. Oh, no, it's in the release folder, my bad. Yes, minus L. Yeah, you can see the dot wasm file is just about two MB, right. And again, looking at it in the length of being it more energy efficient, small binary size for our file. So we spoke about the WebAssembly side of things and why WebAssembly is ideal for serverless. Serverless in itself is both more energy efficient and hardware efficient and thereby also cost effective. And to talk to you a bit about that is Kate. Hi, everyone. So we just talked a little bit about WebAssembly. And so I want to take a couple steps back and talk about other ways that you've thought of packaging your applications or isolating your applications. So if we go back to the slide there, we can see that one way that we're really familiar with isolating your applications is virtual machines and virtual machines kind of initiated cloud computing. It started this concept of being able to have multiple applications on the same physical hardware. And the way it did that was by isolating the entire operating system. And with virtual machines, there was some amount of scalability. You were able to bring up a new virtual machine in a few minutes.  And this resulted in more monolithic types of applications that were isolated in their virtual machine and stayed there and contain and continue to preserve those physical hardware resources. Then we moved on to a new way of isolating our applications, which was containers. And this created a smaller, isolatable unit. And you would just package in your application along with its dependencies. And this created a situation where you could start up new instances of your application in a few seconds.  And now we've moved on to a WebAssembly world where it takes milliseconds to start. And you're able to isolate them in these small WebAssembly unit with linear memory isolation. And this creates a world where we can start up applications and instantaneously right when they're needed. And this comes into the world of serverless or functions as a service. And so if we go to the next slide, we can talk a little bit about what that serverless word means. So serverless can be one of two things in a way, it can be a type of application like I was just explaining, where it's short lived and event driven functions that happen upon a request, or it can also be thought of as a development development model, where you don't need to manage any servers, or any of the back end infrastructure, and therefore it is serverless. And these two definitions of a type of application and development model come together to describe functions as a service or fast, which you also may be familiar with that term. So whether you've heard of it in the form of fast or serverless, we're talking about the same thing. So why should I care about serverless? So we talked about it a little earlier, it's moving forward in that smaller isolatable unit that's faster and event driven. But also when we talk about serverless, we can talk about how with serverless, you can be more and more focused on your business logic. You don't need to think about all the infrastructure behind it, you just think about your business logic that you want to execute on a certain event. Beyond that, serverless leads to faster scaling, like you're saying, it can start instantly. And therefore, if you need to scale up the number of units you have, you can do that instantly. And then finally, you get a better utilization of hardware. So the more units that you can put on a machine, the better utilization you have of that hardware. And all that comes together to lead to cost savings, this wonderful piggy bank we have, and environmental benefits, like we were saying, it has two of those parts of our formula, it has operational emissions are reduced, because you're only running things when you need, and embodied emissions are reduced because you need less hardware to do more. So digging into that less hardware to do more. One way to achieve that is through greater multi tenancy. So multi tenancy is the concept of where you can have multiple independent applications and often independently owned, so they might be owned by different tenants as well, running in a shared environment. And what multi tenancy does is it brings the cost of running a system closer to the value that you get out of a system. So you can think of the value of a system as the long term average traffic of a system or long term average use of a system. And the cost of running a system is the peak use at any given time because your system needs to support the maximum load at any given moment, even though what people get out of the system is about the average amount that it's used over time. And a lot of in this idea of focusing on multi tenancy and the idea of bringing the peak closer to the average. There's a great blog by Mark Brooker that we've linked here if you want to kind of dive into that concept. So to kind of visualize this idea of bringing the cost of the system closer to the average use of the system or what you get out of that system, bringing that peak closer to the average, we generated some random numbers here in order to kind of simulate what this might look like. So basically what I did is I used a random number generator to generate a load between one and 10. And then I at the same time then plotted what was the sum of all those loads between one and 10, which is the yellow line or the uppermost line on the graph. And then what is the average? So we can see on these these graphs that you have two horizontally dotted lines. The top horizontal line is the peak use of the sum use of a system at any given point. And then the lower line is the average use of the system at any given time. And the goal is to bring these two lines as close to possible, so that the peak use and given time is as close to the average use at any given time. And you can see when we have two tenants or just two randomly used amounts that the peak in the average, the peak is about 1.7 times the amount of the average. However, when we throw two more tenants into the system, you can see that the use starts to balance out. We're seeing these peaks and these eddies kind of forming one line. And that's creating a situation where the peak and the average are closer together and the ratios only 1.26. So just this mock scenario shows that the more independent users you add to a system, the more likely they are to balance out to the point where that what you're getting out of the system is really close to the what what you're spending on a system or what you need to support in that system. And all this leads up to the idea of how can we get as many tenants on a system as possible. And so we talked about this briefly when we're talking about VMs versus containers versus WebAssembly. But to see this visually, we can see how you can think of each wave of cloud computing as also increasing multi-tenancy. We can have a few virtual machines on our hardware with virtual machine isolation. And we can have dozens of containers on one unit of hardware with containerization. And with WebAssembly, we can have thousands of applications, WebAssembly applications or WebAssembly functions on a single unit of hardware, because it has a higher level of multi-tenancy. And if you're looking at this image here, you may think that something is missing. And you might be familiar with micro VMs, which aimed to be the next wave of multi-tenancy beyond containers. And let's talk a little bit about micro VMs, or you may be most familiar with AWS's firecracker VMs. So when the firecracker team at AWS was conceptualizing the firecracker micro VM, they actually created a paper to kind of discuss the process that they went to went through. And it's called firecracker lightweight virtualization for serverless applications. And the firecracker team at AWS released that paper in 2020, firecracker micro VMs came out around in 2018. And basically what they walked through in this paper is how they went about defining what this ideal serverless unit would look like this unit that could be instantly started, instantly started up and achieve a high level of multi-tenancy. And they defined six areas, or six characteristics of an ideal serverless unit. And so I want to talk through each of these. And then maybe you'll recognize how WebAssembly could satisfy these as well. So first of all, an ideal serverless unit needs to be isolatable. So we've talked about that with VMs, they're isolatable with containers, they're isolatable and with WebAssembly, they're also sandbox. So the key thing to a serverless unit is that it needs to be able to run next to all these other applications and be fully isolated from it. You need to be able to support a high level of density on a single machine. So you could run thousands on a machine with minimal waste. So we're using all of those hardware resources. You want to have as near native to performance as possible. So you don't want the fact that you're isolating this unit to be too much of a detriment to its performance. You want it to be compatible. So if I am switching to serverless, that paradigm of application, I shouldn't need to change the way I build applications too much, I should be able to use my favorite libraries and use my same operating systems and platforms as I've always loved using. It should be fast switching. So this is the idea that I should be able to start, execute and bring down this function or the serverless unit as fast as possible. And that's part of the utilization of hardware. So I need to be able to run it and bring it down as fast as possible so that other applications are also able to get their share of resources and I'm not hogging them all. And then soft allocation. So this is the idea that you should be able to over commit your resources. So I should be able to schedule 1000 applications to a node under the assumption that even if the node can only handle, say 250 at once, the idea is that these applications are all independent enough that we can assume that only 250 are being used at once. And that also assumes that the other 750 are taking up very minimal resources when they're not being executed. So if we go to the next slide, we can then look at this comparison explicitly between Firecracker Micro VMs and WebAssembly. So the team at Firecracker made a unit that satisfied all these characteristics. And WebAssembly uniquely also satisfies all these characteristics, making it a very good serverless unit. Both of them are isolated, they have different mechanisms. So WebAssembly with its linear memory and capabilities based security that Sohan mentioned, and Firecracker Micro VMs with a virtual machine monitor and KVM. They both can support great density. The paper shows that they were able to support 1000 on a node. And so were we when we did stress testing, but one thing to note is with Web Assembly, we were able to do a lot more, or we were able to do just as much with a lot less resources. So in our load tests, we only had a 32 gigabyte RAM machine and only eight cores while they had a lot beefier machines when they were doing their tests. With performance, both of them are near native. And fast switching is another part where WebAssembly once again jumps ahead. So with a Firecracker Micro VM, it takes about 125 milliseconds to start, which is why oftentimes they'll do some prewarming to bring that down a little. While with WebAssembly, you don't need any prewarming and you're sometimes below one millisecond times and oftentimes around one, one to five milliseconds. Soft allocation, we didn't test that in our load testing that we did, but with Firecracker Micro VMs, they were able to oversubscribe or the hardware resources as they desired. And then compatibility. While Firecracker Micro VMs are limited to Linux and KVM, WebAssembly is OS and platform agnostic. However, library support is where it maybe takes a downfall is that these libraries need to support Wazze and more and more are. But there is still some limitations there. So we talked about the characteristics of an ideal serverless unit. So what we need to be built into the technology in order for us to want to adopt it or use it. But what makes a unit adoptable? What makes me as a developer want to use a completely different way of building my applications? And there's four things we can think of. One, it needs to be language agnostic. I shouldn't need to learn a different language or limit my language choice in order to use a new type of software. It should be cross platform.  It should be portable. So I need to be able to distribute my application from one location to another. And then finally, I should be having as good of a developer experience as possible. And what comes with a good developer experience is good tooling, a robust ecosystem of libraries ideally. It needs to be very debuggable and easy to test locally before I put it in my production environment. And we're seeing with WebAssembly more and more developer tooling coming out. And the portability really does make it so that there is an incredibly good developer experience for serverless that we haven't had in the past. So to kind of bring this in together, we wanted to show a demo of how we were able to create high levels of multi-tenancy with spin applications. And a lot of this came from we were building out a cloud and we wanted to know how many spin applications can we place on a single node in our cloud? How great of a unit is this WebAssembly unit? And so in this demo, I want to show how on my MacBook Pro here, and we prerecorded this, I basically set up for me on cloud, which is our environment for hosting spin applications. So what that entailed was a single node, nomad cluster, your typical cloud services, logging services, storage, networking, and spin. So spin is both a tool for creating applications, and it's also a runtime. So inside spin is the bosom time runtime, and that it will execute and isolate our WebAssembly applications. And then we deployed 500 spin applications to this one machine here. And in just 10 seconds, we brought up and down 10,000 instances or invocations of those spin applications to show how fast it's scaled up and scaled down. And we'll see CPU spike up and then immediately drop all the way back down to show how instantaneous the resource usage jumps and comes back down. So you can see here, this is the nomad portal brought up locally on my machine. And we have those cloud, those typical cloud services, you have traffic for networking, Bindle for application storage, which is specific to WebAssembly, journal for logging. And then you can see spin MT, which is our multi tenant spin. So this one spin binary that for executing all of our applications. And then we have spin garbage collection, which is basically just cleaning up your spin applications after you've deleted them, which is another way of removing any extra resources that aren't needed at the moment. And so I'm deploying 500 spin applications to our nomad cluster. So you can see now we have 500 nomad jobs and each one of these jobs basically just did these optimizations and that pre that head of time compilation that Sohan mentioned, to make sure that they have even faster startup times. So now we're looking at our resource portal usage portal for nomad, and we can see that we have CPU on the left and memory on the right. And CPU is pretty low right now, it's around like the 15% point. And just on the right, we have our terminal with the endpoints of all of our applications. So we can see that there were 500 and they're all in the format of an HTTP Rust application. And just the the URL and we can see that when we ping one, we expect a simple hello for me on we had hello CNCF earlier response. So for load testing, our cloud, we built our own load testing tool, we wanted to be able to hit a bunch of endpoints, which a lot of tools didn't support. But you can see that it has the same flags as many load testers you may be familiar with such as these. So we're here saying that we're having 25 concurrent users sending requests, and that each concurrent user is sending 400 requests. And then we're adding a point zero one second jitter here to throw off a little bit there. And total that it's going to send 10,000 requests, and it's going to send 10,000 requests to that 500 endpoints here. And you'll see a CPU now spiked to almost 90% here. And then now it's coming all the way back down in just that 10 second interval, we pinged in that actually it ended up being under six seconds. So 5.8 seconds, we pinged 10,000 in some requests to our 500 applications. So that just shows how fast WebAssembly is and how scalable we only used all that CPU when we needed, and it scaled up and down as we expected. So very dynamic, very fast, and very resource efficient. And so now I'm going to pass it off to Sohan again to talk about another resource that you can optimize with WebAssembly. Yeah, thanks, Kate. So I mentioned earlier in the talk about those two lenses to at which you can actually look at you know, being more looking at your software carbon intensity, which is being energy efficient, and being hardware efficient. So serverless AI inferencing is potentially one way to actually look at this as well. So AI is the talk of town. Everyone is talking about Generative AI and large language models.  So typically companies and programmers are renting powerful GPUs that are running in the cloud. And these are running for a longer period of time and requests are being made in terms of either inferencing or like image generation. Now, regardless of whether you make one request a month or like a million requests a month, these CPUs are actually running in the cloud for people to use. So another way of actually looking at this is to do this serverlessly as well. So instead of having GPU running in the cloud or, you know, running containers for a longer period of time, we were actually able to time slice a GPU that's running in the cloud and use it for AI inferencing. Because you know, a dedicated GPU in the cloud is both carbon intensive and it's low and it can be expensive. So how this works essentially is there is a time slicing and for any request, you can actually essentially make AI inferencing request to a large language model that's running in the cloud. And you will get, you know, whatever AI inferencing request you make. And we at Fermion, we actually built this along with a partner called Civo. Civo is a hardware partner and they essentially use a company called Deepgreen. Now what Deepgreen does is fairly it's it's quite interesting if you ask me. So they turn unwanted waste heat from one system into a desired warmth for another system. And what this means is they're using cloud GPUs and their actual GPUs are immersed in a particular kind of oil. You can see the image there and the heat from these GPUs are actually captured and they're transferred to other things that potentially need heat. Now this is a startup and they're actually in production right now. And they're using the heat from these CPUs to warm a swimming pool somewhere in or near London. So it's a very real world use case of using like an energy in this case heat from running something in a GPU to a place that actually needs warmth in this case, a swimming pool. And what essentially this could potentially unlock is AI inferencing that is actually carbon neutral. So when you make an inferencing request to a large language model, not only are you using serverless computing to be energy and hardware efficient, you're also transferring some of the heat generated from running that piece of hardware into something useful. Right. So the cost or the carbon intensity of that LLM request in itself could be either carbon neutral or very close to being carbon neutral. Right. So this is a great real world use case of how both serverless and WebAssembly came together, you know, to make software a little more greener. So we have thrown a lot of interesting and hopefully new, informative, you know, concepts at you today. For some resources, you can actually look at building your first WebAssembly app using spin. It's very easy to get started. Just go to github.com slash fermion slash spin. Also check out serverless AI inferencing fermion.com slash serverless AI. And if you're interested in reading more about carbon neutral AI inferencing, we also have a blog post that goes into the in depth, you know, the nerdy stuff around like GPUs and energy and cloud and all of that. So check that out. Anyway, that brings to us an end for this session. Please join us on our discord server. We have a discord. If you go to fermion.com slash blog slash fermion hyphen discord. Feel free to connect with both Kate and myself on LinkedIn and reach out to us if you have questions about serverless, what WebAssembly or software sustainability from Kate and myself. That's it. Thank you and have a good rest of the day. Bye.


So the boomtown effect is an idea that came out of the 1970s by a researcher in Gillette, Wyoming, who is observing what was happening in families in an area where there was rapid development of natural resources. And the idea is that a small community, an isolated rural community in which the extraction is happening, has a large influx of population that needs to work in that industry, whether they're there because of the specialized technical skills they bring or because they're looking for work in that industry. Population mushrooms, the community can't, doesn't have the capacity to respond to that population growth immediately. There's growing pains. And as a result, families break down. There's domestic violence. There's depression and other mental health issues. Substance abuse, crime, sort of all the social ills that are associated with that kind of development was documented then in that early development. That boomtown model is what we have started with when it came to shale development. So just trying to understand what happens when you have rapid growth in a community, particularly rural communities, we're here in the Marcellus. We've seen more of that kind of development. And trying to understand how communities adapt are affected and how families in particular and individuals are affected by that development.


living in a world that is more technologically advanced, more medically advanced, more connected than ever, we are the sickest, most depressed, suicidal, hopeless, despairing generation ever. So something's missing, something's happening, something's going on. It's beginning to fragment the edges. The information age got us to where we are, and we'll always have a part, of course, in our future. But the world, it started to break down and the fault lines, like the San Andreas Fault in California, the hairline cracks are appearing all across the globe, and people are starting to say, what is it that's going on? How come we are so advanced and yet we are so desperately needy of things that the advancement do not speak to? And I think my version of this coming age is called the age of human flourishing. That's my name for what's coming next.


So let's take a look at problem 3.5, and again, don't watch this video. Remember a main goal of our course is to develop your problem-solving opportunity, and you only ever have one opportunity to solve a problem. If somebody shows you how to solve the problem, you will never ever again have the opportunity to solve that type of problem. So this particular video explains how to solve the problem of finding zero minus five, but the instant that you finish it, forever after, anything similar is not going to be a problem. Zero minus eight. This is not a problem because you will know how to find it. And again, after you watch this video, you will never again have the opportunity to solve this problem of finding zero minus eight. And again, problem-solving opportunities are extremely rare, so you have to ask yourself, are you ready to lose forever an educational opportunity? Your education will be worse after you watch this video because you will have given up a portion of it. All right, so assuming that we're ready to give up a part of our education, let's go ahead and tackle this problem. So let's zero minus five equal x, and we want to find this zero minus five using our various properties and definitions. So let's take a look at that. So first off, our definition of subtraction, well, that's a subtraction. We go look up our definition of subtraction, and a subtraction says that any time I have a subtraction, I also have an addition. Our definition of subtraction tells us that this and this are tied together. So by the definition of subtraction, I know that zero minus five equals x is the same as zero is equal to x plus five. Well, now here's something that's worth noting. Again, pulling our definitions, I have the sum of two things gives me zero. Well, my definition of additive inverse says that if I have two things that add to zero, they have to be additive inverses of each other. So that tells me that x is equal to the additive inverse of five. x is negative five in common language. Now let's see if we can generalize that. Well, I can apply exactly the same logic to anything zero minus a. Zero minus a, whatever it is, well, that tells me that zero and x plus a have to be the same thing, and that means that I have to have the additive inverse of whatever a is. And so in general, when I look at zero minus a, it's got to be the additive inverse of a.