I think the winner got to start. Okay. Thank you for coming back. Thank you. Thank you. So we will just continue on carrying from where we left before the break. Actually during the break I was talking with a few people and Ronnie came to me and said, you know, I want the whole lot. I don't want just half truth. I want the whole lot. And that's exactly what we deserve. You know, when Jesus says in the book, there is no hierarchy of illusions. There is no difference in miracles. That's what we deserve. We deserve the eternal life. We deserve that. We deserve the ultimate. And I guess if I was asked a few years back, we're talking about practicality. When we talk about practicality, we want to talk about our lives because that is our daily experience. And a few years back if I was asked what is my life, I would probably say my life is made up of my possessions, what I have, what I own, situations, what I experience in terms of different situations, maybe my relationships.   But really, if I must now, what is my life? I would say it is actually made up by decisions, every moment, it's a decision. And then it comes down to whether this eternal life is in the awareness, is in my experience or not by my decision. So it becomes, it's not about situations anymore, it's not even about differences, different relationships, different things that I own, it actually comes down to the decisions. And yesterday we were talking about the number one question, what are the number one questions that we were asked when we travel around. And I would say that question, one question that is asked a lot is how do I know which one is the Holy Spirit and which one is the ego. It is a very good question because when we start to ask that question, at least we start to think, I want to make decisions. If decisions are what is about in my life, then I want to make decisions with the Holy Spirit. And that is a very good starting point because that is how we give the illusion back to the light. We want to give over our mind and we want to give over our decision making back to the light because actually Jesus says in the Course, decisions are the subtotal of the beliefs. So how we make decisions reflects back what we're believing in. So when we give over the decisions to the Spirit, then this question comes, okay, what is the Holy Spirit? How do I know? That question is asked a lot. But I want to say make a better question when this question comes to your mind. A better question to ask is how willing and how much commitment do I have to give over this particular decision right now to the Spirit? What is the percentage I want to give this one over? Completely, or 80% or 50% or 20% because the clarity comes from our willingness to listen. So it's not a question of how do I know, I'm confused, I don't know. The question is always about how committed I am to listen. And a lot of the times we were in probably seeming crisis and we say, okay, Holy Spirit coming now. But then the next 23 hours we're making one decision after the next based on the old beliefs and together with the ego without us even realizing it. It's like an autopilot. Then a moment of crisis I realize, okay, there's some crisis here. Where are you? It's really about how much we're inviting the Spirit to make decisions with us in this moment. Actually it's not even on the timeline, it's not even about in the next five years how can I have you make decisions with me? What about this moment? And how much I want you to make decisions this moment? So it actually becomes very, very, very practical. Very, very practical. It is about daily experiences, it is about daily decisions. It is about this moment. So I just want to let this lead whatever we want to talk about the next hour and keep it open up and see whether there are questions that you want to explore from here. Yeah, I think a metaphor that can help us out too is this thing we know about AI and artificial intelligence and virtual reality and when we talk about movies when you go to a movie theater and you watch a movie, that's like a version of virtual reality. It's been actors, actresses, producers, writers, directors, it's all been put into a product. When you lose your sense of being a person as you go into the story you kind of give yourself over to the virtual reality of the movie or in the case of even live theater someone's standing up and starting to yell at the actors forgetting that it's a stage play and getting so wrapped up into play that start engaging with it. And as we move along, we see it's not only movies, I mean in human history robots have been advancing and advancing and advancing, being able to do more in businesses taking over for humans doing it, just the robots doing it in military, in photography, in filming, drones. Now we have unmanned flights, there's also drones, you can buy drones. You can buy drones and they're quite high-tech what they're capable of doing. Surveillance, recording, of course the military uses them for bombing and all kinds of things and if we look at smartphones and iPads and the way that things are going with the technology more and more time is spent in human lives interacting with these little miniature supercomputers using for example apps before Steve Jobs, the founder of Apple before he passed away he did know what was coming next before he passed away, he said it's all going through the apps people are going to be using apps for everything and he accurately forecast that but if you look at the time and effort that's spent on these little devices in a way they're like little drones, we ask them to do all kinds of things for us and make human life more convenient and more direct, let the app do it let the app find the restaurant, let the app find the parking so there's becoming more and more reliance on that. There's even science fiction movies, Bruce Welles did this movie years ago I think it's in my movie watchers guide to enlightenment, it's called Surrogates where the robots have developed and been so highly developed that human beings decide to interact with the world through their robot selves they're stronger, more handsome and beautiful, they don't have diseases they do have to be maintained in other ways but basically in that movie Bruce Welles and his partner basically they go and they lay on some kind of apparatus, plug into their surrogates and the surrogates do all the interacting the surrogates go to work, the surrogates go off and have sex the surrogates do everything, they go to the surrogates selves and then the users are just back there behind in a world where everything the movie pretty much opens up where there's a bit of an argument about when are we going to take a vacation and the wife is basically saying well why don't we send our surrogates to Hawaii and Bruce Welles is like I don't want to send the surrogates where are we going on vacation and everything it's gotten to the point where the surrogates are being used so much that the humans are basically they're staying in their rooms and they kind of go out or stay plugged in in different ways and get fat they're not exercising, the surrogates do everything and you can see the direction with different kinds of technology as well while surrogates are substitutes, smart phones are helpful for communication but they also can be very distractive because they're capable of all kinds of things and the mind can get lost into those things and get away from purpose so when we start to look at purpose or as Francis brought up, decisions Jesus has a very interesting line in A Course in Miracles because he says a decision is a conclusion based on everything that you believe so every decision you seem to make in this world is just a conclusion based on all of your subconscious beliefs you might use a computer analogy, you know, when you have programs running on your computer you might sometimes your computer seems very slow because there's either too many programs open and running or you have a virus that you're unaware of that's using a lot of your processor energy and your computer is very sluggish so you literally have to go investigate to find out where the virus is and remove the virus the ego is like a virus in your mind the ego is where all strain and stress comes from all fatigue when you feel like you're sluggish and you're slow and you have low energy and all these kind of things it's like the ego belief system is a virus and your holy precious mind that was created by God is now about a parasite that is draining the power and the vitality from what seemed to be the Christ mind that has fallen asleep is now dreaming of a world of separation so a computer expert might say well we might have to clean your hard drive and clean your whole system, find the virus and remove the virus but even if you look at it in terms of surrogates and having your smart phones people are encountering that now they use their smart phones for so many things and then it starts to be like there's a glitch in the matrix they get a little sluggish they don't respond, you're supposed to tap on the glass and they're supposed to respond immediately and you tap and tap and tap and they're like this does not compute it's too much, there's overwhelm there's information overwhelm, app overwhelm they're getting apt, they're getting sick with apps those are all just symbols of putting all this investment in things of substitutions of we might say the complexity of letting substitutions take over for your life very much like the movie where you basically forget that you're dreaming and you get caught up in layers and layers and layers of dreaming and you forget that you're dreaming and then you can't even hear the wake-up call it will take a very strong wake-up call to wake you up because there's so many layers upon layers upon layers of dreaming so what A Course in Miracles does is it simplifies gives you a mind training system with the workbook to take you back through these beliefs and get you back so that your life in this world is not a robot just acting and reacting based on ego beliefs and most of us know that that's how the human condition always acting, reacting sometimes we react so quick where did that emotion come from? I didn't know I had that stubbornness in me or that anger or that anxiety just rose up so quick out of nowhere it helps us clear away these beliefs so that we can be more spontaneous and spontaneous moment by moment following the spirit's prompts for us which is to unwind us out of these false beliefs that's the way to release the virus is to let the spirit guide you the human construct, the human being would not know the answer because the human itself is like a robot acting and responding on the surface of consciousness and the human has no way of finding an answer to the problem of being human Einstein said you cannot solve the problem at the level of the problem so why would we think that we should keep trying to solve all of our issues and problems as a human being on the level of the human being? that's what Jesus is saying in the Course he's saying you've got to go to the level of the mind in order to solve this if the body is like a puppet and you've got a crossbow and a puppet master and the ego is pulling your strings and you seem to be developing illness or symptoms, stress, fatigue you've got to get back and switch the puppeteer from the ego to the Holy Spirit and you have to do it in a systematic way that will work so Jesus is very practical he says basically that the ego uses the body for pride, for pleasure, and for attack three things and the Holy Spirit uses the body for communication one thing this sense one is simpler than three you start to realize wow if I give myself over to that one then I can be unwound from the matrix and I can be unwound from this robotic sense of feeling at the mercy of something that I can't even smell or taste or touch I can get in touch with the task master the ego in the mind that is the belief in separation that's where all of this craziness in mind the insanity is coming from so suddenly a course of miracles becomes your best friend in the sense if you're practicing with it because it's going to give you most direct the most straight shot back into peace of mind and all that really is asked of you is your willingness to give yourself over to it we don't have to write the book we don't have to figure out the book we don't really need to analyze it and break it apart and try to figure out anything all we have to do is use it those are the only two instructions given for the workbook don't do more than one lesson a day and as best as you can try not to make exceptions to the lessons that's wonderful too it gives us a workbook that we can use in any situation imaginable and there's only two guidelines not 10, 15, 102 guidelines so you can see that he's trying to make this pathway back to spirit as simple and direct as possible instead of being a robot and the ego would say oh you're no robot you're an autonomous human being the ego will tell you how amazing the human body is and you have a mind that thinks it will tell you you have a brain that thinks because the brain is a projection too but it wants to even make it seem like the brain thinks and it will tell you you have a will of your own God gave you free will in your creation no free will is back in heaven this is imprisoned will that's what we're talking the ego gave you imprisoned will and God gave you free will but free will isn't choice free will is perfect happiness God's will for you is perfect happiness that's what the will is and it's truly free it's happy in this world it's in prison will and then the human being acts out this in prison will in the matrix you know basically Neo was asking Morpheus and basically Morpheus is saying I'm trying to free your mind he says before he leaps from one building across into another building I'm here to free your mind and then he jumps across from one building to the other and all Neo can say whoa like you've got my attention he's trying to free the mind out from these unconscious beliefs at one time Morpheus takes Neo on a training program and they're walking down the street and I'd love to watch that scene because Morpheus is gliding down this sidewalk street in a busy major city and he's not touching anybody he's just gliding down even though the characters are moving in the other direction and Neo is getting bumped with everyone he encounters because his mind isn't trained he doesn't know that it's a simulation it seems very real that's why he keeps bumping up against things that's a good analogy for the human race the reason we seem to bump up against things as a human being is because we have internal attachments we've got belief attachments we've got thought attachments and when we look at the great yogis and mystics and avatars amazingly they seem so calm they seem to be gliding through time and space almost laughing going ha ha ha like Morpheus is doing when he's doing the training video he's not serious at all he's basically using the training the training program as an instruction for Neo until it ends when he says Neo were you paying attention or were you looking at the woman with the red dress look again and then when he looks back freeze it the whole program freeze it there's an agent with a gun pointing so it's like the whole street scene is just a simulation it's just a device that Morpheus is using to teach how to free the mind he's beginning to teach you are not at the mercy of all these images you are at the mercy of your belief in your conditioning and programming of these images now let's take a practical example we want to bring it down a little closer to home does everyone know now that they're inventing self-driving cars you know that it's happening now cars that drive by themselves now originally there was some malfunctions that everyone got real spooked when there was a crash with one of these self-driving cars and there was an attendant that was there in the car while this car was driving itself and the attendant died that gets the human stirred up you might remember 2001 a space odyssey did anyone ever see that movie when the computer Howell decides to take over the mission and all the humans who are watching the theater go whoa there's a machine it's after the human we're root for the humans Howell must be stopped we have the matrix where the machines and the humans there's many movies coming out now about AI let's bring it down to cars because we like our cars Nick you like your car and drive your wife's car very fast and she says and's car but we like our cars so let's use the car analogy self-driving cars now they've picked out of all the cities in the world the practical the practical area for they're going to set loose a bunch of self-driving cars in Singapore now it's coming we're going to have self-driving cars you're on the highway someone cuts you off you start screaming and you look there's nobody behind the wheel how are you going to project your anger on a self-driving car well let's take a moment to look at a self-driving car how do these self-driving cars work except for programs sounds like the born ultimatum and the born identity how born has all this information at his fingertips well now these cars better have a lot of information because they're interacting with what seems to be the human in Star Trek the board would assimilate the humans and then they'd make these creatures that were half all this apparatus of machine and half human we're getting to the point where we're setting cars loose now in human land and that's going to be an interesting experiment but think of it the cars are programmed now there's a movie I use in my movie Watcher's Guide to Enlightenment it's called Solaris where George Clooney is a psychologist and he gets set up on this planet and there's these beings that show up that supposedly aren't real beings but they're just collections of memory but they're kind of like one sided they look real they look like real human beings but they're made up through the use of this energy up in Solaris and at one point there's a scene in the movie where basically he's saying to this character you're not real and the character says and you are to George Clooney in other words imagine it's talking to one of these self-driving cars it cuts you off on the highway and put a dent in your fender and saying listen, you're talking to the car you're not real this isn't a Walt Disney movie you just put a dent in my car and you're not real and then the automated car going and you are then you start to get to this question of who is real and what is reality and that's exactly what we have to start to come to that's what AI is starting to bring into our awareness with all these movies and these inventions we have Siri talking back to us on our iPhones and there will be more sophisticated versions of Siri that will come out I have tried asking Siri what the meaning of life is and sometimes she is stunning an occasion with her answers around the meaning of life it sounds like she's got some course in miracles programming going on in there for the Steve Jobs we have to get to a point where we have to realize that what we see as real isn't real and that it's all programming that all of this world of cosmos the black holes the stars the galaxies the quasars it's like the Truman Show if you're enjoying a beautiful landscape and you're looking out at the lake and you're watching birds fly over the lake that's part of programming too those birds have been programmed to fly that lake looks like a lake but it's all like a holodeck in Star Trek it's all a holodeck we have to start to realize that we aren't living in a real concrete world but this is a digital world this is a holographic digital world that's nothing more than a projection of our minds and so we can't keep telling ourselves well I've got the practical things to deal with in the real world and then I've got this mental thing that's going on because the practical things in the real world is this mental thing going on it's all mental young kids will say mom don't go mental on me well all of us have gone mental and we've forgotten that it's mental and now we think that there's a physical and a mental but there's not two things going on here and that's the purpose of the workbook of A Course in Miracles he will have lessons number one, nothing I see means anything number two, I've given everything I see all the meaning he has for me and then when he finally gets to lesson number four he starts talking about thoughts before in lessons one, two, three he's talking about perceptions but not in lesson number four he's talking about thoughts then he goes back number five, I'm never upset for the reason I think he's talking about thoughts I'm upset because I see something that's not there he's back to perceptions I see only the past he's talking perceptions that everything we perceive is the past that's number seven, I see only the past these are his first lessons in his workbook of re-training the mind he's going to go back and forth between thoughts and perceptions and he's going to teach the mind re-teach it help it remember that my meaningless thoughts are showing me a meaningless world my mind is preoccupied with past thoughts I'm just perceiving the past imagining that I'm still in the past not that the past is over and gone and healed but imagining that I'm still stuck in something that he says is over and gone it was over long ago this world, this cosmos is over long ago think about that when you go to watch a movie in the cinema you're watching something that's already been produced the movie's over they're not making a movie while you're watching it they've already made the movie it's in the can in the old thing now it's in the digital it's in the memory but you're really watching something that has already been filmed that is just this pre done packaged thing called a movie and you're reacting with it as if it's happening to you right now and that's exactly what's happening in the mind the movies the cell phones the robots, the drones the technology is just reflecting back to us that we have forgotten who we really are and we're just caught up in the past we're just replaying rehashing separation over and over and over and we need some real good training from a master to get us out of this it's a very hypnotic, it's like a trance we're caught in a human trance we need to be lifted out of this human trance so the more that we talk about this and the more we go into this the more it should become obvious that what Jesus calls mind training and of course the miracles should become your top priority because why would you continue to invest in effects when they're already over and gone why would you continue to try to fix problems at the level of form when you can't fix problems at the level of form it goes against all our conditioning if we think we have no money in our bank account we have to go work to put money into our bank account we're still not aware that it's all thoughts if we think we have to do all these things with our houses, our cars, our yards this series of problems that confront us every day and if you have a good day and you solve most of them, you've got to face another day of problems and another day busy, busy, busy now there are those that try to figure out the world I don't get this why would you try to figure out a destructive device why would you try to figure out a hallucination why would you try to figure out a smokescreen there is one point in the course where Jesus defines this linear perceptual world as an impossible situation so when you try to fix aspects of your life in form you are trying to tinker with and fix an impossible situation this hologram is literally not created by God and therefore it is impossible and yet when you put your mind's energy on trying to fix it you are trying to fix an impossible situation that's like trying to put your head and your skull through a six foot concrete wall you can keep banging away on it but I have no doubt that the concrete wall is not going to be moving skulls were not made to go through six feet of concrete most people would laugh really that guy is crazy local that's an impossible situation trying to put a skull through a six foot wall of concrete but when we try to fix the form we are trying to do the impossible why do we like consciousness teachers even better why do we like non-dual consciousness teachers because there are a great majority of dualistic teachers and we have already seen that in religion heaven and hell you know the good ones and the bad ones and do this and you get to heaven and do that you go to hell we don't need anymore dualism here we are going nowhere fast if we try to follow dualistic teachings but when we get a good non-dual teacher then Jesus basically said you would do well to follow a peaceful teacher well to me that's what I like about the course is because Jesus is a transcendent non-dual teacher he has transcendent duality completely I don't know about you but that's somebody I would like to learn from I would like to learn from the master the way the truth in the life thank you very much I've tried it the other way I think I'll go with a little bit of the way the truth in the life now I think that's a good sign when we we start to give ourselves over we may have people say oh don't become a Jesus fanatic but I don't know about you but I want to become devoted to the way the truth in the life I think I could learn a lot from the way the truth in the life you can call me a fanatic if you want to but I still want to be shown by a way shower who has transcended time and space to me that's just good common spiritual sense to follow one who has transcended time and space and for many of us that's the feeling we get when we pick up a course of miracles we go whoa whoever wrote this book is not in time and space we get a feeling that washes over us like whoa like with Neo with Morpheus whoa I better pay attention here that's why actually when I first picked up the course I used to have all these books by my nightstand and I loved reading all these different books and philosophies I put them all away I even cease reading the newspaper I was so riveted with the course because I thought oh my gosh it feels somehow like eternity is speaking to me and somehow that's very important when eternity calls I want to answer the call like it's somehow very important and all of us have that calling somewhere deep inside of us so I really feel like Francis is saying the focus becomes more our decision making capacity and who am I making decisions with at this moment becomes a very important question who am I deciding with Holy Spirit decide for God for me be my partner be my companion be my comforter and we can't any longer say that we can't tell the difference between the ego and the Holy Spirit because the entirety of A Course in Miracles is helping make it exceedingly clear of the difference between these two purposes these two voices in our mind one is the still small voice that always loves us that never commands that never demands it can be compelling but it never will command or demand it can't be louder without violating our freedom of choice there are many answers from the Holy Spirit that we have received but have not heard because we were just too terrified to hear the guidance sometimes we get those little nudges those little nudges but we're too terrified of following the nudge not because we're afraid of what will happen next but because we're ultimately afraid of where is this nudge leading me and where will it take me where is the end where is this all going to end yeah eternal life is where it will end the ego doesn't like that so with the time we have here before our lunch that's an interesting starting point that's what we just talked about what about those decisions you know do you see how important it is to be guided in your decisions do you see that my questions are around wishing to know your opinions on what I call or I've heard called spiritual bypassing and I've noticed some Jesus' teachings that Jesus' decisions were to go out into the dream a separated world and heal the sick and comfort the despairing and you yourself said I believe our brother and sister cattle in the solution line and try to bring comfort and fear and confusion and it seems to me that those things are the right thing to do and it it seems to me very important so I'd like to hear more about where spiritual bypassing and it kind of sits with with that thank you, that's a very good question I have given some talks where particularly with of course of miracles and of course of miracles students or teachers I think the greatest spiritual bypass in working with a course of miracles is this phrase, it's all an illusion is if the very premises underneath the course is like a cliche with everything and so it's kind of like trying to go around and spread the course of miracles pixie dust it's almost like if I repeat that mantra enough it's all an illusion that eventually I will experience enlightenment so then we go back and we look at Jesus in his example those three years of public ministry hospitals and not once does Jesus tell everybody it's all an illusion he demonstrates it with his attitude 100% of the time and he speaks it 0% so I would say that as we work with the course one of the most helpful things you can think of with it is wow, it's all for me in other words it's all for my mind I'm learning these deep metaphysical truths I've been giving a training program but I'm not here to try to convert people to convince people I'm here for a transformation of consciousness where the presence of love can come radiating oozing from my being with everyone and everything and oftentimes this comes up when we talk about your biological family your parents children I mean I know that people have tried that and oftentimes they report it's very very difficult some very interesting reflections come back and you tell your parents it's all an illusion I know there have been parents who have repeated this to their children over and over and over they try to teach the course conceptually to their children and the only good thing about it is after a while the children start to point out to the parents all the time that their lives contradict their teaching oh yeah mom you said it was an illusion you look pretty upset today it's all a piece of mind I don't know what's going on there I had a group of students back in the 1990s that basically they wanted to come to the lakeside and so they're all around me and they're asking me all these metaphysical questions but they brought their children and the children really don't want to be a part of the metaphysical talks they're going to go run through the forest with the dog that's what's important to them play with the dog so they're playing with the dog running through the forest and they come back and at one point they went to everybody and they did stop for maybe like five minutes to talk about God and it was really beautiful to listen to what the children had to say about God very beautiful things and then they go back off playing with the dog about five minutes of metaphysical talk well at one point the children come and say we want to go swimming and the parents were like well you can't go swimming unless we're watching you and the children were like what's wrong? are you afraid? do you think we're bodies? you don't trust us we might drown and the parents look at me like what do we do? because suddenly they've been teaching the course verbally to these children right back at them in terms of transfer of training so the parents were like let's move our discussion down by the lake so we can keep an eye on you and then again the children were ready to run in and swim in the lake and they go no the parents said no no not unless you have life preservers on there's no life guard here why do we have to wear life preservers? do you think we're a body? again the screws got turned in right away and that's what's going to happen if you go around and you indiscriminately try to teach the course verbally over and over I've seen people at work where people start talking about the course at a restaurant with the chef and the cooks and when it gets to be rush hour this whole thing about time being an illusion is flying back at them because you have to be at the point where you can demonstrate what you are teaching before it makes any sense before there's a congruency before there's a consistency there what business do you have telling the dream figures or telling the figures how they should live their life if you're not demonstrating yourself and in full demonstration of it for three years he was literally healing the sick raising the dead and casting out demons and still he wasn't telling everybody that it's all an illusion even with all of that he didn't even do that so that's probably the biggest example of a spiritual bypass is Course in Miracles students even in groups when I was up I'm sad my cat died I feel upset it's an illusion, your cat's an illusion going to visit somebody in the hospital who's in traction they're all wound up and taped up and everything is banging on their knee what are you doing in here, it's an illusion we're not here to verbally say it's an illusion we're here to practice forgiveness to practice the internal clearing and beliefs and judgments in our mind so that our attitude can be like the B attitudes of the Bible so our attitude can teach love and compassion in every single situation in which we're presented and that's what a wayshower does demonstrates transcendence through attitude through state of mind and if you're going to teach spirituality then it would be the one thing I would recommend is make sure that you come into fruition you come into the practical application and demonstration of what your words are when parents try to teach children things like don't smoke don't drink you need to exercise more your diet's terrible the kids are what, watching the parents to see if the parents smoke, drink exercise what the parents are eating because what, if you try to teach a child something that you don't demonstrate yourself then there's an incongruity there and that will come back the children will say why should I quit smoking when you smoke you see, there's a real basic hypocrisy that gets pointed out immediately and I would say lies in spirituality so a spiritual bypass could be dismissing something when it hasn't really been fully exposed from the unconscious mind and that's a very good question, I mean that's a question of consistency and integrity I still have a question hand over there do you just have a little with me into the world I found a particular help in there's a pain in the body of actually filling the body with light particularly the painful area and was I bringing God into the world because the body seems to me I'm a yoga teacher the body seems to be such a helpful tool to use to press those ideas yeah I think when I hear about those kind of things again everybody is approaching this from their level of understanding and from your level of understanding bringing light to a particular part of the body where there seems to be pain is I would say what's going on in the mind is focusing back to the light and the reflection can be that the pain goes away very much like if you have a shift in mind or a change of mind, a change of heart that it could be symptom removal it's really where is my attention you're bringing back the attention back that way there is a very famous teacher named Louise Hay who basically wrote a book, You Can Heal Your Life and basically she again was going to use the body as like the varometer not the cause but she was going to take the symptoms that would appear like like a pain here, a pain there and she would trace it back and of course there's many traditions that have done this Native American and many original traditions where they look at the symptom and then they take it back to the consciousness and she would do that and ultimately where the healing actually occurs in a lasting way is the release of the self-concept with a false identity that's being held in consciousness that's where all the symptoms disappear and so you start where you start you may start where there's something it's more like a piecemeal approach I have a pain here I'm going to send light here and the spirit is like good, good, that's okay just like even taking medicine you know taking an Advil for a headache or something like that is magical but there's a belief in that and therefore there's nothing wrong with it and there's nothing wrong with Gandhi using herbs for his treatments and so on and so forth it's still magical but it's helping reduce the level of fear which is very important we can't deny that reducing the level of fear is as important as it is and when we say okay and take me to the bigger picture what's the broader picture where is this all heading it's releasing this false identification with the body and the world and coming back to Nirvana or to pure spiritual connection so I think it's good to be easy on yourself and even when you find things that work when they seem to eliminate the pain temporarily or reduce the fear you can feel gratefulness for that there probably will be advances in medicine and quantum machines that will help more and more the human race to alleviate some of its pain and suffering in a temporary way but it will be spiritual inquiry like Ramana Maharshi what is the I who am I that ultimately will take the mind back among other great techniques and devices to realize the pure spiritual identity so there's nothing wrong with these things but I'm talking about the general practice as you as you go through your life of just taking a look at what am I perceiving and if I'm perceiving pain there must be some kind of distortion in my lens because God didn't create pain so I must have some kind of ego distortion and then having the willingness to go as Francis said desire the holy instant desire to go back toward that pure beingness that take away all the struggles of the world one thing I could think of is that Jesus with the women at the well he said to her drink of me and you will never thirst again it's wonderful to think of that in terms of pain Jesus saying drink of me and you will never see this pain again that puts it in a higher context and that gives you the impetus for this inner work whereas the ego wants to distract away from that and say oh just get concerned about all the forms and the effects and so it's a big difference when you say look into it I found that very helpful too so what is the purpose of this pain to keep looking and then it dissolves somehow it's not there the more that you focus your gaze so to speak your attention on uncovering and exposing the false the less you will see of pain and guilt in your perception in other words the more that thoughts and beliefs are kept hidden and pushed to suppress down in the unconscious the more they will seem to appear in the projected world and the more that they're exposed it's like it's like playing ollie ollie income free okay all you false beliefs and thoughts amnesty you're gonna grab amnesty now just come on up you're free to come up now no penalty you can come and turn yourselves into the Holy Spirit for free right now the more we're able to practice that in our daily life then the more innocence we perceive reflected back to us in the world so it's beautiful you know you start to see symbols of innocence flooding your awareness and then you know oh this is good I'm moving in a good good direction we talked a little bit about the role of feelings which the ego uses to make the public concrete and real but how we can let Holy Spirit use it I love what Francis says whenever I ask a question when we're organizing the talk he says yeah that feels good or you know if it feels good for you then do it but yeah can you talk about feelings and how we can move from ego to giving them to Holy Spirit and using that to come out of our self-concept yeah that's interesting that I actually have put in my books I know in Awakening Through a Course in Miracles I ask Jesus for a map of the mind and then emotions and feelings are on the map and the feelings are actually very close to the perceptual realm so everything that we perceive in time and space is very closely connected to our emotions in fact in Awakening Through a Course in Miracles Jesus says you will look upon that which you feel within so if you have pain you will perceive a fearful world and if you have love you will perceive reflections so the emotions and the perceptions are very closely linked and now when we've met with you and we've talked about this process we'll call it a defense mechanism called intellectualizing intellectualizing of course in miracles even would be starting to use different words and phrases and everything has bypasses over the top of the emotions and you can tell that when somebody just wants to use all of an illusion anyway and not even get in touch with the emotions of hurt or grief or jealousy or envy that there is almost like trying to bypass the emotions and use some kind of phraseology that is spiritually correct politically correct I'm going to use my spiritually correct metaphysics and if you don't deal with those emotions if you don't welcome those emotions if you don't use those emotions as like barometers then you're not really using one of the most helpful tools that you have available to you so I'm always encouraging people to get in touch with their emotions when I do workshops or seminars or long retreats I'll do a lot of experiential exercises that are designed to bring those emotions up we may watch movies that will help bring the emotions into awareness but you can't have a change of mind unless you can get in touch with your emotions and emotions are also lead into what lies underneath and beneath the emotions which are the thoughts if you just stay on the realm of perception words and cliches and phraseology you might say that you can only seem to pursue an intellectual understanding of something which isn't understanding at all it's just more conceptual gobbledygook and this is a great temptation with the Course of Miracles one time there was a gentleman who was the scribe of the Course who was quite an intellect in terms of her persona and same with Bill Bedford she explained at last a pathway to God for intellectuals so of course the miracles is over 1200 pages and it came as a response for an intellectual pathway to God you have to retain the intellect you're not supposed to retain the intellect when you use the Course it's to take you back to this childlike sense of wonder and glee and connection but the temptation of those that are drawn to the Course is to avoid experiencing the Course in Miracles by getting locked up into conceptual identities and conceptual phraseology so it's good to be aware of this because the emotions are being avoided when there's these intellectual gyrations that are going on and it might be well to ask at some point in the middle of the intellectual gyrations and how are you feeling right now you see how that brings the focus back into something very simple and direct feeling and even better is to watch your own mind if that's a pattern to say oh I need to get really in touch with my feelings because they're helpful they can be used by the Spirit to help take me deeper and that's the goal is to go deeper into an experience sometimes I have been I find the Course's framework very helpful inward into the emotions because you can just go forever into anger feeling it and it doesn't end or guilt and feeling it doesn't end can you talk a little bit about these powerful feelings of guilt and shame about the original sin the idea of the ego so when we feel that was guilt then when we put it in the right framework it's a lot more helpful to it helps a lot to come out of it more easily yeah the emotions can be so intense at times where it seems like these survival kind of mechanisms and interpretations and reactions can come in but I would say there was a does anybody ever remember rational emotive therapy Albert Ellis rational emotive see how he was taking cognition and he was taking emotions and he was saying let's work with both because both are involved in the healing rational emotive therapy and I would say any type of therapy or practice or spirituality that just emphasizes one aspect of human consciousness and dismisses the rest it's not helpful it's a complete system Jesus says this course has everything that you need it's a very highly sophisticated mind training program designed to deal with all aspects of consciousness not to dismiss some I've even seen some therapies that focus only on emotions and nothing else they totally dismiss cognition and I've simplified the whole human experience which is amazing the more you read about it and you look at it and observe it and they'll try to dismiss cognition for example by saying get out of your head all of human history is reduced to get out of your head so I like to engage with people I say okay what do you mean feel the love feel, feel, feel, feel it's all feelings you've probably encountered that get out of your head or they'll reduce the whole of human history into the left brain and the right brain don't you like how that's simplified get out of your left brain and get into your right brain that's the whole problem you're in the wrong half of your brain well what's the left brain that's your rational self and rationality will never get you anywhere actually when you read A Course in Miracles Jesus has a lot to say about rationality he uses it in a helpful way he would have you get to your assumptions underneath your rational connections and see that you have a lot of faulty assumptions that have to be questioned and he does say would you rather be right or happy meaning you've got to go really deep to get at those assumptions but Jesus doesn't dismiss cognition or rationality and so what we start to realize is am I willing to practice the Course and really get myself over to it is really important that's where we have the healing am I willing to just practice what's offered to me and trust that it's designed and given to me for healing for rapid mind training because I think intellectualization or conceptualization what it does is this temptation to try to figure out a problem and analyze the problem as if by doing that I can find a solution in the same frame of mind that I have a very intellectual mind and I've noticed the temptation of trying to define and analyze a problem when it happens even in terms of sickness you know what happened what in the past caused this present moment really but we were talking the other day about when the problem of separation happened Holy Spirit fixed it in that very instant so the answer is given in that very instant if this whole cosmos and all the problems and conditions happened and the solution arrived in that very instant then really practically what it says is we can focus on the solution which is given because there is no separate problems really there is no separate moments and every moment is a repetition of choosing this separation in the mind then boom this whole world is playing out this desire by presenting all kinds of separate problems for us to solve but if we remember really the solution is given in that same moment then our mind can be relaxed and can be freed up from trying to look at the problem and what went wrong in the past you know instead we can look at okay what is the solution now because actually Jesus says in the Course you are not responsible for the problem you are responsible for accepting the correction right now because the problem is not really created by God or by us so our sole responsibility is to accept the answer and it is very very practical it is a very very practical approach when we come together in everyday life we don't sit down to discuss what went wrong who is responsible for that what happened in the past what is the issue metaphysically and practically it's not the best use of our mind it's not the best use of our time the time is used to go back to the solution when we come together normally doesn't really matter what is the question is let's play together to receive the answer and to the extent our mind is willing to let go of the definition of the problem and the temptation to analyze it and try to solve it by ourselves we can receive the answer sometimes it looks not related to the problem but it is the answer regardless let's move on let's receive and follow receive and follow so that's how we glide through life like morphias we our life becomes simple we receive and follow receive and follow and know and experience that by doing that actually it's solving the problem there is the only problem is the belief in there is a problem there are situations so as David was talking about in order to really purify this desire to do only that to receive and follow the emotional aspect that we need to allow we need to permit our emotion to come up that's important the temptation to try to analyze the problem and solve it is the temptation to bypass the emotions the temptation to keep control because when the emotion comes up we lose control I don't know what's underneath that I don't know what's going to happen there's a lot of fear of losing control so in our you know practice in my own pathway just allow the emotion to be what they are is extremely important it's actually against our conditioning because if I start to cry the conditioning is something is wrong people would jump in to say don't cry or let me fix you let me help you and that's the conditioning but no our goal is not to fix at the level of the form our goal is to allow this emotion to come up sorry I have a question I experienced well I went into psychosis I've had a lot of extreme emotions and I I love to act I want to experience everything fully sorry I keep getting like my head is trying to figure out what to say and it's like very very annoying I was going to say about the anger but it just seemed important to let everyone know that it's not a problem it's not a problem when somebody's what you think it's you I need to know that when I see someone going through a problem it's something in my perception of me and I just like I'm always okay and everybody worries they say stop stop crying or stop being angry and that fuels it because I say no I need this can't be life I can't be controlled I can't be like I can't live like this and I try and express it and I never get the chance to because I always get reflected back my fear because I can't feel like I can and I just want that's why I'm always chasing to be on the stage because I'm like it's my place I need to be there so people can hear but then there's all this confusion it's beautiful in the sense that it's like it's so strong for you I just hear you have such a strong call for healing that you are getting much much much more in touch with your emotions than seems to be the norm seems to be socially acceptable reminds me of a black and white movie I saw years ago called The Elephant Man where it's a man but he's so disfigured that people interpret him as an animal they don't want to be around him and everything and finally during the film you sit there and you watch the whole film and then you know he's like I am not an animal you know he has to verbally because it seems like everyone around him is perceiving his disfigured body as him being an animal so as intense as this is as painful as it is to seem to be a very emotional being in a society of the stiff upper lips or whatever you want to call it you know it just seems to be a big contrast it's the more in touch we are with our emotions that's actually since there are barometers that's the desire, it's a reflection of the desire to come closer to who we really are to be emotionally in touch and see I've seen it play out because I go to 40 countries around the world so like when I go to South America for example and I'm going down to Venezuela and Colombia and Argentina and this and this and this I have these awakening gatherings I've been going down there since 19 around 2002 was when I first started going down 2002 or 2003 and I would do these enlightenment gatherings and invite everyone but like 93% women show up 95% women show up 97% women show up but I'm not doing women's retreats I'm doing enlightenment retreats and I'm inviting everybody to come but the women show up and a small few of the men show up and the macho men don't show up for my enlightenment gatherings why is it that the macho men is not showing up at the enlightenment gatherings because the bravado the strong silent stuffing down of emotions not being raised not to cry I actually always get attracted to guys who don't muscular and I find that maybe there's something in me that's actually not very emotional because I think people assume that I'm very emotional and I see a hardness in myself they're very strong that's where you have to trust you have to trust that the Holy Spirit knows best always even with the Course Miracle people don't always know that Helen and Bill that we learned from Absence from Policity the book that Kent wrote that Helen and Bill were brought together to help bring the Course and deliver the Course but Jesus says that they have no dynamics how many of us have ever grown up I study psychology therapy and I've never heard therapists say complimentary ego dynamics you know but Jesus can because he knows in the greater plan that people are drawn together in a way that Bill's suppression and repression and Helen's projection brought together we had a book called Helen and Bill and they act out each other very good so you can see there's a perfection in this plan it's all working together so good right okay it's lunchtime but it's actually called David actually we call him Bill


Right hello, Simon Benjamin here again. What I'm doing now is just presenting a few, essentially, outtakes from Lecture 7 and really from Lecture 6 as well. Things that didn't quite fit in to a reasonable one-hour time budget, but I do think are going to be interesting to people who like to really get into the techniques and the maths. So the three things in this little outtakes bonus lecture are one, some stuff about that example that we did where in diffusion, where we had a bunch of pipes all connected together, what if there are only two pipes and so it's a finite problem, a problem where the initial conditions only go from a certain point to a certain other point. That's a nice example to think about, to practice generalizing into a periodic function. And then two things from Lecture 7, some tricks to do with doing a Gaussian integral and using some ideas from contour integration. And then the big one is transforming a certain integral into the error function. So hopefully those are interesting for you if you're into the real details of things. And here it comes. It's a nice time to talk about wise choices when extending our function. So let me copy this diagram and think about a related problem. Now we've said that if we have a function that's only defined between two points, we can extend it by making it periodic. Let's imagine that we had a pipe like this but it's a fixed length of pipe and it only has one valve in the middle. In fact it's just, it's equivalent to one of our cycles here, so let me finish the diagram. There we are. So it's exactly the same parameters, characteristics that we were dealing with before. We can even use the same symbols for the initial density. But it's only one piece of pipe. It's sealed off. It's total length is 2a. Now we would like to be able to solve that using the techniques we've just used. And we might be tempted to say, well all right, let's just make my function periodic. I'll make it exactly the function we were just dealing with because, hey, the thing isn't defined. Let's say that it's defined from x equals 0 to x is equal to 2a. And it's just, it doesn't exist outside of that regime. So surely I can do whatever I like outside of there and it will all be fine. So what did we have? We had something like this. That is everything that can be said about that finite pipe problem. So then why shouldn't I, let me draw what we're proposing, why shouldn't I extend it in the way that I've drawn, which will get us just exactly the scenario we've just looked at. The thing only has been set up in this region here. So I can do whatever I like, can't I? Well, if I do that, then the problem I'll be solving is the one that we just looked at. And we know that what will happen is we're going to get a diffusion, we're going to get a curve that shows all our sharp edges are softening out over time. So we got this kind of thing. Now, if we extended our finite pipe this way, what that seems to be saying is at the end 2a, we have somehow got material that's, our density is dropping down. So that means that at this end, I guess we're saying soon after time t equals zero, our density starts to drop down at that end. And similarly, x equal to zero soon after time t equals zero, our density starts to go up, which is this region here on our diagram. So these regions are not behaving intuitively. The reason is that we've mapped it onto a problem where right next to the sections that are defined, we have abruptly different densities. And that's an inappropriate mapping of our problem. And we can see why, you know, we're getting this anomalous, unphysical behavior. So what should we have done? What would be an acceptable way to map our Fourier, to map our finite function into a periodic one? Well, this is what we should do. I'll sketch it. There we are. I've marked on in red the danger areas where we were going wrong before. And in the new diagram below, what I have is I've extended out our defined function by mirroring it. So now the complete period of one function is, for example, it goes off my diagram a little bit, but it would be from minus a all the way through to 3a. That's one complete cycle. So and then then it's allowed to be periodic and to drop back down to the phi one level. Why does that help? Let's focus on this this middle part of the diagram, where now we don't have an abrupt change. We have the very opposite, which is a kind of mirroring, right? So this green line that I'm drawing is where our finite function that we are using, we can imagine it's being mirrored because we've got a full region of the higher density phi two on either side of width a before it drops down. Why does that help? It's a symmetry argument again. Think about a little region near to a, so I could just imagine a little slice here spot on the end there. That is in the center of a region of high density. No material is going to flow into that region by crossing my green line. So what will never happen? This is very similar to something we looked at in the last lecture when we realized we could do two problems for the price of one. This kind of thing that I'm drawing with my arrow, my orange arrows, that never happens. We aren't going to get flow of material that comes from one half to the other. That's because we're right in the middle of the high density region. So all that's going to happen is that material is going to flow outwards from that. So that's why it's safe to then put a divider in there because material wouldn't have wanted to cross that line anyway. It's like a still point in the problem. And if we had, if I had continued my diagram out to minus a, we could make exactly the same, well in fact we can make exactly the same remark at zero. So whoops, you need to do that. So here's another mirror point because my better periodic function continues out to minus a before going back up to the high density. This is exactly the same argument. Material will not cross the zero line. It will only flow in from the high density regions. So that's another still point in our problem where we can safely cut it. So that's what we should do, whereas the example above is the worst case because we've created these points of rapid diffusion exactly where, according to our problem, we have sealed ends of our tubes. So I hope that makes some sense. That's why I mentioned, I think all the way back in a much earlier lecture, maybe lecture two, that what we need to do when we extend the finite function out to be periodic is to watch for this kind of thing and to be smart about how the new period, essentially be smart about the period of the new periodic function so that we create these still points at the end of our problem. Of course, I took two kind of magical steps there, right? So in order to not take too long, I jumped two things. And let me just remind you what they were. One of them was I said we could just drop those shifts, those little imaginary shifts on our integration. And the other was I just announced that the integral of our Gaussian is root pi. So let's do the more boring one first. How can we get the integral of e to the minus y dy? It's a good question to ask someone who thinks they're good at integrals, right? Because it looks quite innocent. Like, yeah, I can, oh, wait a minute, how can I, it won't integrate as it's written. Now there's a very, very strange trick to do this. What we'll do is we'll define that integral, we'll give it a symbol, which I don't think we're using for anything else, which is b. It's clearly going to be some value, right? I mean, if we sketch it, it's just the area under this thing, which I've drawn really badly because it goes down to zero. And so it's some finite area, but what is it? Here's the trick. We actually figure out b squared, and then we take the square root. We do it in a really funky way. So b squared is, of course, just equal to this integral squared. But then we can write that in a different way. We can say this. So I've just written the same integral twice, just using a different dummy variable. I've used x as the dummy variable on the right. Well, I can do that. It's just a dummy variable. I know that I can use a smiley face if I want, but I'm not finished by any means. Now I've combined those integrals quite legitimately. I'm just have a look to see if you consider that the step that I've just taken makes sense to you. But normally, you would go in the other direction, because you would notice that two integrals, an integral over two variables can actually be pulled apart into an integral over just one of those variables times an integral over the other. Normally, that would be the direction you're trying to go in. But we're deliberately making things more complicated because it will actually give us in the next line something that's much nicer to integrate. The final trick, then, is to say here, we're integrating over x and y. I can think of that as integrating over the plane just with the x and y coordinates. It's not a complete coincidence. I've used those particular dummy variable symbols. What I can do then is I can switch to polar coordinates, which sounds like it's going to be even more complicated. But wait and see. So there we are. That's just the integral above now written in polar coordinates. So where you have dx dy, you may remember that we now need to sweep out a bit of area using the polar coordinates theta and r. And we should use r d theta for sweeping out a bit of the angular direction and then dr for a bit of the radial direction. And now we can do this integral. So the integral over theta is trivial because nothing depends on theta. So this is just the integral of something it regards as a constant d theta. So it's just going to pick up a 2 pi, and we can put that in front, leaving us with this very simple integral. And now it's one we can do. That r that we have multiplying the e to the minus r square, that was the thing we were missing at the beginning that stopped us being able to do the integral. Now it's trivial. So let's do it. So that's the integral with its limits. We've just needed a factor of minus 2 divided by a factor of minus 2. Great. And we can see that at the limit infinity, this will be 0. But at the limit 0, e to the minus r squared is just 1. And so we'll have an extra minus sign because that was the lower of the two limits. And we end up with the 2's cancel out and we just have pi. But if b squared is equal to pi, that means that b must be equal to root pi. So that's a really, I think that's one of the more surprising and strange ways of doing an integral that I know of. You can't do the original integral just by standard techniques. So you compute instead the square, but then you're going always in a direction that seems to be making things worse. You take two integrals that happen to be, that can be written as factors multiplying one another, and you complexify that into making an integral over two variables just so that you can eventually get that extra r factor in front. So the more interesting one really was why is it okay to drop the small imaginary shifts from this integral here? That is a deeper question. So let's remind ourselves of what complex numbers are like. We can draw the Argan diagram where we have the real axis and the imaginary axis. And normally when we do an integral, we're just integrating along the real axis, maybe from minus infinity to infinity as here, or maybe from some fixed point to another fixed point. Let's imagine we were integrating from minus r to r, and let's write this integral in that case, and then we'll let r go to infinity in a moment. So what we're really being asked to do here is a weird integral. So just making, instead of an infinity, just using this finite real value r for a moment, what we're being asked to do is to integrate from here to here of our function e to the minus y. Well, okay, but what does that mean? Here's how we can actually work it out.  Now, again, this seems to be making things more complicated. Why am I now having to think about a path integral? The reason is there's a beautiful and powerful result that when you integrate around a closed path in the complex plane, it's zero unless the function that you're integrating goes to infinity inside that loop. But in this case, our function does not go to infinity inside the loop. It doesn't go to infinity inside any loop that's finite in the imaginary direction. This certainly is because we've just got our gamma factor that just takes us a certain distance off the axis. So our function has no infinity anywhere close to our loop that we're drawing here. And so that means that the complete integral here must be zero. So there I've written out all four sections of this path I want to think about. And adding them up must be zero because the integral around the closed path, as I've described, is zero. So here I'm this is the first integral and there's the second one and the third one is the normal one, if you like, that's the one that goes along the real axis and there's the final one. Now what can I do next? I seem to have made it into a very complicated problem. It's not that bad.  So now I want to let r tend to infinity. And so this one and this one will individually go to zero and that's because they are after all e to the minus y squared and the major part of y squared will be that real r which is going to infinity so that will just kill it. Doesn't matter if there's a little complex thing multiplying it or not, it will still be down down to zero. So because those individually go to zero and I know that the sum of all of them go to zero, it must be that the two remaining integrals cancel each other out. One is just minus of the other. So that means the following. But we're there. We've arrived because the thing on the right I can just absorb that minus sign by reversing the order of the integral and now I see exactly what I set out to prove, which is that the integral over the shifted line which passes through, has an imaginary part to it, is just equal to the integral along the real axis. So there we are. That's what we wanted to show. That completes the last trick that I needed in that proof. This, by the way, is a glimpse at something called contour integration, which is a really powerful technique because often when you have a hard integral, if you could just see it as a section of a path in the complex plane and then use the fact that the closed loop must be zero, that gives you a very different and very powerful way to solve integrals. Anyway, that's enough of that. That was that detail sorted. There we are. I've just introduced a symbol meter, which is defined as x divided by root dT. Again and again we see this x divided by root T and then root of whichever constant we're using, alpha if it's the temperature problem, d if it's the diffusion problem. And there we are. That's about as neat as I can make it just by changing variables and introducing a constant. It's only helped a little bit versus the original form, as you can see, but it has cleaned up the exponential a bit. What can we do now? How can we actually attempt to do this integral? It's another tough one. They're all tough in this lecture. There are three functions there, really. There's the sine, the one over eta and the eta the minus eta squared, which is also called a Gaussian. And we've met that a few times in this lecture already. I could attack it with, I could try integration by parts or the usual tools, but actually I'm going to bring out another really heavy piece of equipment, a very, very powerful trick for doing integrals. I'll write it down and explain it briefly. Here we are and it deserves its own box, I think, because it's a pretty amazing thing. I'll explain it briefly. So this is the form of Planche-Reyard's theorem, not a name I can really say properly, I think, and it's from 1910. So we're catching up, right? So we started off with Fourier and now we're up to 1910. So we're almost within the last century in terms of the maths tools we need to take things on. So it's getting pretty, it's getting pretty state-of-the-art in terms of the kind of maths we normally use when we're tackling undergraduate problems. What does this one do for us? What's it saying? And actually I've missed off a couple of asterisks. It's basically a way to take an integral that you don't like the look of and hopefully change it into one that you like more. What this says is if you have an integral, and so it's over here, it's the one on the left, and it's a product of two functions, and you happen to know what the Fourier transforms of those individual functions are, then you can actually just instead do the integral of the two Fourier transforms multiplied together, which might be nicer. Now this asterisk means the complex conjugate, but that won't actually trouble us because the choices I'm going to make G will essentially be the Gaussian, so its complex conjugate is just itself. So this is, to say it one more time, you have an integral to do, you can see that it's a product of some functions, could be more than two, but if you group it into two products of two functions that are then multiplied together, and you don't like the look of them, you don't see how to do that integral, you can just say well what would it look like if it was the product of the Fourier transforms of these two, maybe I will like that integrate integral better, and that will be the case here. So we just have to make a good choice for what are f and gr. Now notice of course that inside this orange box that I've written, I've written it in a sort of standard notation, x is a dummy variable, k is a dummy variable, so it doesn't matter if we now write it out with eta or whatever, dummy variables are just instantly changeable to any other symbol as you know by now. So still on the screen at the top here was the thing we were trying to tackle, how am I going to break this up? I'm going to say that that is one of my two functions, so sine of some constant beta times eta over eta is one of my two functions, it's the f function, and this other one the Gaussian is my g function. What I need to do is write down what the Fourier transforms of these things are, but fortunately we've done them before, so there's no work to be done, we'll look at what they are and we'll decide whether that's going to make the integral nicer, which it will. Okay here's the first of those Fourier transforms, the Fourier transform of the sine eta divided by eta is actually just a top hat function, I've sketched it over on the left here, it's equal to zero everywhere except in a region near the origin, so f of k, capital f of k is equal to a half if k, the magnitude of k is less than beta, that is the Fourier transform of the input function there. Now that may or may not look familiar to you if you've attempted the problems that go with this course, because it was one of the tasks a couple of sheets ago, a couple of problem sheets ago, to go in the opposite direction to start from that top hat function and ask what's the Fourier transform of that, but because of the close relationship between the expression for the weighting function and the expression for the original function when we do a Fourier transform, if you've gone one way you kind of can go the other way, so the mathematics for that you've already worked for and it is actually quite an easy one to work out, it's also very similar to the one we did in the lecture course where sorry in in the lecture itself where we had a triangular single triangular tooth in the middle of a zero everywhere else, anyway that's that's what that one is, how about the other one, okay so this one we actually met earlier in this lecture, the Fourier transform of a Gaussian is just another Gaussian with a bit of a scaling and a scaling both inside the exponent and a pre-factor, where did we meet that earlier, let me show you, you probably have forgotten this is a long lecture I know, so back when we were thinking about a pulse of energy, our first complete solution here marked with the blue arrow was a complete solution but it still had an integral in it, so we decided to have a go at that and at one point we were trying to do this integral here and we succeeded, now that if you look at it is exactly the right format for a Fourier transform of a Gaussian and what did we end up with, we ended up finding out that there was a root pi factor and the output Gaussian, the Fourier transform had a factor of one over four up in the exponent, there we are, we know both of our Fourier transforms, we don't have to derive them, great, let's see what they look like, do they indeed look nicer, multiply together in the integrand than the things we couldn't handle, so there they are and there is the integral that we wanted, the first thing to notice is that our top hat function has just introduced a factor of a half and has limited our integral instead of being from minus infinity to infinity, it's from minus beta to beta, well that's fine and our GK function is just a Gaussian in there with its root pi factor, so this has ended up just being an integral over a finite range of a Gaussian, we can tidy it up a bit, since it's an even function, I can just take half of the range from zero to beta and double the value of the integral, but I'd like to simplify that exponent, so I'm going to switch to a variable that takes care of that fraction of a quarter there, okay just to change a variable to what I'm calling K prime just to simplify the exponent there and now I'm going to tidy it up a moment line and actually going to drop that prime from the K because it is just a dummy variable, there we are, that is as neat as I can get that, so we certainly did some serious work on that integral, but let's write out what our complete solution now looks like using this, so this was a solution for S of X and T and the X and T are actually hiding inside that beta constant, let's write out what the whole thing looks like, right so that's the end of this little outtakes video and yeah if you've got to the end of this then well done, that's pretty hardcore, all right maybe see you in lecture eight


The study investigated the effectiveness of adding palm kernel shell ash, pKa, rice husk ash, RHA, and waste steel particles, STP, to the morphology and strength behavior of AL-6061-T6 alloy. The results showed that the responses were greatly affected by microstructural evolution. At 4% STP, 2-4% RHA and pKa increased the tensile and flexural strengths, while 4-6% decreased them. Temperatures between 700 and 800 degrees Celsius favored response improvement, while those between 800 and 900 degrees Celsius were detrimental. The optimal mix was found to be 4.81% pKa, 5.41% RHA, and a stirring temperature of 803 degrees Celsius. The model was validated to have a maximum deviation of less than 5%, indicating its reliability for future predictions. This article was authored by Abiyomi Atawale Akenwand, Olamarwajusona Desana, Adilu Atasogia Deteran, and others.


So, today I will talk about, do you know Papers We Love? You ever heard of it? Papers We Love? Nothing to do with that. I just stole the title. Perfect. Because I liked it. But we're just going to talk about papers that we use in Elixir and existing research that we use in Elixir to implement stuff that we have in the language. My username on the internet is that. My name is Andrea. I work at a company called Community, which does like messaging. This is an article that came out recently. 100 Music Stars are giving the fans their phone numbers. That's what we're doing. We are the phone numbers. If you're interested, more just talk to me later. We're hiring remotely as well, so just come talk to me. And I come from Italy. You've probably heard of it. My favorite thing about Italy in the world, has anyone been at my talk the day before yesterday? It could be in light. OK, we'll recycle a bunch of jokes. I'm sorry. But my favorite thing about Italy is Italians that are mad at food. So Italians get very mad at food when other countries make Italian food, because they don't do it right, apparently. So they have these beautiful Twitter accounts. Just go look at it if you want, where there's screenshots of Italians that are getting angry, especially at Americans, but generally angry at people that are doing Italian food.  Obviously, there is no spinach chicken pasta recipe in Italy. In Italy, a recipe like this is crime worse than a murder.  It's very passionate people.  Yes, very. We're not offended. We're actually vomiting, told you lots of vomit stuff. This is for Americans.  It's beautiful. Then we have defeated people. I really don't understand why you do this. Just people are defeated. So happy that there is an ocean between us, guys. Positive thinking, right?  So lots of passionate, very passionate people in Italy. Anyways, we'll talk about Elixir. Has anyone used Elixir before here? Perfect. Anyway, Elixir is a functional, concurrent, full-tolerant distributed programming language that runs on the Erlang virtual machine. And it's a relatively young language. It started coming out in 2013, roughly. 2012, 2013, roughly. So it's a pretty young language and it has gained a bunch of traction and I'm part of the Elixir core team. That's why I'm talking about this. I'm the guy middle, bottom middle and we're six people and none of us are academics in any way. Some of us have like computer science degrees but we're not academics but we absolutely love existing research. We love finding about things through existing research because there's a lot of, as you may know, there's a lot of existing research that's very interesting and that solves a lot of problems. So when we have to solve problems in our language, we often reach out for existing research even if we're not academics, right? You just go read paper and most of the time they make a lot of sense. We're gonna discuss three things. Three problems that we, where we use research to help solve them and they are formatting code and different data structures and property-based testing. So let's dive right into it starting with formatting code. So formatting code means that you run a tool that takes code written in whatever style you have and it turns it into a uniform, automatically formatted layout, right? So we really wanted this in the language because it's very welcoming to newcomers. It eliminates a whole category of discussions about style which are horrible and boring and also I always want to be right about those discussions. So if we build a formatter in the intellectual, I can be right more times and it also gives like benefits for consistency, right? When you're writing code, it's easier to read code that's written in the same style across community, across companies, across teams. So we really wanted this to be in the language. What is the hard thing about writing a code for matter? Usually you could just take AST and just turn it into some string and it makes sense, right? The hard thing is that you usually want to print code or format code with a line length limit, right? You want it to fit in a given line length. You don't wanna go on forever because otherwise you could just format everything to be like every line to just be as long as you want and it would be much easier.  This is an elixir map. It's like a hash or dictionary in other languages and you have two keys and you have different things. How do you, so if you have let's say a line length of 30, this fits so the formatter can just take the AST for this map and just put it, print it as a single line. But what if the nice transition? What if the line length becomes 25? Now we need to, the maximum line length gets set to 25. Now we need to change how this is formatted in order to fit, right? So it could become something like this, right? So it becomes a formatted thing. If we shorten the line length even more, you can split even more and you can see how the formatted needs to take a bunch of decisions in order to figure out how to print code in a way that fits the line length, right? And that's the main problem, basically. We started out with this paper from John Hu, the design of a pretty printing library. And this paper introduces a concept of algebra documents. So an algebra document is a thing that you can render in, you can use to introduce some logic into rendering pieces of text, right? And a few examples of documents are simple texts. So that's exactly you can't break. For example, if you have a variable name, you can't break really that into multiple pieces or new lines. So you have this text, you have concat, which is a way to concatenate multiple documents and possibly breaking them in the middle. You have something like nest where you say, if this breaks nested by a few columns and that's used for indentation when formatting. And then you have something like line, the first is a line break. So you have a few documents that you can compose and then have logic to handle them based on the line length, basically, right? So if we wanna see an example, if you wanna write a list, you can say like, just write a parance, then concatenate with the first element in a comma, second element in a comma, third element, and then the closing parance, right? If you print it without any line limit, it's gonna print like that, right? It's just gonna fit all on one line. We can use line and force a line. So we can use parance and then the line with all the elements. We can nest the previous thing so that when there's a break, the break is nested and you can see it's indented. And so that forces the indentation and it forces the breaks. Another paper by Philip Waddle called A Prettier Printer also introduces the concept of groups, which is what we use as well, which is a way to basically say, to have a unit that can either be split or not split. So in this case, like the unit is the whole list. Like this whole thing can be split or cannot be split, but if it gets split, it should be split altogether. That's a thing, right? Otherwise you can end up with where you have like a parance, one, two, and then three on a new line. But we wanna make sure that either you print on a single line or you split the whole thing on multiple lines and that's what a group is for, right? So when you are dealing with these algebra documents, the most important thing is, again, having a hard line length. So when you have to decide, you basically, when you are rendering, you have to decide whether you want to render the document as a single line or replace the concatenations with breaks and render the document on multiple lines, right? So you have to choose. The problem is that Elixir is an eager language. It's not a lazy language, it's a strict language, right? So when you call something like this, it evaluates the arguments before evaluating the choose function, right? And in this case, it would have to render doc and then it would have to render the replace concat with line break doc, so a document where all concatenations have been replaced with line breaks. It has to choose and it has to evaluate both of them and see like if the first one fits, then it's okay. Otherwise it has to go with the second one, right? The problem is that this is exponential, right? Because you have to explore all possible scenarios before you can actually choose the main, right? It's an exponential problem, it's not really, like it's very, very, it doesn't scale very well and it makes it impossible to write practical things, right? So fortunately, we found another paper called Strictly Pretty by Christian Lindig and this paper explains how to do strict printing. So it explains like a different approach to formatting and to dealing with algebra documents that is strict and this was implemented for OCaml in the paper. So it has a very similar approach to the original paper which was implemented for Haskell but we were able to turn our formatting into strict formatting so that it works for our language. We also ended up adding a bunch of documents. So like color, for example, to have stuff that's colored in the terminal, we can use this. We're nesting with a cursor. So like nest as far as the cursor is instead of a fixed number of spaces but the idea is that we were able to, based off of this research, we started with a problem, we started with a solution, it didn't apply to our language, we found someone that already solved the problem for our language as well. So we applied that and then with the abstraction that we found in the research, we were able to extend this and create our own things that we need for our own purposes, right? So it was very, very useful. Diff in data structures, this is like, so the idea that we wanted this because when you have two tests, when you have a test and you're asserting that two things are equal and they fail and the test fails, we want to know why it failed, right? And here it's CCC but when you have like a big piece of text, for example, it's harder to see why it failed. So we wanted something like this where you have a diff of the things that are different basically. So it's much easier to see, it's in like a normal github and it's much, when you have a large data structure, this is unbelievably useful, like it's very, very useful to be able to point out to where the differences are. And so to do this, we started with this paper, we called an O&D difference algorithm, it's variation by Eugene Myers and this paper basically is about finding the shortest edit script to turn a sequence into another sequence and basically it's like finding the shortest path in a graph, right? That's a problem that it's solving and the way that it turns, edit script is basically a sequence of commands that can bring you from a sequence to another sequence and the commands are add this, leave this alone or delete this basically. So with these three commands, you can bring for example, any string into another string where you can say just add this letter here, like leave this part alone, remove this letter there and you can transform a string into another string. This is useful for, so the O&D complexity is important here because this is useful for things that are not very different. So if you have two sequences that are not very different, like two strings that are pretty similar, like the ones that we saw over here, if they are really very similar, this algorithm works very well. The D in the O&D is there related to how similar the sequences are, so the complexity of the algorithm is based on how similar the two sequences are. So it's good for things like source code changes because you usually don't have a lot of source code and you don't have to do big changes all the time, you usually do small changes. It's useful for things like DNA strand mutation, which is, I have no idea even what it is, but it's mentioned in the paper. But we were able to basically turn this paper directly into an implementation, so we have here list.mires difference and as you can see it takes two lists and it gives you an edit script, so the edit script for us is just EQ, that's the command for leave this part alone, then delete an element, then leave this other part alone, then insert another element, so it's just an edit script. And once you have this, it's really just a journey into a diff, you just colorize this, right? You colorize the delete as red and the add as green and leave the rest alone. We were able to do no modifications to the paper this time, so we were able to just take the paper and implement it in a lecture and it worked and it was very nice that we didn't have to think about this and figure it out. We also improved the situation a little bit by finding this other paper, string matching with magic trees using approximate distance. This tells you, gives you an idea of how similar two strings are, very fast, in a very fast way, and now we use this to decide whether we're gonna do diffing or not. So if we have strings that are relatively small and similar, we do diffing. If you have huge strings in the test failures, for example, we just don't do diffing because it would take too much time, right? Because that's property of the algorithm is that if the strings are very different, it takes time. So we were able to improve the situation a little bit for us by not doing the diff in that case at all. So that was very nice. We could really just basically take the research and apply it to our language and we didn't have to think about anything. And property-based testing, then it's, this is a more complex problem. Actually, we ended up not having this feature in the language. It's now shipped as a separate library, but we researched this a lot. And if you don't know what property-based testing is, it's basically a way of testing where you take, instead of giving exact values to things that you're testing, you come up with the shapes of values that are, that should work with your code. So for example, a list of integers, that's a shape. And then you find out properties of the output of your code. So for example, if you have a sort function, a property of the sort function is that the length of the list that it sorts is the same as the length of the original list, right? So that's a property that applies to every possible input that you give to the sort function. Every list of things, so that's the shape. And property-based testing basically takes the shapes, takes, to take the shape definition, takes the properties of the output and generates a lot of possible random data and it verifies that the property remains, right? That's property-based testing. This is an example of what I just mentioned. So we have generated a bunch of random lists with the shape list of term. So any list of any term, in elixir, sorry, the terms are all comparable, so it doesn't matter what you're sorting. Then we sort and then we assert that the sorted list is a list and that the length is the same. So that's a property that's valid for all lists, right? To implement this thing, we started from QuickCheck, this is a original paper called QuickCheck, a lightweight tool for random testing of Haskell programs. This is good, but it gives you a good idea of property-based testing, but it relies very heavily on types to generate things, right? So for example, it's easier in something like Haskell because you can have color, which is red, blue, or green, and then you can just infer what values you can generate from the color, right? So if you have a function that takes the color, then you can implement easy things like easy generators for types and you can say just for example, color is gonna be either red or blue or green, right? So in elixir, we don't have this because it's an end-to-end language that has no types, but we were able, this is not existing research as much, but it's existing code, actually. So if you write closure, you might know test.check, but test.check is a property-based testing framework for closure and we were able to have a very, very similar implementation to this thanks to the fact that closure is very, very similar to elixir in semantics, so it doesn't have types, it has a very similar set of data structures, they're immutable just as well, so we were able to take these, the ideas from the property-based testing and the implementations from the closure.check can make a library in elixir called stream data that allows you to actually, this is actually running code, allows you to write property-based tests and generate data and verify the properties of the data. So we didn't end up, again, adding this to elixir, but the experience was very similar to the other cases where we studied research and came out with something practical. Some honorable mentions of some paper that we really enjoyed, this is called How to Make Haddock Polymorphins Less A Dock, and we use this as the base of implementing protocols in elixir, which is a feature where you have polymorphins based on the data structure, so you define a set of basically functions that you can call, and then you can define implementations in different places for those functions for different data structures so that it looks, for example, you can have collections as a generic idea, and then you can have a module that works on all collections, and there's a bunch of functions like map or reduce or filter that work on all collections based on this protocol. This is a paper for LISP, Recursive Functions of Symbolic Expressions that Computation by Machine. We didn't take a lot from this, but elixir is a homo-iconic language that has macros and the ASC of elixir as elixir code, so it has a lot of ideas that come from this language originally from this paper. This is one that I like, it is Advances in Record Linkage Methodology as applied to the 1985 Census of Tampa, Florida by Matthew Jarron, this is a paper that describes another algorithm for string distance, it's Jarodistance for short, and it's very performant, so we actually have this function called Jarodistance in the Elixir Library, if you wanna do just diffing, or if you wanna get the distance between two strings in your production code, this is what you should use, not the diffing algorithm. And then there's one called ITERRT, Teaching an Old Fold in Neutrics, by John Lado, this is not a paper, I believe it's an article somewhere, a monad read or something, I can even remember, but it's still research, and we use this as the base for when designing the language, as the base for enumerables, which are our collections, polymorphic collections, it's a way to have a generic way of implementing something that can be enumerated, and can be where the enumeration can pause and continue, and you can implement this for multiple things like we implemented for lists, we implemented for lazy streams, where the data is lazy, we implemented for things like reading a file can be a stream where that emits lines, so we have a very good abstraction and it was heavily inspired by this. So the conclusion for this is that existing researchers is very nice to have. I recommend that everyone, when you're trying to solve something that sounds like a computer science problem and doesn't sound like adding a route to a web application, if you have to figure out a problem that sounds complicated, just go look at the research because there's a good chance that they're gonna be surprised how many things have been solved by other people. For me, it's probably better than me, that's the part that I like, that they solved it probably better than I would, so it's very nice to be able to have this existing research and the thing that I like the most about this is the research really tends to solve problem in a very good way. So when you read papers, usually it's a very, they're very focused on finding a general solution or a very simple solution or for example, a solution where you have a very, very simple core of things that you can compose, like very simple primitives and composition, so a lot of focus on that so that you can build more complex abstractions but starting from very simple components, so that's very, very nice. And then what we did is usually just modify this lightly so that it can be applied to a real world or to a real needs, but all the base ideas and the base algorithms that we use are often, they often come from existing research, right? And that's all from me. Yep.


Hey folks, it's Leanne coming to you from day one of IMAX. It's the Breakfast with Pacific World at the Venetian. Pacific World is a global DMC that we use for some of our clients that do global programs. So it was important for me to come here and meet some of the suppliers. But a theme I'm already seeing emerging and it hasn't even, the show hasn't even started is some of the sustainability initiatives that a lot of our suppliers are doing. And Pacific World is one of them. They have this great program called Bring Change With Me. And when you talk to each destination, they're going to outline some of the sustainability initiatives they're doing for their clients and for their clients' programs, which is really cool. And the other sustainability initiative, which is so awesome, and thank you IMAX for this. I was an NIMX last year, so this is the second year of you guys doing it, kudos to you. But look at the name badges.  There's no plastic holder for the name badge anymore, no lanyards. Yay! So you can either bring your own lanyard or some of the hosted buyer groups have branded lanyards that you can use. So really proud of IMAX in this initiative because it's thousands and thousands of classic name badge holders that they're saving. So those are my sustainability observations on day one of IMAX 19. Have a great show everyone.