the name of the Father and of the Son and of the Holy Spirit. Heavenly Father, thank you for the beautiful way that you made us body and soul. Help us to understand ourselves better, that we can grow under the influence of your grace and be transformed by your love, that we can become saints. Send your Holy Spirit to guide us and give us wisdom this evening. We ask this through the intercession of our Lady and St. Joseph, through Christ our Lord. Amen. The name of the Father and of the Son and of the Holy Spirit. Amen. Amen. Thank you for that beautiful prayer, Father. Thank you so much for coming here and being with us tonight. We're so excited to have you. And we are excited to continue this journey of healing from the Avila Army. We've been doing a series on healing, some of our extra exclusive webinars for our monthly donors. And that's kind of what inspired this webinar with you tonight. And last time we did a talk on healing memories, kind of going back and asking the Lord to reveal some of those places where there may have been hurt. And I think we'll be really neat to dig into in this webinar is some of those feelings that come up when we encounter this memory. So we might have recollection now of a place that's been wounded in our heart or something we're holding on to. Maybe we've done forgiveness work and we really worked on forgiving the person and, you know, discernment of spirits, understanding that this is hard for me, but we still may have some walls up there. And there might be parts of ourself that are blocking a deeper relationship with Christ that we're not quite aware of yet. And so that's why we have you here tonight to talk to us about some of these parts deep down in our heart and healing those. So, Father, I know you have a presentation and I'll kind of let you take over from here. Great. Well, thanks so much and thanks to all of you for coming this evening and it's a joy for me to talk about these things. I wish I had followed all of the previous presentations so that I wouldn't repeat anything, but hopefully this will be sufficiently fresh. And I'll just give a presentation and then I'm happy to make this a discussion and maybe Anne will be able to even leave me a little deeper into some particular areas that would be helpful for you. So happy to do all of that. But let me just share my screen. I made some fun pictures that always makes this a little more interesting. And here we go. And I love the title. Anne and I kind of came up with this in dialogue a little bit and then she really did a beautiful job capturing the ideas and bringing out, well, some things that I think are so important and has been so much a part of my life. I'm a Benedictine from St. Vincent Archabi in La Trobe, Pennsylvania. So I'm not a Carmelite, but I love the Carmelites. And I spend a lot of time giving spiritual direction and I've had the privilege of getting to know a lot of individual hearts. I also collect things. So I read a lot and when I find things that are helpful because they capture the experience of people I'm working with and I find them valuable for healing for myself and for others. I tend to collect them and then try to put all kinds of things together and that takes me in Dominican directions and psychological directions and anyway, all kinds of fun things. So I just want to start by referencing Anne's email. I love this little email that she shared with us in the invitation. Be Not Afraid, that's my title. We hear that, of course, from St. John Paul and we repeat that kind of thing quite often and we know that Jesus says that 365 times in the Bible, which you can always remember because where Jesus doesn't say it, God says it or the Bible says it, I suppose, 365 times as many as there are days of the year. And Anne gives us this little scenario. Dear Anne, we are told that fear is from the enemy. The Bible tells us over and over again, do not be afraid. So we renounce fear in Jesus' name. But what happens when we renounce fear or anxiety, shame, anger and many other feelings, but it doesn't go away. So it's a great question and I think is, yeah, one we can all identify with in various ways. And I would say there's one thing that happens is we have the right idea that our faith life should help us. Let me just say it really simply that way. We have the idea like it should make a difference that I'm Christian and so I should be able to like use some Christian powers to help things that are immediate difficulties in my life. And I run into difficulties with fear, with anger, with certain kinds of pain or shame or anxiety or these kinds of things. So I should be able to like use my Christian powers to overcome those things and therefore have a happier life. And at a certain level, that's all correct. It's just sort of getting the pieces in the right places that is the important part, the really important part or otherwise we can end up sort of complicating things. And so I'll try to cover some of those ideas. So just to kind of zoom back, we have emotions. This is one of those things that makes us not angels. I'm not talking to any angels on here. We're all human beings. We all have bodies and therefore we all have emotions. And now St. Thomas Aquinas has his names for these things. But anyway, the term emotions I think captures the idea well enough that comes out of our modern psychological vocabulary. St. Thomas talks about appetites and passions and some other things along those lines. But when we're young, we can think of our emotions as, you know, the word is in there, motion. So our emotions move us. And if we had no emotions, we would not be moved by anything. That's not very interesting. That's kind of flat. We would be emotionless. And anyway, so we have emotions when we're young that are kind of wild. We can think of them like a young pony. And I tried to find a pony that was even wilder than this. At least you can see there's a little pulling of the head away. And it's, you know, vigorous and young, but we know that, well, and they can be a little wild. And we can think back to our own, as they say, every saint has a past and every sinner has a future. We all can probably share things from our past when these things were a little wild. So how do we handle this? Well, one approach that we can take is we can beat it to death. We can beat the life out of it. We can beat all of the wildness out of it. And we can end up with a dead horse, or a mostly dead horse that's kind of emaciated and doesn't do much. And in fact, not only does it not do much, it becomes a burden for us because we can't actually get rid of it. We end up carrying it around with us. And so this is, you know, and this is the kind of thing. Now, this is one of those places where I need to slow down. I'm not energetic about ideas, but these ideas have are connected with people. And so I just want to slow down here and just reverence this place that may touch on the hearts of some of those who are, who are with us because it's one thing. If we kind of beat down our own emotions, or we try to control them, suppress them, contain them, get rid of them, amputate them. We try to do this in various ways.  And we end up feeling like we're carrying around a dead horse when that happens a lot.  It may happen in some particular areas of our emotional life. And then we can feel like we have this burden that we're carrying around. And this is not how God designed us. So he designed us to form, not just to be wild and not to be dead, but to be formed and strong. And like Astalian, that's how our emotions are meant to be guided by our reason. And we call those virtues, back here in Thomistic land and, you know, the Catechism and the Catholic Church, these things. So we talk about virtues. And when our emotions are full-bodied and robust and strong and vigorous and docile and obedient to right reason, when we live virtuously, we live fully alive. And we're just in these days of Jesus talking about these passages. I came that they may have life and have it abundantly. John 1010. So what does abundant life look like? Well, it looks like an abundant emotional life, a full emotional life, where we can really enjoy good things, where we can really resist bad things, where we can really fight for hard things. And there's a robustness to all of that that's admirable. So we talk about the saints exercising heroic virtue. Heroic virtue involves a lot of emotion. It involves a lot of passion. There's passion in that heroic virtue. But it's been shaped in a way that it's able to really strive for the good and resist the bad, overcome evil, and achieve great goods. So that's God's design for us, this very robust emotional life. So just a little survey. Again, this is kind of domestic. It's really Aristotelian land that St. Thomas brought into the summa and then reshaped in his own ways. And we can do a lot with this. I just want to make a couple of simple points. I'll give a bit of the overview here first, but you may be familiar with these terms, concupisable appetites and irascible appetites. These are some of the, again, kind of domestic terms that float around. And of course, you know, John of the Cross and Teresa of Avalar building on this framework. But I really like Conrad Bars is, he was a psychologist that reshaped psychology to use a domestic anthropology, to use the anthropology of St. Thomas Aquinas. And he renamed these from concupisable and irascible, which, you know, first of all, they're a lot of syllables and they're kind of hard. And they're kind of in, you know, we also know concupisants is this kind of disordered desire that's a consequence of original sin. And irascible has to do with, and who wants to be irascible anyway? It's like, I don't want to admit that I have concupisable or irascible appetites. So no, that's not, you know, St. Thomas wasn't living in our time, but we're weighed down by our own connotation. So Conrad Bars just need, rename these things very simply. And I think helpfully to the humane emotions and to the assertive emotions. And the humane emotions, just the simplest two to think of is when we have something that's good, we feel joy. You can think of a whole variety of examples. The child gets the ball, the birthday boy gets the birthday cake. We get an A on an exam, we get a hug from someone we love. You know, anyway, you can have complex or simple goods and they lead to various levels of joy. But simply said, joy comes from the possession of the good and the opposite. So I use the word evil here just because it's four letters and it fits better on the page. But we can think of the good. And as St. Thomas describes it, evil in our mind tends to have a personality to it. So just to make it a little bit more general, we think of the evil as the lack of the good or the deprivation of the good. The good is missing, the good is not there. And so the birthday cake is taken away from us or the ball is taken away from us. That leads to a certain kind of simple sadness. A loved one is taken away from us. Or we fail an exam. Or we're the victim of bullying or misunderstanding. So think of good and bad in these ways, first of all. And our response to that is sadness. We could use the word hurt here. We feel hurt when bad things happen. So that's a proper emotional response. That's in touch with reality. A bad thing happened and I felt hurt by it. I felt sadness by it. I've lost something that's good and I grieve that. We use the word grieve. I think it's a very helpful one. It's sort of permissible to grieve. And so it's come nicely into our vocabulary. And then we can also think of the humane emotions in terms of a future good or maybe a future evil. We have a desire or an aversion to a desire for the good and aversion for the evil. And then there's another... So those humane emotions, now think of what a heart is like that feels real joy at good things and that feels real sadness at bad things. And even think of the heart of our lady and our lady of sorrows. Sometimes we have the idea that Christians aren't supposed to be sad because it's the joy of the gospel after all. That's what we're supposed to embrace. Well, we celebrate our lady of sorrows and we celebrate her tears and we celebrate her pain and her grieving because she was able to remain at the foot of the cross and her heart felt because a heart that's properly tuned corresponds with the gravity of the evil. No one experienced a greater evil and stayed there than she did. So her heart is really robust to be able to feel all of that. And likewise, the joy. Now we don't get an account of the encounter of Mary with Jesus and the resurrection, although St. Ignatius of Loyola includes that in his 30-day spiritual retreat. But we can imagine the joy that she experienced at the reunion and certainly the joyful mysteries that we celebrate. So our lady was able to experience incredible joy and this is a sign that her heart is really humane. She has this kind of robust humanity to her. We experience someone as humane that's able to weep with those who weep and rejoice with those who rejoice. So that kind of robustness at the good that's present or the lack of good that's present. Now there's another set of emotions that we can think of which, again, the traditional word is the erasable appetites. I like the word assertive emotions or sometimes just the energy emotions. There is a certain energy to do something and this has to do with what St. Thomas calls the arduous good or the good that's hard to achieve. When there's something out there that's going to take a lot of work. I'm working on a degree or I'm working on trying to rescue a person who's really lost or I'm working on my soccer game and really trying to make that great shot from a distance. Now these are not of the same order of thing but when I'm working on something hard I hope that I can get there and I get a certain energy from that hope. Now we're talking about the emotion of hope not the theological virtue of hope although they're obviously related. The theological virtue of hope is a hope in God. But I have this hope that I can do it and when it's right in front of me I surge forward in courage and I take hold of that good. I work hard for it and I have fortitude, strength to do that and I do that for the arduous good. Now I think we're all behind hope and courage and this is where things get another complication. We tend to have some complicated feelings about the feelings of fear and anger but at their basic level anger and fear are God-given emotions and they serve a good purpose.  And fear is when we are facing an evil that we can't overcome and we run away from it. So let me just suggest if a bear breaks into your room right now and you feel a lot of fear that's a God-given gift to help you run the heck out of there because otherwise you get eaten by the bear. We don't want that. So there are dangers that we need to run from there are dangers that we need to fight and God gave us these assertive emotions. Now the assertive emotions have a lot of power to them and so that's where we can end up having a complicated relationship with them because we've sometimes been shamed about our fear and we've sometimes been shamed about our anger and so we've tried to control that by suppressing it and that leads us back to the dead horse image from previously. We try to get our hands on that thing and we've had experiences where we got very angry and it was an angry outburst and it hurt somebody and we regret that and we apologize for that and maybe it's caused some complexities and we'll get a little sense of how some of these things interact but at their basic level the virtuous man is the one who knows how to use his anger to overcome the enemy. Now let's think about overcoming sin or sinful behavior let's think about fighting perpetrators and rescuing victims we can think about anger in some of these ways and again likewise the fear knowing when to run and having the energy to do it can be a good thing. So what do we do with this? Can we control our emotions? This is kind of that, why don't you just renounce it? What do we do about these things? Well our emotions are subject to our reason and in a basic way our emotions respond to the idea that we have you can think of if you saw a shadow and you thought it was a bear fear might rise up in you it may or may not be a bear but your idea was and the reason is there so if you saw a shadow and you thought it was a friend joy, hope might rise up in you so our ideas do affect our emotions our reason affects our emotions but our emotions are not subject to reason like a master to a slave or even the way that our hand is my reason said to move my hand and my hand moved even that's a little bit of a limited operation because if my reason told my hand to play the piano it wouldn't sound very nice to anyone out there so even our limbs are not fully subject to our reason in the way that they will be in the resurrected body so our resurrected bodies are perfectly conformed to our reason that's one of the beauties of that agility of the resurrected body so when my mind tells my fingers how to play the piano and the resurrected body it'll happen not in this body so but our emotions are even more distant than that we can't control our emotions like a master over a slave St. Thomas uses the image of he says it's more like a noble ruler over free citizens and I kind of like that image because sometimes our emotions feel like free citizens who gave you permission to feel fear or joy or sadness or whatever it's like sometimes we have a sense that our emotional life has a life of its own and so we can feel some of that disconnect Conrad Bars uses an image that I like very much he says our emotions are like children that need to be led by the hand and I think that's a very beautiful image because it gives us this sense of they will follow but we need a little bit of gentleness with them sometimes we can get so fierce with our emotions we can end up trying to control one emotion with another emotion the sort of classic thing in Christianity is we have also a kind of suspicion around our concupisable appetites around our humane emotions because a related word with joy is pleasure and we get kind of suspicious about pleasure well I'm enjoying too much now this is even worse in America with the Puritans what do they say that the Puritans have this fear that someone somewhere out there is having a good time so sometimes we can have this kind of complicated relationship with those emotions and one of the patterns that can form is we can end up sometimes through fear we can end up controlling suppressing our joy or our pleasure or our desire that goes along with that and make it like I'm not allowed to have any of these things I'm not allowed to want these things I'm not allowed to enjoy these things and fear can do that and then we can have some of those reinforced structures of fear that came from the outside as we were scolded for a hand in the cookie jar or as we got the idea that feeling anger isn't allowed in this house not allowed to feel angry and then these things can end up getting suppressed by fear sometimes we can use anger also to suppress some other emotions so we can end up having some of these knots that start to develop in our emotions so the first thing is to realize our emotions are God-given and they have a purpose and they need to be trained and formed not controlled and shamed and suppressed so thinking of them like children sometimes our emotions still need to grow up a little bit but we don't have them grow up by beating them up we help them to grow up by leading them with love and a really important part of this I'm addressing all of you and I'm hoping that you'll apply some of these concepts in your own life but I also want to make the very important point this isn't something ultimately that we only do alone so we can certainly practice alone but it often requires the help of another and fundamentally it always requires the help of another in the sense that part of that process of moving from the pony to the stallion always involved the affirming love of another and sometimes we miss some of that along the way some of that can be filled in after the fact by entering into healthy relationships where there's affirming love I'll define that here in a moment but I love this passage I think it was even before he was cardinal Joseph Ratzinger, our beloved Pope Benedict later on wrote these meditations on Holy Saturday which are just magnificent if you look up Joseph Ratzinger Holy Saturday you'll find the meditations I'm happy to share these slides of course you can copy the web address there but listen to this part anyway it's in the context of something else but he describes this so beautifully he says, if a child had to venture out alone through a wood on a dark night he would be afraid even if he were to be shown a hundred times that there was nothing to fear he is not afraid of anything specific to which he could put a name but in the dark he feels insecure an orphan he feels the sinister character of inner existence only a human voice could console him only the hand of a person he loves could banish the anguish like a bad dream there is an anguish, the true kind nesting in the profundity of our solitudes cannot be overcome by reason but only by the presence of a person who loves us so we're always going to be involving another in our healing journey there's always going to be that involvement of another it's not a matter of learning all the techniques and then going off and practicing them on our own because God made us for each other for community, for communion if we were able to become totally self-sufficient normally the word we use for that in Christianity is hell, that's total isolation where I don't need anyone for anything I even worship myself that's the full expansion of self-sufficiency that's not what we're made for we're made for relationships so there's no shame around needing someone and sometimes we end up in that place where it's like I'm really afraid and I can kind of argue my way out of it but it doesn't make the fear go away ultimately I need another person who can hold my hand who can reassure me sometimes they even say the words that are in my own head but they don't reach my own heart unless I receive them from another and so we should never feel shame around needing someone else who just reassures us, supports us affirms us, consoles us we're made for relationships and if I have a certain weakness there I need to be reinforced I scare myself or I'm scared by something where I face a bear of different kinds a spiritual bear or a physical bear and I'm trembling and I can't stop myself from trembling but I can be held by another and that can bring peace to my heart and so the goal is not to get over that now there are some things obviously that we can also do on our own in prayer and sometimes we can work ourselves in some places and we can have some deeper self-understanding and that's all good too but these things grow together we support each other so what is this affirming love and here I think Conrad Bars just does us a great service and he has a number of books that I really appreciate Healing and Feeling Your Emotions or Feeling and Healing Your Emotions but there's a little book Born Only Once which is some of the ideas and then he has some kind of scientific, complicated books and some other things like that that really get into the details he gives the whole tomistic framework of psychology that he developed with Anitrua anyway this is a very simple a very fundamental concept going with what I just described about needing another I need another in a particular way and he describes this as affirming love I want to take a couple of minutes to go through this he says your affirmation you are feeling firm and strong you can see that word affirmation it has firmness in it and that's what gives us strength and kind of holds us together and helps this process to move along that I can work with my emotions in this good way moving towards that stallion but I need something to hold the whole operation together and that comes, that's a gift from another so your affirmation you're feeling firm and strong you're possessing yourself in joy you're feeling worthwhile starts with and is dependent on another human being who is aware of attentive and present to your unique goodness and worth separate from and prior to any good and worthwhile thing you may do or can do so he starts at the innermost level it's a first of all an awareness and attentiveness to the unique goodness and worth of the person so that I really, I love you for who you are not because you did a great thing not because you were nice to me not because you raised your family not because you're a good Catholic not because you pray a lot because you are a human being because you are made in the image and likeness of God I love you because of your own unique goodness separate from and prior to any good and worthwhile thing you may do or can do second is moved by feels attracted to finds delight in your goodness and worth so I allow myself to be moved by you I can study you like a scientist and say you are good you are unique for these six reasons check, check, check I'm going to write you down, take some data or I can encounter you as a person and I can open my heart to you to be affected by you there's actually a vulnerability in the listener as well as a vulnerability in the speaker and that's the kind of listening by the way that I teach in spiritual direction the spiritual director needs to be vulnerable open to your unique goodness to be affected by it to be moved by it to be touched by it that I'm not just cold and distant analyzing you but that I'm open and able to be moved and affected by you so I allow myself to be moved by feel attracted to and this is, we're talking about not sexual attraction here we're talking about the attraction this is a beautiful person this is a good person, remember good attracts evil repels so I'm attracted to your goodness finds delight in your goodness and worth but without desiring to possess you or use you or change you so I see you for who you are I affirm you in that and just moved by that I'm going to own you or possess you I don't have an interest in you and you're going to be part of my scheme or I'm going to take advantage of the fact that you've got all the connections and we're not doing a project just for who you are it's an unconditional response and then third, permits his being moved by and attracted to you to be revealed simply and primarily by the psychomotor reactions visible, sensible, physical changes which are part of his being moved so in other words as I encounter you you can read in my face you can hear in simpler ways in me when I started doing spiritual direction on the phone you know I'd be nodding my head and then I thought this is not working because this person cannot see that I'm nodding my head so I had to develop some way of making little groans yeah I see but they're kind of spontaneous responses you know when you come into a room I had this gosh such a touching experience this will be really helpful for you so my mother who I just love with all my heart and really taught me so much of this by her example she declined over the last 8 years of her life from Parkinson's disease to dementia Louis body dementia which is different than Alzheimer's this is maybe a unique description from my experience but if you've ever had the experience of kind of falling asleep when you're trying to talk to somebody this might be my problem primarily but anyway and you can't quite remember what you just said you might have just said something but you might not have in that space like everything was present and she had a hard time sort of holding a thread anyway there was one time I went to a visitor my dad was her full-time caregiver and I always you know I went on my visit to him and when I came in the room she lit up like her whole face was I mean she could not have expressed her delight at seeing me anymore profoundly I mean it made me feel like a million bucks I just I felt like I was the greatest thing in the world that's an affirmation response so she doesn't want to use me possess me contain me it's not because it's something purely for who I am now we're not going to necessarily have that kind of response for everyone we see but it illustrates this point that's the kind of spontaneous gift and so this is the way that Conrad Barr summarizes affirmation he says in affirmation I give when I'm affirming you I give the gift of you back to yourself in other words you get to experience yourself as a gift through me so you're a gift for me and you experience yourself as a gift through me that's what an affirming response is and that's what gives us the strength then to do a lot of the other things to have the kind of interior freedom and the self reflection and to shape the emotions and to respond in different ways that helps me to be in myself that helps to ground me and help me to be in my you know by myself I'm going to come back to that that phrase here in a moment so so that affirming love this is this is one of the great gifts we give to each other this is normally the kind of thing that we're receiving a lot from our parents you know this is like a mother Conrad Barr uses this nice image of water he says water has this quality that it perfectly shapes itself to the contours of an object you know think of a fish or you know a coral or algae or something like that water totally shapes to the contours of that object but water also shifts and moves and it gives room for that object to shift and move it doesn't control it it's not rigid and so it continues to conform to it water also kind of overlooks the blemishes right you know everything looks a little bit better when it's under water it it does the air brushing effect you know that our zoom lenses also tend to do and then water also cushions the blows if something tries to hit that water is going to slow it down and it's not going to be struck so much and he says so affirming love has that quality like water that it holds without controlling manipulating adjusting you know and it exposing it holds and then he says of course the perfect example of this is the water bag of the mother's womb beautiful right that's what we started in and in that way it's a womb like quality we might say to affirming love that it holds that way and conforms it expands it makes room and embraces so now I want to take us another layer deeper and recognize that you know not only do we have all these emotions and I've already kind of alluded to this we have the sense of emotions almost being like their own personalities they seem to have a life of their own I use the example of building you know leading them like children we have this horse but if we were honest about it we've got several horses in there you know and sometimes they're going against each other and that's the kind of thing that St. Paul says I do not understand my own actions I do not do what I want but I do the very thing I hate for I do not do the good I want but the evil I do not want is what I do you know this is like St. Paul's distress and we have this kind of thing and we express it in language sometimes like this you know there's a part of me that wants to ask for help but there's another part of me that's afraid and shuts down you know so we describe ourselves in parts there's a part of me that wants that there's a part of me that doesn't and we have this kind of inner conflict and almost like separate personalities without well I guess I could say you know if we really push this to it it's extreme we could do something like dissociative identity disorder multiple personality disorder you know that's a that's kind of a strange thing out there in the psychological literature and none of us are in that place but we do have this way of experiencing ourselves I pulled some examples from the movie inside out which I think is just delightful it's a you know it's not perfect but it's descriptive and evocative of some of these ideas so anyway you know these these parts are like little personalities in us and you can think of how you experience different parts in different situations you know the languages around us is that parts get activated in different situations you know there's a part of us that's playful and carefree maybe you experience that when you're with your children or your grandchildren you kind of get into it and it's like they're playing house and you're playing house I was playing with my nephew you know when he was about six or something now he's brilliant he's 20 something now but anyway when he was little he had this Noah's Ark and you know anyway I'm not the best with kids but I was giving it a try you know I was down there on the floor with him and I was moving the animals you know into the Ark and he just looks at me like with disgust he's like Uncle Bono how it works and I'm thinking I have a master's degree in theology I know how Noah's Ark works what are you saying to me I kind of get alright you tell me the rules of the game we'll play you know so anyway sometimes we get playful in different context you know there's a playful carefree part of us maybe there's a part of us that's a little more detail oriented careful that part of me died I think when I was five I'm just playing but you know we also have different parts with different strengths you know but maybe there's a part of us that's social or engaging there's a part of me that comes out what I'm teaching what you're experiencing now is not what my confer is experienced here at the monastery necessarily you know there's a sort of animated thing that comes out and you know sometimes there's a tender part of us you know when I'm listening to myself you caught that at the beginning because I get so into it I get excited about sharing these things and then I suddenly realize I'm talking about dead horses and people are like you know so that's where I have to move back into I got to engage the tender listening part of me that's worked with with so many hearts because there are so many that have been wounded and have you know parts of their emotional and I'll say this for myself too when I was at the point of entering the monastery gosh I'll tell you the I was baptized when I was 21 I really came to know Jesus first when I was about 18 and as I developed a real relationship with him when I was about 20 I guess I was experiencing some other Catholics who could cry and people moved by that I hadn't cried since I was 12 and in one moment in prayer I was there in the chapel and I was really struggling and I said like what's the deal why haven't I cried and then I was thinking back to what happened when I was 12 and it was not one of my dad's more stellar moments you know he was really angry with my brother and anger terrified me and I was like heaving sobbing I was so terrified by this and and then he even came and my dad who is just a beautiful person I mean I just can't I'm ready to canonize him in just in so many ways he's really a marvelous person but he was really upset with my brother there had been a whole other series it's my older brother you know I had told on my brother that's what facilitated this whole thing and so I'm also like there's all this mixture of guilt and fear and a whole mess of things in my poor little 12 year old body and my dad came into the room one time and he looks at me and he's like why are you crying stop that which is the worst reaction right well I couldn't even stop I was like so crushed by all that so anyway I I was going through this memory it just came up really spontaneously when I was there in the chapel I was praying and I was like why can't I cry and then this memory came back to me it was the last time I remembered crying and and then I said God where were you you know I didn't even know you I didn't know anything about you where were you in my life I got angry I was just kind of yelling at the Lord and then I kept I kept in that image and I remember what happened there my mother in that moment when I was like heaving sigh my dad came in yelled at me all this kind of stuff my mother held me and I could feel in that moment my head just like against her stomach and just her holding me so tightly and and comforting me in that moment and I just had it was like right there the Lord said I was there with you and I realized that he was really in my mother and was loving me through her in that moment and I was able to receive that in a way I hadn't been able to receive that all those years previously and was able to find a lot of healing and and my whole my whole Christian life really I've been in the monastery that was 25 years ago and I'd say it's been a steady journey of really recovering tears you know allowing that that part of me that got so exiled in that moment a part of me just got suppressed by my father's anger and and then I wasn't able to receive my mother's love in that moment but really received it kind of later on and then you know had a lot of affirmation a lot of support in the Christian community that allowed that part of me that could really feel sadness and could feel pain to have some breathing room so that I can you know I can cry with people and and and really share their pain so parts oh boy I'm just gonna say a couple more things and then we'll do whatever we're doing after that I guess so so we do have we have parts and there's also a we also have a self so we're not just a kind of random assortment of parts this is one of the things that the movie inside out is missing it could be kind of implicit but there is a seed of consciousness there is a self and I think it's helpful to think of the self as like a conductor over instruments parts are like instruments in the orchestra and hopefully I illustrated that you know there's a part of me that's able to be social and engaging there's a part of me that's able to be tender and listening there's a part of me that's able to teach and these kinds of things and I do better if all of those parts are sort of free to move it's like a conductor that's able to move those parts and work through those different aspects of my personality I don't want to make this sound too bifurcated but and then we know that we're in self when we have these different qualities we feel compassion creativity curiosity confidence courage calm connectedness clarity presence persistence perspective playfulness patience so I think that gives you a sense of the kind of freedom these are the qualities of a real internal freedom we have breathing room and we're not judging ourselves controlling ourselves forcing ourselves we're not we're not self critical or or or self indulgent for that matter we're not dragged this way and that way we're not addicted and compelled you know we hopefully that communicates that sense of real freedom in ourselves what happens like I was just describing with my own experience is when we get wounded it causes a certain disharmony now my what happened in my wounds that that fear of anger is that fear really suppressed things and suppressed some of my my tenderness and my my tears that that capacity for to feel fear and sadness that way so that can get suppressed and we can end up so so parts of us get pushed into extreme roles there's a there's a part of me that should be able to sort of hold things in and you know maybe prevent myself from feeling the extremes of of pain and sorrow that I was experiencing but that gets pushed into an extreme role and nuns really suppresses that thing or the inside out image you know as anger gets in the driver's seat right that sense of it takes over and then it drives the show and now I'm not in self anymore there's not compassion and connectedness and clarity and you know and confidence and courage all these things now it's like the anger is driving the show or the we tend to have well first of all exiling so a part gets pressed down and pushed away and again the process is really there's a very positive quality to all of this because you know it's not a it's not a bad thing it's trying to reduce pain so that's the that's the goal of these these structures is to reduce my my pain you know when I when I felt that extreme pain all of that gets kind of pushed down in order to to limit the amount of pain that I feel and and but the the process is that it ends up exiling so I lost a part of myself in the process and and that's you know we don't want to lose a part of ourselves and then that exile bears that burden so I I was burdened under probably the words of my father you know like stop crying and you know and then that kind of gets into this this whole this whole structure and that little part of me gets pressed down it carries this burden and then anytime that there's a you know that gets threatened that that could come out then my protector steps forward and takes over again so what would happen when I encountered something sad I would just go numb and that happened for for years I just would shut down when I felt something sad and I could even I was very attentive but I was sort of attentive in an anxious way when somebody would start crying around me when somebody would start sharing something like that just numb and and shut down so our our protectors tend to fall into two groups managers and firefighters you know managers are things like perfectionist parts of us as long as I do everything right everything will be alright you know there's a part of us that can be working really hard I know a woman for example who's her mother had to go to work her father didn't make enough money she was a little bit later in the game and you know her older brother is seven or eight years older than she is and her her mother had to go to work and her mother got really stressed out at work and her mother came home and if everything wasn't okay in the house like things weren't clean things weren't prepared her mother could get angry get upset about that and so she learned from an early age to be super sensitive and well she's probably naturally sensitive but she used that sensitivity to protect herself I'm going to figure out all of the things that might upset my mother and I'm going to make sure that everything is in order and that's a kind of perfectionist part that can develop we can do that around religious things too a kind of sanctimonious part that's like I got to do all the religious practices right I got to do them right you know and that can get pressed into us if I don't do them right then bad things could happen we can sort of develop that that kind of thing but it's trying to protect something that is sensitive or wounded in us there can be a dutiful part I've got to do everything that I'm told and if I don't do that then you know bad things could happen we can kind of control food control schedule so a lot of different ways that those managers can be active now again the managers are good the fact that somebody is sensitive that they can anticipate problems that they can be dutiful that they can be religious these are good things so it's not bad in itself it's just that when there's that dynamic we can end up getting pushed into extreme roles and it can become too much another set of protectors are firefighters things like binging blanking numbing like I described we can be binging on various things alcohol sexual indulgence we can have angry outbursts we can run away so again these things are not necessary the capacity to enjoy food or a healthy sexual life or sexual attractions certainly a sexual life for those of you who are married but you know having a sexual attraction is anyway it is what it is and there's a good in the opposite in the fascination with the the opposite sex or whatever the heart can be moved by things like I said anger in itself to overcome the bad to overcome what is wrong is a good thing and running away can also be a good thing but again when these get pushed into extreme functions then it's problematic so the last slide just a little so I've just given you a lot of conceptual framework if I had another hour I might take you through an exercise but anyway a couple of simple takeaways the first thing is we should learn to love our protectors one of the things that can happen is like I have this exiled part and then I have this perfectionist protector and then that perfectionist causes me problems because it gets me stressed out and I end up controlling other people and other people don't like my perfectionist and so then I try to control my perfectionist and maybe I even try to renounce my perfectionist or I try to you know like use other structures and that's where this going back to that renouncing fear renouncing anger I can end up renouncing parts that protect me rather than you know trying to understand and that would be the starting point is if I have this this part of me that's not functioning well or is causing some problems maybe it sounds weird to say this but like ask that part what it's doing what are you afraid would happen if you didn't get everything right what are you afraid would happen if you didn't eat you know like a court ice cream right now what do you think would happen what are you afraid would happen if you don't do all of the religious practices and sometimes when we ask that question it will reveal the deeper thing well then you might get really hurt then you might get abandoned then your mother might get mad now some of you like me my mother died a number of years ago you know and it's like how is my mother going to get mad but anyway these are emotional structures we develop these things from early on so just first of all loving our protectors they're trying to help now they're not always doing that in the best way and sometimes it's causing some problems but they're trying to help so we love our protectors and then they can help us to connect with those exiled parts which often are like little children in us because they tend to well they have they're vulnerable and sometimes they didn't develop as much and they're little parts in us you know the part of me that wasn't able to cry because I suppressed that 12-year-old part needed to be welcomed connected with and we can start to connect with those and then understanding the burdens that they're carrying so again maybe it's the fear of being hurt maybe it's the condemnation maybe it's the shame of what others think of me maybe it's you know what my father said or my mother did or my teacher did or the nun did or whatever there's different kinds of burdens that we can end up carrying and there's a way that we can move toward forgiveness and let go of some of these burdens sometimes there is a lie that it can be appropriate to renounce I'm gonna say one more word about that in just a moment and then I'm going to be done it may also be a matter of feeling the pain so part of reconnecting with an exile exiles tend to carry some of that pain or that the hurt whatever caused them to be exiled they tend to still carry that and we have to be willing to welcome that and that's where when we've suffered very difficult things you know it can be hard to revisit that pain and that's why it's so important to do it together you know coming back to that affirming love having someone that can really hold us in place who can work through it with us that we can feel in that person's presence that we can share the burden and then of course we're doing this with Jesus and he really comes in through the person who is with us and then may come in as I described you know an experience and prayer that Jesus came in and really helped to connect with that exile and helped me to receive the love that in fact was there we discover that maybe you talked about that in the healing of memories but God was always there many times we didn't receive maybe the love or the support or the courage the help some of the things that he was providing at that time sort of like I didn't really receive although my mother was holding me I wasn't taking it in when I was 12 I took it in when I was 21 you know that's the sort of beautiful thing God saves all of it up for us and is still willing to give it to us so hopefully that wasn't too much gives you a few things this language of parts that I'm describing is called internal family systems is the sort of psychological model that puts some of those parts together and there's a wonderful website actually if you look up Catholic IFS IFS stands for internal family systems if you look up Catholic IFS it'll take you to soulsandhearts.com and there's really some marvelous folks there who are all very Catholic these are friends of mine and I can vouch for their faith beautiful beautiful people but really developing that IFS model and others are also familiar with it Claire I know so soulsandhearts.com and ITC is the internal therapist community if you go to TOC it'll take you to a list of topics which is pretty helpful and then as I mentioned Conrad Bars is another place to follow up with born only once is the kind of really straightforward most accessible text but then something like feeling and healing your emotions is a beautiful one and many others there's actually an audio book by his daughter Suzanne Bars that you can get on like iBooks or whatever and it talks that she gave to priests a number of years ago very beautiful so those would be some continuation points for you as well so with that you've already abused your patients thank you so much for enduring all of that and i'll hand it back to Ann to do whatever is next thank you so much father and I know you have a busy night tonight you've got more stuff going on do you have just a few minutes for some time I have time yeah yeah I did have a question in the chat box so it's kind of interesting it sounds like someone's realizing that they might have a part of themselves it's a little judgmental that might be judging the other parts like overeating or other parts they have so what do you how do we view these things as being judgy and overeating well these are sins we're so good at taking them to confession how do we really love that part like what does that look like yeah it's a great question and I just getting all of the human dimensions of this we could add a couple of layers but I think it's so important to get the human parts right so hopefully it wasn't too tedious in all of that first of all it's worth mentioning if I can say it and then I'll lead that into your the question directly but you know there are spirits so the renunciation thing isn't completely off the rails but spirits have a way of hitting us in their weaknesses right so we need to understand the human structures that are underneath it and that's where the ultimate healing takes place and so there can be a spirit of fear that agitates our fearful part right so you see there's really two different things happening there now the we can end up removing that spirit of fear and still have that fearful part which is still going to be in need of healing and kind of in the ways that I described but just so I complete that piece one of the things that I like about unbound for example is the human dimension so that longer time of an interview and any other healing model that would have that kind of connection because interaction with another person is so helpful I prayed with a woman who had been through terrible childhood abuse and she really it was like she relived it in my presence and went through it it was so beautiful and then we were at a place because she was able to feel it and connect with it then we were at a place that I could also help her to forgive and renounce and some of these things and she had tremendous for it just really very very beautiful she had been through counseling she had done a lot of other things but it was kind of that combination of things it was so beautiful for so just to observe those things first of all and then this question of sin you know it is so we know that the culpability for sin is mitigated by a number of psychological factors and the catechism recognizes that through things like habits addiction you know these various of course ignorance and compulsion and that is part of what happens that image from inside out of the angry part being in the driver's seat or what I described from my own experience my dad wasn't thinking through all of this and decided to yell at me it was a spontaneous moment where in fact he was already feeling out of sorts like his children were out of control he's failing as a father he's got all this stuff going on in him and then anger takes over and says that thing so where is sin and where is this sort of acting out of our woundedness well god knows that's the basic answer right god knows so do we bring these things to confession well certainly we can and we should we did something wrong we apologize for that we struggle with it so we bring it to and confession is a healing sacrament and when we expose that painful part that failure when we expose our emotional difficulties in pain when we expose that in confession that way it can be a beautiful way the combination of the human and the divine the human and the spiritual to communicate the grace of the sacrament to counter very beautiful so now the judgmental part to come back to that so we can end up layering protectors as I mentioned there's a you know we might have a firefighter that that binges let's say and we know that binging is wrong and you know so then there's a judgmental part I'm not supposed to binge and so we shame ourselves into not binge it now we haven't actually gotten to the the heart of the thing which is why was I binging with it's not just because I'm a bad person you know it's like there's there's a deeper part of me that I'm trying to put out this pain now it's not always obvious and this is again where the conversation sharing this with people working through some of these things is helpful but we might be able to you know ask that that binging part like what what are you afraid would happen if you didn't meet that court ice cream you know well then I would really have to face how alone I am or I would really have to feel my my sadness over what's happening I'd really have to anyway it's it's amazing what will emerge from that when we you know and we we can ask Jesus that to we can bring that into the whole inner world of prayer we can also bring that into the world of conversation and sharing with someone that we can be vulnerable with that way now we might have to address the the judging part of us and now again we don't want to we don't want to shame the judging part of us right but the judging part of us is also trying to help it's trying to manage this behavior and it's not doing it very helpfully necessarily maybe it's suppressing it maybe it's controlling in some way but I want to say well you know I understand why you're why you're judging and and we want to work through this but would it be okay if we just we look at the behavior you know if we look at that that binging part or we we bring this before the Lord and likewise we can use scriptural images really the Ignatian exercises in Scripture really work with parts because if you if you put yourself in the passage you end up engaging different parts of yourself and maybe that that judging part needs to meet the Pharisees in the in the adulterous woman you know and and see that Jesus doesn't judge that part Jesus loves that part of us and he doesn't want us to sin he doesn't want us to hurt ourselves and to continue these dysfunctional behaviors but but he but he loves that part and so sometimes that can help our judging part to settle down a little bit and and we can allow God's mercy and forgiveness to enter in there great thank you that was a wonderful answer to I I think too sometimes it just starts with an openness to being aware that the part exists like oh hey I see you you know and that's a part of yourself that's been working so hard over time trying to keep you safe and keep you from harm so sometimes it just needs a little hello to kind of be able to step aside and let the the Lord come in because even you might be in prayer and you can have a block there you might be trying to meditate on the scripture and you just can't get there because a part might be just saying no we're not going to go there that's that's way too scary to be you know if we're not going to be judgmental because that has kept us out of trouble and it's kept us successful and we there's no way we can go down that path so yeah it's really beautiful someone's asking this great question what if you don't have anyone to share these emotions when they come up to share them with um well certainly we can we can share them with Jesus in prayer you know that's that's certainly a good thing sometimes it's hard to make that connection and uh and we don't necessarily need to share them when they come up we can we can do that also a little later enter back into that maybe note down something that happened and then bring that up in spiritual direction or bring that up when we're with a close friend we can revisit some of those places and allow ourselves to get back into that experience sometimes just calling memory to mind is enough to sort of bring up some of the parts some of the feelings that are going on there great thank you and then I want to unmute Claire for a second are you still there Claire she was going to add a comment here can you hear me yes there she is I'm at your own risk I've got a house full of kids that are all a little wild after a full day at school I just want to thank Father Boniface so much for that for his talk tonight and I uh I wanted to just encourage everybody this the conversation about Conrad Bars and the miracle of affirmation is has been life changing for me so if you haven't read any of his work or become familiar with this idea of affirmation and this emotional birth that we all have to go through in order to become whole persons I first I took a Christian anthropology course in college that introduced me to his work and it's been especially as a mother it's been transformative for the way that I parent and then I interact with people and I did a paper on uh oh can we lose her doesn't look good well we will let her come back let's go ahead and mute so uh just a couple more questions real quick would it be helpful or a bad idea to imagine these parts and imagine talking to them I sort of go both ways in that in my personal experience but a lot of people do imagine the parts and again I understand that in the right ways I mean we don't have little creatures running around in us but I find especially for myself but imagining myself a lot of times those exiles I connect with a part of myself that when I was like you know nine or twelve or six and and seeing it as little and like a child really helps me to be compassionate tender you know some of the managers I have I have a directie a priest who really took to IFS and he goes and then my diplomat came out you know he looks like the guy in Monopoly with the monocle and the top hat so anyway he's very lively he had been a stand-up comic at some point you know but anyway he had this very lively sense of images and images can help us to connect with personalities and can help us to engage so you sort of you know try it on for size and see how it goes it one way or the other and really invite the Holy Spirit to give you that you know image or what what if a spiritual director had poor boundaries after having shared some of these wounds and they took advantage of your vulnerability it's our next question I mean depending on how seriously we're talking about taking advantage we may want to report that to the diocese and get a new spiritual director if we're talking about something more minimal like I don't know anyway I could take that in a whole variety of ways I suppose but that's really not good if that's yeah so just depends on what take advantage means there that's something that may need to be reported at worst get a new spiritual director in the middle or something that should be worked through at least so okay thank you and then just a quick question about Conrad Bars which Claire messaged and said she apologized for the disconnection but what would you recommend as his best book again it kind of depends on what you're looking for I've gotten let's see so like I say if you're just going to get one book I think that born only once is a good starting point it's the most accessible and you can get right into it as I say in a way even better than that those conference talks from Suzanne Bars are really beautiful at several levels she's a sweet person and having the tone of voice to go with it it's presented to priests and so it's a very catholic and expecting a mature audience it's called a boat of the heart I think or a boat of love I think is the name of it but if you look up Suzanne Bars with a Z and on like iBooks you find that and then otherwise I would say so a little more robust than born only once is healing and feeling boat of love great unaudible perfect exactly feeling and healing your emotions is very beautiful for the kinds of things that we're talking about wonderful I think that's all the questions I hope I didn't miss anyone but father thank you so much for your time today this was a wonderful presentation I really appreciate it and would you mind closing us with a blessing of course so happy to thank you for the invitation and so so wonderful to be with all of you thanks for your hunger for growing knowledge and faith and holiness and love let us pray Heavenly Father we thank you and praise you for how wonderfully and fearfully you have made us capable of tremendous goodness and sometimes way down by various wounds and pains and inner disharmony help each of us to find the healing transformation inner freedom that we need to be saints the saints that you have made us to be charging forward with heroic virtue and loving others as you love us and I ask you to pour out your blessings on all of my brothers and sisters may almighty God bless you the Father and the Son and the Holy Spirit amen thank you God bless you everyone


Hi, I'm Zor. Welcome to a new Zor education. I would like to continue talking about Bernoulli distribution, Bernoulli statistics, as part of this advanced course of mathematics for high school students. I do suggest you to watch this lecture from Unizor.com because it contains notes and problems and solutions, etc., etc. and exams for registered students, so it's like a whole course for either self-study or just as an auxiliary material for the regular school. All right, so we were talking about the problem and its solution and right now I would like to basically exemplify whatever I was talking before about Bernoulli statistics with three problems, which is actually one problem turned three different ways. There are three very important characteristics when you are talking about statistics. The volume of samples which you have, like number of experiments, the margin of error you would like to have or you already have based on whatever you have and the level of certainty, the probability that your evaluation is correct basically, that's what it is. So these three parameters, statistical parameters are very much related to each other and these three problems which I'm going to present today are exactly how to evaluate one parameter based on two others. Okay, so let's consider a situation when you have some kind of manufacturing facilities and they manufacture parts for, I don't know, car parts, whatever and there is a quality control. So the quality control takes a sample of, let's say, 10,000 parts which were manufactured in this facility during a certain amount of time and they found that 300 of them are defective. They don't pass the QA control. Something is wrong. So now why it happens is a different story. I mean it depends on what kind of problems they have identified with these 300. Now as the person who is probably more interested in financial situation with this particular manufacturing facility, I might be interested just to know how probable the manufacturing of the defective parts is. Obviously if I have a choice between two different manufacturing facilities to invest my money, I would like to invest into the manufacturing facility which is more reliable, which has less number of problems like this, etc. So I would like to evaluate how big this actually is and I can do exactly the same with another facility, have another number of parts taken for quality control and number of results but how I can compare it. So I have to compare with certain mathematical validity. So my first question is, I would like to be able to evaluate the probability of manufacturing a defective part with a certain level of certainty and my certain level of certainty is 0.9545. Now it's not just an arbitrary number. I mean if you remember the normal distribution has sigma rules. Now sigma rules for normal distribution is as follows. If you have a certain bell curve and that's the statistical distribution of random variables. Now this is interval of one sigma around the mean. So it's from minus sigma to plus sigma, from the mean value, mu. Now this is minus 2 sigma plus 2 sigma and this is 3 sigma minus and plus. So the probability of random variable with normal distribution to be within one sigma from its mean, which is relatively narrow strip of values. So one sigma would be 0.6825. Two sigma rule is, so what's the probability to fall within mu minus 2 sigma and mu plus 2 sigma? That's obviously bigger. That's 0.9545 and this is exactly the number I have chosen. And the 3 sigma interval, that's a very wide interval around mu. 3 sigma would be 0.99, I think 73, final mistake. So that's the reason why I have chosen this particular thing. So with the probability of 0.9545 or I would rather say with certainty level of 0.9545, I would like to evaluate the probability of manufacturing a defective part. Now obviously my best approach would be just to divide 300 by 10000. Now why? Well let's just go back to the definition of probability. Now one of the definitions and probably most natural one is that the probability is related to frequency. So if you would like to know what's the probability of certain event, you observe occurring or not occurring of this event during certain number of experiments. And as your number of experiments goes to infinity, then the statistical frequency of occurrence of this particular event would tend to some number which is defined as a probability of this event. Now obviously open question is whether the Riesel limit, whether it's a unique limit, et cetera, et cetera. But that's besides the point. Now the frequency approach to definition of probability is kind of natural and everybody understands it. So if I have 300 out of 10,000 defective parts, well then it actually prompts me to say that most likely the real probability of manufacturing should be somewhere around 300 divided by 10,000, which is 0.03. So my best estimate for mathematical expectation of the event manufacturing the defective part would be 0.03. Now in the previous lecture when I was talking about solutions, I have suggested that the best way to approach this particular problem mathematically is to consider every test which I have made in my quality control and I've made 10,000 tests. Consider this to be a Bernoulli random variable which has value 1 or 0. 1 means the defective part, 0 means it's good part, not the facts. And we are interested in the real probability p of this random variable to take the value of 1. So we have experimented with this random variable and in the series of 10,000 experiments we have come up with 300 over 10,000 frequencies. Now if somebody else makes another series of 10 experiments, well he will have different obviously number, maybe 310 or 250 who knows. So what I have just did, what I have just done and I have calculated basically the frequency which can be expressed as the following. If the result of the first experiment is x1 and result of the last experiment is xn where n is equal to 10,000. So these are results of my experiment with xc. I know that 300 times I have 1s somewhere here and the rest I have 0s. So basically if I will summarize them and divide by n, that would be my frequency or sample mean as we are saying. So again the sum of Bernoulli variables is actually the number of times this event occurs because we have assigned 1 when it occurs and 0 if it's not. So their sum divided by n would be my sample frequency in this case is 0.03. Now if I make another series of n experiments, I would have another number. So basically I would like to say is that this is actually a single value of some random variable and random variable is eta which is equal to xc1 plus etc. plus xcn divided by n where every xc1, xc2, etc. is exactly the same way distributed as xc and they are all independent. So they all kind of represent each individual experiment. So I have 10,000 experiments, I have 10,000 random variables. Each one of them is 1 with a probability p is 0 probability 1 minus p and their sum divided by n is basically a probabilistic picture of whatever I have done. So what I have done, I took one particular single value of eta, one single series of experiments and I've got this particular number. Now as you know in Bernoulli variables the mathematical expectation of xc is it takes value of 1 with probability p and value of 0 with probability 1 minus p so the whole thing is equal to p. So mathematical expectation is actually p. That's why this which seems to be kind of the same mathematical expectation should be as xc right? Mathematical expectation of eta is what? One ends can be brought out of the expectation and then some of these mathematical expectation of sum is sum of expectations and each one is exactly the same p as xc. So I will have np divided by n so it will be exactly the same p. So mathematical expectations of these two are exactly the same. That's why single value of eta which I have obtained might actually be an approximation of the real p. And how good is this? Well we are talking about this that the good measure is a variance. So what's the variance of this? And we were discussing it in the previous lecture. Variance of eta is variance of c divided by n as we have discussed previously. And again it's very easy because variance is a quadratic thing right? It's supposed to be taken out in a square so it will be 1 over n square variance of a sum. Variance of a sum is sum of the variance so it will be n variances of c divided by n square which is variance of c divided by n. Now what is the variance of c? Well variance of c is equal to p times 1 minus p. That's what I have derived in the previous lecture and we were derived many times before in the variable explanation. Alright so I have the variance and the fact that this denominator contains n is very encouraging. It means that as n grows my variance is getting smaller and smaller. Now variance is a measure of deviation from the mean value right? So if this is a variation of the mean then this is a variation of the mean. This signifies the deviation from the mean which is smaller and smaller as n grows. So that's a good thing. So our distribution becomes more and more concentrated around its mean value. And that's why even a single value of our random variable eta might be a good approximation of its mean value. So mean value is p so that's what I would like to know and I don't know it. But single value of eta would be a good approximation for the mean value because all the values of eta are concentrated around my mean value. And how well they concentrated, how close they are that's the measure and the measure is actually getting smaller and smaller which is a good thing. Now another assumption is that this sum with relatively large n is very much close in its distribution to normal distribution. We have spent many times actually discussing this issue. This is the central limit theorem when the sum of random variables under relatively liberal conditions is distributed closely to a normal distribution with the same mean and variance as the sum. So I actually can say that eta is almost normal random variable with mean value p. So the mean value is here that's my p and the variance this one which is getting smaller and smaller as n goes to infinity. Now how can I estimate where is my mean value p if I have only a single value of this random variable? Well I can do it using the sigma rules. I know that my let's say 2 sigma interval around the mean value is the interval where my random variable falls with this probability 0.9545. And that's the certainty level which I would like. So basically I can say that with this probability with this certainty level this random variable eta would be within 2 sigma interval from the mean. So all I have to say is that my 2 sigma interval around my unknown probability p is actually the margin of error which I need to establish. So I can say that whatever the value here is which is 0 point the value of frequency which is 0.03 it's a good estimate of the mean of this particular random variable. And the quality of this estimate is measured as follows with the probability of 0.9545 it's within 2 sigma interval around the mean unknown mean. But I don't care actually because I'm talking about this is my estimate and I know that the mean is within 2 sigma range from it. So it's around plus or minus from this from this way. Now that's great but I don't know my sigma because it depends on variance of xi and xi is again depends on unknown probability p. But here is what I have suggested the previous time as far as the solution to this problem. Now this is not a good solution let's put it this way but it's a very practical solution in many cases. Now again my variance is equal to p1 minus p divided by n right. Now what I have suggested in the previous lecture is yes I don't know p times 1 minus p however this is 0 this is 1 this is function. 1 minus x it's a parabola right. 0 and 1 are the points where it intersects the x axis and its maximum is in the between which is one half. And if it's one half then the maximum is equal to one quarter. Now if you don't care about these because the probability cannot be less than 1 or greater than 0. So I can say that my maximum of this is one quarter so I definitely know this right. So now this is already something which I don't know because I know n it's 10,000. So I can say that my variance is less than 1 over 4n which means my standard deviation is square root of variance which is less than 1 over 2 square root of n. So although I don't know my variance exactly of this variable eta I know it's upper bound. So if I will use this as my 2 sigma it will be a wider interval than reality in reality. So at least it's some measure of evaluation. So what is this? Well n is 10,000 so this is 1 over 200 and now I'm talking about rule of 2 sigma right. Now 2 sigma is 100 which means that the real probability would be within 0.03 minus 100. So it's 0.02 and 0.04 with certainty level 0.9545. So this is actually a very simple problem which I have spent lots of time discussing and I just wanted you to understand that you cannot just say that the frequency is 0.03 which means probability is somewhere around 0.03 if you do not define somewhere around. Now somewhere around means the following it's better probably than this because we have taken the upper bound but at least I can say that the real probability would be within 0.02 and 0.04 with this certainty level. It's not 100% certain by the way. Probability can be significantly greater or significantly smaller than this. But I cannot, based on whatever I know right now, I cannot say anything better than this. So that's something which is good. Now two other problems I would like to go much faster and their purpose is you see again right now we had n and we had the certainty level p. Well, I use lowercase p. This is not uppercase p which is the probability of c to have the value of 1. And what I have derived from this? I have derived the margin of error which is 2 sigma which is 0.01, 100. Now two other problems I will just change something. I will be given one particular, two particular parameters and define the third one, different third one. So that's the end of this first problem. We have defined based on the number of experiments and required level of certainty 0.9545 I have derived the margin of error. So from 10000 from certainty level 9545 my margin of error is equal to 100. Alright, let's go to the next problem and it will be much easier in this case since we basically know what we are doing. By the way, I do suggest you after you finish this lecture to go to the website Unisor.com and read the comments because they are also like a textbook basically. It's my notes for this lecture which I have written before starting it. Alright, now what if under the same circumstances I would like to narrow my margin of error from 100 to 5000. So to basically reduce it by half. What would be the certainty level in this case? Certainty level of my evaluation. So basically what I am saying is that the probability, this is uppercase, from 0.025 to 0.035. What would be the probability of this being true? So I reduced by half. So going back to whatever I was just saying before my margin of error was equal to 2 sigma. Now I would like to reduce by half. So my interval would be half of this one. So it would be single sigma rule. Now single sigma rule for normal distribution is this. If we are requiring more narrow interval around my average, my sample average, my sample mean, then obviously I cannot say it with more, I can say it only with less certainty. So I know that within larger interval the certainty is 0.9545. But if I would like to say that it's actually much closer I cannot be as certain. So my certainty level goes to a single sigma. So what is in this case probability of having this thing? Well obviously this is 0.6825. Because everything else is exactly the same. So all my calculations, my n is the same, my number of defective parts is the same. So my sample average is also the same. And I am requiring 0.005 interval around it. So it's from 0.03 minus 0.005 which is this to plus. And since I have already calculated my sigma which was equal to 1 over 200 which is exactly this one. That's why I have chosen this one. That's why I have applied rule of single sigma. So that's my second problem to establish the level of certainty if my margin of error is given. Now the first problem was I have established my level of certainty and then I have found what my margin of error should be. And in that case when that was 0.9545 my margin of error was greater 0.01100. But if I would like to actually be satisfied with a smaller certainty level I can narrow my interval in half. And the third problem is what if I would like to have a certainty level and I would like to have a certainty level to sigma. And I would like actually to have a little bit more precise variation. So I would like my margin of error to be this small. So with my 10,000 experiments I can achieve this margin of error only with this certainty level. But now I would like to have more certainty and to do this I have to have more experiments. The question is how many? Well let's just think about it. Now sigma if you remember was equal to 2 square root of n, right? And that's why if I would like this to be equal to 0.005 just one second. No, I would like, sorry, I need this certainty level. I would like to have certainty level 0.9845 but I do not know my n. That's my problem. So with this certainty level what interval I have to be satisfied with around my mean value? It's 2 sigma, right? This certainty level is associated with the 2 sigma rule. So I know that if I am on the 2 sigma minus and plus 2 sigma then I will be within 0.9845. So I need 2 sigma to be equal to 0.005 because that's the margin of error which I would like to have. Which means that 2 divided by 2 square root of n is equal to 5.000 which is 1.200. So this is square root of n is equal to 200 and is equal to 4.000. So if I would like to reduce by half my interval relative to my first problem where I was actually requiring this probability but I was satisfied with 0.01 margin of error. If I would like to reduce margin of error by half my number of experiments should go up by 4. That's because the variance is a quadratic function. So if I would like to have this precision, so the probability of my p to be within 5.000 of my average value, if average value is 0.03. If I would like that to be equal to 0.9845, so if this level of certainty is required then my number of experiments should be 40.000. So this is basically three typical problems which statisticians are solving all the time. The first problem, let me just make a quick summary. So the first problem I was given number of experiments and I was given the level of certainty and I have derived my margin of error. Second problem I also was given this but I have defined my margin of error to be twice as narrow. And then I have derived that the probability of my variation, my certainty level was actually smaller. This was 0.9545, this was 0.60 something. And the final problem was the third one. If I have the level of certainty and margin of error, what is my number of experiments which I have to basically get into? I don't know which problem is more prevalent. It seems to me that sometimes experiments have already been done than either of these guys. But sometimes if you are planning experiment then you have to really think about what the certainty level you would like to achieve and what's the margin of error you would be satisfied with. And then you will derive the number of experiments you have to do. And let me point out another very important aspect of this thing. Now you remember that the real variance of eta, eta being c1 plus c2, etc. divided by n is equal to variance of c divided by n which is equal to p1 minus p divided by n where p is the probability of c to take the value of 1. Now what I have done, I have done this. Now how good is this? Well obviously if p is equal to 1.5 that would be exactly equal. Now if p is, let me go back to the graph. This is my graph y is equal to x1 minus x. This is 1, 0, this is 1. So somewhere in the middle, yes. It's very, very close to this maximum value of 1.25. But if you go to the both extremes, so if your event is either very unlikely or very likely then this particular variation really not good at all. I mean the real variation, real variance would be significantly smaller than this one if my p is closer to 0 or close to 1. So sometimes it's a good estimate and whatever we have derived was relatively good. But in some other cases it's not and it's not good whenever my events are rare, too rare or too frequent. Now speaking about defective parts, is it rare event or is it frequent or is it like 1.5 probability, 50-50 as they say. Well that's supposed to be a rare event. So the real probability should actually be close to 0. And in this particular case, well let's say the probability is 0.03 which is my evaluation of the probability. When obviously this times 1-0.03 would be significantly smaller than 1.5. It would be something like 0.0, like 2.8 approximately, right? It's significantly smaller than 0.25 which is 1.25. So our evaluation was really not very good in this particular case. And what we can do is we can really make this significantly better and smaller, therefore. However it will not be with 100% certainty. So that's another level of uncertainty which we can introduce to improve this particular variation of my variance. But again for the price of losing certain amount of certainty. Now this will be a subject of the next lecture where I will spend certain time basically to better evaluate this variance. Not 100% certain but better. Let's put it this way. So then we have to really choose what we prefer to have absolute certainty in this evaluation. And then we will have another uncertainty because it's still a variation of the variance and our variable can go outside of this interval. Or on the top of that uncertainty to add another uncertainty of evaluation of this variance more precisely than this. Which would narrow our interval but again it will reduce the certainty level. So as you see statistics is a really tricky kind of a science but it's a science nevertheless. Alright, thanks very much. I do suggest you to read the notes for this lecture on Unisor.com. Thanks very much and good luck.


Hey, this is Brett, and this 2012 Chevy Corvette 3LT Z16 Grand Sport is stock number 12764Z. We are here at Summit Automotive in Fond du Lac, Wisconsin, your new and used sports car headquarters. This 2012 Chevy Corvette 3LT Grand Sport has the 6.2 liter V8 LS3 engine, and in this particular car it has 436 horsepower. This car has been fully-safetyed and inspected by our service shop, it has a fresh oil and filter change, all the fluids have been checked and topped off, and this car is 100% ready to go. We're going to go all the way around on this car, inside, check out the trunk, start it up and take a look under the hood, Inferno orange metallic is the color, and we shoot all of our videos in 4K, so if you have HD capabilities on your computer, tablet, smartphone or television I highly recommend turning them on right now because it is your best way to check out the quality, condition, options, and cleanliness of the car before seeing it in person. And if you like the video and how we do things here at Summit Automotive in the lower right hand part of the screen, consider clicking the subscribe button to our YouTube channel, and then click the bell notifications and you'll get updates on the videos we do each and every day here at Summit Automotive. On this one, the front rims are 18 inches and they are chromed alloy rims, has Goodyear Eagle P275 35ZR18 tires in the front, and in the front they have right around half the tread left. You get the drilled rotors with that Grand Sport Z16 package, front fender is in really nice shape and it's in these scuffs or scrapes, the headlight lenses are crystal clear and it does come with the HID headlamps. Front bumper and lower valance are in really nice shape on this car. I didn't see any scuffs or scrapes or major imperfections and the hood is in very nice condition as well. Passengers side headlamp is in nice shape and the passenger side fender, no major scuffs or scrapes on there. And we'll take a look at this Inferno Orange Metallic, it's got just a little bit of metal flake to it, it's really a cool looking color. You can see just how nice that paint is, the clear coat is really nice too. And as you go down this side of this 2012 Chevrolet Corvette Grand Sport 3LT, take note of how clean that body is, how reflective and mirror-like that paint is, and it's reflective and mirror-like that paint is. We take these HD videos, so whether you're far away or you're close by and you just can make the trip down but you're still interested in purchasing the car, you can see the car, hear the car and have confidence in the vehicle that you're looking at before you even get here. So when you do get here there's absolutely no surprises and you can make a smart and informed buying decision from wherever you're at. And if this video helps you make that decision, let your salesman know that you saw the video that it was helpful and that Brett sent you. So on the back tires we have P32530ZR19, so these are 19-inch rims in the back, and the back tires have just a little bit less than half the tread left, not quite as much tread as the front tires, it's still a little bit there. Coming around to the back of the vehicle, rear bumper is in excellent shape, no major scuffs, scrapes or anything like that. The spoiler is in nice condition as well. Now this one has the dual mode exhaust and I'll show you exactly what that is. You can see you get the dual exhaust there with the quad tips, but then you get the valves right there. So they open up and you can see there's actually a valve in there. So that opens and closes to give you more airflow and that's what gives you the extra six horsepower with that dual mode exhaust. Take a look inside the trunk here, so this one comes with just a couple extra things. Trunk air is pretty clean and we have a battery charger or battery tender, I should say, a Corvette one. We have the other Maptis, so it comes with two Maptis, one for the west coast, one for the east coast. You get your original letter of authenticity, instructional DVD, and then you get your Corvette handbook, driver handbook, so it's pretty cool and that comes in this nice box here. You can see that the shocks are holding up that hatch nicely. And then the other thing with this car is that it comes with a car cover and then a box for all that stuff that you just saw in the trunk. As we come around the driver side, just as clean as that passenger side, no scuffs or scrapes on that back quarter. And this back rim is just as nice as the rest of them, very nice condition on that rim. Driver side door looks really, really good. This whole car is extremely clean, very well maintained, power mirrors inside. The three LT package gives you the black leather interior, there are no rips or tears on those seats. You get the Corvette logo stitched into the headrest, and a lot of times these will be really war right here, but this one's in really nice shape. Both these front seats are heated and power, and it does come with factory floor mats. Power windows, power locks, power mirrors, memory driver seat, and Bose sound. We'll hop inside, check out the miles radio on these Corvettes. I do have to start them up to see the miles and everything, so we'll start it up here. Starts right up. You can change that first, that's the previous owner's name, 9,183 miles on here, instrument cluster is very nice and clean, comes with the leather wrapped steering wheel. Audio controls on the right, Bluetooth controls on the left, paddle shifters, and this one does have heads up display, you can see that that's working nicely. The other thing is that this one has the telescopic steering wheel, so not all of these Corvettes have this feature, so I always like to show that, push button start, information center, you do have the factory radio, AM, FM, and Sirius XM radio capabilities, and you can see it does have the NAB system, and this is the east coast disc that's in there, so that's working nicely.  Center console is in nice shape, I didn't see any major scuffs or scrapes on that. And the passenger side, the floor mat and seat are in really nice condition, smells very clean inside this car. Headliners in nice shape, you do get home link buttons for your garage door security systems and lane systems, on starting SOS capabilities in the mirror as well as a compass display. And we'll just listen to the exhaust real quick and then we'll check out under the hood. It's kind of a quiet exhaust, but I would personally like to thank you for checking out the video today, and hopefully from this HD video, you'll have been able to verify the quality condition, options, cleanliness of this vehicle. This one is in really nice shape, like I said, and under the hood we have the 6.2 liter LS3 V8 engine, engine bay is very clean, runs very smooth, and once again this car has been fully safe and inspected by our service shop, has a fresh oil and filter change, all the fluids have been checked and topped off.  And there is your emissions sticker. And you can see that those HID headlamps are super bright. I would highly recommend this 2012 Chevy Corvette 3LT Grand Sport in Inferno Orange Metallic for make quality and condition standpoint. I don't think you'll find too many that are nicer than this one. And to see more pictures of this car, one of our other 450 new cars, trucks, SUVs, minivans, wranglers, halftones, three quarter tons, one tons, corvettes, Camaros, challengers, chargers, mustangs, GT500s, you name it, we gotta go to that website right there at www.SummitAuto.com. Full pictures and descriptions of every single vehicle from two locations all at SummitAuto.com. And if you'd like to check out more HD videos, you can go to www.youtube.com. Remember to like, subscribe, and share on this video and all the videos that you see there. Click the bell notifications, you'll get updates on the videos we do each and every day here at Summit Automotive. In fact, in a second you'll see a link to subscribe to our YouTube channel on the upper left. A link to more Corvette videos like this one on the upper right. Link to this vehicle on our website on the lower left and a link to one of our latest YouTube videos on the lower right. Click those, check us out. We're super excited to help you with this ultra clean 2012 Chevy Corvette 3LT Grand Sport Z16 in Inferno Orange Metallic. Thanks again for checking out the video. Remember to like, subscribe, and share.