Well, hello and welcome to Understand Men Now. I'm Jonathan Asley of JonathanAsley.com and I'm so excited to be doing this live stream for you today. Our topic, he's just not that in you. Five signs he's not interested in long term. All right, really quickly before we get started, if you're brand new to my YouTube channel, please hit the subscribe button, hit the bell so you can be notified of new videos. And if anytime during this video, the content resonates with you, please hit that like button so I can be seen in the YouTube algorithms.  It's direct, a little tough love and a lot of heart. And occasionally I use expletives to enhance a sentence. So if an F-bomb or two isn't your cup of tea, I suggest logging off right now. Lastly, these are my thoughts, my perceptions, my opinions by no means do I suggest this is the truth. You have to decide the truth for yourself. I'm a contrarian, so I see the world a little bit differently and if my content does spark some curiosity from you great and if it doesn't, that's okay too. All right, let's jump into, he's just not that into you, five signs, he's not interested in long term. Okay, now I know you'd much rather hear about the five signs that he's into you, but here's the thing, I find that a lot of women are holding out for the wrong guy over and over and over again. So I wanted to lean into this conversation today and maybe you can glean a different way to approach the dating, mating or relating process. So now here's the thing, I want us to go backwards in time a little bit because back in the day, 70, 100 plus years ago, the average courtship was less than eight weeks. I repeat that the average courtship was less than eight weeks and whether it was arranged marriages or you met someone in your town, if you wanted to get laid, you basically had to get married. You had to make the ultimate commitment with someone and because they made the ultimate commitment with another person, they were actually more invested in trying to make the relationship work out. And so these days, a lot of human beings, men and women alike, rely on strong chemistry to initiate the relationship process because these days were meeting total strangers for the most part. Let me repeat that, we're meeting total strangers, which was unlike 75, 100 thousands of years ago because you probably met someone in the tribe you were in or the village you were in or the small town you lived in or maybe even in your work environment. So there was a chance you had a level of familiarity with this person that helped ignite the relationship because maybe if you grew up in the same town, you shared the same values, your lifestyles were blendable and if you had chemistry, then the relationship took off. Now the challenge with today and in particular with midlife is that today, as I said a moment ago, we're meeting total strangers. So we lack that sense of familiarity, that sense of connection and maybe even the sense of shared values or even lifestyles that can work together. So there's a lot more moving parts in the process. Let me repeat that, there's a lot more moving parts to the process than the fantasy that the men are just gonna claim you because these men are hunters and they chase relationships. Wait a minute, let me say that again. Men are hunters and they chase relationship, Jonathan. That's the belief many of you have about the idea of hunting. The idea of hunting has nothing with men being hunters has nothing to do with men hunting relationships. They might hunt sex, but it doesn't necessarily mean they're hunting relationship. So this is one of the fundamental problems in the dating process is we don't know people and we don't know their intentions. We don't know what they truly want. And I see this from men and women as well. Ladies, I know you are all relational and you want relationship more than men, but quite frankly, doesn't mean you're any better at the process just because you tend to want relationship more than men. And yet many of you will dive on the sword believing that you're more altruistic because you want relationships more than men. And I'm not saying all women out there, I'm saying a lot of you. So let's just agree that men and women are rather clueless in the dating, mating and relating process. And this is especially true for midlife. And I know a lot of women that don't think otherwise, I can tell you as a coach and let me tell you something, every single time I work with a client, they all say the same thing. I know what I want. I know what I want. I know what I want. Then they go through my proprietary coaching program that I created and after six weeks, they all say the same. Jonathan, why didn't they teach us this in school? Why didn't my parents teach me this? Why didn't I learn this before I dated that knucklehead or married the wrong guy? Yes, we all need to be reeducated, not even reeducated, we need to be educated on how to actually even be in a healthy happy relationship. And sadly, most humans don't know how because they're not operating as a grownup. They're not operating as a grownup. So if you want to read a great book, how to be an adult in relationship, this would be a great book to read to start. And maybe if you're dating someone, buy a copy of this for them as well. Because I got to tell you, men and women act like children in the dating process. And you're probably going, Jonathan, what does this have to do with the five signs? Okay, I'm gonna get to that in a second. So I wanted to set the stage of where we're at and why we have so many problems. And the reality is, is for midlife, because men aren't on the hunt for a wife in midlife. Let me repeat that, they're not on the hunt for a wife to make babies with. Most men and women have a capacity, only have a capacity to be in a casual relationship, a casual relationship, where they're basically experiencing connection and sex and maybe a little bit of companionship without any forethought or any intention of pursuing it from a partnership base, from a partnership base. And I'm gonna talk about that in a little bit, okay? But I wanna establish this base that men and women alike are operating from the place of casual. So ladies, when you're talking to a guy on a first date and you say, hey, what are you looking for? You know, when you say, are you looking for a relationship? And he said, yes. Well, here's the thing. Your definition of a relationship might be very different than his definition of a relationship. But you too heard the words of relationship and he says, oh yeah, I'm seeking a relationship and you're hearing, well, he wants to spend three or four days and nights a week together doing shared activities, hobbies, mutual interests, spending time with family and friends, traveling together, teamwork, building schools, both in our personal and professional life, intimacy, both physical and emotional intimacy that leads to getting married or living together. That might be what you're thinking and he's thinking, yeah, I'd like to see you once a week at my discretion, okay? Until you learn to ask better questions, which we'll talk about in a moment, you're gonna be stuck in this loop over and over and over again. And what's the definition of insanity? Doing the same things over and over again, expecting different results. So what are five signs? And by the way, there could be dozens of signs that he's not interested in the long term. These are five that I wanna share with you today. I might do a part two at some point. But let me put on my trusty glasses. Here's my notes. He's just not that any of five signs he's seeking. He's not interested in long term. Okay, number one. And folks, you already know this one.  I'm gonna repeat that. Communication with each other and planning dates with each other begins to fall off. Now, I know a lot of you ladies put all the responsibility on the men to initiate communication and the men to initiate dates. And I'm here to say, I'm a big believer of two people traveling like they're on a two lane street together in mutual effort. So if you put the expectation always on him to communicate and to initiate dates, well, first off, you're giving the job to the wrong person, first and foremost. But I'm here to say, when you're active participant in the process, it takes the pressure off of him always being active in the process. So what happens is if you basically have an expectation that's all on him and he's not interested, it's gonna start to weigh. However, if you start initiating those phone calls and start initiating times to get together and you notice he doesn't engage with you, that's a great sign, he's not interested in long term. So rather than wait months to see his behavior go like this, why not treat the process right from the get go of a two lane street because you're gonna weed out the wrong guys much sooner in the process rather than because again, you took off like a rocket because you had this great chemistry to begin with and then you find it fizzling because he's not intentional about the process. And we're gonna talk about that a little bit more in a second. All right, number two. Oh, he hasn't suggested meeting your family or your friends nor has it been vice versa. So he hasn't introduced you to his family and friends. Men who are genuinely serious about a long term relationship are excited to introduce you to their family and friends. Now, you may not wanna do this on the first, second, third, five, seven, then nine, 10th date, I went through that. First, six, seven, eight, one, first, second, third, fourth, fifth, six, seven, eight, nine, 10th date. You may not do that because you don't know if you wanna build a relationship with someone. However, when you've agreed that you're in a relationship together and you've had sex together, that's about the time to start incorporating your life together, start blending some of your lives together. And if he avoids either meeting your family and friends or he avoids introducing you, by the way, a man could meet your family and friends but they might avoid the other way around or they might do it the other way around. They might introduce you to their family and friends but avoid yours. These are signs when it's not mutual in this process. That's a sign that they're not interested in the long term. Now, there's exception to the rule. Sometimes there's shame in with people's families on both sides, believe me. I love my sister with all my heart. I shouldn't throw her under the bus like this but there are times I don't wanna introduce her to people and I mean, she's a great woman but sometimes she drives me nuts or my brother drives me nuts but I certainly, not but, and I would certainly introduce them but I might have some reservations at times but that's the exception, not the rule, okay? So if they're not actively introducing you to their family and friends or vice versa, that's a good sign that they're not interested in long term. Number three, their energy is off. He begins to feel distant, he begins to feel distant and most likely there might be some chaos going on in his life. In other words, his house isn't in order and I don't mean his literal house. I mean, his figurative house is in order. Maybe it's his professional life, maybe as a contentious divorce going on, maybe as issues with his children, maybe as physical issues. When a man starts to become distant, starts pulling away, there is a good chance there's some chaos going on in his life and he'll start expressing that chaos as his exit clause to let you, so their exit clause is basically this, they lay the foundation of the problems going on in their life as a way to say, I'm not ready for a significant relationship. I'm gonna repeat that, I'm not ready for a significant relationship. So they'll start laying the crumbs of all the problems going on or crumbs, crumbs, crumbs, crumbs, of all the problems as a precursor to saying I'm just not ready for a serious relationship. I find it interesting why they don't lay these crumbs on the first, second, or third date and it's maybe because they're laying the crumbs of I wanna get laid, I wanna get laid, I wanna get laid. All right, so if their energy is off, he begins feeling distant and there's chaos going on, there's a good chance he's laying the foundation to exit the relationship.  This is because for men, sex can be a very emotional experience for us beyond the physical and so when a man is pulling away sexually, that's because it's a sign that he might be moving on unless he has some pre, you know, unless he has some erectile dysfunction or some other issues going on, most men at midlife are still rather horny even in their 60s and 70s and while they might not wanna have sex with you five times a week or twice a day or three times a day, certainly most men want to have a regular healthy sex life with someone so if they start pulling away sexually, that's a pretty good sign.  Let me repeat that, he starts picking fights, he complains about you or he criticizes you. Men and women do this very often is that this is a precursor to sabotaging the relationship. I'm gonna repeat that, it's a precursor to sabotaging the relationship because let's face it, a healthy happy couple can agree to disagree about things, certainly you can not necessarily see the world the same way and yet, if somebody is habitually complaining, criticizing or picking fights, there's a good chance that's a precursor to wanting to exit the relationship. The problem is a lot of guys, they tend to nest in relationships, so we almost pick fights as a way to get you to break up with us. Let me repeat that, we pick fights, so you break up with us. This isn't all men, this is a percentage of men that do this, but again, if you're starting to see these signs, less communication, not introducing you to family and friends, starts pulling away distance because there's chaos going along, not initiating sex as frequently and picking fights with you, there's a good chance that he's getting ready to end the relationship, he's not gonna go long term. So what's the solution to this? What do we do knowing this information? Folks, I'm a big proponent of asking better questions right from the get go to determine if you're on the same page. One of the reasons why I created my private coaching, by the way, there's a link below, and if you wanna schedule a free discovery call with me to see if working with a coach is right for you, my area of expertise is to teach you how to ask better questions right from the get go before you get too involved with a guy based on your personality and how to vet for emotional maturity. I'm gonna repeat that, how to vet for emotional maturity, going back to do you wanna date a boy or an adult in relationship, okay? That's my area of expertise, so check out the link. So the solution is learning to ask the better questions right from the get go to determine if you're on the same page. But Jonathan, you're not supposed to interview someone on a date. Bullshit! It should be an interrogation. You wanna interrogate the motherfucker, right from the get go, folks. Stop this passive way of dating and start being intentional. Start using radical honesty to pre-qualify your prospects. In fact, one of the exercises in my private coaching is called radical honesty, pre-qualifying your prospect, folks. What's the definition of insanity? Doing the same things over and over again and expecting different results.   And if you're not familiar with my book, What the Heck is Self-Love Anyway? There's a link below to get my book. I am all for empowered energy for men and women to be empowered. Has nothing to do with masculine and feminine energy. It's about being in your individual empowered energy. So you don't have to put the label on it, just be in your empowered energy.  Let me tell you something. If a guy likes you and he's into you, you can ask the tough questions right from the get-go. And if you need some help with that, you might wanna also check out this book. Are you the one for me? Are you the one for me by Barbara DeAngelis? I love, love, love this book. It is such a great book. Look at how thick that is. Folks, you will improve your dating prospects 10 fold just by ordering this book. And I'm here to say, if you stop treating the dating process from the traditional rules-based way, and by the way, I got the updated version of the book, The Rules, Dating, The Do's and Do's from a Digital Generation. Let me just tell you something that this book suggests in the back. The rules taught a generation of women how to successfully play hard to get in the process, which has helped millions of women get Mr. Right. Let me tell you something. Playing hard to get temporarily gets the wrong guy into you. I mean, Pete, that temporarily gets the wrong guy into you.  Don't play games. Don't use hard to get. Don't lean back. Start leaning into being a better detective. And let me just tell you something, folks. If you haven't learned human behavior by now, then you better start. And I highly recommend ordering these two books attached by Amir Levine and Rachel Heller and Getting the Love You Want by Harville Hendricks and Helen Hunt. Folks, these two books teach human behavior. If you don't start understanding human behavior, you are behind the eight ball. But let me tell you something. Do you wanna go out on one date that goes nowhere, two dates that go nowhere, five dates that go nowhere with one, two, three, four, five, six, seven, eight, nine, 10 different men?  So you can avoid those five signs that the guy's not interested in you because you can actually determine this sooner rather than later. All right. I think I set it up to cover the topic. Now it's time for Q&A. So for those who are on the live stream right now, there's a chat box where you can post a question, write the word question, and then post the question thereafter or purchase a Super Sticker or Super Chat. If you purchase a Super Sticker, Super Chat, all the funds go to a scholarship fund in the name of my son, Connor Asley. There's a picture of Connor in the Obey shirt. He's my son who passed away a few years ago. And in his honor, I've created a scholarship fund to defray the cost of personal development for those who are in need and also to donate to personal development causes that are near and dear to me like the Hoffman processor Insight. So purchase a Super Sticker, Super Chat or write the word question and post the question thereafter. We are gonna jump in the Q&A. And by the way, if you're listening to the recording right now, just I'll do my best to read them succinctly so you can know what's going on. All right. So let's check out the Q&A board. All right. Coco writes, how do you cope if your partner would be open to seeing others he wanted to? How do you cope? Okay. Coping. You cope with self-love. Folks, here's the thing. If the person you like or the person you're dating wants something different than you, you have to understand what a standard and what a boundary is. A standard is what you want in the, specifically in the area of relationship is what do you want in a relationship? So let me give you an example. I seek a relationship where we spend three or four days a night a week together doing shared activities, hobbies, mutual interests, spending time with family and friends, traveling together, teamwork, building skills, both in our personal and professional life, intimacy, both emotional and physical intimacy that is all exclusive, leading to either getting married or living together. That's my standard. My boundary is, if you have the need to date other people, bye-bye, boundaries are simply what's okay and what's not okay for me. And you could simply say, if this is the case, you know what, I'm seeking a relationship where it's monogamous and exclusive. What are you seeking? You just ask the question.  That's what I'm looking for. Not Jonathan Asley, but I'm pretending to be the guy. Does that feel good to you? That he wants to date multiple people and sleep with multiple people? If that feels good to you, then go for it. And if it doesn't feel good, say, homie, don't play that game. Homie, don't play that game. Next, or next out. So that's how, so coping with it, I think the challenge is that you're, the coping part is a representation that you want him to behave different than he is. And you need to cope with the idea that he doesn't want what you want. So then you're hyper focused on it being about what you, well, how do I say this properly? I'm got tongue tied here, so forgive me for a second. If you have to cope with it, it's because you're in a misalignment that you're misaligned to your own self-worth, self-esteem, self-confidence, self-reliance, self-discipline, which is all wrapped up in self-love. It's not about coping. It's about integrating the loving within yourself. And listen, folks, if you can't, it's gonna be very hard to be in a fully committed relationship, in a healthy, happy way.    So it's not about coping, it's about loving on yourself and that's my invitation for you. And I'm sorry that happened for you. This was a great question. I really appreciate it and I hope I helped. So thank you so much. Thank you, Coco. All right, let's go swimming if we have more questions.  I ask questions right away. Way to go, Jennifer.  Let's see, let's go swimming, let's go. If you have a question, post the word question or purchase a super sticker, super chat. Gina wrote, Jonathan, how do you tell the difference between a man who's not interested or a man who's really shy? Okay, great question. So shy men tend to be quiet people. They tend to be quiet, they tend to be quiet. They oftentimes might be HSP. And from what I understand now, roughly about 25% of the population is HSP, which is highly sensitive people. So they might be shy because it might be information, might be, I say information overload, might be that when there's a lot of connectivity, they tend to go inward. Again, I'm not an expert in this area of human behavior, but shy people tend to be a little bit quieter. Shy people tend to be a little more withdrawn. They prefer smaller groups than crowds, okay? That just tends to be that way. With that said, what they don't do is that they're still consistent in communication and planning dates. They want to get, they're open to exploring, getting to meet your family and friends. They will still initiate sex. There isn't, if there isn't chaos going on in life, they're not planning their exit clause or exit strategy. And lastly, what was my last one? And they're not picking fights with you. Shy people don't necessarily pick fights. So the difference is the disinterested person is doing all the things to sabotage the relationship. The shy person isn't sabotaging it. Most likely the shy person doesn't feel overly safe. Maybe they lack a little bit of self-love. So I have a solution for you and I recommend this. I would purchase two copies of the book, eight dates by doctors John and Julie Gottman. Purchase two copies of the book, eight dates by doctors John and Julie Gottman. Let me tell you why. These, this book has created great questions to talk to one another. Look at these chapters to talk to one another about the important things in a relationship. And what this will create is intimacy, intimacy between the two of you. Intimacy means into me you see. And I've got another book I recommend. It's called Oral Sex, Talking and Listening Your Way to Passionate Intimacy. Folks, so what if he's shy? You can break him out of his shyness by talking with him about deeper things. Talk to him about deeper things instead of the surface conversation. How's your day going? Is your day going good? Hope your day is going good. Is your day going really good? I've been thinking about you. I hope your day is good. This is about 90% of the bullshit rhetoric that goes on between men and women and their text messaging. How's your day? Like that's the best they can do. They lack depth. You know, it's interesting.  But it's interesting. I had a woman email me today on a dating site and I mentioned that we live quite a bit, quite a bit of distance from one another. And what she wrote back was a real clear succinct understanding of what I was saying.  I can understand what you're talking about. It's not easy to do those things like spontaneous, let's do Netflix and chill or watching the sunset together or going for bike ride. There's a little bit more work involved. What I most appreciate it was she went beyond the surface. And this is what I'm doing my best. It's why I scream at the top of my lungs.  This is why I highly recommend reading the book, Making Love, How to Make Love All the Time by Barbara DeAngeles. This has so much great information to go deeper than the surface that most humans are dating these days. And let me just say something, ladies. The wrong guys run away quickly and the right guys lean in. In fact, they actually appreciate that you're making this effort. So it takes all the pressure off of us when you start in it. Again, the right guys appreciate this. If they're genuinely interested in you and they're genuinely interested in long term. You know, the challenge with most people is they're just not into each other enough to make the effort. And I'm here to say there is a way to make that happen by asking better questions and becoming intimate.   That's what intimacy stands for. So that's my invitation for everyone. And going back to your original question about the shy guy, the difference between the shy guy, he's usually just quiet, but he's engaged. And that's how you can tell the difference. Okay, Gina, thank you so much for that question. I really appreciate it. All right, let's see what else we have. Purchase a super stick or super chat to tell me you're appreciating me right now. I'd really appreciate that as well. All right, let's see. We have a question from C.O. Mama. C.O. Mama, co-mama, okay. I have high standards, but I've been told that I'm high maintenance because I know what I want and I don't put up with the yes. Okay, thank you for telling me that. You didn't ask a question. So what is your question? By the way, folks, when people criticize, by the way, okay, I'm gonna go off, here's the thing.   It's not constructive criticism to tell someone you're high maintenance. Now, if they're going to maybe express what it is you're doing that's different than someone else, I can appreciate constructive criticism, but The Four Agreements, be impeccable with your word. Always do your best. Remember that don't make assumptions about others and understand that people's projections or criticisms of you is often a projection of themselves and that's what I was leaning into there.  However, it doesn't hurt to get constructive criticism at times and I will tell you that entitled behavior, a lot of women act very entitled. I was watching a video earlier of a woman who says, I will not go out on a date with a man unless he takes me out to a fancy dinner. I will not go out on a date with a man unless he takes me out to a fancy dinner.  This was a TikTok video. That is riddled with entitlement.  That's an element of high maintenance and both men experience high maintenance from women who have expectations and yet are unwilling to give it the same level that they wanna get. So with this said, I'm not suggesting that's you.  However, if you need constructive criticism, hire me, talk to a good friend. By the way, be careful of your female friends. Talk to a male friend who actually knows you. Maybe that would be the person to get advice from. Or hire me, schedule a free discovery call with me to see if working with a coach is right for you to see if you're genuinely high maintenance or not. And by the way, I can figure that out relatively quickly based on my initial questionnaire I give client when a woman works with me. So just remember, you might need some support and some help on that. So who was that that post that question? Coco, thank you so much. I appreciate that. Or it wasn't Coco, it was... Oh, I don't remember who it was now. Ko Mama. Okay, thanks so much. I wanna thank Ouija for the $5 Super Sticker. Thank you so much for that. I appreciate you making this environment much better. I appreciate your comment on that. Thanks so much. All right, we are rocking and rolling today. Question from Katina. How to tell he wants a second date? First date was great, but not sure how interested he is. Okay, that one's interest, that's easy. He plans the date. That's how you know he's interested. Now, if you got on a first date with someone, usually a guy who wants to see you will either lock you up for the next date at that moment before the date ends, or he's contacting you very quickly, usually within one or two days. At the very most, you'll have to wait one or two days. That's how you know. There's really no other way to know. He either says it right afterwards and he makes a plan or he does it a few days later. That's the sign he wants to see you a second time. The problem here with dating is we... Folks, we have to understand that the getting to know you phase is challenging because a lot of times we're dating with a lot of doubt. In other words, unless there's amazing chemistry between two people, there's always gonna be tons of doubt. Ladies, you're feeling doubt whether or not you're attracted to him, whether or not he's a good person. He's feeling doubt about you, so there can be reservations about a second date. By the way, this is one of the reasons why I encourage women to call the guy up and say, hey, I had such a great time with you. I'd like to show you my appreciation that you treat on the date. I'd like to show my appreciation by taking you out for drinks Thursday night or Friday night, which works better for you. Now, if he's not interested, he's gonna say thank you or he's gonna go or he's not gonna respond, okay? But if he is interested, now you've established the second date. So folks, stop playing the rules-based way of expecting men to chase. You can make effort too. You can. It's okay.   I'll be in my masculine energy if I ask a guy out and that's gonna intimidate him. Look it, unless you got a shotgun pointed to his face, unless you're physically bigger than him, you can't intimidate him. Only a weak guy gets intimidated, but do you wanna be with a weak guy anyway? So you can make effort as well. That's my invitation for you. All right, thanks so much. I appreciate that question. All right, I wanna thank Kim Turner for giving me a few good questions in order to vet a new date. My favorite first question to ask someone, what does commitment look like for you? What does commitment look like for you? So folks, commitment, you guys know my standard. Commitment looks like this. We spend three or four days and nights a week together doing shared activities, hobbies, mutual interests, spending time with family and kids, traveling together, teamwork, building skills, both in our personal and professional life, intimacy, both physical and emotional intimacy, all in an exclusive relationship where we either live together at some point or get married. That's what commitment looks like to me. Here's what most guys are gonna say. Huh? That's a deer in the headlight. What does commitment look like? I don't know. I don't know. I don't know. But the problem is ladies, you don't know what commitment looks like for you. I'm gonna tell you something. I had a coaching call a couple of years ago. A woman calls me up, telling me about the relationship she in. She says, Jonathan, I want more commitment from the guy I'm with. We've been dating nine months. I'm like, great. What does commitment look like for you? But Jonathan, I just want more commitment from him. I'm like, great. What does it look like for you? But Jonathan, I just want more commitment from him. Great. What does that look like for you? But Jonathan, like she thought screaming was actually describing. Screaming doesn't describe anything. So saying it louder didn't change. You did not know what you wanted in this particular case. So coming back to Kim, ask the question, what does commitment look like for you? And listen to how he responds because then you can determine if maybe you're not on the same page or you are on the same page. That's a good question. Another good question to ask someone is, how fucked up are you? And I'm just joking.  I've noticed a lot of guys seem really fucked up in the dating process.  You say it with humor. You say it with a tongue in cheek, but you'll be surprised.  I mean, a smart, intuitive man won't, but most men are unconscious. So if you do it in a fun way, just saying, hey, I've noticed a lot of guys seem really fucked up in the dating process. Is this normal?  You say it with a smiling face. He might divulge his dysfunctionality and you might be able to go bye-bye much sooner. So those are two quick questions. You might want to try, Kim. Hope that helps. Thanks so much. All right, let's go swimming. Liz Taylor says, let's be real then. I agree.  My girl, I dated in high school and her husband passed away a year ago as well. So I'm sending you a big hug of love right now. I'm sending Kim Turner, sounds like Scooby-Doo. I don't know. Thanks so much. I appreciate that. All right. Kelly says, projections of the past can get to you if you let it speak life into new love, less doubt and more questions. Exactly. Robin says, Jonathan, you sound like Scooby-Doo. I didn't think about that, but thank you. Hey, Doug is in the house. Doug, I find that things that might have actually worked can easily fall apart between the first and second date due to doubts by each or the other things happen. Yes, Doug brings up a good point. So folks, I've had great first dates. And as a matter of fact, this happened within the last four or five months. I had a really nice date with a woman. Then the next morning I woke up going, I don't wanna see her again. I was feeling resistance. And I didn't know why. I was just feeling some resistance. And as I explored it, I came up with a lot of rationalizations in my head, but I was just feeling resistance. Sometimes we feel resistance because our intuition is saying, no, no, no, no, no. And not because she was a bad person. In fact, she was an amazing person. When you reached a highly attuned level in your intuition, your intuition speaks to you in a very silent voice because that resistance wasn't fear or anxiety, it was just like, wow, I'm just feeling resistance. So it is common from the first to second date, from after the first date to maybe hit a wall. And like in my case, I'm pretty highly attuned to my intuition, but that's very common. Listen folks, it takes about a hundred hours of face-to-face time, a hundred hours of face-to-face time to develop the first stage of trust in a relationship. Let me repeat that. It takes about a hundred hours of face-to-face time to develop the first layer of trust. And trust is built through layers. So just understand this. This is why, listen, some women have learned to date like men. Men don't get attached to the future outcome. We might futurize with you. Listen, when men are excited and we're horny and we're feeling lust or limerence, we might plan your entire future with them on the first, second, or third day. Usually it's the first or second day, okay? We have a habit of what's called futurizing, meaning we try it on for size. But here's the thing. We are never attached to that outcome. Ladies, the minute you like a guy, you are attached to the future. You are so hyper-focused on the future instead of appreciating the experience. And when you're focused on the future, you've created an expectation. And as my friend Guy Blue says, expectation is the mother of disaster and desperation is her twin sister. If you create an expectation of a future with a guy, you are setting yourself up for failure until you've actually established a deep, rich, committed relationship together, committed relationship, and you are co-creating the relationship together. This is why I continually recommend reading the book, Eight Dates by Doctors John and Julie Gottman, purchase two copies, read it together before the penis goes inside the vagina. And if you wanna learn how to actually develop a deeper relationship, I highly recommend reading a couple books. You might wanna read the book, Mating and Captivity by Esther Perrell, and you might wanna read the book, Spiritual Partnership by Gary Zukov. So Esther Perrell, Mating and Captivity, Gary Zukov. Let me tell you why you wanna read these books. Folks, you're all dating, most of you are dating under the premise that men are the leaders of the relationship. And you're hyper-focused on chemistry. If you're not familiar with my relationship iceberg, here it is. Above the water line is attraction. And as you can see in the tip of the iceberg is chemistry. Below the water line is shared values, blendable lifestyles and emotional maturity. And as you start checking the boxes, you become more and more attracted to one another. Most of you folks are winging it when dating and you lack any intentionality. But Jonathan, I don't wanna put pressure on the guy by asking good questions. Folks, stop being afraid to talk to men. If you listen, read my book, chapter one, speak your truth, deal with kindness. And then later in the book, chapter nine, if it's sincere and from the heart, you can't say the wrong thing to the right person. So folks, stop being afraid to leaning in, leaning in. Leaning back doesn't work, leaned into co-creating a relationship. Write these words down, co-creating a relationship. It's the two lane street and it happens from the very first date. I shared this story before, I'm gonna share it again. I'm going off on a tangent here for a second. I'll never forget, I had a first date with a woman and we went to a dive bar for our first date. I mean, she was really excited about it. She was, I mean, she told me she was totally up for it. And I bought the first round of drinks and when it came to the second round of drinks, she pulls out her credit card and I go, no, I got it. And she goes, no, I got it. And I go, no, I got it. She goes, no, I got it.  What she did next blew me away. She put her hand on my arm. She said, Jonathan, I really appreciated that you treated the last round. Would you allow me to show my appreciation by treating the next round? Can you receive my love? I mean, she didn't use the word love but that's what in essence she was doing. Can you receive? Folks, in that moment I was floored. In that moment I knew this woman could be a partner in life because you know what she did? She said, Jonathan, you mattered and I'm willing to invest in you. Folks, the dating process should be a mutual investing process, a mutual investment process. And if you're investing more than him, then it's misaligned. And if he's been investing more than you, it's misaligned. When it's done in a two lane street that is your greatest chance for success. And while it didn't work out with this woman, she had major trust issues. And by the way, I'm the worst person to date if you have trust issues because I talk to women on the phone all day. But she had trust issues and I couldn't be with someone who has trust issues. But you know what? She showed up like a potential partner right from the get go. And that's what I invite. And that's what I mean by co-creating. It's a two lane street, it's mutual effort to get to this because when you create a bond with one another that's strong and can't break it apart.  All right, I think you get the gist. By the way, Doug, thanks for jumping in on that one. I really appreciate it. I hope you found value in what I shared. Thanks so much. All right, Giselle says 50-50 very important. No, it's 100-100, 100-100, not 50-50, 100-100. I know it's semantics, but I just want to make sure that everybody gets that distinction. So thank you so much, Giselle. All right, another one says 50-50, no, 100-100. All right, Catherine says I agree. I've been guilty of being attached with expectations about the future early on with a guy. Thank you so much. I appreciate you sharing that, Catherine. Laura says, wow, that statement was an eye-opener. Thank you so much. I'm happy to hear that. Kim says, could we talk you into doing your next video in a Scooby-Doo voice? Scooby, Scooby, Scooby-Doo. Oh, we're shaggy. Kimberly says, question, have we completely ruined our chance at a future by sleeping together too soon before emotional attachment?  Now, that's the exception, not the rule. Folks, if you follow my work, folks, everybody repeat after me before the blank goes into the blank. Everybody write it down before the penis goes inside the vagina, purchase two copies of the book, eight dates by doctors John and Julie Gottman. That's what you should be doing to see if you're on the same page. Stop dating in a passive manner and start dating intentionally. How many times do I have to scream this over and over and over and over? Wait, Scooby-Doo-Bee-Doo-Boo-Doo, over again. All right, folks, I think you get the gist of where I'm going. We're gonna take one more question before we wrap up or you can purchase the Super Sticker Super Chat tell me you appreciate me. That would mean a lot to me. Goes to that scholarship fund in the name of Connor. Here's Connor, oh, he's so cute. All right, last question of the day. Nicole says, what dating sites would you recommend? All right, so folks, before I get into which ones I recommend, I just wanna say this. The days of meeting organically is becoming increasingly hard. The days of meeting organically, unless you're in an environment of single, eligible people, it's gonna be problematic. In fact, online dating probably now represents 50% of all new relationships for those over 45 years old and there's a good chance that number is gonna be hitting 80% in the next few years. The sad thing is online dating is gonna be the way most people meet these days. So it's important to first create a stellar profile. Folks, I wanna show you something. This is a screenshot of a picture I took this morning from a woman. This was her dating, a picture on her dating profile. That was her picture and at the top she says, felt cute but I might delete later. That is a grotesque picture. I'm sorry, that's a grotesque picture.    So it's not about which is the best dating site, the question really becomes, are you gonna put a great representation of yourself? So folks, just as an example, I'll show you mine. I will show you mine. So my first photo, crisp, clear. You can see what I look like. The next photo, crisp and clear. You can see what I look like, self love club. Next photo, my kid's dog, crisp, clear. Quality photographs, smiling. Next photograph, a body shot. I'm wearing sunglasses but you can see I'm not a big chunky guy. And last but not least, or second to last, here's another one, my book.  Can you see that? And lastly, these are the books I read. I put together a stellar dating profile. By the way, this is on Hinge. The dating apps that I like are Hinge, Bumble, Soso on the league, Soso on Tinder, and then match.com. Those are the five sites that I'm on. I prefer match, Bumble, and Hinge as my primary sites for meeting people. Now, someone might be saying, well, Jonathan, how come you haven't met someone?  And I just don't have patience for someone who puts poor effort out there. I just, I really don't. If you're not willing, if you're not willing to put a great representation of yourself out there, then why should I even bother investing in you? This is my beef with a lot of you ladies out there and men as well.  So, I'm here to say, start with a quality profile. Write a great essay. Let me read you my Bumble essay, just to give an example. This is my Bumble essay. Bum, bum, bum, bum, bum, bum, bum, bum. Bear with me, Bumble. Okay, so my Bumble essay says, for the past four years, I've been on a dramatic journey to become vulnerable and authentic, seeking a woman ready to explore the depths of intimacy. You up for deep, meaningful conversations and a slight warped sense of humor. I'm your guy. If you're a fan of A Course in Miracles, are you? Fan of A Course in Miracles, are you? Seeks empty nester. I mean, I think there's a lot of good content in there, but most of you are writing this. Wah, wah, wah, wah, wah, wah, wah. Wait, I'll do that again. Wah, wah, wah, wah, wah, wah.  It's like the Charlie Brown, the school teacher. Wah, wah, wah, wah, wah, wah, wah, wah, wah, wah. Scooby-Doo. So, shift your narrative. Put together a great essay out there. Put together a great profile. And if you need some support on that, check out the link to a free discovery call with me. I'll turn you on to a great company that will help you create a great profile. And as far as the best sites, I like Bumble because I like that women make the first move. Do you know why? Because women get hundreds of messages a day from guys. When women actually reach out to a guy, they tend to be more interested because you guys are ladies, you are inundated with men. And I like the ones who make effort. That just happens to be me. That's not a beta male, Jonathan. That doesn't mean I'm passive. I just appreciate that they make effort. It tells me they're a little bit more interested in the average woman. I like hinge, really good site, and I do like match.com. So, to answer your question, that's the ones I like and I hope I helped. All right. Well, I think it's time to wrap up today, but before we do, we're gonna say, Robin says, all right, Charlie Brown. Elaine says, you're funny. Wait, who just, who just, someone's got my picture, walk user. Someone stole my picture and created a profile. I just blocked them. All right. Anyway, folks, I think that, oh, anyway, I think this is a good place. Someone says, thank you so much. I really appreciate that for answering my question. You're very great, or very welcome. All right, this would be a great place to wrap up today. First off, I wanna thank you all. If you found value in this content, please tell your friends, share this video. I'd really appreciate it. And also, if you'd like some support, check out the links to the books I recommend, my membership group, and certainly, if you'd like some support and coaching, check out the free discovery call with me to see if working with those coaches right for you. All right, I'm gonna wrap up this video as I always do. First off, giving myself a big, gigantic job at the barricade of self-love. I'm gonna reach into the camera and give you a hug of love if that's okay. I'm gonna ask you to turn to a friend, a pet, a teddy bear pillow, and give Iter them a hug of love because hugs are a great source of love. And let's face it, we could all use more love in our lives. I wanna say thank you to Robin, to Linda, and Nicole, to Maggie, to Melissa, to Jennifer, just to name a few. Missy, Suzanne, Jennifer, thank you all so much to Weegean and all you others. I just wanna say wishing you a super duper, wonderful evening. Bye-bye now.


Okay, so let's start. So we have, start with u over zon, matrization theory. So X normal, if X is normal with a countable basis, the second countable, right? Countable basis implies X matrizable. So it's stronger with regular, okay? Regular is okay, but we prove this. A regular space which is with a countable basis is normal, but that I will not prove. So proof, lemma. There is a countable collection of continuous functions, fn from X to zero one to the interval zero one. So n and n, countable. Such that, given any point X in X and neighborhood u of X, given any point and every neighborhood of that point, there is an index n such that fn, so it's X zero, well. Given any point X zero in X and any neighborhood u of X zero, there is an index n such that fn of X zero is bigger than zero and fn of the complement of the neighborhood is zero. This is an important lemma, okay? It's on the rest is easy. Okay, proof. This is the orison lemma, proof of the lemma. So we have a countable basis, okay? So let b be a countable basis for X, second countable. For each pair of indices, a, b, so sorry, for b equal bn, n and n, so this is also countable. Be a countable basis for X, bn, for each pair of indices, let's say nm such that, so we have this bn, this is on our basis. Such that the closure of bn is contained in bm by the orison lemma, so we apply the orison lemma, choose a continuous function, f and m, so it depends on these two indices, f and m. This is not the same n, okay? Then this is countable also in two indices, so no problem. f and m choose a continuous function such that, so orison you can separate closed disjoint sets, okay? One is bn closure, such that gnm of the closure of b is equal to one, so it's one on this, and the other closed set, it's a complement of bm, the complement of bm, and gnm of the complement of X minus bm is zero, so this is a lemma of orison, okay? You can separate disjoint closed subsets, okay? Yeah, all right, now it's g, okay? So I call it g now, so, but these are all fs of course, but in another order. So this is a countable collection of continuous functions, okay, which depends on two indices, g and m, this is countable, okay? And now we need this property, there is an index, for any neighborhood, there is one of these functions with this property, okay? So this is the property. So let's see, let X, so what is the notation? X zero in U, any neighborhood U of X zero, so let X zero, so consider now X zero and the neighborhood U as in the lemma. So there's a basis element which contains X zero as contained in U obviously, so there is choose a basis element, bm such that, such that X zero is in bm contained in U. So this is the basis, no problem, yes, thank you. So now we have this situation and we choose obviously a basis element, bm such that bm X is contained in U, but X is regular, okay, normal, X is normal, regular sufficient here, what does it say? Well, maybe it's regular, it's better here because normal is for close ups, that's regular as for point, a point, okay? So regular, anyway, it's normal, but maybe better to try and figure it out. So given a point and the neighborhood, so this is a lemma, no, which you prove, not, I made by picture, okay? If you have a neighborhood of a point and there's a smaller neighborhood, such that the closure is still contained, and given a neighborhood of a point, there's a smaller neighborhood of the point, such that the closure is still contained in the larger neighborhood. So we have the smaller neighborhood, the smaller neighborhood obviously contains, again, a basis element, still smaller, okay? Because it's a basis, okay? So there is, X regular, there is a BN, a basis element, BN in our basis such that X zero is in BN closure still, and this is contained in, and then of course G and M has what we want. So this implies that G and M, where's our G and M? It's bigger than zero, G and M of BN bar is one, and G and M of, what were X minus BM is zero. So X minus U is zero, okay? So this proves the lemma, right? So now we have G and M in two indices, but it's countable, and now we call it FN in one index, okay? This is our, this is the lemma. And now the proof of the theorem, so the idea is, I didn't say that, but the idea is the following, so we define a function F, continuous function F from X, X, we have to prove X is matrizable, okay? And so we embed it into our omega, and this has a product topology for the moment, product topology. Well, also it works with the uniform, but let's take the product topology. So how do you find, F of X is equal to, so we have this countable collection of functions, FN, okay, so we take these functions, F1 of X, F2 of X, and so on, so it's N of X, N and N. This is a definition F, okay? And now we want to prove that this function is an embedding, okay? The claim is, F is an embedding. What is embedding? Well, we will see in the proof. It's a homeomorphism onto its image, okay? Homeomorphism onto its image, embedding, homeomorphism onto its image, that's an embedding. And then of course, that's nice, no? Because if it's embedding, homeomorphism, what does it imply? This implies that X is homeomorphic, homeomorphism, to what? To its image, F of X. And what is this? It's a subspace of X. No, subspace of what? Of our omega. Our omega is matrizable, okay? This is matrizable. I gave the metric, okay? The theorem and what is the right metric for our omega is the product topology. So our omega is matrizable. So this implies any subspaces matrizable. The subspace of matrizable to space is matrizable, okay? So subspace of a matrizable to space is matrizable. It's the same metric. And this implies X is matrizable, okay? F of X. That's the idea here. This is the idea, okay? This is embedding. F of X is matrizable. So we embed it into our omega. So this is a proof. So I have to prove that F is an embedding, right? Also the uniform topology would be okay, right? Because this is a metric space even, okay? Defined by a metric, okay? So it works also with some modification. But here we take the product topology. So I have to prove this claim. F is an embedding, okay? Then we are done. Okay? This is the idea here. We construct enough continuous functions to the real numbers. And then we take all this countable number, okay? Uncountable, our omega, our uncountable is no longer with the product topology, you know? The uniform topology is in all, okay? So, well, anyway. So this is, now I have to prove only this claim, okay? Well, what means embedding? Homomorphism, so proof of the claim. So embedding, homomorphism, so it's injective, okay? F is injective. So that's the first, F is injective. That means if you have two different points, then you should find one of these functions which has different values in different points. So let X, Y be different points. How are they called? Whatever. X and Y, yes? Let X, Y be in X, X different from Y. So X is T1, T2, okay? X is T1. As before, X is T1. What does it mean? There's an L value of X, which does not contain Y, the other one, okay? Now we do the same game as before. We find two indices, L and M, such that as before, what I did in the lemma, okay? As before, as before what? There are BN, BM in our basis, such that X, what is our point? X zero before, now X is contained in, no, I forget, BN closer, contained in BN or what did I write? BN closure, yes, BN closure contained in BN, okay? That's as before with X zero, exactly the same. They are BN, BN. So there is an FN and then we have our GNM, okay? So GNM, so what was FN, this is some FL, some, I don't know which one. FN, M of X and BN closure, what was it? It's one, I think now, and GNM of Y. But Y is the complement of BN, okay? So it's zero. So this function is one here and zero on the complement of BN, that's the original lemma, right? These are the two different closed sets. This is one here and the other one is a complement of BM and that's zero. So GNM, X is zero, so for some, FN this happens, okay? And this means that F of X is different from F of Y because these are all these GNMs. So it's injective. The second is, it's continuous. Well, this is easy, no? F is continuous, since Y, why it's continuous? What? All component functions, this is product topology, okay? Since all component functions, coordinate functions, whatever, FN are continuous. And here in the, if it takes the uniform topology, we have to prove something still, okay? Because this is a larger topology, you know? So continuity is stronger, okay? But for the product topology, no problem. And then the last thing is that F is, so what is the notation? F is a homeomorphism onto its image, homeomorphism onto its image. So we have to prove that F is a homeomorphism onto its image. So what remains to prove here? Remains to prove onto its image, which I call Z. That's the image of F of X. So this is a subspace of our omega, the image, okay? We prove that for each open Z, which is called U in X, F of U, open, okay, open. It's open, so for each open Z, U in X, F of U is open. The image of open Z is open, where in Z. Not maybe in X, that I don't know, in our omega, okay? In the image, we are restricting to the image. It's open in Z, which is the image, that's important. So that we have to prove, right? Okay, that's the last point. So we have to prove that for each open Z, F U is open in, so take any point here in F of U, okay? Let, which is called Z, whatever it is called. Z zero in F of U. F of U is open here, so we have a point here now. We have to find an open Z in Z, which contains this point as it's contained in Z, okay? The usual thing, open, okay? Open means, for every point, we find an open Z, which contains a point, is contained in our Z, which we want to prove open. So let zero be in F of U. So let X zero be in U, so it's the image, F of something, such that F of X zero is Z zero. It's in F of U anyway, okay? So we take a pre-image in U. Now, we have this point X zero, okay? And we have our collection of functions. And we have a neighborhood of U. So what was the lemma? For each point, each neighborhood, we find an index N such that F N is bigger than zero in the point and zero in the complement of this function. That's the main point, no?  It was one, but bigger than zero, okay? And in the complement of U, F N of X minus U, it is zero. Again, the lemma, okay? The lemma, so we apply again the lemma. So let V, by definition, V is a pre-image of, so pi N, what is pi N? That's a projection on the Nth coordinate of r omega, okay? Projection onto the Nth coordinate as usual of r omega. So one here, projection of the Nth coordinate, pi N minus one of the interval, zero infinity. So we avoid zero, okay? We take the, so this is open, open, where's it open? In X for the moment, okay? Pre-image of an open sector. But that means, of course, that W, which I'm not interested in X, I mean open in X here. I'm not interesting, so this is V, intersection Z, there are too many notions here, V, Z. So V is this pre-image and Z is the image, okay? Sorry, I wrote something wrong, open in where? R omega, okay? I was, something was not okay. But I didn't, so this is a projection from r omega onto its Nth coordinate, okay? So this is open in r omega. But we are not interested in r omega, okay? We are interested in the image. And so I intersect now with the image, okay? So this is open in Z now, clearly. This is open in Z, this is the image of F of X. So this is in r omega, we are now, okay? And now this is the set which we, so the claim now is again, well, one claim after the other. That's okay, this is our set. So claim again, what is our point? Our point is called, where is it? That's zero, okay? This is the point we choose in the image. So the claim is X zero is contained in W. This is open, no? This is open in Z, open in Z, in F of X. And this is contained in, where it should be contained. What is it called? F of U. And then we are done. So this implies F of U is open, Z, which is F of X, no? Then we are done, okay? So Z zero is in W since, so this is immediate. Since pi N of X zero of Z zero, this projection, what is this? This is pi N of F of X zero, yeah, this is FN of X zero. So this is bigger than zero, yes. Pi N of Z zero is bigger than zero. So we are, so this is okay. And second, so what remains is W is contained in F of U. So take a point in W, let Z be in W. Then Z is equal to F of X for some X in W. And X, we are in F of X, okay? But F of X is not sufficient, we need F of U for some X in X. And pi N of Z is where in zero infinity. Z is in W. That many notions, too many notions, now W. You always have a new name for everything, no? But that's from the book. So this is the image, okay? We are in the image anyway of X, and now we are also in V, positive coordinate. Now we have these two things here. Okay, since now, pi N of Z is equal to what? Is pi N of F of X, no, F of X is Z, anyway. And this is F N of X.  Where does it vanish? Outside U, this was our neighbor, what? This means that X has to be in where? In U, F of N vanishes outside U, no? But F N of X, so this is bigger than zero, sorry, okay? I might better add that. So pi N of Z is this, is F F of X bigger than zero, okay? This is bigger than zero, because we are in V here, in the pre-image of volume zero. And where N is also, so this means X is in U. It has to be in U, because F N vanishes outside U. So we have to be in U. And this means that F of Z, Z, what is that? Z, which is F of X is in F of U. So we are proving this here, no? Any point here is also here. And that's the end of the proof. Okay, well, we have to concentrate. There are many, this is not taken from the book. There are many names here, no? So one has to look, what was 1W? What is V? What is that, no? Maybe too many names, but one has to concentrate. What is our set, okay? Anyway, the proof is not difficult. So the main part is the orison lemma, okay? To have all these functions, F1, F2. So this is the proof of the orison matrization theorem, okay? Well, and all the last theorem is much easier. It's a consequence of this one anyway. I finish with the following theorem, which is also very nice. Also orison matrization theorem. So this is a complete solution. If x is compact, suppose x is a compact space, and x is matrizable, if and only if x is matrizable, then, well, anyway. If and only if x has a countable basis. For a compact space, this is a complete solution, okay? Of the matrization problem. If x is compact, then matrizability and second countability are equivalent completely, okay? For compact spaces, this is the solution. Here the proof is now easy. That's nice, okay? We don't prove the general matrization theorem, no? We know second countable in general is not sufficient, okay? It's not necessary, okay? First count, it's between first and second countable, the general matrization. Well, the proof is we have two directions. The interesting is this one. So x has a countable basis. This is a horizontal matrization. So compact implies normal, okay? X compact, that you have to prove, implies x is normal, anyway. And if x is normal and second countable, then x is matrizable. And this is a horizontal matrization theorem, okay? Which we proved. Normal, second countable, x is matrizable. So this is corollary, x matrizable. This is horizon matrization theorem, okay? So the other direction is also interesting because this is one of our exercises, which I like. So what now, x is matrizable, compact, okay? X compact matrizable, so exercise. X matrizable, compact implies, what you have to prove, x is second countable, okay? X has a countable basis. This is the easy direction. You remember this exercise, okay? So there are two exercises, one we did already. This is if x is matrizable and it has a countable dense subset, then it is a countable basis. That's what we did. And this is the second of this. If it's now it's matrizable and compact, then it has also a countable base. What? Say again, I didn't. So if x is compact, compact space is normal, right? A compact house of, of course, okay? Is that what you mean? Compact house of, oh, sorry, sorry. There's something wrong, right? Compact house of, yes. Very often compact includes house of, but not with us, okay? So I forgot that. Of course, house of we need, okay? Okay. Compact house of, we need a compact house of space, okay? If it's not house of, it's not matrizable, right? So that's certainly the first necessary condition for being matrizable, okay? So we need a house of space, yes. Thanks. Compact house of means normal, right? And then normal second countable implies matrizable, yeah, okay. And this is our exercise, right? I hope you remember that, okay? Yes. So what is the idea, so proof? Well, let's do it as an exercise, proof. This was the exercise, it's the exercise in the book. So matrizable compact.  One over N, one over N. By open balls of radius one over N. This exists now because it's compact. You take all open balls of radius one over N, this is an open covering, so you have a finite sub-cover, okay? So no problem. And let B be the union of all of these BN, N and N. This was a hint in the exercise, right? This was a hint. Let B be, so B is countable, okay? This is clearly countable. Even a countable covering would be okay, still for countable, right? Well, anyway, so B is the basis, okay? Now we have to prove that B is the basis. B is the basis for the topology of X. So what means basis? So now it's okay, okay? This is the, ooh, the matrization, the second. Compact house dot space. So what means B is the basis? This means that if you have an open set U open, if you have a point X in U, you shouldn't be able to find the basis element which contains X and is contained in U. Then the lemma says this is the basis, okay? For the topology. So we have this situation again. However, X is matrix space, matrizable, okay? So what you find is, I make my picture. You find the ball, okay? Which contains, we center X and contain in U. So this is the ball, D, X, for some N, no? One over N, epsilon. And then I take some one over N immediately, okay? One over N. Now we want to find a basis element. So what we do, what I do is, I consider half the radius again, okay? Half the radius. One over two N. No, no, sorry, one second. I apply for two Ns, okay? So I have an open covering of balls of radius one over two N now, okay? So this is our N, okay? And now I pass to two N. So let X, it's one over two N, they cover. Finally many, but they cover, okay? Let X be B, D. So now I find another point which is called, whatever it is called, Y, radius one over two N. And this in B, so this is in B, how do I call this? Two N, no? B two N, one of these, so contained in B. So I consider these balls, okay? N is this one. So here's some, so it's in this, obviously, but it's somewhere, this is one over two N, so the point Z, Y, what is it, Y, it's here, okay? Half the radius, somewhere here. And now we have this ball here, okay? This is this ball, Y one over two N, which contains X, okay? This contains X. So what we need, it's contained in this one. Which is clear from the picture, and then it's contained in U, and then we are done, okay? So the point is that Y one over two N however is contained in this one, B, D, X one over N. Why Z? Well, you take any point here, okay? Z, so take any point here, where in the, this one, Z, okay? Then the distance of Z and X, okay? You have triangular inequality. So this implies that the distance of X and Z, since distance of X is smaller or equal to what? This is one over two N, and this is also one over two N, okay? One over two N plus one over two N. So one over N. We need smaller, okay? And that's it, so we have this. So this is the lemma, okay? This is the exercise, okay? This is the proof of the exercise. Okay, that finishes the general topology part. And now we start immediately with, so the nice theorems obviously are, lemma of orison, orison matrization, and this second orison, okay? By the way, I looked, so orison was from 1898, 1924. And the general matrization theorem, it proved in 24, all this stuff, okay? It's, there are three names or two, three names by, so one is snagata, Japanese, independently, okay? Smirnov and Bing also has some version. They all have some version, okay? General, so there are three, two, three groups of people who independently prove the general matrization, which I didn't tell you, okay? We have to find the condition between first and second counter, okay? Normal, okay, normal we need anyway, okay? But we need something between first and second counter. And this was quite subtle. So this was more or less from 1950, okay? Proof, 1950. So that means it took 25 years to find this condition, okay? After orison, it took another 25 years, no? To find the right condition, which is subtle, okay? You can have a look in the book, what is the condition? Some existence of special kind of basis between first and second counter, okay? So this is also historically, it's quite interesting, okay? Okay, maybe, he died with 26 years now. Maybe if he would have gone on doing mathematics, maybe this would be, I don't know, when he obviously would have also thought about that, okay? After this, after his first paper, when then maybe we have 1935 or something about this, of course, history. Okay, so now, it's good. So this, we can forget not everything, but almost everything. No, no, something we need, but homotopy and fundamental. The first part will be very formal, okay? And maybe a little bit boring, but the second part, then we have applications and that is very interesting again. But the first part is formal, okay? So I have many definitions in there, so. So definition, what is homotopy? To continuous maps, f and f prime from x to y are homotopic, and we write that f is homotopic to f prime. So this is the notion of homotopic. Not isomorphism, okay? Homotopy is one, just one law. If there exists a continuous function, a continuous map, map and function, let's just say most. Capital f from x cross i, i is the interval zero, one, so this is interval zero, one, as you know, zero, one. Close interval to y, such that f at time, so this is a time interval. f at time zero is f of x, and at time one, f of x one is f prime of x.   What is a homotopy? Homotopy is a continuous deformation from f to f prime, okay? And so a continuous deformation from f to f prime. That's intuitively what a homotopy is, okay? Can the form continuously this map f to a map f prime? That's the definition of homotopy. Example, first of all, this is a equivalence relation. So homotopy, so observation, remark. Homotopy is an equivalence relation on the set of continuous maps from x to y. What is equivalence relation? So f, the first is f is homotopic to f, no? By constant homotopy, okay? By the constant homotopy. So constant means f of x, t is constant, is f of x. Constant does not depend on the time, okay? So this is trivial. The second, what is the second? So f homotopic to g, f prime.  And how do you define g? g of x, t is equal to f of x. You just reverse the time. From zero one, you go from one to zero, okay? So this is the second one. And the third one is if f is homotopic to g by a homotopy f. And g is homotopic to f, g, what's the next, h, no? By a homotopy g, then we have to define a homotopy from f to h, h, okay? So then you can think of how to define h. So how do you find h? So what you have is we have f from, we have f, which go, so this is my kind of picture which I will use, okay? Here we have f. Here we have g. And here's the homotopy between f and g, which is called f, right? This is the kind of notation, f, g, homotopy, f. So this is a picture of x cross i, okay? This is a time interval here on this side. And then we have a homotopy from g to h. And this is called g. So it's defined here, okay? This again is a time interval, okay? So we have to put it together in a good way. So h of xt is equal to between zero and one half, we take f, f of x, two t, no? And between x of, between one half and one, we take the other one, which is g of x and now two t minus one, yes. h is continuous, y by the pasting lemma. We have on two parts, it's continuous and then, okay? So you have this lemma, pasting lemma, okay? So it's an equivalent, right? Examples. First, every map from f, x, every map, a continuous map, of course, f from x to rn, let's take rn here. Standard, rn, analysis, rn. Every continuous map, f from x to n is homotopic to a constant map. So let's see this. This means it's not very interesting. Seen from point of view of homotopy, maps to rn are not interesting, okay? They're all homotopic to constant maps, which are trillion, you know, trillion maps. So let's see this. So we have to find a homotopy from f to a constant map. So we have, so we have f of x, which constant? Well, I don't care, x zero, okay? Here we have an rn, this is an rn, right? f of x and some constant, zero. But it doesn't depend on the constant, so I call this z zero, okay? And now we just move f of x for each x continuously to this point. So what is the homotopy? So f is homotopic to the constant map. I write this way in z zero, okay? This is a constant map. In the point z zero, so we are in rn here. The constant map, okay? And so this homotopy. So what is the homotopy? H of x, t is equal to, so this one, okay? So at time, whatever. At time zero, we want f of x. f of x, at time zero, so one minus t. That's good, no? At t equals zero, we have f of x, okay? And at time one, we want z zero. So plus t, that's it, okay? So now at time one, we have constant, okay? At time one is constant. So what is this? This is a line, no? This is a segment. So we just go on the same. This works only in rn, okay? In outer space, we don't know how to do something like this. So this is called straight line homotopy, okay? Because it follows straight line, okay? Straight line homotopy. So we will use this. This is a straight line homotopy. In rn, only in rn, in outer space, if you don't know what is a straight line, right? So we have a vector space. We have, okay? This sum in rn is a vector space. So this is straight line homotopy. Second example. So take a path, f from zero one to x. Path is continuous map, okay? Take any path. So this means then f is homotopic to constant path. Again, not very interesting. Why is this? Well, it's almost the same as this, no? So we have homotopy, h, x, t. So what do you take? f of, x is bad now, okay? Because this seems we are here, sorry, okay? x is bad, x is the image now, okay? So I take s, t, okay? This is better, s, t. So what do you take? Well, depends where you want the constant, okay? You can take any point, but the first point. Let's take the first point. So then I have to write s times, let me try, one minus t. So if t is equal to zero, we have f, okay? If t is equal to zero, we have f. If t is equal to one, we have f constant in the end point, okay? That I don't want, I want the initial point. So what is s? t times s, well, sorry. One, I wrote one, let me try, one minus t times s. So if t is zero, we have f. If t is one, we have f of zero, the initial point, okay, yeah? So the constant map in the initial point, okay? This is the constant map. In the initial point, f of zero. In some sense, you see the homotopy, okay? It's clear what is this homotopy. It looks like this. So here you have, the picture is this, no? You have this and you have some f, okay? And now you have this homotopy. What happens in the homotopy? Well, you multiply with, intuitively, this homotopy with this, at time one half, you just go to half of this, okay? Between zero and one, the reparameter was. And then, at time three over four, you just go to this point, okay? And then, finally, at time zero, you stay all the time at this point, okay? So you see, so in time zero, you go all the way, okay? In time one half, you go half the way. Half velocity, okay? Or maybe you stay here. You gave us the same velocity and then you remain here, okay? At time three over four, you go just to this point, one over four, and stay there. And at time one, finally, you stay all the time at this point, okay? So one homotopy is this one, okay? This means, this is not interesting for pathos also, okay? So we have to, but we want, so what we do now, this we don't want, okay, for pathos. The general definition of homotopy is what I gave, okay? For pathos, I have to modify now, okay? Why? Because this is not interesting, otherwise, okay? Every path otherwise would be homotopic to a constant path and constant paths are trivial pathos. No, not interesting pathos, okay? So now, modification. Modification of the notion of homotopy for pathos. Only for pathos, okay? Only for pathos. What we do, we fix this point and we fix the end point, okay? We are not allowed to move these two points. So in some sense, we fix it here, we fix it here by some nail, and then we can move in between what we want by continuous deformation, okay? But these two points, we are not allowed to move, okay? So we cannot go back to the initial point, okay? With everything, so a definition. And this is the definition of path homotopy. That means, of course, that the two pathos, if you fix these points, the two pathos have, we need the same initial and the same end point, otherwise, we cannot compare, okay? Right? So let F and G from the interval to XP pathos with the same initial point, so what is this? F of zero equal G of zero, and the same end point, F of one equal G of one. So we have this picture there, no? We have F and we have G going. Then F and G are the same, okay? Well, path homotopic, but I will not use, for pathos, the homotopy is this definition, okay? So it's path, but we say just homotopic. F and G are homotopic as pathos. If there exists, there is a continuous map, capital F from, now we have I cross I, the time interval to X, such that. So as before, capital F of, now I have to write S, no? Because X is not good. At time zero, we have F, at time one, we have the other one, G. So these two means homotopy in the general sense, okay? That is homotopy. Homotopy in the general sense. But not for pathos, this is not sufficient, so now we add F of zero, this is the initial point, T. We always have the point F of zero, which is also G of zero, okay? And at the end point, F of one, T, we always have F of one. These points, we are not allowed to move. G of one. And so this, all together, this is path homotopy, okay? So the picture looks like this. And I will use these pictures, which is very, so down we have F, here we have G to pathos, and here we have the constant, okay? In the point F of zero, which is also the point G of zero. And on this, we have the constant in the point F of one, which has to be also the point G of one. And here we have our homotopy. And we write, again, F is homotopic to G. And in the book, I forgot, he uses some other sign, which I've not used, I forgot which sign even, okay? He uses something like this or P, path homotopy, okay? I will not use this, okay? So I just write this, okay? Also for path homotopy. If F and G are pathos, this is always path homotopy, okay? So this is the definition of path homotopy. So again, the same remark as before, this is an equivalence relation, but where? So a remark, path homotopy is an equivalence relation on the set of pathos from a fixed initial point X zero to a fixed endpoint X one, okay? These two here. From a fixed initial point, from the set of pathos in X, of course, or space, from a fixed initial point X zero in X to a fixed endpoint X one in X. And the proof is the same as before, okay? You just check also that everything goes well. I mean, if it's constant here on both, then also the map which you defined before is constant on this, okay? No problem. So this is a path homotopy, okay? Homotopy, important notion in general, okay? Homotopy, path homotopy for pathos. Because it's not interesting otherwise for pathos. Okay, for pathos, we have a product. We want to define a group, okay? Using pathos, a group, okay? Fundamental group. And we need a product. So product of pathos, it's another definition. Let F be a path, X is fixed in X from X zero, from X zero to X one, and G a path. So of course, if you want a product, the second one has to start, where the first one finishes, no? Then we have, and G a path from X one to X zero, X one, X two. So we have this picture. This is X zero, X one, this is F. And then we have G, which goes from X one to X two. This is G, okay? Then F, first F and then G. That's a product, the product we write in this way. First F, then G. Then FG from Y to X. So how is it defined? F times G of, well, no, S or T, I don't know. No, the T is the, let me take S, okay, the parameter. So it's equal to what? S before, between, for S between zero and one half, we take the first path, F of two T. So this is twice velocity, okay? And for S between one half and one, we take G, but also with twice velocity, with double velocity, twice the velocity, okay? No, it's okay, yes. So this is a path, which is called the product. It's a path. Why is it a path? Again by the, pacing them, you know? That's why it has a name. So it's used everywhere. It's a path, which is called the product of F and G. So again, clearly defined only if, defined only if, let's emphasize again. Defined only if F of one is equal to G of zero. Then the product is defined, otherwise there's no product. So X zero, X one, so this is X one, no in this situation, okay? This is the X one here, yes. So we have a product now, which is not always defined, but anyway. What do we need for, we want to define a group, right? What do we need? We need associativity, no? And then we need identity element and we need inverse element, these three things, okay? For this product, we have no chance, okay? Because a path is a path, okay?  But this is not, so we have to pass to a homotopy. If you want a group, we have to pass, pass to a homotopy, okay? So definition, for a path, f from X, from I to X, let, so this is not, the equivalence class, you always denote like this, no, in general. F be the path equivalence class of F. The equivalence class of F is an equivalence relation. Be the equivalence class of F with respect to path homotopy. This is a familial notation, right? The equivalence class you very often denote by these parenthesis, okay? Let F be the equivalence, and then definition, let, again, let F and G be pathes with, so the condition F of one equal G of zero. Otherwise there's no product, okay? Now the product is defined. Then we have the definition, define F, but now I want to, not pathes, but equivalence classes of pathes, no? The usual thing, you, so this is the definition, and you take the equivalence class of F times G, okay? So this is a product of equivalence classes, no? Not of pathes, product of equivalence classes of pathes. What do you have to prove? That is well defined, okay? Which is well defined, the usual thing. Which is well defined. Well defined means does not depend on the choice of representatives. So what do you have to prove? You have to prove if F is homotopic to F prime, so if F is equal to F prime, no? That means F is homotopic to F prime by a homotopy F, right? And G, we have another representative. So this means G is homotopic to G prime by a homotopy G. Then we have to prove that F times G is homotopic to F prime times G prime sorry, homotopic to F prime times G prime, okay? And so this implies then that F times G is whatever it implies, F times G is equal F prime times G prime, okay? Yes. So we have to define this homotopy here, H. And now we get a picture, okay? So what do we have? We have F, where is F? Homotopy F between F and F prime. And then we have G between G and G prime. And here it's constant, okay? Here's the same point, F of one is G of zero. So this looks good.  So we define H of S, T equal two. And now the interval, which I have as a parameter which I have to change is S, not T. S, here's the interval, that's okay. That looks anyway good, okay? But here I have to change. So between S between zero and one half. So what I take here, here I take F of two S, T. And S between one half and one, I take the other one G, two S minus one, T. Sorry? Now you say this is a product between F and G. We don't define a product here. Yeah, for any fix T, it is a product of this path and this path. Yeah. But I don't have names for this. So one second, what I want to say now is that then this is this homotopy, okay? At time zero, we get really the product of F and G, okay? So H of what? Of S, at time zero, we have this product, so I'm getting tired. So at time zero, we have the product of F and G. That means for T equals zero, H of S, T, at time zero, this is F times G of S. And at time one, this is F prime times, so then we're here, times G prime of S, by the definition of this product, by definition of H and of this product, okay? We're doing here exactly the same as we did for F and G, okay? By definition, by the definitions of H and the product of two paths. So that's more or less what you, and at the time, in the intermediate time, we have the product of this path and this path, no? Yeah. But I didn't give names, so I don't know. Okay. So again, F is, H is continuous by the pasting, okay? H is continuous by the pasting lemma, okay? It's always the pasting lemma. F is, H is continuous by the pasting lemma. Well, so the time is finished, so we go on tomorrow. This is, omotope is important concept, of course. Probably you know, I don't know. Omotope, path, omotope. Then it's natural product of paths, no? And we want to agree, so tomorrow we define a group. This is very formal, this last second part today and tomorrow also, okay? The definition of fundamental, it's very formal. And then you say, well, many definitions, no? But then the fundamental group is important concept, okay? In mathematics, so, and then we have very nice, so this is the first part here is very formal, but then we have some very nice applications, which are very concrete applications, okay? Or fundamental group. So tomorrow we go on with this.


Good afternoon everyone. I hope you had a good lunch because otherwise it's not fair to talk about fairness on empty stomach Thank you for joining me today So all actors in the field are working intensively on policy design for the use and development of AI All initiatives put in the center the call for AI to be fair ethical and just But what is it? What does it exactly it means? It's an open questions that I will try to unpack in this presentation using a multidisciplinary approach So the computer science literature refer to more than different more than 20 different notions of fairness Each paper spent a lot of time on arguing why the suggested notion of fairness is the fairest The most just and the most ethical in my paper in my presentation I argue that the complexity of the various policy domains that algorithms are Implemented in require different solutions Therefore, there is no hierarchy between the different notions of fairness and one is not superior over to the other So the legal and social frameworks surrounding each policy domain Require a notion that is tailored to the unique to its unique characteristics What I'll do is that I will address the three main Groups of fairness notions in the computer science literature I will address the sub notions of each group Determining to which policy domain each one of the fairness notions Is most suitable for Let's start with individual fairness the first group the focus of this group is the individual Regardless of his or her group affiliation and the idea is that everyone is equal in front of the law The first sub notion in this group is the unaware approach It's called for equal protection, but in a traditional way of viewing equal protection as colorblind So the algorithm should be blinded and unaware of any differences between people and the only prohibited Attribute attributes by law such as sex or gender cannot be included in the algorithm Legally, we already know that colorblindness doesn't work because success is not just a matter of Effort and talent, but also a matter of access to resources that you have or don't have depends on your group affiliation Computationally, it's very easy to design an algorithm that doesn't take into account trace or gender, but There are many factors that could serve as proxies for the protected attributes. I Think that individual fairness in the unaware approach can work only in cases where the group of people that we are comparing between is quite homogenic Still in the realm of individual fairness Fairness through awareness call for treating similarly situated people Similarly not everyone And Legally the idea behind this approach is that regulation by its nature seeks to differentiate between individuals and the question to ask are When it's legal to classify People and what is the basis for the classification? so I Will demonstrate with an example in the criminal justice imagine that there is a study that show that If you are a black defendant and if you have five priors or more you will be considered risky But if you are a white defendant and you have two priors or more It's enough to consider you as risky the similarly situated individuals will be black defendants with five priors or more and white defendants with two priors or more This notion is quite promising But it's very hard to determine the metric the computational metric that will identify the similarities between individuals group fairness approaches is the second biggest group it includes many Subnotions that the common denominator between all of them is that not all groups have the same starting point in life The best is to integrate differences in the equation and not to ignore them Legally group fairness equal affirmative action Basically favoring a group of individuals That have been historically disadvantage in order to give them a equal starting point Affirmative action is a civil mechanism that could That has been approved in court and by the legislator in a very narrow set of cases and these are the cases that can be used in a computational sense as well The first group notion approach is the coupling it's called for creating one algorithm per group So compass a risk assessment tool using criminal justice have two versions General compass and compass women and the creators of compass justify having that because women Compose a very small part of the criminal justice. So their claim is that if we don't have a specific tool for women their unique Characteristics and needs will be ignored. So ignored so Compass takes into account economic Marginalization trauma and other unique characteristics that are special for women But the question is that do we want to allow that as a society? Do we feel comfortable with having compass men and compass women and how about having compass black and compass white? Okay, the second one the second approach in group fairness is statistical parody This one called for making sure that the outcome is distributed equally in accordance With the total population. So if I have 100 Loans to grant I should give 52 men and 52 women Because woman composite 50% of the society computer scientists dismiss notions that are based on Dismissed this notion quickly And consider the following example So if I'm the CEO of an IT company and I'm trying to hire a couple of individuals I meant to use algorithm that is based on statistical parody But one might tell me that it's not a good algorithm Because I will have to admit less qualified women in order to satisfy the 50 50 Percentage, but I want to argue that Using statistical parody will actually solve other problems because we all know that the reason why we have less women in IT related jobs prestigious IT related job is not because they're less qualified But because maybe the ads that advertise this kind of jobs they Women don't reach them. They're not published for women or when they are they are Kind of design in a very hostile way toward women So I think it's a good example and the same could be applied for school admissions Equalized odds is the next group fairness notion It recognizes the fact that there is no algorithm that predict 100% correct in all of the cases and it's called for equalizing the errors that the algorithm may So the errors that the algorithm make are called false positives and false negatives and Equalizing them is complicated because society value them differently If I'm a utilitarianist against again in criminal justice I care about the total happiness of the greatest number of people and I care about public safety I wouldn't mind putting a bit more people in jail in order to make sure the public safety is there But if I'm in it focusing on the individual I'm an egalitarianist I probably remember that our criminal justice is centered on the beyond the reasonable doubt standard And I have to be the most fair toward the individual What is the error rates that our society is willing to tolerate is a very hard question both legally and computationally The third group causal reasoning based approaches was developed because of two unique characteristics of machine learning that have been discussed here before The first one is that machine learning algorithms are based on correlations and correlation does not imply causation and also the fact that Machine learning algorithm lack explain ability and the combination between those two can harm due process So causal reasoning based approaches will only take into account the factors that it has been proven But experts that they caused the outcome It shouldn't be surprising that we can't satisfy all notions of fairness so campus the tool for risk assessment that I mentioned before It gives a defendant each one a score from low to high that determines the risk of recidivism Pro-publica and use outlet in the US Conducted the investigation into campus and concluded that it's biased toward black Because among defendants who were released from jail after two years among black defendants People who didn't commit any other crime 42% were labeled mistakenly as high risk and the algorithm did the same mistake among white defendants only in 22% of the cases Of course the developers of campus descended from this conclusion and they said that campus is fair The and the core argument between Pro-publica and North Point the developers of campus is a misconception of fairness Pro-publica wanted equal opportunity they wanted Black and white defendants low risk defendants to be to have the opportunity to be classified as so and North Point wanted individual fairness. They are claiming the law doesn't allow us to treat black defendants differently and Given the difference in the base rate between black and white defendants the gap is that Pro-publica is referring to will always be there But in fact none of their approaches address the most important issue and it is the fact The differences in the base rate and the fact that black defendants are overrepresented in the criminal justice because of historical reasons So what developers can do that in order to better address algorithmic fairness? The first and most important point is to clarify their Clarify their approach to fairness and to basically show whether other notions of fairness were to were examined before the chosen one was Before the one that has been developed was chosen and also having a lot much more Information about the society that the algorithm will be implemented in is crucial From the point of view of the policy makers It's very important to clarify the laws and regulations But this is a tricky one because law by its nature is developed is designed to be broad in order to accommodate as many Cases as possible, but for the algorithm. It's the opposite the more specific you are better the prediction that you will get So balancing between the sue is very important It's also very important to audit the results of the algorithm so To conclude All models are wrong, but some are useful is a quote used To teach students in statistics classes that the the models are wrong because they Represent a simplified version of reality But what I hope I started to convince you in my presentation is that most models are right But it depends how we use them The variety of fairness notion is big and I expected to grow this this diagram The notion that is working for credit scoring might not be the same notion that will work for criminal justice And it's very important to be aware of the very specific details of each case Thank you