Welcome to the show, Jill. It's great to have you with us. Thank you so much for having me. It's great to be here. Now, as a fellow imposter, Johnny and I were laughing earlier. How did you discover or find out about imposter syndrome first?  I have so many imposter stories of my own. It's hard to know where to start. But I mean, I guess where to start is how I kind of discovered this was a thing, which was when I was applying to graduate schools, it's a whole long story that involved some mentor telling me that I should apply to go to school in Boston. And I didn't really want to go back to Boston because Boston was home. But I decided that I would apply anyway. And I kept it a secret from my family because I didn't want them to pressure me. And then I looked at the stats to see the acceptance rates. This was at Boston University.  So, okay, it's fine. Kept it a secret. Couldn't take the guilt. So I finally confessed to my parents, to my dad, actually. I'm applying to go to Boston University to work with David Barlow. And my dad says, Dave Barlow, the clinical psychologist. And I said, yeah, how do you know? My dad's like this business guy. He doesn't know anything about the mental health field. And he says, oh, I play golf with that guy. I was like, you're kidding me.   And I did. And he said, you know, very impressive credentials, yada, yada. And I ended up getting into the program. And to this day, I still worry that the only reason I got in is because my dad has played golf with this man. And so that, you know, I think that was really kind of the beginning. And actually, the way I even knew to look out for it is I met with a mentor prior to going to Boston. And he sat me down and said, look, you're going to go to grad school and you're going to constantly think I don't belong here. I didn't deserve this. I'm a fraud. And I looked at him and thought, how did you know? Like you're reading my mind. How did you realize this would happen? So it became clear that this was maybe kind of a universal phenomenon that many people, especially students and especially more successful people, tend to experience. Yeah, that was my exact experience in graduate school myself. I had a mentor who put in a good word and I got into the PhD program at Michigan. And I immediately felt immense amount of guilt and self-doubt that everyone was smarter than me. And somehow I lucked out and I still feel it at times when I look back and think about my research and should that have even been published? Do I know what I was talking about?  They would come take boot camp and express these immense feelings of self-doubt and not know where it's coming from. And yet at the same time, everyone in their life outside says, you're amazing. You're incredible. You're so driven. You're so successful. But yet internally, we don't feel that way. And what does the research suggest on where imposter syndrome is coming from? Yeah, I mean, it's a great question and I think it's complex and I think it might come from a number of different places. You know, first and foremost, you can pretty much always find an evolutionary explanation for something. And really, if you think about early humans, you know, we didn't have fangs and we didn't have claws. We had each other and we're social animals. And, you know, so we would constantly check our standing in the group because to be part of the group, you had a survival advantage. You know, people who hunted and gathered and traveled by themselves were more likely to die, right? And so making sure that you genuinely belong in a group, had a survival advantage. So I think, you know, first and foremost, we've evolved to be people who engage in social comparison. That doesn't so much explain but then why the imposter syndrome. And I think that that develops for two reasons. You know, one is this like social, cultural, historical context, right? So like, think about, for example, women just a generation or two maybe ago, you could be a secretary, a nurse, a mom, that's about it, right? And that wasn't very long ago.  And you know, you can look at cultural context and historical context for a number of different groups. You know, Jim Crow was not that long ago, right? And these are like very strong messages about who does and who does not belong. So, you know, I think that's part of it. Maybe a more current example would be like affirmative action where there's been this like unintended messaging around, oh, you were only given this position because of your race or your gender or whatever other quality, not because of your hard work or your competence or because you deserve it. And then I think the final factor are the individual learning histories. And it's funny because this can work, the totally opposite things can work to have the same results. So for example, if you have parents who withheld praise, who every time you got a B said, well, why didn't you get an A? You're smart. I think you could have done better. You know, that can result in that imposter syndrome.  Or, you know, the participation trophies is a similar example. You know, you sort of know, like, I didn't do anything to work for this, to deserve this. And I think, you know, a complex combination of all of those different factors can lead to this. And it's apparently occurs in 70% of people at some point in their lifetime, which is just, I mean, that's crazy. That's, I don't know if any other phenomenon you see in that many people. And who's in the 30%? Right. Well, interestingly, people who don't have imposter syndrome, research has shown they're actually more likely to cheat. So the people who are imposters are the ones who don't have imposter syndrome. Right. And that's where Johnny's favorite Dunning Kruger effect comes in. That's exactly right.  Right. We have to laugh because many people view it as, oh, it's just part of growing up. And, oh, I get it in college, but many of us feel it well into adulthood and beyond as we're striving in our career. It's not this temporal, oh, I had it in my youth and now I got beyond it, but we can have these feelings throughout our career. 100%. And I was telling you guys before we started recording, I immediately, when you reached out and invited me on the podcast, my first thought was, me? Are they sure that they actually want me? You know, I see that you have some of my heroes have been guests, Gretchen Rubin and Dan Harris. And I'm like, I don't belong with Gretchen Rubin and Dan Harris. So it doesn't seem to just diminish on its own. And what happens is people think if they just keep achieving, like if I just do this next great thing, then I'll feel like I'm worthy and I belong here and I deserve it. But it can actually do exactly the opposite of that. You know, there's this like, well, I didn't get caught this time, but the more I get away with this, the higher the chances that they're going to figure it out the next time. Right. Right. There's also the more success or achievement I have, the higher the expectation of my knowledge or expertise. So now I feel even more like a fraud. It's very difficult to focus on the right things, as you were saying. And certainly with social media, where we tend to look at how many followers does this person have? Obviously they know what they're doing because people seem to enjoy it and they're following them. Because my follower count isn't where it needs to be. I'm certainly not playing in there on the same field. And it's an arbitrary number when it actually comes to your talent stack and your skillset. Absolutely. And you could have all those followers and either think I don't have enough or as many as this other person who I see as my metric for success or you could also have millions and say, I don't deserve these. Where did they come from? They all think that I deserve these follows but I don't have anything important to say. So it is this kind of empty. The achievements are the thing we think are going to make it feel better. But it can work in that way for the short term. But it typically just kind of perpetuates the problem. With that, for young folks who have a lot of immediate success, let's say they just happen to be dealt with a great hand for singing or painting and they get known for that talent and they are praised and thrown all this admiration at their very early age. They haven't earned it. And then later on when that initial wave starts to move into other places and they're left wondering what is it with them and why couldn't they hold it and maybe they were faking it the whole time. Whereas when you have fought tooth and nail for every follower that you have and the work that you've put in, you feel confident. You realize I did that. That was the work that I put in and it gives you a certain level of fulfillment, satisfaction of I deserved everything that I have gotten. Yeah, so I think there's kind of two different things I'm hearing you say.  Or like you have been handed things that maybe you didn't work for or maybe you don't deserve. And I think that is a phenomenon that's far less common. Not to get political, but Donald Trump comes to mind that he was handed millions or billions of dollars right out of the gate. He definitely does not have imposter syndrome. But what happens more commonly is the ladder that you're talking about, which is I did work my butt off to get to where I am, but I still don't necessarily feel like I deserve it or I'm good enough. Like people who have imposter syndrome have a really hard time. They can't internalize their successes. It's like no matter how many successes I have, it doesn't accumulate as evidence that I am not a fraud. And that's the sticky part, right? Like that's the trap there is you can't climb out just by doing more. The feeling that everyone else around you can see it and you can't. So everyone around you treats you differently for this, but internally you're having the struggle that I don't actually deserve what it is that you guys all think I'm deserving of. Right, right. Now I was fascinated to learn that there are five subtypes of imposters and I'd love to go through those for our audience. I know that I identify with one and we'll see if Johnny can guess and vice versa. But many of us did one imposter syndrome is a newer phenomenon that we're learning about and then you have it and you're like, oh wait, there are different subtypes of this? Okay, I'm fascinated. So what are these five subtypes if you could walk us through? The term was coined in 1978, which is relatively new, all things considered and I think it hasn't really gotten a lot of media attention until maybe the last decade or so. And I was actually interested to learn of these five subtypes too and this comes from Dr. Valerie Young, who's an expert in this area and has written a book in this area. And so the first is the perfectionist and that one's like fairly self-explanatory. It's the person who sets very, very high standards, high goals, high standards.  They all end in that sentence, right? That ending of the sentence. The next one is the superwoman or Superman or superperson. And so this is like the workaholic, like the person who just works and works and works and pushes him or herself harder and harder and harder to have that sense of being enough and to measure up. There's the natural genius, which is the person who believes that in order for your smarts or your competence to count, it has to come very easily to you. So if you have to work hard at it, it doesn't really count in there for your fraud. There's the soloist. And so that's the person who thinks you should be able to go it alone. And if you have to ask for any help or support, you're inadequate and therefore a fraud. And then the last one is the expert. And that's the person who bases their worth on the level of knowledge or expertise they have. And they're always trying to get more and it never quite feels like enough. And it's a big threat if something sort of reveals that they don't know everything or have all the expertise. So which one are you, AJ? So for me, I'm the expert. And it didn't even dawn on me that this was my sub-type until last summer. I was having lunch with a mutual friend, friend of a friend, I should say, a mutual acquaintance of a friend in New York. And he was very fascinated by what we do at the Art of Charm. He's doing very similar work. And sitting down at lunch, and he's asking me a lot of questions about myself.  And I don't understand. Like you are an expert. And I'm like, I would never classify myself as an expert.  And he's like, you've been doing this for 15 years.  You are not inexperienced, working with thousands of clients in person, coaching them.  And there's no way that I could call myself an expert. And I think a lot of that really was wired in in my undergraduate experience of just being surrounded by Type A people in pre-med and then going on to graduate school and joining these labs with literal experts in their field and constantly being around people that I thought were far smarter than myself. And I just never, ever feel like I stack up to that level. And he couldn't finish his lunch. He was so frustrated with me. He's like, I've only been doing this a few years and I would consider myself an expert. And your level of knowledge in this area, it is incredible. I can't believe you don't view yourself as an expert. So I kind of left that lunch thinking about it. And I'm like, am I being too humble? I don't know. I just, I don't feel it. It doesn't feel right to me to call myself an expert. You know, I've been fortunate enough to interview other experts on this show who I deem as experts. So I feel surrounded by other experts, but I would never call myself an expert. So in seeing that in prepping for this, I was like, huh, I guess that is my subtype. I never would have imagined. Yeah. It sounds like it. And it speaks to how much of this comes down to a feeling rather than data or facts.  But, you know, a lot of what's out there right now is change your thoughts, like learn how to think positively and like look at all your accomplishments so that you can convince yourself. And, you know, if that works, that's great. But that has never worked for me. And it sounds like it also hasn't worked for you. And in a way, you know, the more this person was like, but listen to all the facts and evidence I have to prove to you that you're an expert, the more your mind goes, yeah, but, yeah, but, yeah, but let me give you all of the counter evidence that shows you that's not true. And I get in arguments with my fiance, Amy, about this. She's just like, you have too much humility. You're too humble.  And I'm like, no, I can't call myself that. I can't justify it. And exactly that, even when there's a preponderance of evidence data and facts, my emotional state won't allow it. So it's so fascinating. And I know many in our audience, we've had episodes on perfectionism. That one's a pretty obvious one. The superhero I know many in our audience probably resonate with as well, just having to outwork everyone, just constantly being in a state of motion, working, working, working, and never quite feeling like you measure up. It certainly has to go with the cultural. As AJ and I both grew up in the Midwest, we had working-class factory dads. So the idea of being this expert, it is, it's very hard for both of us. I even know for myself, when somebody asks me in for this line of work, can I have your expert opinion or looks to me, I always say the same thing. I'm like, you can have my opinion as somebody who's been studying this for close to 20 years, but I'm not going down the, I'm not going to answer to the expert role. It's still different going. I know, isn't that funny? I have, I don't know how many times I have started writing an email, a document where I'll say something, you know, I'm trying to pitch a talk that I'm doing. And, you know, I have expertise, backspace, backspace, backspace.  It feels, it feels false. Like it's being fraudulent. The one that I found the most interesting was the soloist, the idea that asking for help reveals you as a fraud. And, you know, I think in my own journey, there have certainly been times where I've been terrified to ask for help, especially in graduate school, because you get that feeling that, well, this is a dumb question. Even though they'll say, there's no such thing as a dumb question, we want to help you. But in the back of your mind, you feel like if I'm asking for help, that means I'm not good enough. That means I don't belong here. When everyone else makes it look so effortless. And I think that's a big problem for a lot of us who are suffering with imposter syndrome is it's very hard for us to read anyone else's internal state. And sometimes two imposters will bump into each other and not even realize it. And that's why I think it's so important to normalize this and talk about it and share that even people you look up to and people that you would view as an expert are feeling these exact same doubts that you're feeling. And it means you're in the right place because it means you care, right? And I think that's the other important take away from this because there are so many frauds out there who are happy to take the expert role, who are happy to give their opinion and cheat their way to the top. The fact that you care so deeply about this and you second guess and doubt your own value means you're in the right place. You are doing exactly what you need to be doing and you're doing a great job. Don't let it stop you. 100%. And if you think about, well, if I were to be found out, if somebody were to uncover that I'm a fraud and I don't belong here and all of that, what is my true fear of what would happen if that occurred? It means whatever this role is that I play. And this can happen in any role. We typically think about it in professional settings or student settings, but you can feel like an imposter as a parent or as a friend. I mean, really any role that you play. And so then what's the fear if I'm found out, then there's a threat that I could lose this thing, right?  I mean, that may be extreme, but there's often a really deep fear and fear isn't always rational, right? So even if it seems extreme, that's often what's underlying that. So it's a really important point that this shows up exactly because these are the domains we care the most about. You don't feel like an imposter when you're watching Netflix. Like, oh, I don't deserve to be binging on this series. That's ridiculous, right? You might love to watch those shows, but those just aren't the arenas that these kinds of self-doubts and anxieties show up. They show up in the places that you really care about. Anyone who is involved in self-development is constantly gonna be pushing themselves outside of their comfort zone. I mean, to get comfortable with that feeling and being able to redefine it so that you can move through it or be comfortable in it is going to allow you to take on more and more roles. The way our culture is right now and everyone is applying themselves that has the opportunity to build companies in any field that they want doing whatever it is. They've always had a passion for it. And of course, if you get on to Instagram for the first time and you see somebody, such as Gary Vee, who manages to pump out great work all the time and you're trying to learn how to do this, it's incredibly, it can be humiliating to see your work compared to all the work that is around you that is gaining steam. And it's only an opportunity to see how far that you can take it. I've also, in my line of work, I've had people ask me what sort of clients we work with and they're like, what kind of problems they might have and when we bring up the idea of imposter syndrome, I hear it all the time, like, really? People feel like that? And I'm like, well, you wouldn't because you are sitting at home watching Netflix. You aren't pushing yourself into the unknown, trying to better yourself and learn. Yeah, I believe you should chase the imposter syndrome and it's a little counterintuitive and it took me a while to realize that this is a good feeling and I need to keep pushing myself because I'm doing something that matters enough to me that I am judging and I'm doing it in a way that is actually based to a degree in my wanting to improve and my wanting to get better. I'm not resting on my laurels, I would never call myself an expert because I know there's more knowledge to be gained, there's more experts to interview, there's more growth that I have in front of me and I think younger and earlier in my career, when I was younger and feeling this immense doubt, I think it is something that isn't talked about in school and unless you really have a mentor say to you, hey, this is normal, I've felt this too, you can feel very alone and isolated in those feelings and I know for myself, when I express that self-doubt to my family and to my friends, they laughed at me. They said, don't worry about it. I don't know why you're even thinking that and that can be very disheartening to hear because it doesn't obviously align with your emotional state and it's not as easy as just, oh, think something else or just fake it or believe it till you make it. Well, it doesn't work that way if you're feeling such intense self-doubt internally. So what can we do to start to counteract these feelings and move forward from them? Well, first I want to say I wish that we could identify who that 30% is that doesn't feel this way because then they're not the people that we should be expressing this to. You know, when I told my dad that I had done this panel on imposter syndrome and he's like, what the heck is that? And I explained it to him and he was still just like completely baffled, had no understanding of how this felt and I thought, oh, you're in that 30%, right? Because I think when, you know, you're exactly right when we talk to the 70% who can relate to this and this is related to what can we do to make this more palatable is you end up having that common humanity. You know, you see like so many of us are all in this together. It's not that everyone else has the key to life and is successful and is confident and has no self-doubt and we're sitting here in this little imposter bubble by ourselves, really the great majority of people feel the same way. And when you know that other people feel this way, it promotes a lot of willingness and bravery to move forward. And, you know, after we did this panel on imposter syndrome, we had so many people reach out, I had put together this panel of very successful professional women and this professional organization we're involved in and the people watching were just like, how can the president and, you know, the person who wrote 10 books, like, how could they possibly feel this way? And so if they feel this way and are still able to do what they're doing, then maybe I can start doing some braver things too. I don't have to wait until I feel confident and certain. I can feel unconfident. What's the opposite of unconfident? You know, I can feel uncertain and self-doubt and do it anyway. And I think that's the biggest key. And the other thing I want to point out about comparison is, and this is going back to something Johnny was saying earlier, notice how we tend to only compare up.  Like no matter how high you go, you're probably not Einstein or Newton or a president of the United States, right? So that's another one of those traps where we tend to compare up and look at how we don't measure up there, but we don't tend to look back to where we used to be, which is I think what Johnny had been saying, or where other people are. And I think gaining that perspective that we're in this together, that we're doing a lot better than we used to be doing or better than lots of other people, and not to say better, like I need to be better to feel better, but just to gain that perspective of you're putting yourself in a trap if you're always comparing up because there's always someone who makes more money or has a bigger degree or whatever the case may be. So I think in terms of like what to do, first and foremost, it's getting in touch with values. Like what really matters in my life? Who do I want to be? How do I want to be? What matters in terms of the way I want my life to go and to look?  And then the second is to then look at like, okay, when I see that person, what gets in the way? So I'll give you an example. Like for me, one of my missions is to try to share evidence-based principles from psychology out into the world, especially with people who might not ever walk into a therapist's office. And so that means public appearances like this or doing big webinars and talks. And it makes me nervous, but it's really important to me. And so when I keep that Y close by, then I have a reason for why it is worth it to feel uncomfortable. And then the second piece is, okay, so if what could threaten to get in my way is I don't deserve it, I don't belong, I'm a fraud, those are the thoughts. And then the feelings of uncertainty, self-doubt, anxiety, those are the things that threaten to get in the way of those values. And so what can I do instead? Can I change my relationship to those thoughts and feelings so that they don't get in the way? And like I said earlier, you can try to change the way you think about it, and if that works, that's great. I just haven't found that that's been particularly useful for me.  That shows up every time I'm about to do something that feels really important to me. And then to choose, like, if I listen to that thought, is that going to move me in the direction of that life I want, or is it going to move me away from that life that I want? Yeah. Have you seen any evidence or data to back the idea that with us spending more and more time online in these profiles that we've made for ourselves on these platforms, being certain characters, that is playing a role in bringing this out when we're trying to function with our friends in real life, where the connections that we're making has much more nuance than the asynchronous communication that we're having online with people. That's a really good point. I mean, I think what it makes me think about is kind of this idea that technology and social media has created this sort of false representation of what's really going on in people's lives. Sometimes you hear it called the highlight reel. And so it appears that everything you're doing is amazing, and so you must feel very confident and you are so successful and that's so different from where I am. But I don't know if that answered your question. I feel like you were asking something slightly different from that. It's just that we are spending so much time online and because we're putting up our highlight reel and now we're out in real life and we want people to see us as our highlight reel because we've gotten so many likes and so much engagement of this person online. And now here I am. Basically, I don't have the computer doing the work anymore. I don't have the filters doing the work. I don't have my... It's me naked. Yeah.  That there's a potential that they could find out that what you're presenting online isn't really the real you. Yeah. And I certainly feel as I'm older now and I at least have the ability to think more critically about social media and what I'm posting and what I'm consuming. I do at times feel very nervous for the younger generations who are living and growing up on the screen where growing up, my comparison was to my friends in the neighborhood and I had a middle class upbringing. So my comparison was not a rich kid in Australia and what they're eating for lunch. It was just my buddy down the street whose parents were middle class like mine. And I think it's leveled the playing field in that we can see into everyone's lives and at the same time it's created a lot of these psychological barriers to our own self-development improvement and self-image. And it is a little nerve-wracking and that's why I try to speak so openly about my own struggles with it even to this day. And I had a conversation last week with one of our coaching clients and he's like, you guys have been in business for 15 years and only less than 0.01% of businesses make it that long. And I'm like, I would not deem us a success. We still have a lot of work in front of us. So to exactly your point, I'm driven to look forward and I'm not spending enough time thinking back to, you know, 15 years ago when I hit record, would I have been happy with a million downloads? Well, we hit 200 million. So why am I not happy now? You know, you look at the bar that you set for yourself a decade ago and you've exceeded it in every imaginable comparison but now we've moved on to the next comparison and the next room and who's slightly ahead of us, not who's at our level or who's behind us who we can bring up. And I think that's the other big piece for me in my journey with imposter syndrome has been in those moments where I feel a lot of self-doubt and I feel really critical of myself, I look to serve others and not feed into that egoic state of like searching out the likes and the adulation but instead I go, well, who else can I help support right now? And I'm fortunate that in my coaching career I have a lot of opportunity to do so and with my clients who are struggling with it, I say, hey, help out a peer, help out a younger sibling, just taking that lens away from yourself and your ego being in the driver's seat and putting it on, how can I help this other person has really helped me in those intense moments of self-doubt where the imposter syndrome rears its ugly head and makes me not wanna get out of bed and not do this podcast and not share all this great knowledge with the world. Well, I think that is by far one of the best things that we can do that people who have achieved some success by any kind of objective metric whether you feel like you're successful or not both to share those experiences like we were saying before everybody have their like, I don't know, imposter syndrome anonymous group, right? Like my name is AJ and I am an imposter, right? And we get that common humanity thing but I think the other thing that that does is that it brings other people up like I was saying before like it gives other people the courage to go forward and to try to do these things anyway. And I think a close cousin to that is being part of communities with other people who are similar to you. So for example, there's research that shows that when black men and women attend historically black colleges they're more likely to go after success and they're more likely to achieve it when women go to all female colleges the same thing is found. So when you put yourself into groups where you're not necessarily with the majority culture and comparing, right?  You can get support in those places. So, you know, for example, I belong to two women's groups within my professional organizations and it's really the support and the cheerleading that comes from there that, you know, I ran for a board position and didn't get it the first time and I felt like almost humiliated and normally I wouldn't have gone for it again and it was because of that women's group that I went for it again and I got it the next time. And so I think that can be something that's incredibly powerful and in fact, there's a woman, Tiffany Doofu who wrote a book called Drop the Ball and she, the big side of her business right now is called The Crew and what she does is she actually finds groups of professional women and sets them up with each other so that they, you know, the idea is like if when we have each other we're more likely to pursue and achieve our goals and so she actually has created a business where she finds those groups for people, which I think is really cool and there's a good amount of evidence to suggest that those things do bolster people and encourage them to move forward even when they're experiencing self-doubt. Yeah, you know, I think the being authentic and being vulnerable and owning this and finding a group that is willing to create that space for you to be authentic and to be vulnerable to own this can uplift you and I found that in my own career whether it's the entrepreneur groups I belong to or even later tonight I have my men's group and we're all from distinct backgrounds different upbringings and in that Monday session we can talk about these emotions that we're feeling that maybe we don't want to share with our best friend or maybe my fiance I feel a little nervous about sharing with it creates a space where we all feel supported in that and we can work through it and I know we try to do the same in our X Factor accelerator by, you know, pushing each other to take risks and then supporting each other if we fail in that risk taking which is all a part of success not every step for art of charm has been forward Johnny smiling we've taken two, three steps back we've tumbled down a couple rungs it happens but you dust yourself back off and you have some support from other people cheering you on and you can go further than you ever thought possible and I just want to add to that for all of us here we work by helping other people and so we have that always in our back pocket so our work is going to lift others up and so we're always we have a lot of people around us and AJ and I it is our clients who have come through X Factor our boot camps who listen to the podcast who write us letters that no matter where we were and the evolution of this company over the last 15 years we're like well we can't stop look what we're doing look what we've achieved look at the lives that we've changed so onward and upward and I don't know how we're getting there but we're going because those people want to see us do all they want to see us help others it's very difficult if you don't see that direct effect or have it shown to you look what you have done look what your words have done look what your support has done for me you have to continue on when you're going at it alone and certainly as an entrepreneur it can be difficult especially if you're just getting started you're doing a lot of things that are in the unknown you're spreading yourself completely thin because you're doing everything and you're doing it all poorly because you're learning all of it and you don't have the feedback of other people being able to experience that work on the other end yet but it's coming and if you're doing work that's going to benefit those around you that you're going to find that support easily well and I think you're really talking about values right now you know what yours and values are different from goals like goals are endpoints and outcomes and we like to think that we have full control over those things but we don't but you do have control over the choices that you make and that you can feel doubt or you can take three steps back you know with the company and you can still choose to show up every day because commitment and giving back and right like helping bring people forward these are all things that matter to you so you keep showing up and you keep doing your best and you hope that it moves back in the direction that you wanted to but you can't really know and you have to be willing to do it even when you're feeling uncertain or insecure or having self-doubt or anxiety or any of those things now we are fortunate that we are in supportive environments and we found groups and sought out people who will have our back and even internally in the company you know Johnny and I work to help each other in those moments where we're feeling down but how does this work in a competitive workplace where you're trying to strive and really performance matters and you're seeing everyone else perform at a high level now you're feeling imposter syndrome being vulnerable and open might backfire and might make you look bad and I do feel for those people who are in careers who are facing that exact challenge what is your advice for them who may not have that supportive workplace may not have a family or peers who view them as having imposter syndrome or even able to help them see through it yeah it's a great question and I think you know there are certain contexts where the choices you make are about survival in some ways and you know when we were talking earlier about how this develops and learning history and experiences we've had you know we can all look at how often we've been reinforced for staying at the office late and working your butt off and being the person who does more than everybody else right this doesn't exist in a vacuum these are real experiences that are happening you get punished for not showing up and you know being the badass and you get reinforced for being the one who does more and that's clearly real and it may not be strategic to go into your workplace and admit that you feel like a fraud to your boss or even to your peers but I think the same principles still apply and it's you know if you can't control how other people are going to respond and you happen to know you work in a corporate culture that doesn't accept these kinds of things you can still be connected with your values no matter what you know and you can still notice all the thoughts and feelings that get triggered in that work environment and you can still make choices that are moving you in the direction of those values even when you feel imposter syndrome and doubt outside of that the pieces we were talking about about joining a group or sharing it with others because of common humanity you may not do that at work you may not even have family or friends you can do it with but you can look online I'm sure if you look up hashtag imposter syndrome there's probably millions of hits you know there's resources everywhere or like you were saying you know join a men's group there are other ways that I think you can still get support even if it's not within all of the different settings in which you belong and I think another exercise that has worked for me in these intense moments of self-doubt is to simply verbalize them you know they tend to carry a lot more weight when they're stuck in your head and they're fused to your being and your entire body feels it but when you verbalize it and you say I feel like a complete nutter failure it doesn't hold as much weight anymore when it's out of your head and you've actually said it and I think many of us don't journal those thoughts we don't we don't actually process them in a healthy way and that's part of this and there's a fear that if people see my imperfections they will judge me negatively but in fact the exact opposite happens because think about who you connect with do you connect with someone who's genuinely perfect as if that's even a thing or do you connect with people who are flawed and I actually recently posted my worst reviews for my book I have a book that came out in January and I posted a couple good reviews and then I posted my worst reviews and part of that is I'm not you know like I only want you to read this book if it's going to be helpful to you and it's not a good fit for everyone and it feels important to sort of not just put the highlight reel out there like to put out this other piece and I felt so vulnerable I was like having physiological anxiety symptoms I lost sleep worrying about it and then of course the response is like oh my god thank you so much for showing that you're an imperfect human being like it means more to people when you show them your humanity than when you just show the highlight reel of all of your successes Yeah well I know many of our clients feel disconnected and lacking in that depth in their relationship and a lot of this is self-reinforced because all we're trying to do is put our best foot forward and only show the good side and only allow people to feel our most confident presence and in actuality in my men's group and in the work that we do with our clients it's in those moments where you share and you're authentically vulnerable about what's going on that deeply resonate with others in the group and the connection that's formed over that is far greater than oh we went on the same trip I've been to the same island oh I drive the same car and all these other things that we externally give value and status to And who's more successful the person that does every single thing perfectly on the first try or the person like Edison who famously was quoted as saying or I guess it took a thousand tries to get the light bulb right and a journalist asked what it was like to fail a thousand times and he said I didn't fail a thousand times it was just a thousand step process to get to the light bulb but even if I mean if you had only done it in one try like that doesn't to me that's not successful the person who fails and keeps trying and keeps trying and persevering and persisting like that's actually the mark of a successful person it's not the person who never fails and we don't tend to look at that side of the equation I think also with the internet there's a lot more or we like to think there's a lot more eyes on us than just hanging out in the neighborhood and I always laugh and I was guilty of this in the past as well of what if I put this out and then we start catastrophizing right like what if a million people see it and they all hate it and I'm just gonna be inundated with hate if you're getting a million eyeballs on something that you created you have a whole set of other problems that is gonna be much more fun to work with so the worst thing you can think of the probability of it actually happen is low and if it does well let's celebrate that you just got a million eyeballs everybody would love to have a million eyeballs on their worst worst work there's no such thing as bad publicity so they say right PT bar number someone says that exactly I think I want to speak to you you were talking about I forget exactly what you had said AJ but it was something about like getting hooked by these stories you know fused with these stories and one of the things I do constantly and it sounds silly but it is super helpful and it's a way to kind of get on views to kind of detach from these thoughts and stories is I call that imposter voice that inner critic I named her and I named her Sheila I don't know why Sheila I apologize to the Sheila as it just came to me one day and so when that voice pops up like who do you think you are you don't belong you know like who do you think you are to think you can write a book you're not you're not a writer you know it's my instant shorthand to go pipe down Sheila and not in a way that's trying to suppress the thought because the harder you try not to think something the more it's going to be there but as a way to just kind of externalize it as a thing rather than like getting all cut up in it as if it is my identity does that make sense yeah yes and that's why I love verbalizing it as well because I think it really diffuses that thought and emotion from my being and and places it in the exact place it belongs outside it happened it's there and on to the next amazing thought and on to the next thrilling pursuit and posting those bad reviews did the exact same thing all that nervous energy it it just took all the wind out of its sails like once it was actually out there I was like oh this actually made these less painful so it's that naming it and calling it out and putting it out there rather than like hiding it as the secret that it just you know you're taking the power away well you brought up a point earlier that I think again going along with this highlight reel that many of us see in the content we're consuming is you know there's a goal to make everything look effortless like you never really get the full highlight reel of all the tries you know you watch dude perfect on youtube and they just do this crazy trick shot they don't show you the hours or days setting it up and all of the failures or maybe once in a while you'll see a blooper reel but for so many of us and in in building anything and achieving anything you want there's so much failure involved that you have to get comfortable with it and the more that we could talk about those failures the more that we could welcome on other guests like yourself who are willing to be vulnerable and open about those failures I think it's important for all of us to realize that just the other side of all that failure is that exciting effortless highlight reel that we think it's going to be but it's just never that way and in starting this podcast you know I've coached other people to start podcasts and they they go well how did you get so good and I'm like because many of those episodes never aired we have episodes that you don't hear because they weren't our best our best work we didn't feel it was a great conversation and it didn't air I wish I would have aired them maybe you'd see the full process you know but we all seek perfection and being the best version so many of us don't realize that the condensed highlight reel doesn't show all the effort and of course it makes it look effortless but just because it looks effortless doesn't mean that there wasn't a lot of effort put in on the back end and to your point celebrating that effort you know and when I have kids that's exactly what I want to do is celebrate that effort not the outcome the outcome will come with enough practice and time that will be there but it's the effort that really matters I want to say that when and I can't cite where this comes from but when they look at the most successful people in the world or maybe it's the most successful entrepreneurs and they find the one thing that they all have in common it's that they have failed more than most people and so it's back to that Edison thing is that it's not the failures it's that they failed and they didn't quit they kept going and kept trying and kept going and kept trying and sort of never took no for an answer and that is that's that growth mindset I think a lot of it has to do with the bottom up learning process being taken away from a lot of children as well where they're just going out and they're falling off the jungle gym for doing stupid stuff and they've learned the hard way that perhaps what we were doing on it wasn't the best way to have fun I now have a broken arm and we laugh on the show but we talk about how helicopter parents have turned into lawnmower parents and they're just mowing out of the way any of the obstacles but all those obstacles are what allow children to learn perseverance and to shake it off and to get back up and I know from my youth the idea of playing music live on stage was to me the most fun and I had seen pictures that just seemed like the artist like Jimi Hendrix on stage looks like he's in this moment of transcendence that I want to feel and so as a musician to continue putting myself in that position to get on stage to hope it one day to feel that moment that was was pictured in that picture and only to come up short time and time again as we were learning our instruments and learning to perform but what we wanted overridden, overrode all of the bad shows that we've played until finally having that moment on stage and going oh this is what I fought for for all those years and what I'm going to continue to fight for for the rest of my being because that moment in music or in sports or writing where where we hit our flow state and we end up chasing those moments for the rest of our lives but in order to catch that there there needs to be well at least for me there was something that that was better that made all the failing worth it right and when you talk about Lawnmower parents or sometimes they're called snow plow parents you know if your parents write your college essays for you and you get into college I mean here's the recipe for massive imposter syndrome right same thing like if you're just I mean not that you can hand someone a flow state but if you had you know achieved the Jimi Hendrix experience huh no pun intended you know right off right off the bat you know you lose a lot when you give up that process of of learning without a doubt well even in our coaching programs you know over the years when we started I would say I probably talked to a parent once a year and now it's almost once a week where a parent will reach out to us and they've identified a weakness in their child's social skills and they're worried about what is going to happen when they go away to school or when they're doing these virtual classes now and inevitably I'll get on the phone with the child in question and the child in question is not interested in doing the work doesn't really care about what it is that we teach and you know Johnny and I are sitting there scratching our heads going well okay you are setting your child up for failure if you're not even getting buy-in from them on what it is that you're trying to smooth over and I think a lot of parents are being a little overprotective and realizing that you know some of these challenges some of this adversity early on is actually helpful for them to build up that self-value and self-worth to not be facing imposter syndrome later in their career to have work through these moments and I think the parents probably have an I'm a bad mom or I'm a bad dad story going on that's driving them intervening and trying to make this happen and you know if instead we were talking to these kids about their values and letting them be more of the architect of their experience you avoid a lot of these problems down there yeah and I love talking to the kids and the parents who are fully on board and want to grow and get better but it has been interesting to see parents getting so far ahead lawnmower or snow plow of all adversity and you know when I first hit adversity it was it was tough for me but thankfully I had scraped my arms on the jungle gym and I had not made the basketball team in junior high and I was cut from the tennis team and I had faced all that adversity that we now as parents try to keep our children from facing so we love asking our guests to give a challenge to the audience something that our audience can do over the next week to push themselves and and maybe the parents can give to their kids to to face a little bit of adversity to grow and get better oh I love this question I think it would be to notice one thing that you really feel like you want to at least dip a toe in but you don't think you're ready like if you're telling yourself well I'll do that when right so when I have this much more knowledge when I have this much more experience when I have this much more confidence then I'll do that thing and so I would challenge people to search for that story and then where it shows up do one thing one small action it doesn't have to be the whole nine yards one thing that moves you in the direction of doing that thing now rather than waiting because that's a trap that day often doesn't come you know I say to clients all the time you know I'm never going to make you do something you're not willing to do and notice I use the word willing I don't say that you don't want to do that you're not ready to do because if I'm asking you to face your fear and do something difficult you're never going to want to do it you might never feel ready but you just have to feel willing or be willing I should say you don't have to feel willing as long as you are willing to do something even if you're uncertain uncomfortable imposter speaking up and do it anyway so it's that willingness that matters absolutely the waiting for the perfect time the right amount of money education the right location the perfect day it doesn't come and when you look at all of those people as you said you are successful they weren't waiting they tried and they tried again and they tried again that's right and it may be the case that you're right that it's not the right time and so for example like I have a podcast too that's called psychologist off the clock and I feel really strongly about playing big like go for your heroes try to get the best people on even as my imposter is saying who do you think you are that you can invite that person to come talk to you on your podcast and I ask anyway and sometimes they say no but more often than not they say yes and it's like mind blowing every time and then that kicks the imposter syndrome up higher rather than lower because I think oh god they're gonna find out that I'm nobody and they're gonna regret that they said yes to this right so it's that like you don't have to be convinced you don't have to be ready you can ask and if they say no or it fails or you're right that this wasn't the right target that's okay you know it's similar to what Johnny was saying earlier it's like even if that happens it's not gonna be that bad even if you get a million people who say something bad like you'll be able to handle it it'll be fine it'll be a learning lesson but also lots of times good things happen but it's never gonna happen if you wait until you're ready and you don't just go for it play big the last question we have for you we love asking all of our guests is what is your X factor and we believe it's when a skill set and a mindset come together to make you unique and successful I mean the first thing that comes to mind is some combination of authenticity and vulnerability you know I get both in my writing and in my talks and workshops that I do the feedback I get most often is like for example with my book people say I didn't feel like there was some expert talking down at me telling me about how I have to handle my anxiety I felt like I was having coffee with a friend and then it who also happens to have some expertise in this area of anxiety and worry and stress so I think it's that you know I'm not willing to like be here and tell you that I have these same anxieties and thoughts and feelings yeah does that answer the question it's like authenticity, vulnerability like what you see is what you get and I'm going to go ahead and be real with you even about the stuff that's really hard to share sometimes I even cry which is incredibly uncomfortable and of course every time that's the thing people end up liking the most well now our audience is salivating what is the name of your book and where can they find it it's called Be Mighty and it's a book for women with anxiety, worry and stress and you can find it anywhere Amazon or Barnes & Noble you can also find it on my website which is JillStarter.com and I give away a free journal for people who order it on my website and actually right now if people sign up I can send them I'm sending people the first three chapters free so like if you read it and you hate it you don't have to spend any money or if you read it and you like it then you can you know kind of like try it before you buy it type of thing or they could just leave a review for you to post on your social media if they hate it right our audience is going to send a lot of positive reviews your way thank you for joining us Jill it was a wonderful conversation thank you so much for having me you guys take care


Hello and welcome to this Getting Started video for STM32 Cube STM32 SIGFOX software expansion. SIGFOX is a low power wide area network allowing low power sensors to benefit from a planet-wide long range network and so enabling end devices with low bomb cost. The X-Cube SFOX expansion package consists of a set of libraries, open routines and application examples for the STM32 L0 powered CMWX1ZZ-ABZXXX neurata module acting as an end device. It includes an application running on the low power wireless BL072ZLR1 Discovery Kit. In this video we will show how to download X-Cube SFOX, personalize a device and activate it on the SIGFOX network. First let's download X-Cube SFOX from the ST.com website. Open your favorite browser and go to http colon slash slash www.st.com slash x dash cube dash SFOX. Click on Get Software. Click on Get Software at the bottom right to download X-Cube SFOX archive. Accept the license agreement and get the zip file. Run STM32 ST link utility and flash signature generator dot bin located in projects BL072ZLR1 applications SGFX Signature Generator. Configure a terminal to access Discovery Kit virtual serial port and reset the board. The board's signature will be displayed in this terminal. Open your favorite browser and visit the Murata website. You can go directly to the address shown in this video. Create an account and send your device signature. You will receive an email from Murata containing personalization data as a header file and as a binary file. Replace the SIGFOX data dot h file located in the ink folder with the one received from Murata in SGFX push button project. This project is located in BL072ZLR1 applications SGFX SGFX push button MDK arm. Open the SGFX push button project using keel. This tool can be freely used for STM32L0. You will find instructions on ST microelectronics and ARM websites. You can add some user code in main.c. Compile and flash the project.  Board's ID and pack will be displayed in this terminal. Open your favorite browser and visit the SIGFOX website. You can go directly to the address shown in this video. Select Murata then France SIGFOX. Copy and paste the ID and pack previously obtained to the SIGFOX website. Register on the SIGFOX website. You will receive an email confirming your device is registered on the SIGFOX network. You can see on the SIGFOX website data sent by your device each time you push the user button on the discovery board. You can display values published by your device on thethings.io. Thethings.io is an enterprise IoT platform aiming at bringing simplicity into the complex ecosystem of the Internet of Things. Thethings.io enables fast and scalable connection of things to the Internet, allowing you to monitor and manage your devices in real time and get flexible analytic reports. Thank you for watching this Getting Started video, and enjoy your SIGFOX developments with the XCube SFOX expansion package. For more information, please visit www.st.com.x-cube-sfox.


The first of the four ideal piecewise constant filters is the ideal low pass filter and the ideal low pass filter would have a frequency response which has 0 phase. In fact, all the filters ideally would have a 0 phase response and a magnitude response that looks like this 1 between minus omega c and plus omega c and 0 else. Now this is very clearly an illustration of why we need to talk about defined almost everywhere. If you look at this response it is precisely specified for all points between minus pi and pi except at the points omega c and minus omega c. At the points omega c and minus omega c the responses are discontinuous, the responses discontinuous. So it is it cannot be specified the right limit in the left limit are not equal. So at that point it is not really correct to talk about the value of the magnitude of the value of the response. Therefore the frequency response exists at all points except at omega c and minus omega c. And therefore we say that for this ideal filter the frequency response whatever it is I mean by whatever it is I mean there is an impulse response that would possibly correspond to this frequency response. The discrete time Fourier transform of that impulse response is defined almost everywhere except for the points omega c and minus omega c. At those 2 points it does not converge and that is why we need to put the almost everywhere. Anyway so this is the ideal low pass filter. Correspondingly we can have now you know this also tells us why we are calling it piecewise constant. The ideal response is constant between minus omega c and plus omega c, constant between omega c and pi, constant between minus pi and minus omega c. Here it is 0 ideally, here it is 0 ideally and here it is 1 ideally in magnitude. On pieces you can divide the frequency axis between minus pi and pi into a finite number of pieces. And on each of these pieces the response is a constant that is why we are calling it piecewise constant. So the ideal response is that we are trying to meet are all piecewise constant. Let us look at the other piecewise constant responses that we would try to design. The ideal high pass filter, high and low remember is only between 0 and pi. So here the ideal high pass filter would ideally take a magnitude of 1 from some omega c to pi and from minus pi to minus omega c and 0 else. So this is the ideal high pass filter. Of course it is 0 phase and this is the magnitude. So here again you notice it is piecewise constant. It is constant on the 3 pieces minus pi to minus omega c, minus omega c to plus omega c and plus omega c to plus pi. We then have the ideal band pass filter and that is easy again. There are 2 points, so omega c 1 and omega c 2 between those 2 points the response is a 1 and otherwise it is 0 and of course once again it is 0 phase. So here again it is piecewise constant. There are exactly 1, 2, 3, 4, 5, 5 pieces on which the response is a constant. Finally we have an ideal band stop filter and as the name suggests this filter would stop a band and pass the rest. It would pass the rest and stop a band. It would stop the band between omega c 1 and omega c 2 and pass the rest and here again this is 0 phase and it is piecewise constant on 5 pieces this one, this one, this one, this one and this one. It is 1 on these 3 pieces and 0 on these 2 pieces. Now we shall also note that it is possible to obtain the ideal impulse response corresponding to each of these ideal filters and we shall illustrate that by starting with the low pass filter. In fact we have already done that job. We do not need to repeat it. We have already calculated the ideal impulse response of the low pass filter. We have already calculated the inverse DTFT of this for the ideal low pass response and we can straight away write that down. Is that right? And the ideal low pass impulse response is equal to sin omega c n divided by pi n whenever n is not equal to 0 and omega c by pi when n is equal to 0. We want to recalculate it back.


Welcome. I'm going to try a slightly different setup and take you through equations by drawing and the slicing on my iPad. It's going to be a little bit of chicken scratch writing I'm afraid because by default the iPad I can't really rest my hand on it because then it goes out of the presentation mode. So the idea here is that I will try to derive the Boltzmann distribution for a general large system like the one you see on the screen and we want to use this to make sense on what's on the left versus right here talk about order entropy and everything. This is not really hard. It's actually a very simple math. You're going to need to understand the exponential function and Taylor expansions but that's it. The thing that might be slightly confusing is that we can't really assume anything about the system so that the part that is possibly the hardest is this slide where we're going to need to introduce some sort of general observations. Observation is the key word here because I'm interested in my small part of the system. This could be a protein in a test tube. It could be a small lab set up at Alvanova or it could be a brick in the classroom anything really. This part does not exist in isolation but it's part of a larger universe in the rectangle here. The universe I'm going to use a special word for that. I'm going to call it a thermostat because when I only care about energy here if I assume that my small part can exchange energy with the rest of the universe well something exchange energy is intimately related to temperature control and everything and that's simply why I call it a thermostat because energy will usually flow from high temperature to low temperature but that's a parenthesis. So what properties my small system will have is interconnected to the large system. If I have a total amount of energy capital E in the universe if I put a small part of that epsilon in my small system by definition I will have to have the rest in the thermostat. If there are lots of ways of doing this then there's lots of ways I can get that division and then there's likely lots of ways that I will observe this many states or many microstates on the other end if there are a few ways of doing this for instance if I try to put virtually all my energy in my small system there would be fewer such microstates available and it's going to be less likely to see them. I bet that sounds abstract to you so I think we're going to try to jump right into the equations. Remember what I said the equations frequently help you rather than confuse you. We're going to need a couple of definitions here though. When we talk about probabilities the easy way to talk about probabilities of something happening is proportional to the number of states that represent the thing happening whatever the thing is. So the thing here is what I have in the figure right that I want to put energy epsilon in my small system so that will correspond to putting energy capital E minus epsilon in the large system. Let's introduce a completely arbitrary letter for that so that's the number of microstates capital M. That is a function of the energy in general so that's I will write M as M-therm as a function of E minus epsilon and then you would just for now have to buy it that's the probability of this happening that is the probability of my small system having energy epsilon is proportional to whatever this number M-therm E minus epsilon is. In principle we don't know more but well we know a little bit right. This is number of states or something unless you have an infinite energy or something there will be at least one state so we can say that it's larger than zero I need to be able to count. If that is larger than zero I'm also allowed to completely arbitrary introduce a definition I can take the logarithm of any positive number so let's just for convenience start to take the logarithm of that function M and multiply it by a constant. Now you don't know what that constant is it's just unit conversion for that I will use the letter S. Of course you know that this is going to be the entropy but pretend you don't for now because M is a function of E minus epsilon S in general will also be a function of E minus epsilon and for now that's pretty much a winnow and K is just a unit constant. Let's see what that takes us shall we? This is what you had in slide 15 I think a lecture 4. I will take you through this. The very first equation here is just a recap of the last equation for the last slide. S is K multiplied by the logarithm of the number of states. We don't know anything about that function but when we don't know anything about a function it's usually a great idea to start looking into zero's expansion in physics. I'm going to need a bit of clean sheet to do that and I don't have sheets here but at least I have clean electrons. They're green. I've reused the electrons it's environmentally friendly. For a general function let's call it f. I can expand that around an arbitrary point x0 so if f is a function of x I could think of f closed a position x0 by looking at a small displacement delta x from x0 and if I do a Taylor expansion around x0 here that would be f at the point x0 plus the displacement delta x multiplied by the first derivative right df dx. I could use parenthesis and use the argument here but to follow the Finkelstein book he loves this physics notation or just or vertical bar and that means that I evaluate that function at x0 so it's no longer a function but this is a value right and then I should divide this by one faculty but one faculty is one so I'm not going to do anything more there then we have a second-order term that's going to be delta x squared divided by two faculty multiplied by the second derivative d2f dx2 taken at the position x0 and then we have a third-order term to delta x to the power of 3 divided by 3 faculty d3f dx3 divided by x0. I hope you follow me because I run out of screen space now. In general you could of course say that you don't know anything so you will just approximate this with the 0, 3rd or 2nd order term but that's a bit dangerous because remember we said that we wanted to prove that this is universally true right so I can't arbitrarily do something I need to prove that something is needed versus not needed for a general function I can't do that but in this case it's not the general function I have a function s that is a function of the energy e I would argue that both s and e's are proportional to the size of the system for energy this is probably fairly easy if I have what one kilo water under particular conditions if you take two kilos of water the total energy there is going to be twice what I had from the start hopefully by that with s it's not quite as easy and remember that s the total s is the logarithm of the total number of states right if I have many states well that is going to have to do with permutations and that I can put I've had two parts in the system the total number of ways I can organize it would be the product of m1 and m2 so this is going to be the logarithm of m1 multiplied by m2 multiplied by m3 etc but then I can just use the logarithm laws so this corresponds to the logarithm of m1 plus the logarithm of m2 plus the logarithm of m3 etc and that is what I wanted to show right so if you had two parts that were identical the total entropy is suddenly going to be or s which you don't know yet is the entropy is certainly going to be the sum of these so that too will be proportional to the system size so going back to this equation we had on the previous slide both s and e are proportional to the system size which is really cool because that's going to get us some things if we now take the Taylor expansion up here and instead of f we have s and instead of x we have e the first order term well I can't say a whole lot about that that's in principle s right so that's going to be proportional to the system size the second order term look at the derivative here we have a derivative well we have a nominator there that's something related to s and then I divide it by something related to the argument which was e so I have something proportional to the system size divided by something else that is also proportional to the system size and that is going to be proportional not to the system size but it's roughly constant well if it's constant we might need that term too let's continue to the second order term here at the top I have something roughly proportional to this system size s and then the denominator I have something proportional to the square of the system size this term is going to be proportional to one over the size of the system and remember what I said in the first slide we're going to look at properties for very large systems so at the size of the systems goes to infinity this term disappears and that term disappears and all the other higher order terms disappear too so we only have to look at the constant term and the first order approximation and then the limit of large system this is going to be exact not an approximation with that I think we can go back to the previous slide so what I've done here I've used the equations from the last slide exactly the only difference is doesn't say x plus delta x it says capital E minus epsilon the minus sign here is going to change like so we have the 0th order term that's s taken at the value e just as before delta x is now negatives turns into minus epsilon instead of plus delta x and then we had the value of the derivative d s d e taken at the value e so that's exactly the 0th and first order term in the zero expansion this might not look particularly beautiful but if we now take the top equation here again and I would like to go back to the number of states because the probability remember that was proportional to this m let's try to solve for m how do I solve for m well I start with the first equation again right so I divide both sides by kappa and then I take the exponent so m would be the exponent of s divided by kappa that's what I do here but now I need to do this for m of e minus epsilon is the exponent of s of e minus epsilon divided by kappa the first term here is just the exact definition but inverted in the second part here let's use the series expansion I had here and put that into the equation there so then I get first as first order term here so the argument for the exponent I'm gonna have s of e divided by kappa that is a constant term so let's break that out into a separate exponent term that's gonna make life and things easier so that's the first term e of s exponential of s of e divided by kappa multiplied by the second term here so that's this part right minus e dsd that's exponential raised to minus epsilon dsde and then divided by kappa it's the same kappa I had there this is beautiful I know that you don't think it's beautiful yet but this explains everything this entire part here is just constant and we are physicists so what comes to constant I will just scratch that out say yeah whatever it's a constant and then I have some stuff remaining here the probability of observing a state was proportional to this number of microstates and if I say proportional to I can complete it it's the constant on the previous slide and that is proportional to an exponential raised to minus the energy in the small part of the system multiplied by this derivative dsde taken at the at the point e divided by kappa or k sorry I might have been using kappa and k interchangeably here I knew I know that you don't think this looks beautiful but the point here is dsde is something natural in nature it comes out of the properties of the system but if it's natural let's just call that something 1 over t is just a definition and the k we had before let's call that kappa what this will give us is a very familiar equation that this proportionality is going to be proportional to e raised to minus epsilon divided by kt or the Boltzmann distribution which is exactly wanted wanted to prove but the cool thing here so we have not assumed anything about a pillar of gas or anything but just looked at general distributions of energies in system and the properties of the exponential and logarithms quote era demonstrator


Joseph, what are you doing today? YouTube, I'm going to school today. Going to school? I just woke up, so I'm kind of on target. Joseph's first day of school, oh man, oh man, oh man. First day of school, Joseph is so excited. He is, remember, he's inquisitive. That's the six-year-old Joseph, he's inquisitive. He cannot wait to get into that classroom and meet his new friends and play recess, and he just, he's so excited. I have struggled the last couple of days, but I've come to the decision that I'm going to leave you guys here. I love you guys, I love you guys, and I want to bring you on the journey of this life, but sometimes I've got to leave the camera and just soak up the moment completely without hitting record, hitting stop. I love you guys, but this is a moment in our life that it's just, it's just a big deal. It's our, you know, I'll probably film Seth going to his first day of school for you guys, but for Joseph, I just want to leave the camera, just soak it up, just soak it up.  It's a big moment. So, too much, too, too much. So hard on a 14er. You enjoyed that time lapse. What I remembered to grab the camera. Excuse me. It was an honor to share the mountains with you guys today. Water run. That was hard. A monkey on my back that weighed a lot, the most I've ever used for a weighted vest, but made it through, and I feel good. The plantar fasciitis is painful, but you can still run on it. You just got to be on the ball with massaging, taking care of it. You know the drill. But folks, it was providential that I did not bring my camera to the drop-off for Joseph's first day of kindergarten because he was having such a great time and was, when the bell rang or when the whistle blew, he sprinted from the playground to the school and he, you know, he got a little tripped up. He was running next to a buddy and he fell and he hit his chin and hit his, right around his eye and I didn't have my camera with me and I was, you know, 15 feet away from him and I was on him like two seconds later, able to pick him up, give him a hug, tell him it's going to be okay. This is a badge of honor, you know, a little scar on the first day of kindergarten. Like it's a badge of honor.  It's going to be, you're going to be fine. So it was providential. I didn't bring the camera with me today for the drop-off and just know that he's excited. He's excited. He's just, he was like honed in on his teacher when they were lined up before going into the building when we said goodbye. So anyway, all's well and we love you guys. Thanks for coming back. Love you guys. Seek beauty. Work hard. Love each other. See ya.


Metal nanoclusters are atomically precise clusters of metal atoms with controlled sizes, shapes, and electronic states. These clusters can be used as catalysts due to the unique properties such as high surface area, small size, and tunable electronic structure. By controlling these properties, it is possible to tune the catalytic activity and selectivity of metal nanoclusters. This article was authored by Wai Huilei, Xu Anhe Zhao, and Xuankuan Zhang.


I need to start by saying I'm at NIST as a contractor from Strativia, thanks Jolin for inviting. I also wanna say that this is an impromptu presentation. The invitation came, I don't know, yesterday or two days ago and you know. So that's my excuse in case I kind of go over time a little bit. So this presentation will be somewhat different from the previous ones in the sense that I won't go into, the goal is not to go into many technicalities, although I'll mention a few technical details, but it's more to present the NIST project on randomness speakers in some of our perspectives. Okay, so let me start with an introduction. So what NIST sees as a randomness speaker since around 2011 as it tried to define what it wanted to promote as public randomness for public good, is that it should be a service that promotes, that produces timed outputs, so they are well defined in time, of fresh public randomness, so a lot of keywords here. So at a high level description, if you look at these words in blue, these are some properties that we want, so we want some periodicity to produce what we call pulses, like the streams of information that contain some randomness, in the case of the NIST beacon implementation, these are once per minute. Each pulse needs to have a certain amount of randomness, which the NIST beacon, for example, has 512 bits of. Each pulse needs to be indexed so that we know exactly what we're talking about, there's no ambiguity. It's indexed in terms of timestamps and it needs to be signed as well. Any past pulse needs to be publicly accessible forever. And also the sequence of pulses should form a hash chain so that somehow we can keep a well-defined history and sequence. Now what is this good for and maybe not good for? Well, broadly speaking, we think of a main application is to enable public auditability of randomized processes. So whenever randomization needs to be used but later needs to be verified, it's nice to have a service that allows that to be done. It allows for coordination between many parties and it also allows to prove that something has happened after a certain amount of time. If you trust that a particular pulse did occur in the time that it shows, that it's timestamped for. And we always like to give the little disclaimer that this is not good for selecting public keys. Even though the randomness is supposed to be the best quality possible, it should only be used for certain use cases. This would typically be a slide like to be maybe in the end of the presentation but because I'm kind of afraid of not getting there, I just thought of putting it here. Also to give a note that I think actually working on applications of public randomness is actually something that would be very nice for this community overall to work on because we're not there yet, I believe. But anyway, here are some examples of conceivable applications that have been thought of across time. So for example, for clinical trials, somebody makes a study, you need to have some randomization in it to make sure the study is good. Then you have super good results or maybe bad results. People can ask, did you really use randomness or did you kind of cook the results in your favor? So if you have public verifiable randomness, that can be used for this. We've thought of applications of legal metrology where for example, certain instruments need to be verified and using public randomness can basically insert a verifiable timestamp in applications that need randomness. Financial audits, for example, this is an application suggested by the Chilean beacon team whereby in Chile supposedly there's a process whereby public officials need to be selected to be audited. And if it happens that you select people that somehow it can be sensitive, the people you are selecting, right? So it's good to show that this is being properly done. Imagine for example, in a legal system you want to select judges to be in particular court cases. You could use a public randomness beacon for that. And then many applications of quality control to basically select what are the samples you should audit and things like that. Some historical notes about the project that missed. By the way, I've been at NIST since 2017. So a lot of this is prior to my arrival there although I visited in 2012. So in 2011 was the start of the beacon project basically based on the idea that public randomness should be a resource for the public good. In 2012 there was like a big internal grant that allowed NIST to produce, to have this project for implementing a NIST beacon. And also to do research in physics to actually develop quantum random number generators. Between 2013 and 18 there was a beacon service dubbed version 1.0. 2015 there was a nice interesting research result by the physical measurements lab that validated Bell loophole free inequalities. Kind of has to do with causality. It's interesting with respect to randomness. In 2018 we kind of started a new phase of the project. Also around that time the physics measurement labs actually developed an in-house quantum random number generator which today is implemented in the NIST beacon. And until present we have version 2.0 online. And since 2019 there's a reference for randomness beacon which basically is the main topic of today's talk. And we're hoping this year, this has been in draft version for quite a while but this year we should have the final version of this draft published, so no longer draft and also publish the open source code of the NIST beacon. I also want to mention that in 2019 we decided to be more clear about different tracks of the project so that the project is not confused just with the NIST beacon. So the NIST beacon, the NIST randomness beacon is an implementation of this reference. That's what CRS track B, but as track A we want to promote a reference for randomness beacon that other beacons can use. In particular, by the way, I actually wanted to mention this in the cover slide, also an aspect of this presentation that is different from the others is that we're not here presenting a decentralized system. We're actually presenting a randomness beacon that is centralized. But the vision is that this is used, oops. But the vision is that this is used in an ecosystem with many beacons and so that's, you know, it's like an ad hoc decentralization. So we want to, as track C, we want to promote deployment of various beacons by multiple independent organizations and currently there's one in the U.S. which is at NIST, there's one in Brazil, by in Metro, and there's one in Chile. We would like to promote applications of beacon-issued randomness. A lot needs to be done here. And we also support complementary initiatives about trusted randomness. Let me just give an example that I think is really interesting. You can use quantum supremacy to enable certified randomness which is really a very counterintuitive concept. So you can have randomness that you can prove that has been freshly sampled and you can base that on quantum supremacy. As long as you can prove, if you have a little seed that you know, if you have a little seed, you can use it in a quantum computation such that what comes out of that, you can prove that it has been sampled after you had that seed. Really nice concept. Maybe someday we'll have a beacon with this type of publicly certifiable randomness. Okay, I'm already spending too much time here. Okay, beacon reference. So there's a report. You can check it online. It defines a format for the pulses, how a beacon should operate internally, how you can use the fields of the pulse to have a proper use of randomness and it has some security considerations and the final version will be published this year. How does this work? Well, there's a beacon, what we call a beacon app that has all the internals inside and then timely produces pulses. It posts them to a database and then users whenever they want to go there and they fetch pulses, the latest one or old ones. How do they do that? Well, there's a REST interface where you can basically use a URL. You can use different URLs to get different elements, you know, past pulses or the current pulse or the certificate or something like that. All of this is explained in the reference document. Here's, let me just, I guess, point out a few items here. So does this have any laser? I guess not. Just to point out a few aspects. So oh, cool, I have this here. So the reference for randomness beacons specifies that the local randomness for each pulse needs to include at least randomness from two RNGs. So there's one that is local to the beacon app. Imagine this basically as a computer, which also has a clock. We recommend that a second RNG should be outside and protected. So not within reach of tampering by the beacon app itself if it were to be hacked. The signing mechanism should also be protected. You can use multiple RNGs. You can use external entropy. This is an interesting aspect. This external entropy is not for the purpose of improving the entropy of a pulse, but it's more to provide an assurance of freshness. So every time you put in external entropy that can be verified in the external world, you know that it's impossible that whatever randomness comes out of it after it had been pre-computed by even a malicious beacon. That's because we have chained randomness. Yeah, that's pretty much it. And then of course we need to have a time server. And then when we make security considerations, there's a number of things we want to consider. What happens if this part is malicious, but this one is protected? What happens if the time server is malicious? What happens if the signature key is compromised, et cetera? Okay, what is a pulse exactly? Well, a pulse has many items and in the interest of time I can't explain them. Oh, let me just mention the essential parts of randomness. There's actually two fields that we call random something. And there's what we call a local random value that is sampled, you know, it's the hash of at least the outputs of two RNGs. And it's pre-committed one minute in advance of being released. So it's pre-committed in a pulse before the actual value is released in the next pulse. The reason for doing this, this is a feature of version two as compared to version one, is that this is one of the features that allows to combine randomness from different beacons. Essentially you can use this to do a kind of typical coin flipping protocol. You pick several beacons, you get their pre-commitments. And once you have all of them, you can safely use the randomness that they reveal after the fact because none of the, at least any honest beacon could have not been, any malicious beacon could not have waited to know what's the randomness of the honest beacon because we're doing like this two-stage process. Then we actually have the actual random output value which is a hash of all other fields that include the signature, timestamps, indices, et cetera. And it's fresh at time of release. Actually it's fresh within seconds because even though the random local value that is going to show is from a minute before, it also hashes the pre-commitment of the next local random value which was just selected. So this is fresh. And this is the actual randomness that should be used by applications. Let's see. Could you tell me how much time I have just to see what should I skip? Okay, perfect. So how does this work more or less with a lot of details here hidden in the ellipses? So we have a local random value that is the hash of various, what we call raw random values, either at least two RNGs but possibly more. Then you pre-commit it. It's like the CI you have here. So on pulse I you have a pre-commitment of what you're going to reveal in the next pulse as local random value. And then the actual random output in a pulse I is the hash of everything that is over here. And then you have this relation. So there, oh yeah, something also relevant from the perspective of hash chaining is that the random output value of a pulse is actually then also included in the next pulse as in the field the output of the previous pulse. And this is what allows us to have some chaining. Yeah, again there's this little relation here as well. Yeah, so this pretty much gives you a little insight to how the random values appear in pulses. Here's a little snippet of a pulse. As I mentioned, each pulse is indexed with an index with a version. There's a URI, there's the time. There's here are the two random values that I just spoke about. Here's the signature value, the pre-commitment. And here is the output value of the previous pulse. And then actually we have an output value of the previous hour, of the previous month, of the previous year to actually allow what we call a skip list, which is an efficient chaining of pulses. Okay, some features of version two. This is what in a bigger presentation each of these elements would be a slide. So a skip list is what I just mentioned. You can actually check correct chaining between pulses. By correct we mean that there's only a possible, there's a single possible history between two pulses. You can use an efficient skip list, even if they're separated millions of pulses apart, because you can go the first of the hour, the first of the month, the first of the year. Then you go one year at a time and then you connect back to the other pulse. Combining beacons, as I mentioned, you can do coin flipping, kind of a coin flipping protocol using the pre-commitments of various pulses. The reference specifies various timing requirements, some of which we call promises. A pulse, the beacon operator promises that a pulse will not be released before its timestamp. It will not be generated less than a minute before its timestamp and things like that. There's a beacon interface in the reference that specifies how you can get all the information from the beacon. This is actually one of the things that has led the reference to take its time to be published. We're just finalizing that. External values, this is something interesting maybe from the perspective of combining various beacon. So version two of this reference has a field to incorporate external values. As I mentioned in a previous figure, this allows to ensure freshness. So we can conceivably insert in this field, let's say, every hour or every day or could also be every minute, but let's say every day, we could actually, let's say, input a random value from the RAND. And that would show that even if the beacon is completely, if this beacon is completely broken, it could have not pre-computed in advance things beyond a day, right? We can kind of imagine here a cross relation between many beacons that would ensure this to various beacons. And then we recognize that future guidance is needed for some aspects of how to use a beacon, how to combine external values, et cetera. Okay, skip please. I'm gonna skip the example, but this was an example that basically shows, instead of going a million consecutive pulses, you can kind of go step by step and just in a hundred and few pulses, you can combine it into, in a hundred or so steps, you can combine it into pulses, distance to part. And as conclusion, just as final remarks, so the beacon project at NIST really arose out of believing that there's a great potential for public randomness to serve as a public auditability, such as for public auditability of randomized processes. The reference that NIST developed introduced new features for better interoperability, security, and efficiency. And its vision is that there is an international ecosystem of randomness beacon. So even though it's a centralized proposal, it's for use within an ecosystem. Further guidance and promotion is needed, and that's something to be done across time. External values are not yet used in the NIST randomness beacon, but as I mentioned, this is conceivable to be integrated with other randomness beacons. I think that's an interesting community conversation to have. And stay tuned for the soon to come reference. Thank you very much for your time. Sorry, one thing I did not get it. Is it publicly verifiable or like? We need to ask what is publicly verifiable, right? Yes, so you can verify that. So the randomness comes from RNGs, right? So it's not as in the RAND where you know, okay, this comes directly from a pseudo random transformation. What you can publicly verify, you can verify all the hash chaining between pulses, and you can always check that the output value, the random output value that is proposed to be used by an application is indeed the hash of everything that is before and it has been signed by a private key. Right, so the first one is like kind of how to trust it. Come again? The first one to start with the hash chain, right? So it's a sequence of hash chain, but there is a initial, I don't know, genesis or something and that can be arbitrarily generated. But as can all pulses. So this is a substantial difference with the RAND, right? So the RAND is effectively not, it's actually deterministic, right? But it's unpredictable. Here the goal is that it's actually random every time. And for example, we use a quantum random number generator, et cetera. So there is that degree of trust that you need to have in a bit. So you are using that there is no verifiability of the fact that these things is being used. That's what I'm asking. Yes, yes. There is no verifiability, it's a kind of trust. Yes, as in others as well, right? Because there's no verifiability of a secret key. Sure, sure, sure. For example, just for the purpose of the secret key, in each pulse you actually implement a PRF in a sense. I mean, informally speaking, because you are effectively signing something with a key that is supposed to be. Signatory you can verify, sure. Okay, thank you. You're welcome, thank you. So you mentioned you had a draft for a spec and everything. So is it really specifying every step of the generation of the beacons? Or could we say, oh, we can transform D-RUN into a compatible beacons by producing, by using D-RUN as a PRNG to the beacons and then just complying with the spec? So that's a very good question and thank you for asking because interoperability I think is a very interesting concept in this domain. It depends at which level you're talking about interoperability. So the reference does specify a number of operations. So effectively the output random value is a hash of a well-specified sequence of fields and things like that, right? And I don't think that let's say D-RUN has those fields in those manners. But maybe that's not an issue because what matters more is like, okay, what is the actual output value? How would you, is it interoperable that we could use D-RUN's external output value in our external value to somehow have that interoperability? A little more concretely, something that I think could be interesting to talk about in terms of community interoperability would be how do we suggest, how do we provide guidance for a user that doesn't wanna trust D-RUN, doesn't wanna trust any of these beacons but is willing to trust the combination of them? What is the kind of guidance that we give to how they should combine things, right? So, let's say, first thought could be insecure but say, okay, no, just collect the randomness from everybody and hash it, right? But then, oh, okay, but what if that malicious party knows that's what you're doing, so they're gonna wait for all the others to reveal their randomness and then they're gonna produce their own, right? So they could bias the randomness. We have this in this reference, the pre-commitment exactly to already facilitate that. I don't know if, I don't think D-RUN has that. But we could think of how to do it, yeah. Final one in the interest of time. Very quickly, it's all very nice, but why are you doing this? Like, what's the interest of NIST of having this randomness begin? Yeah, so this started in 2011. Actually, it would be nice if I could open the, we have on the website a little kind of historical note and I don't wanna say the wrong name of, it was suggested to NIST in 2011 that it would be a good resource for cryptography to have public randomness. And so NIST as the standardization institute, at least in the US, would be an appropriate agency to kind of suggest that and promote that. So I would say that honestly, I think the most direct answer is that there is a vision that public randomness is a public utility, can be used for the public good. And so this was a project that started as a way of promoting development of randomness beacons. And it has done so at this stage by promoting a reference, it's not necessarily the approach that D-RUN follows, for example, and I think overall that's good, it's good that there's a diversity of things. That's it, but does that answer the question? It's a vision of public good, of being useful for the public good. Wonderful, thank you very much. Thank you very much for your attention.