You don't want to dismiss their feedback if somebody has concerns. Sure, you want to consider them, but you're not putting that extra emotional weight behind it where I'm a bad person or I'm not worthy. It's just, okay, here's some issues that perhaps I can address, if it makes sense for me. Hey, if you want to welcome to Developer Tea, my name is Jonathan Cutrell, and in today's episode we will continue our interview with Kalid Azan. Kalid created better explain.com. Of course, if you missed out on the first part of the interview, make sure you go back and listen to it. And we have interviewed Kalid before to make sure you check out those first interview episodes as well. Kalid is a wealth of knowledge. He has such a great mindset, a great way of looking at the world. And there's so much hope and excitement about such a cold subject, what we see normally, a cold subject as math. So I'm really inspired by Kalid every time we talk, my brain just fires on all cylinders. And it gets me really motivated. So hopefully we'll do the same for you. Now, I'm going to stop talking where we get to our interview with Kalid Azan. Kalid is, you're incredibly good at visualizing, finding these insights, metaphors, and analogies, new ways of looking at things. Perception is really kind of your key, I would say, your key talent is perceiving things in a way that other people will now shift their perception a little bit. Can you share just before we move forward with more theoretical discussion? I'd love for you to share maybe three epiphanies that you've had recently that you found incredibly valuable to you. Sure. And are you thinking of kind of math epiphanies or just in general? Just pick your three favorite. You can do math or anything else. Okay. Let's do a combination here. So one huge epiphany, this is more from a life or creation point of view is just the value of Evergreen. Evergreen in terms of long lasting, it could be content and motivation. And so in my life, I've been working on the blog for 10 years and certain articles. Actually, something like 45% of my traffic comes from articles written in 2007. So that year was, yeah, it's crazy. Like the first year I started, yeah, but yeah, 10 years ago, and I had a lot of back content from my old site that I brought over and I was, I had left my first job then, so I had a lot of time and I was just writing a bunch. And those articles, because they're on math topics, you know, 10 years later, the math hasn't changed. And so those things are, you know, and that's, I wasn't that conscious of that. I kind of suspected, oh, okay, well, this will be useful, but now that I've seen it. So basically, you know, half of my lifetime traffic basically has come from articles that were written 10 years ago. And so the value of just, you know, you're stacking up this brick or this resource, which just, it's going to stay there. And then in, you know, 10 more years, let's keep generating things. So there's that kind of Evergreen content or Evergreen, usefulness from the, from the writing. And then also Evergreen Motivation. So one of my other subconscious realizations, I think, was that it being motivated for a day isn't as important as being motivated, motivated for a year or for a decade or for a lifetime. So if you do something, like if you grit your teeth and you force yourself to do something, you really don't want to do, you might be motivated for a few hours to do so. But afterwards, are you going to be motivated to come back? And so, you know, it's really like just getting a one-off win doesn't, you know, just imagine it's already a year later so that whatever benefit you had from the one-off win has already been long forgotten, the real benefit is whether or not you're motivated to continue. And so this actually reminds me of a quote, which I found pretty true, is that long after, so if you meet somebody and, you know, like a coworker from a decade ago, they say that long after you've forgotten what they did, you remember how they made you feel. Oh yeah. So, you know, and it's like, I have no, it's like, oh, this person, you know, from that company 10 years ago, I don't remember what our project was, but would you want to call them and catch up or would, or if they asked you for a favor now, would you want to help them out? You do that based on the feeling that you remember. And so whether or not your action today is basically based on this kind of more soft and fuzzy feeling versus a very hard specific fact. And so for motivation, I can pull teeth and force myself to do something today, but then in a month or a year, will I want to come back to the project? Because will my memory of the project be that I really, it was unpleasant and I forced myself to do it? So I realized, okay, if I can keep myself motivated or the trick to having a blogger or anything for 10 years, is that you want to be willing to come back to it again and again. Yeah. So that's sort of like the main goal. It's not the specifics of what you did. It's, do you feel warm about the project enough that you want to come back to it? Man, let's linger here on this one for a second because we've got two more piffneys that you're going to share. But I want to say here for a second that there are a ton of people who are listening to this episode and you're looking for some kind of direction, especially if you're super early in your career. And I would say, this is kind of an unscientific thing, right? Motivation is, as we've already obviously discussed a little bit on in this interview, but motivation is really hard to quantify. Of course, you can do something like the fieldgood.txt, you can do something like the awesome jar, you can ask your friends when they see you most alive, whatever your way of quantifying it is. But using motivation as a determinant for what you will learn is a really effective strategy. Like it's the same analogy for working out. The best workout program is the one that you'll continue doing, right? It doesn't matter how hard that one workout was. If you don't do it again, then one workout is going to get you basically nowhere. It's better to do a light workout and we're going to stick with that analogy, I guess. But it's better to do a light workout four times a week than to do the hardest workout of your life one time and then never go back to the gym. So view your learning process the same way. This is a lifelong thing. And if you start down a road that looks boring to you, you're going to be bored. And it's hard to continuously do something that boars you. And certainly at the very least, it's not very fun to do something that continues to bore you. But if you see something that you're really excited about and then you're excited about it the next day and then the next day and then the next day, fast forwarding your brain down the road of what would happen in my life if I learned this thing, that's a really good way to play out the strategy. Don't just look at the salaries that you could possibly earn if you go and learn Java, right? Don't that's not the only factor here. Another factor for your success is whether or not you put in the energy to actually learn it. And if you are not motivated, if you're not excited about it, you're probably not going to put the energy in to do it. Exactly. And along with that is kind of the warmth to come back to it. I remember, so I finally did a report on how many blog posts they wrote over time. And so the first year I did a bunch, I think it did like 40 or something that first year because I had a lot of content. And then in 2015, I only did I think four blog posts. So that was maybe three months between posts. I was like, oh, okay. And then in 2016, I did like 16 blog posts. So a little bit more than once, once a month. And so between 2018, 15 and 2016, the reason I was okay with that was that I didn't have this kind of beating myself up like, oh, man, like you better get on it. You like I didn't have a negative association with coming back to writing. I was just saying, okay, well, I was a little bit, you know, I'm not sure what happened that year. I didn't write that much. But okay, I can come back to it. And it was a gentle thing. I mean, imagine, and for the gym analogy, imagine every time, you know, everybody we fall off the wagon, you know, we get sick or we just who knows? We just get lazy. Anything. It could be anything. And you come back to the gym and the people are like, oh, nice to finally see you back. Yeah. As soon as you hear that, you don't want to come back. You might finish that work out. You know, like, geez, every time I, you know, I get off my habit, if I come back, I'm just going to get, you know, some flack for it. It's that. Boom. You don't want to come back. So I think I had some consciously realized like I didn't control myself saying, oh, you know, finally, you're doing another blog post. It's been, you know, three months. And I didn't have that. So when I came back, I was just writing more frequently and great. But I think like if you have, you know, again, we remember that that feeling, right? Not the fact that I did a workout is that feeling of dread or feeling like you're going to be embarrassed because you go back. And that is a horrible place to be. So I tried to avoid putting myself there. Yeah, that's really good. So we've got two more epiphanies for you to share. Oh, started with the evergreen content, evergreen motivation. Let's see. I think the other one, this is sort of a, okay, this will be kind of a mixed epiphany. You know what? So the first one was sort of more about the site. In general, in personal, this one will be a middle epiphany. And then the last one will be more of a technical one. So this kind of middle epiphany is, I think, the value of empathy. And actually, I think there's a recent podcast, one of your podcasts is on this too. And I just think of empathy is this kind of honesty about what's going on. And just trying to connect to something is just, you know, human to human or program or programmer or writer to writer. And so in the, in the writing world, I, in my mind, I'm trying to write as if I'm talking to a younger version of myself. And the reason I do that is one, it's kind of hard to write for a general audience, you know, jokes and things. If you try to think of a joke that everybody will find funny, it's not going to work. But you find funny. Okay, great. Just put it in there. And then some people get us and people don't. So there's sort of that warmth that I think that comes in. It's this intangible thing. I mean, when you're reading a mathematical, people don't expect warmth. But when it's there, I think it's refreshing. Like, for me, I would want something that's like, hey, like you're a human being. I'm going to treat you like a person who's understanding this not a computer that's trying to read Wikipedia and analyze it. Right. And so I think part of that too is things like even like in postures syndrome, for example, I try to be pretty straightforward about things that we're confusing. So if I'm learning a concept, I mean, the reason I'm writing about it oftentimes is because I struggled with it. And then I finally figured it out. And I want to share what I figured out. And so when I write the article, I'm not going to pretend like it was just obvious to me. Like, oh, this concept just, you know, here it is. And here's, you know, like my big brain explaining to your little brain, what happened? No, it's hard. I was super confused. And for some reason, the tutorials that I've read, they didn't mention this key element. And maybe it was obvious, but I didn't see it. So I needed to make a diagram. And here's the diagram that helped me understand it. And in math, there's so many things. It's really funny because there's concepts in math that were debated for decades. Like the Fourier transformers one is it's a very popular kind of signal processing tool. And Joseph Fourier, who invented it, when he proposed it, it was debated for decades by other mathematicians. Like the most famous mathematicians in all France were debating this for like two or three decades. And finally, they realized, okay, this, this result of yours is true. Fine, let's let's start teaching it. And yet in math class, you're taught it in 45 minutes. It's a one lecture item. And the confusion that you have, you know, students are wondering, wait, is this really complicated? Is this really, is this that obvious? And the professor thinks it is because it's taught in 45 minutes, even though it took 30 years of the best mathematicians, you know, in the 1800s to figure it out. And so when I, when I write something, I say, hey, I found a confusing, I looked at the history. Yeah, it turns out it was a 30 year process. It was confusing. Yeah, super confused. Yeah, it was. It's not just you, like the imposter syndrome, I think it might come from the reverse, which is like the kind of superhero syndrome that people are projecting. So like Wikipedia and other things, they just, they just kind of blandly state facts that were decades of thought by really, really smart people to figure out. And it's just like a blase, like, oh, and this leads to that. And that connection took, you know, 30 years to figure out. Yeah. You know, it's just, so I try to, so the empathy thing is for myself, um, to kind of be honest about what's, what's working or not or what I struggle with. And also to, yeah, when, when I'm trying to write, I try to connect with people, um, just as a human being, and I think that it opens up because also there's sort of a tension to where, um, this is more for real life teaching, maybe than, than writing. But when you're explaining something, you want the person to feel comfortable saying, hey, I don't get this. You don't want them to feel like they're going to be judged or be, you know, ridiculed or something. And, but I feel like a lot of teaching unfortunately has this kind of approach where if you don't get it, something's wrong with you versus, hey, you're actually curious enough to want to know more. Thank you. Like let's figure it out. And another analogy, oh, man, I, I might go over my three-in-site limit here, but, oh, that's fine. It's good. It's what we want. Exactly. I mean, I sort of see confusion as finding, like, a hole in your roof. Like, if you walk around your house and there's water coming down, it's not great, but you're happy you found it, because you can patch it up and now your house won't get damaged and, you know, everything's a little bit better. And so I think we treat, I treat learning and confusion as that is that these are little issues that I can fix up. Oh, like this door isn't closing properly. Let's fix that up. Oh, there's a hole in the roof. Oh, there's like a windowsill, which isn't sealed. Okay, we can fix these up and then the house is that much more pleasant. But I think the historic way that we see it is you have a hundred, a score of a hundred, and every defect is a negative, and then you fail your driving test or something. So you're just hoping, like, a lot of people see it as every issue is something that is wrong and with enough wrong things, I'm just bad. And like, the teacher is an inspector of the house, rather than the repairman. Exactly. Exactly. Exactly. And that's, that's perfect, because the inspector is trying to block you from something. And every issue they find, like, you don't want the inspector to find the, yeah, like the, the leaky roof. Right. You know, in some way you want to know, but you don't want them to know. Exactly. So I sort of changed this, and I think it was again, a subconscious sort of twist where I realized that every issue that I had, if I fixed it, suddenly, I've upgraded myself, it's like finding a bug in your program. Like, don't you want to find the bugs? Because now your program is that much better. And yes, you do want to find them if it's for your own use, but maybe if it's for some evaluation or scoring thing, suddenly, you're kind of hoping the evaluator doesn't notice the bug. And that's a really, you know, it's unfortunate because you're losing out on the knowledge that that would be gained from fixing it and the future improvements. So I sort of had to take that approach where math, every issue I found in math, every confusion was a, in a, actually, this is, okay, I'm just going to keep going with the analogies. I had this post recently on the kind of Mega Man model of learning where I saw this one. Oh, great. Yeah. So this is one of my, sometimes I get these little analogies. So I actually, I'm, I'm not sure, but everybody who grew up in the 80s, they probably heard of this game called Mega Man. You're basically a robot. You're like a cyborg and you go through levels and you beat bad guys. And the really cool thing is when you beat a bad guy, you actually get their weapon. So your Mega Man, and there's Ice Man and Fire Man and Electric Man and there's all these different people. And once you beat Fire Man, you now have a Fire weapon and that makes your fight with Ice Man a little bit easier. Yeah. And then once you beat Ice Man, so you have a Fire weapon or an Ice weapon and then the Ice can work on Electric Man, then you have Electricity and then you can use that on a different guy. So what's interesting is in Mega Man, you actually want a lot of enemies. You want a ton of bosses because every villain is a new tool that you get near tool belt. And then eventually, once you have, you know, 10 of these tools, you can go fight the big boss and the big boss is that much easier because different parts of the level can be beaten with these different tools. So it's a, it's a great metaphor for learning, which is that, oh, I learned this concept and it helps me unlock this other concept and this, these two concepts together help me get this third concept. Yeah. That's how I see math is it. Oh, once I understand exponents, it helps with this other thing and I understand radians and I understand imaginary numbers and exponents and radians and imaginary numbers, they help me with oilors formula, which helps me with the Fourier transform, for example. So you can basically get these little tools and help you versus attacking this really tough concept with the kind of standard weapon, which doesn't have any advantages. So it's like, oh, wow. So like you sort of look forward to it. And of course, Mega Man has like 10 sequels because people love it. It's like, oh, you know, there's tree man and fish man. You can have every, you know, every now and can be a potential ally. So you basically have all these sequels. People love playing Mega Man and there's, there's more and more. And then the alternative is something like Tetris where Tetris is basically a race against time. It's, designed to break you like, sure, yeah, exactly. You know, you don't really win Tetris, right? You survive it until you lose. Everyone will lose Tetris. Everyone will lose. Exactly. Like there's no, and that's how learning is for a lot of people is that we're just going to find your breaking point. Oh, you passed this class. Okay. Let's give you this other one. Oh, you answered this question. Let's give you this other one. And so Tetris, you know, there's, I think, I don't know, six or seven shapes, like the L shape and the square and the kind of zigzag shape and so on. Imagine if Tetris gave you more and more shapes, like newer and more intricate, like an X shape, like a double U shape. You'd be like, no, no, I don't want anymore. It's hard enough already. Like more impossible. It's more possible. You're making more difficult. But in Mega Man, you want more bad guys. So it's weird. And Tetris, you don't want more bad guys. Tetris would be great if it was just L shapes or just squares. Yeah. That'd be perfect. Because then you can, you feel okay. But Mega Man would be really boring with just one boss, right? So, you know, and it's just like, wait, why in these two video games, one, I love the enemy is the other one I hate them. And it's because of the structure. Tetris is like this pressure cooker trying to break you and Mega Man is this kind of exploration. And you get better and you sort of improve like an RPG, you know, you're getting better with more enemies. And so I realized that learning could be like that where unfortunately, we have the Tetris model and the Mega Man model. I think would make us feel a lot better. So I, I think I just stumbled upon it for myself where if I really understood something is now an ally versus these tests that are just designed to find your breaking point. And, and, and, you know, even if you survive Tetris, what does it mean? Like, you don't, I feel like you might learn a little bit of skill in the process, but you don't have like a tool, so to speak. You just, you kind of went through the gauntlet and that's it, you know, survival is the goal there. I was talking about something kind of similar to this with a couple of friends recently. My wife and I are expecting our first child this summer. And so our minds are certainly on education. Thank you. Our minds are on education, you know, already, of course. I mean, the kids not going to be able to do anything until he's at least, I guess, you know, six months before he really even knows that he's alive. But, you know, so, but we're thinking about education. We're looking at schools in the area. And because we know it's going to come, you know, before we know it. And some of the things that we were discussing with with a couple of friends of ours, one of them was the idea that when I was in college, I took a bunch of Spanish classes. And it wasn't elected. It was actually required that I take these Spanish classes. And we debated the value of that, right? You know, I'm not using it. I've forgotten most of it. It really hasn't provided any, you know, at least visible or direct value that I can identify after college. And maybe it did then, or maybe there's something in my brain that works better as a result of it. But it's an indirect correlation at best. And perhaps, you know, there's nothing there at all at worst. It was a waste of time entirely. I don't think that it was a waste of time entirely. But I do think that the way that it was taught made it less valuable to me. And so we got onto the subject of memorization because most of what I did in Spanish class was memorize, right? And the problem is there's so many so many classes where memorization is kind of a fundamental skill. But we don't really have a class that teaches memorization to kids, right? We don't really have that as a formalized, you know, teaching a kid how to memorize something. What class would that be in? Well, it's not in one of the major subjects. Maybe in English. So memorizing things, children learn so quickly because they're in the environment that they're having to learn about. And they use associations and stories and all of the multi-sensory inputs that they have. And they learned super fast. Now, the biological side is really compelling as well. It's very interesting to go and study this. I'm not going to belabor the point about baby brains. But I do think it's important to start recognizing this idea that, you know, you have allies. And what I viewed my Spanish test as was a huge barrage on my memory ability, right? Like that's, that was all it really functioned as in my, in that class. I never really felt like I was learning as much as I was just like testing my ability to cram. And it was never really particularly valuable to me. Whereas in a different class that I took as an ethics class, we were presented with different paradigms of ethics. And then every test was actually an essay. This was hugely different obviously because it forced us to really articulate the full learning process, right? We had to articulate all the way through rather than, you know, saying what did, you know, multiple joys, what did this person believe was the most ethical way to go about punishment or whatever, right? We didn't have to do that. Instead, we had to compare our own perceptions and really go through the process of learning enough so that we could re-articulate it to another person. That was so much more of a memorable and valuable class to me. And I believe that every class could be that way. This is not like a judgment on learning foreign languages at all. I think there's plenty of value in learning foreign languages. But the way that you learn it, you know, are you really going to provide yourself with an ally or are you doing exactly what you're talking about with this, with the Tetris blocks, right? Those tests were just really fast Tetris blocks that were thrown at my memory. Exactly. And I think, I mean, most people, it's funny because language learning and math are very similar in that people study them in school and then have very little intuition. Nobody says, oh, yeah, my high school Spanish class, I feel great about math or Spanish now because I learned in high school. Same thing for math for most people is that, hey, I studied math in high school and now I love it. It's like, no, no, it's gone. I think it's gone. And we sort of continue to do the same approach to things and it doesn't actually work. And so actually, languages are good example. So I, similarly, I took it in high school and a little bit in college and I wasn't really that comfortable with it. But then now I chat on Skype sometimes with the language partner. And so there's no, it's not a memorization. I'm not trying to, hey, can you quiz me about going to the bank or something and like all like integrating it, right? I'm just integrating it. Just trying to say, hey, let's just have a conversation. And so I'm, you know, just using my vocabulary that I have. And there's a lot of things like, so you know, the game taboo where you need to describe a word without using other words. So it might be something like airplane and you need to say the word airplane without using like flight or ticket or something. So I've realized, oh, wait a minute, that game of taboo, I'm getting somebody to guess a word and I can't use the word directly or these other related words. Well, that's actually what it's like to speak a foreign language. Like, hey, how do I say, I don't know, like door or something? And if you don't know the word for door, you can say, well, it's that thing in the house that's between rooms. And then they say, oh, door, you're like, yeah, that's what. So you could basically, you know, like I'm playing taboo when I'm talking Spanish. I'm playing taboo essentially in my head where I know a few words and I can stream and that's actually maybe my analogy brain going an overdrive. It's like, okay, how can I refer to something without using it directly? And so and it's fun and it's not memorization. Then suddenly I hear the word and then it kind of, I'm, you know, a couple times with that and sticks a little bit more. And so again, that isn't taught in school, right? In school, you get punished. You didn't know the specific word for door. Oh, that's bad. This is getting someone to see. Oh, yeah, the thing between rooms or it's not a window, but a door, you know, like you can basically get someone to understand what you're talking about. And it's really just about communication, language is about communication. And then math to me is about these really beautiful concepts that if you understand them, you'll start noticing them. So for example, people always say, when will I use math? And that's like to me, that's unfortunately it's presupposing that the purpose is to be used like that versus it's when will I notice? Like to me, it's kind of saying, when will I use the color red? You know, like you don't really use it. I mean, you notice it and you say, oh, but red is sort of kind of energetic. So if I want to convey a sense of energy, maybe I'll use red. So, you know, when will I use a circle? Well, it's symmetric. Like if you understand a circle intuitively, say, oh, it's very symmetrical. And there's all these properties. So if I want to and it's kind of unifying. So if I want to get this concept of unity or symmetry, maybe a circle is a good place to go. And so to me, math is kind of a set of these colors, almost so to speak, right? Each color has maybe like an emotional vibe to it. Like green is very earthy and wholesome and red is like energetic. Yeah. Blue is calming. So it's like, oh, okay, a circle has these properties and a square has these properties in a certain kind of equation as this property. And so when I'm trying to do something, I almost look at metaphorically. Like I don't need a literal circle, but the idea of a circle is helping me think about something. Oh, yeah. That's exactly where I was hoping you would go with that. The concept of properties and using properties of one thing as a system of creation or as a system of understanding something else, right? The idea of a circle, I mean, there's so many things as a software developer that you can build with circular structure underlying that you never actually visually see or use a circle, right? Like there's so many things that can be that can be accomplished by understanding the properties of a given thing. The same thing is true going back to our Spanish discussion, right? The same thing is true because you start learning how grammar is structured, right? You start learning how different languages use and how there's like a minimum number of parts for a sentence to make sense in any given language. And that may be different for one language than another. And you know, you can use these same structural or property-based things to inform the rest of your world. Today's episode is sponsored by Headspace. If you don't know what Headspace is, let me set up this scenario for you. Everything that we do, everything that we engage in, we need to practice. There are many different ways to practice any given thing, but everything that we want to be better at, we have to practice at it. And one of those things that we all as developers really should aspire to become better at is the practice of focus. We need focus in our lives and we need mental clarity in our lives to be able to produce the best work to solve difficult problems and to reduce the distractions around us, right? These are things that are not really, they aren't really optional for the average developer. We can't allow ourselves to be distracted and also expect to level up in our careers. Now, as I said, there are many ways to practice just about any given thing, right? You can practice focus by actually going through your day and then evaluating how well you focus. That's kind of a passive way of practicing focus. An active way of practicing focus would be something like meditation. And that's exactly who our sponsor is today. It's an application that makes meditation simple. This is a iPhone or an Android app. You can find it in the App Store and you can try it for free. It's Headspace, right? Headspace is sponsoring today's episode and they are also a company that is growing incredibly fast. They have over 10 million downloads worldwide. This concept of meditation is taking hold. There are plenty of people who are benefiting from it and then sharing their stories. And it crosses over the boundaries of different cultural norms, it crosses over belief boundaries. So if you haven't tried meditation, I would highly recommend this, especially as someone who uses your mind each and every day. Your mind very much so needs something like meditation to work properly. So go and check it out. I've used Headspace for over a year on and off. I'm not super great at my meditation practice. I'll be honest with you. But every time that I feel unbalanced or I feel like I need a little bit of clarity, I need to have a jolt of inspiration. Usually the first thing that I go to is meditation. And the first thing that I think about when I think about meditation is Headspace without fail. So they are building world class engineering team, as I said before, with TeamsBase and San Francisco and in Los Angeles. So if you're interested in joining a company that's working to improve the health and the happiness of the world, not just a small group of people, but everyone in the world can benefit from meditation. You should apply. You can go to headspace.com slash join dash us. Of course that link will be in the show notes. You can go to directly to spec.fm slash headspace all one word to go directly to that job page. Thank you again so much to Headspace for sponsoring today's episode of Developer Tea. Exactly. And I think that's ultimately the goal of education is they say we're teaching how to learn or something. And while I appreciate the sentiment there, I feel like it's so vague that is really hard to like if I say, oh, we learn math because it helps us learn other things. Like I like that that's often is you know math teaches you how to think. I see that a lot and I like the sentiment, but unfortunately it's so vague. It just sounds it's like it's not really helpful. And so I like to use these very specific analogies like, hey, a circle like you're probably never going to draw. Well, I mean, maybe you'll draw a circle for some reason, but the concept of a circle, let's say in a program, well, that's a loop. A loop is a circle is a loop. We're just going to move in a circle until we have a condition that breaks us out. And so that's your honest circular path. And then eventually you go off an tangent. You say, okay, we escaped. We escaped the circle. And so, oh, a tangent. What is a tangent? Oh, it's touching the circle at one spot. So you basically loop around and then you zoom off. And that could be like a go to or a jump or a return or a break. So I mean, I'm just thinking this now. It's, oh, okay, there's like a geometric intuition for what's happening in a program based on a circle and a line. Oh, interesting. And that's just for software. What about for exercise? Doing reps of something. Okay, you're doing a circular pattern. You're going over and over. And then maybe or you have like a high intensity training where you have sort of a fast loop and a slow loop. And okay, what's happening there? You're going around in a circle, but at one point you're moving faster than the other. So there's all these intuitions that can come. And that only happens though. If you really, I mean, a circle is something that we're very viscerally comfortable with. Like we we've seen circles so much in our lives and we're comfortable. So I don't feel bad using a circle as an example, but something like a parabola. Oh, like for most of us parabola, like like I wouldn't I wouldn't say, oh, it's kind of like a parabola, like a parabola. It's in the scary land of we had to memorize it. We don't really get it. But like, so I could keep going on. But once you once you have an intuition for something, it gets in that familiar circular territory. Yeah. Now it's like it's an ally. Like a circle is a math ally. Like you can use that in so many scenarios because you're really comfortable with it. But a lot of other concepts are these tetris pieces like parabolas and ellipses and hyperbolas. All these things are thrown at you and you memorize them. And unfortunately, they're not allies anymore. So my goal is really to build to turn as many of these concepts into allies. And then it's fun because when you have that approach, oh my gosh, like can you imagine having like learning about a shape as useful as a circle? Like it's almost like the first time. For the first time, it's like, wow, I didn't know. Like imagine I said, hey, there's a color you've never seen before. But it's super calming and it makes you excited and calm at the same time. And you've never seen it. Wow. Okay. I would love to show you that color. That'd be amazing. Like maybe we find out that like our eyes are capable of some other color that we've never seen before. Actually, I think Fuchsia is one of those. This is I can't quite remember, but I think Fuchsia is like a constructed color. Yeah, it's one of these like, it doesn't, it's one of these things where it's created by the combination of colors in our mind in a way that isn't, it's not like a physically, like we can't decode it properly. We can't decode it properly. Yeah, there's something about it. I can't quite remember. And maybe afterwards we can, or I'm sure listeners can inform me, but there's something about Fuchsia, which it has some property. It's almost like a psychological color more than it is a like a physical color. That's interesting. So yeah, it's it's almost like black is like the absence of color. Right. Right. So like, like it's not and white is the combination of three colors. So white doesn't really exist on its own. It's the combination of things. And I think Fuchsia has some some other property like that. So imagine there's these things that are out there. And oh my gosh, can you show me? And that only happens again because we're excited about getting more Mega Man weapons. Exactly. Exactly. Excited about these these new shapes. Yeah. Man, that's good. That's very good. And it's inspiring to think that, you know, there's so much more that we can understand going back to your repairman analogy. And then we'll go to our third epiphany. But the repairman analogy of having holes in your roof and that kind of thing, you know, when you when you look at problems as or when you look at skills as discrete from everything else, you're kind of missing the idea of how your brain works. Right. So more than it being a discrete problem like there's a stain on the rug, a lot of the times that we that we have problems in our brain or not problems, but missing information or incomplete information, it's more like the circuit breaker is is cut or like there's a there's a problem with with something with your plumbing. Right. It's going to affect maybe everything in the house. Like it could affect your understanding of everything, your perception of everything could change and it could be not, you know, not just everything, but it could be 50% of the house. Now it doesn't have power because this one circuit breaker flipped. Right. View your brain the same way because, you know, now that you have this knowledge of of a parabola or now that you have one of my favorite videos or videos or articles that can't remember that you did was about the magical number E, I believe it was E, was it E? The the interest number. Yes, yes, that's E. Yeah. Yeah. All I remember is that it is it is this concept that gaining interest over time and and how important that was for my understanding of, for example, my finances, right? It's a totally separate separate conversation then, oh, what should I put into my bank account? It has different implications and the how you think. Even though I'm not sitting down and doing, you know, long form math calculations to determine my retirement, I am using that intuition to inform the way that I think about retirement. Exactly. And that's one thing I wish was taught more in math class too is that the goal, it's sort of, man, it's almost like the theme like in English class, you know, you read literature and then we talk about the theme. So like you read a poem or, you know, a story and you might discuss what it's trying to convey and you're not like there are the facts of the story and the facts of the poem, but there's this kind of deeper meaning and I feel like in math class, we don't say, okay, well, here's the concept and here's a deeper meaning. I mean, acknowledging that you're going to forget most of the details like E, like, yeah, for most of it's okay, you know, what is it? And for, I'd say for most, I mean, myself too, until I really started working on it, I didn't have like a good intuition, but already that intuition that yeah, it's involved in interest rates and it's about kind of compound interest. Okay, that's enough of an intuition just to put you in the right path of but why it's there. So if you see it in a formula, you say, oh, maybe there's some interest being accumulated and the interest could be it could be monetary. Maybe it's biological. It's a population that's growing. So you're getting interest, which is your population or maybe you can actually have negative interest, which is like radioactive decay. So it can be used like as and so that's oh, what's happening? Half life. Half life. Exactly. And so you have this very comfortable, like, oh, he just represents the process of gaining interest or losing interest. Oh, interesting. So things that are changing over time and they're kind of getting more and more or getting less and less versus like a stat like like a line keeps the same progress every time. So you're getting, you know, $10 forever. But with your bank account, the more you have, the more you make. So now it's improving. It's 10, then 11, then 12 and so on. So E, like you kind of intuitively know, oh, it should be E and not like it's like a just a regular number here. So right. Yeah. And that's and that's all the intuition that you really need. Like often, yeah, you're not computing things directly, but it's just being comfortable with it. It's kind of like the way that programmers, especially formerly trained, if you've taken an algorithm course, you look at, you know, big O complexity, right? You have a log or you have, you know, I can't remember all the like in squared, all these different levels of complexity for algorithms. And the whole point of those is to determine, okay, over time, how does this algorithm actually actually work? How does it become more complex with a larger data set? Does it take longer with a larger data, larger data set? Or does it, you know, does it get better with a larger data set? There are certain algorithms that do that. And if you don't understand, you know, the way that those to get that intuition, you can look at a few graphs and say, okay, if it looks like this shape, then it's basically, it's this type of O notation, right? I may not know the exact O notation, but learning, for example, what an exponential graph looks like. Well, now, you know, that's probably not the algorithm that you want to choose. Whereas what a logarithmic graph looks like, you know, I heard that described as the opposite of an exponential graph, which that was such an simple explanation for something that confuses so many people. What is a logarithm? Well, it's, it's the opposite of an exponent, right? Yeah. That's, that's a basic and perhaps incomplete explanation that gives you an intuition for the shape and the, the way that that changes over the course of a graph or over the course of inputs rather. Oh, man. And I knew every little back and forth here is great because this is giving me more and more intuitions. And so one intuition for logarithms, this is one of my favorites because logs, they sound so complicated and people like, I never use logs in real life. Like exponents, maybe, because interest and I can understand, you know, maybe populations that people can perhaps perceive that they're using exponents in some way, but logarithms, I mean, come on, who uses logarithms in everyday life? And my, my intuition, though, is that logs are basically, if exponents are the output or the result, logarithms are kind of the input. So for example, if you, if you look at your growth of your bank account, that's the, that's the result. But the logarithm is actually your rate of return. Oh, yeah. Basically, or like your stock market, like it went from this, you know, the portfolio went from like a thousand to 1500 over 10 years. Okay, so that was the result. But the input was a certain percentage growth. So the logarithm kind of finds the root cause. And so I had this sort of analogy that like logs are like time in a sense and then exponents of the result went happened over that period of time. So you can sort of see it as an input output kind of cause and effect. And so it's like, oh, okay. So oftentimes we notice effects. But then if you want to ask the question, well, what was the cause, then a log will help you find the cause. So it's like, oh, okay. So like you don't, and another, oh man, I'm going to keep going here. I could. So we had this interest rate. So everyday logarithms, well, interest rates are basically logarithm. And oftentimes because they're, they're computed, especially for rates of return, right? Like you compute an interest rate based on what happened. You don't, you don't set out knowing the stock market's going to go 10%. It just happened to go 10% because you found it out after the fact. And then another analogy is when we talk about the kind of digits, so we say, oh, this is like a five figure deal, a six figure deal, a seven figure deal. That number five six seven, that's the log of the of the deal size. Oh wow. And so yeah, it's like, oh, but why do we, why don't I say it's a deal of 50,000 or 100,000? It's like, well, that isn't as important as it kind of the rough order magnitude. Yeah. The scale, exactly. And the cool thing is you're able to talk about a huge difference, like 50,000 to, I don't know, 50 million. That's a big jump. But they say, oh, it's a five figure deal, six figure, seven figure, eight figure, nine figure. Suddenly, you're on the scale, that's a lot more reasonable. And so things like page rank, I'm not sure if Google still uses it, but they used to, you know, measure the authority of websites by their page rank. And it was basically a logarithm of like the number of links or something like that. I think that the number of links that we're pointing. So CNN might have had eight, eight digits of links or traffic. And a small site would have two. So you have a scale that goes from two to eight. And it's because it's two digit number of, or you know, amount of visitors versus eight digit number of visitors versus saying 200 visitors a day to, you know, 800 million people a day or something. So you're able to take a huge scale and kind of compress it and walk it down. And so then like the last intuition is for something, if you think about the effort involved to increase the logarithm, like going from one to two digits, not too bad, two to three. Okay, you know, you're going from like the 50 to 100. Okay, three to four, four to five, five to six. Oh, that's a big jump. Six to seven. Oh, so it's getting harder and harder to increase that digit count. Every digit that you've gone through, the next one is 10 times more difficult. And so that's why logarithms, they grow so slowly, like exponents, they started the explode. They basically say, the more I have, the more I make and the more you know, the more I make the more I have it, it keeps going, going, going. Logarithms are the opposite saying, okay, well, you got to, you know, the seventh level, well now to the eighth level is 10 times more. Oh, like 10 times. But like Tetris, exactly. Like in Tetris, the more stuff that's on the screen is even harder, you don't have as much room and it gets harder and harder and harder. So exponents are sort of faster and faster and faster and logs are slower and slower and slower. And so, and that might be like if you want to put the breaks on something, you put a logarithm on it and suddenly is really hard like getting paydrink nine, nine digits of traffic, getting 10. Oh my gosh, 10, like even like a Richter scale, for example, that's why earthquakes, they, you know, around eight or nine is like the most because every digit you're adding is like 10 times more, more strong. Yeah. It's really hard, you know, you're basically fighting. I think maybe like the, the asteroid that took out the dinosaurs might have been like a 11 or 12 or something, I'm not sure, but it's, you know, because even if it's a thousand times more, it's only a few more digits. Yeah. So it's harder to, it's really hard. So you sort of have this scale and that's like, oh, wow. So I explained in this way, oh, it seems natural, it's fun. It's an ally versus see it in your life, right? Yeah, exactly. Another physical example of a logarithm would be like losing weight, right? So if anybody who has, who has been at your largest point in your life and then you went on a massive diet of some sort, you know that the first couple of days you're dropping pounds like like crazy, right? Like it's like the first week you can, you can lose five pounds in a week and it feels like a large amount of momentum. A lot of people end up stopping their diet because they don't understand this basic principle of, of rate, right? So as you lose that weight and you're getting skinnier and skinnier, the amount of weight that you lose, so one pound of 200 pounds of body weight is only what, 0.5% of your, of your body weight, but a pound of 150 pounds, right? Exactly. Is significantly more. And so even if the rate percentage wise that you're losing of your body weight stays the same, the actual gross amount of weight that you lose changes. And if I'm not mistaken, it changes basically logarithmically. Yeah, you can, it's kind of this one over X factor. And actually, this is, oh, this is getting to the math of it, but like logarithms, the natural log is derived from that one over X pattern, because you're right, like one pound over 200 compared to one pound over to 199, then it's one pound over 198 and one over, so you have, you have, you kind of this one over X pattern and logs basically derive from that, where as you go, like the additional pounds, it's more and more effort, or it's, it's harder also to, to take away, but when, once you have so little to lose, getting that last, you know, five pounds out might be really hard when you're 150 versus when you're at 200. And the same shape would apply to things like productivity, right? Like your, your own output, you may have massive jumps of productivity if you're doing nothing and then you do something, well, that's a hundred percent jump, right? But for you to go to 200 percent productivity, maybe significantly harder than going from zero to a hundred. Exactly. Another analogy too, I don't really follow baseball that much, but, you know, like a, like a, I think like a meteor, so they have a batting percentage. So out of a thousand, attempts, how many hits do you get? And so, you know, an average player might be like 250 or something, let's say. So that's, you know, 25% of the time they're, they're hitting the ball, and then a really good player is 300. And then an excellent player is like 350 and like an outstanding player is 400. And so adding 50 extra hits, it gets harder and harder. I don't, I'm not sure what the record is, but, you know, if somebody was hitting 500, you know, 500 or a thousand, superhuman, it's unheard of. So every extra hit gets harder and harder to increase your percentage of hits that you're getting. And so there's a lot of things in life like that where it's like this asymptotic kind of like it's, you know, each step is harder than the one before and the higher you are, the more difficult it is. And this is why very rarely, when you watch think something like the Olympics, very rarely, well, you see somebody who's way out in front, right? The slivers between superhuman and incredibly good, that slivers very small. But the sliver between average and incredibly good is pretty big, right? Like that you can, you can train and train and train. I heard this actually on once again, I'm going to use his name, Episode of Tim Ferris, but he was speaking with someone about gymnastic training and the guy is he's trained a ton of world champion gymnasts, right? And he said at this level, every single minute of training, every single thing that you do is putting you like milliseconds of difference away from your competitors. Like the heavy, the weightlifting champions are like a five pound plate difference or a two and a half pound plate difference. And it's so interesting that we get so addicted to massive changes and massive progression when really at the top performing levels of most things, it's very small differences. Yeah. And this is great. And you know, so my hope and dream is that in the future, people will be comfortable saying, oh yeah, like the progress is logarithmic. Yeah. We're getting logarithmic. And like I would love just people to be that comfortable. We could say, oh, you know, I'm in kind of a circular pattern. Okay, I get you, like you're kind of in a rut, you're in a circle. Hey, I'm kind of like progressing logarithically. I would love it if in the future people just were that comfortable. Yeah. That's, you know, my goal really is to help people reach that level of comfort. We're math, it's a set of ideas that in addition to being metaphors, you can't actually compute with them. Yeah. This is like, you know, like a theme in an essay, it might inspire you, but it's not like you calculate based on it. But in addition to helping you describe something, logs can help you log a satellite or something. You know, it's sort of, you know, it's useful in a practical sense, but also just metaphorically. And so I think, yeah, so, oh man, this is great. Like, yeah, nice little logarithm discussion. Yeah, we went way on. Well, I guess I'll have to use word tangent now. Perfect. Perfect. Okay. So let's shift into this, the third epiphany if you have one lined up ready. Oh man. Okay, this is good. So let's see, one of my, it's a recent one. So this is, I guess, more of a technical thing. Actually, and this will be good for programmers too. It's kind of an information theory example. And I like this one too, because it's about noticing patterns. So I'm not sure if you're actually maybe you're familiar with the highway system. So like, you know, the 50 users developed and they kind of put it on a grid. And of course, you nobody, nobody told me like the way the grid worked when I was in driving school. I mean, you sort of figure out patterns a little bit, but basically the US interstates, there are, you know, they go north to south and east to west. And so on the west coast, you have things like I five, like in Seattle, there's I five and it goes from Seattle all the way down to San Diego. And then there's I 15, I 25, 35, 45, 55, 65, 75, 85, 85, 95. And then I 95 is in Boston. And you can take that all the way down to Florida. So you have these kind of interstates. It's just saying, yeah, left to right. And it's the odd numbers. And then you have these east to west interstates, I 10, 20, 30, 40, 50, 60, 70, 80, 90. And so I'm in Seattle and I'm from Boston. And so just not even looking at Google maps, I can say, you know what? I can drive an I 90 from Boston to Seattle. Huh. Yeah. It will be, you know, 3000 miles or something, but I can do it. Or hey, wait, you know what? I want to go to Florida. So I could take I 90 from Seattle to Boston. And then I 95 from Boston to Florida. Or I could take I five from Seattle to San Diego and then take, I don't know, I 10, I guess, because the lowest one I 10 all the way across to Miami, let's say. And so suddenly it's like, whoa, okay, we put all these numbers on a grid. And the properties were, okay, so we have a few properties. There's even odd. And that's sort of mapping to North, Southeast, West. So it seems like the evens are East to West and the odds are North South. And then we're also using multiples of five. So it's like five, 10, 15, 20. So the major roads will be kind of a multiple of five. Like a nice clean number. Yep. But then sometimes you have these other interstates, which are like 295, 395, like in Boston, there's 195, 295, 395. It's like, oh, what are those? And so if there's a three digit number, those interstates connect to the bigger one. So I 95 will connect to 95. 295 will also connect to 95. 395 will also connect to 95. It's like, whoa, okay. So these three digit numbers are sort of smaller interstates that are connected to the bigger ones. And what does that first digit mean? Like the one and the two and the three. And it turns out that means something. So an odd number there, they call it kind of a spur road. It kind of connects to 95 once. So 195 will kind of shoot off of 95. But an even number like 295 will actually loop back. And so it's kind of a, it's like a circular, usually around a city. So you have a city and then you have the main highway, like 95. And then you have sort of a loop around the city. And that's kind of an even sort of like 495. Oh, there isn't a 695 that I know if a 695 would also loop. And so it's like, oh, interesting. So just intuitively, you know, okay, I'm on 95. And I'm going to take one 95 is my exit. One in one 95 is never going to hit 95 again. It's just going off. So it's like, oh, wow. So what we've done is we've taken numbers, which have all these properties, like even odd, how many digits is it divisible by five? Always propagating with them. Exactly. And we're mapping to all these properties. And that's kind of the beauty of math, which is that it's very abstract. I mean, a number, you know, when we're counting, nobody was thinking, I'm making these numbers. And later on, we'll have all these properties. And then we'll map them to highways. It's just that no, we discovered them. Math it shows us. And then the question is, wait, what other properties are there? Like we've done even odd, we've done, you know, the number of digits. And so then a fun, this is an article, I said, okay, well, another property of a number is whether it's prime or not. So you could say, okay, so it is a divisible by any other number. So three is prime, five, a seven, but not nine, nine is divisible by three and three. It's like, oh, wait a minute. It could be use that. So you could imagine that if you had like local roads, so local routes are usually low numbers like 20 or 15 or three or something. So you could say something like, if I had route three and route seven, maybe route 21 connects them. So if I have, if I promise to say that the local roads are individually prime numbers, and this is, it's kind of nerdy, but it's kind of fun, is that, okay, if the local roads are prime numbers, which are things like two, three, five, seven, like small numbers, then the roads that connect them are when you multiply. So if I'm on route three and I want to get to route seven, I'll take route 21. If I'm on route three and I want to get to route five, I'll take route 15. And the cool thing is with prime numbers, there's kind of this guarantee that 15 can only be reached by three and five. So this is sort of a math properties that they say numbers have a unique prime decomposition. It sounds so nerdy, but it basically just means that there's only one set of prime numbers that will get you to that number. So yeah, like 15 is only reachable by three and five. So it's kind of like, whoa, so like if we wanted to, we could have these other roads that were labeled. So you could even without looking at Google say, okay, I'm on route three, I'm going to look for route 15, and that'll put me on route five. Great. Or maybe, you know, and who knows, maybe there's other properties, like I'm going to be sneaky here, maybe there's other properties that we can use as well. And so I love this intuition of just the number system has all this knowledge in it. And it just knowing even odd is enough, like I can get around the country with even odd, like left to right, north south, I can drive from Seattle to Miami without knowing anything, or even to Texas. I could say, okay, maybe I'll go halfway through, I'll go on I 90 about halfway. And maybe it's I, I don't know, 45 or 35 or something, which takes me not to Texas. So I could just navigate in my head without knowing anything about like the actual roads. And so numbers, there's all this information there that we can sort of pull out. And so this is kind of information theory, which is, yeah, like, you know, assigning the properties and like programmers uses with like bits, right? You have like a like a eight bit number and each bit represents some property. And you say, okay, like the color or something is on or off as a first bit. And if it's, you know, left or right as a second bit. So you sort of cram all these properties into the number. And that's sort of what we've done with the highway system. That's so interesting. You know, you could use it even further. If you start, if you apply the same concept, right? So if we take those properties and let's say a company like Google and maybe they've done this, but to route from where you are to another location, they use those properties rather than using something like edge finding or like rather than actually running all the routes. So that's to determine, you know, what is the next best turn? They use that numbering system to say, I know for a fact that if you want to go from here to, you know, somewhere a thousand miles to the west, that most likely you want to hit these particular numbers. Exactly. And then they can, they can derive only from a number graph rather than looking at math, you know, a map data. They could derive from the number graph the possible routes and then eliminate a bunch of computing problem, right? It's a really huge opportunity. And it's just because we used some kind of encoding of information so that we could rely, it's like a protocol. We rely on that information being encoded in this particular way. So that instead of observing and re-measuring, we're using, it's like memoization almost, we're memoizing the fact that these two roads connect in the number. That's very interesting concept. Exactly. You're kind of pruning your search space because you can maybe optimize the rope, but you know that in general, you don't need to look at every possibility. You can say it's going to be an east west and it's going to be probably in the 90s because we're in Seattle or something. So yeah, that's that's actually, I didn't think about the rope planning element of it, but you've basically, because you have the grid system, you don't need to do this pathfinding as a first pass anyway. Oh, that's really cool. In particular, if you can get the Latin long of the two endpoints and determine how far these away from each other, then you can say it's like a 99% likelihood that you're going to take an interstate. And so then you start eliminating things. I'm sure if we were to talk to somebody on the Google Maps team, they'd be like, well, yeah, of course, we'd, but, but discovering this stuff is really enlightening, isn't it? Exactly. And this is the kind of exploration that I hope, programming and math, it's kind of this what if it's like, oh, what if we added more properties to the numbers? And what if we, and the thing is like decimals, maybe there's, you know, 95.1 and 95.2, kind of like, you know, radio stations, but maybe that point one decimal can mean something. Maybe it means it's like the number of lanes in the highway or the speed or something. Like you could have all sorts of properties encoded. And so it's just really fun to think about. And I think this is when people talk about, you know, everybody should learn to code and so on. I don't, I personally don't know if it's that necessarily. I think it's that everyone should, it would be nice if people had more of a programmer's mindset where you don't know, you don't need to know JavaScript or something. It's, you know, the average person doesn't need to create things, but having a mentality, which I think programming gives you that, oh, I have this information and what can be fit? And, oh, what else can we do? I mean, most people, you know, they're familiarity with systems, because it might be the highway system or, or maybe the library, you know, do we decimal system or something? That's kind of the extent of it. And I think programming, you learn sort of the ins and outs that you have a bite and you have a binary number. And there's all these little properties you can put in. And so like an ISBN number or other things can be, you know, maybe they're encoded in a way that has all these useful properties. And instead of just being an auto-incromiting ID, there's all these things that you can add to it. And I think that's sort of like the intuition that I hope people get from programming versus the specifics of like a four loop or something. I mean, for most people, I don't think that's that useful. It's more, hey, can we be structured about how we approach things? Listening to today's episode of Developer Tea, my interview with Kalid Azad, Kalid is such a great thinker. And hopefully you were inspired by him like I was. Thank you again to today's incredible sponsor, Headspace. If you are not meditating yet, then I would recommend you go and check this out. Especially if you haven't meditated because you thought it looked weird or it looked too spiritual or something like that. There are plenty of people of all different beliefs, all different backgrounds that are using Headspace to improve their mental health and even their physical health. There's some studies that show that meditation can improve even your physical health. So go and check it out headspace.com. If you're interested in working for a company that has mental health at the front of their vision all the time, then go to headspace.com slash join dash us, or you can get a spec out of them slash headspace and go directly to that job page for Headspace. Thank you again to Headspace for sponsoring Developer Tea. If you don't want to miss out on future episodes, make sure you subscribe. And I haven't asked for these in a while, but I would love to hear your reviews. You can always go and leave a review on iTunes. Thank you so much for listening and until next time, enjoy your tea.