In today's episode, I interview a returning guest, Kalid Azad! Kalid is the creator of BetterExplained.com. Today's episode is sponsored by Headspace. Headspace offers you guided meditation that you can take with you, and does so in a beautifully made native app experience. Headspace is also hiring! Head over to https://Headspace.com/join-us to learn more about the openings.
In today's episode, I interview a returning guest, Kalid Azad! Kalid is the creator of BetterExplained.
Kalid's first interview
@BetterExplained on Twitter
Today's episode is sponsored by Headspace. Headspace offers you guided meditation that you can take with you, and does so in a beautifully made native app experience. Headspace is also hiring! Head over to https://Headspace.com/join-us to learn more about the openings.
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. part of the interview. Make sure you go back and listen to it. And we have interviewed Khaled before, so make sure you check out those first interview episodes as well. Khaled 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 Khaled. Every time we talk, my brain just fires on all cylinders and it gets me excited. So hopefully we'll do the same for you. Now I'm going to stop talking. We're going to get to our interview with Khaled Azad. Khaled, 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. Now 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. 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'd 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, 10 years later, the math hasn't changed. And so those things are, and that's, I wasn't that conscious of that. I kind of suspected, oh, okay, well, this will still be useful. But now that I've seen it, so basically, 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, it'll just keep generating things. So there's that kind of evergreen content or evergreen usefulness from the writing, and then also evergreen motivation. So one of my other subconscious realizations, I think, was that being motivated for a day isn't as important as being 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, it 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 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 blog or anything for 10 years is that you want to be willing to come back to it. And so, I can pull teeth and force myself to do something today. 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 epiphanies 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, you know, this is kind of an unscientific thing, right? Motivation is, as we've already obviously discussed a little bit in this interview, but motivation is really hard to quantify. Of course, you know, you can do something like the feelgood.txt. You can do something like the awesome jar. You can ask your friends what they, you know, 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, you know, do a light workout. And we're going to stick with that analogy, I guess, but it's better to do a light workout, you know, four times a week than to do the hardest workout of your life. And that's the best workout program that you'll continue doing. And that's the best workout for your whole life, one time, and then never go back to the gym. So, so view your learning process the same way. Like, 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, to continuously do something that bores you. And certainly at the very least, it's not very fun to do something that's, 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, you know, fast forwarding your brain down the road of what would happen in my life if I learned this thing? You know, 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? 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 I wrote over time. And so the first year I did a bunch, I think I 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. But and then in 2016, I did like 16 blog posts. So a little bit more than once a month. And so between 2015 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. Like I didn't have a negative association with coming back to writing. I was just like, 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, you know, we get sick. 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, as soon as you hear that, you don't want to come back. You might finish that workout and you're 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. Land blast. Boom. You don't want to come back. So I, I think I had subconsciously realized, like, I, I didn't cajole 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. Like it, 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. Um, I think the other one, this is sort of a, okay, this, this will be kind of a mixed epiphany. You know what? So the first one was sort of more about the site, um, in general and personal, this one will be a middle epiphany. And then the last one will be more of a technical one. So, uh, this kind of middle epiphany is I think the value of, um, empathy. And I actually, I think there's a recent, uh, podcast. Um, one of your podcasts was on this too. So I just think of empathy is this kind of. Honesty. Honesty about what's going on and just trying to connect to something is just, you know, human to human or, or, or programmer to 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 something that you find funny. Okay, great. Just put it in there. And then some people get it. Some people don't. Um, so there's sort of that warmth that I think that comes and it's this intangible thing. I mean, when you're reading a math article, 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. There's not a computer that's trying to read Wikipedia and analyze it. Right. Um, and so I think part of that too is, um, things like even like imposter syndrome, for example, I try to be pretty straightforward about things that were confusing. Right. Right. Right. Right. Right. Right. Right. Right. Right. Right. Right. Right. Right. 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 more, you know, I was super confused. And I, for some reason, the tutorials that I 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. And in math, there's so many things. It's, it's really funny because there's concepts in math that were debated for decades. Like the Fourier transform is 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 of 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 a 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 it confusing. I looked at the history. Yeah. It turns out it was a 30 year, you know, process. It was confusing. It was 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, 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, you know, it's just, so I try to. I try to do things for myself to kind of be honest about what's, what's working or not, or what I struggled with. And also to, yeah, when, when I'm trying to write, I try to connect with people just as a human being. And I think that it opens up because also there's sort of a tension to where 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 ridiculed or something. Right. And so I think 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, I might go over my three insight limit here, but Oh, that's fine. That's good. It's what we want. Exactly. I mean, I, I sort of see confusion as finding a, 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, we treat, I treat learning and confusion is that is that these are little issues that I can fix up. Oh, like this door isn't closing properly. Let's fix it 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 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, and like, 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, even though, you know, in some way you want to fix it. You want them to know, but you don't want them to know. Right. 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, 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 things, suddenly you're kind of hoping the evaluator doesn't notice the bug. And that's a really, you know, it's, 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 advance. Oh, 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. Yeah. So this is one of my, sometimes I get these little analogies. So, yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. 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 in your tool belt. And then eventually, once you have 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 great metaphor for learning, which is that, oh, I learned this concept, and it helps me unlock this other concept. And these two concepts together help me get this third concept. That's how I see math is, 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 Euler's formula, which helps me with the Fourier transform, for example. So you can basically get these little tools that help you versus attacking this really tough concept with your kind of standard weapon, which doesn't have any advantages. So it's like, oh. Oh, wow. So you sort of look forward to it. And of course, Mega Man has like 10 sequels, because people love it. It's like, oh, there's Tree Man and Fish Man. Every noun can be a potential ally. So you basically have all these sequels. People love playing Mega Man, and 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. You don't really win Tetris, right? You survive it until you lose. Yeah, everyone will lose Tetris. Everyone will lose. Exactly. 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, 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 or like a W shape. You'd be like, no, no, I don't want any more. It's hard enough already. More impossible. It's more impossible. It's more impossible. You're making it more difficult. But in Mega Man, you want more bad guys. So it's weird. In Tetris, you don't want more bad guys. Tetris would be great if it was just L shapes or just squares. That'd be perfect because then you feel okay. But Mega Man would be really boring with just one boss. And it's just like, wait, why in these two video games, one, I love the enemies, 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'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 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 even if you survive Tetris, what does it mean? I feel like you might learn a little bit of skill in the process, but you don't have like a two-step process. And so I think that's a really good way to get better. So to speak, you just, you kind of went through the gauntlet and that's it. 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 already, of course. I mean, the kid's not going to be able to do anything until he's at least, I guess, 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 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. I don't think that 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 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 learn super fast. Now, the biology, 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 was all it really functioned as in that class. I never really felt like I was a kid. I never really felt like I was a kid. I never really felt like I was a kid. I never 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, it was 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? And so I think that's a really important part of the study. We had to articulate all the way through rather than, you know, saying what, you know, multiple choice, 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 think that's a really important part of the study. 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 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. 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 language is a good example. Similarly, I took it in high school and a really good example. And so I took it in high school and a really good example. And so I took it in high school and a really good example. And so I took it in high school and a really good example. And so I took it in high school 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 the things you're 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 I, if you don't know the word for door, you could 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 them. And that's actually maybe my analogy brain going in 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. And then suddenly I hear the word and then it kind of, I'm, you know, a couple of times with that and it 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. Yeah. Getting someone to see, oh yeah. 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 languages, but 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, 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 math? And that's kind of like, when will I use math? And that's kind of like, 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, you 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 and blue is calming. So it's like, oh, okay. A circle has these properties and a square has these properties and a certain kind of equation has this property. And so when I'm trying to do something, I almost look at metaphorically, like I don't, 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, of one thing as a system of creation or as a system of understanding something else, like the idea of a circle. I mean, you, 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, 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. For a Spanish discussion, right? The same thing is true because you start learning how grammar is structured, right? And you start learning how, uh, how different languages use and, and, and how there's like a minimum, uh, uh, number of, 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, or property based things to inform the rest of your world. So today's episode, is sponsored by Headspace. If you don't know what Headspace is, uh, 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, uh, 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. And I'm going to talk a little bit about that in a minute. So today's episode, we're going to talk about 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, these are things that are not really, uh, 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 an iPhone or an Android app. You can find it in the App Store and you can try it for free. It's Headspace. 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. 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 a world-class engineering team. As I said before. With teams based in 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 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. They say we're teaching you how to learn or something. And while I appreciate the sentiment there. I feel like it's so vague. That it's really hard to. If I say we learn math because it helps us learn other things. Like I. That's often. You know math. 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. It's we're just going to move in a circle. Until we have a condition that breaks us out. And so that's. You're on a circular path. And then. Eventually. You go off on a 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. But say oh okay. This is. 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? When you're doing reps or 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'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. Uh oh. Like for most of us a parabola. Like I wouldn't say. Oh it's kind of like a parabola. Like a parabola. It's in the scary land of. Ah we had to memorize it. We don't really get it. But like. So I could keep going on. But once you have an intuition for something. It gets in that familiar circular territory. Now it's an ally. Like a circle is a math ally. Like you can use that in so many scenarios. Because you're 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 discovering a new color. 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. Like 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. I can't quite remember. But I think fuchsia is like a constructed color. Interesting. Yeah. It's one of these like. 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 a listener 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 interesting. It's almost like black is like the absence of color. Right. Right. So 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. Yeah. And I think fuchsia has 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. We're not excited about 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 look at problems as. Or. And when you. Look at skills as discreet from everything else. You're kind of missing the idea. Of how your brain works. Right. So. More than it being a discreet problem. Like there's a stain on the rug. A lot of the times. That we have problems. In our brain. Or not problems. But missing information. Or incomplete information. It's more like. The circuit breaker. Is cut. Or like there's a problem 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 a parabola. Or now that you have. One of my. Favorite videos. Or videos. Or articles. I 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. Okay. Yeah. All I remember is that it. 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. It. Has different implications. Into how you think. Even though I'm not. Sitting down. And doing. You know. Long form. Math calculations. To determine my. Retirement. It. I'm. 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. It's sort of. Oh man. It's almost like the theme. Like. Like in English class. You know. You read literature. And then we talk about the theme. So like you read a. 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 the deeper meaning. I mean. Acknowledging that you're going to forget. Most of the details. Like E. Like. Yeah. For most of us. 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. That's enough of an intuition. Just to. Put you in the right path. About 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 E can be used. Like. And so that's. Oh. What's. Half life. Oh. Half life. Exactly. And so. You had this very comfortable. Like. Oh. E 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 a line. Keeps the same progress. Every time. So you're getting. You know. Ten dollars. Forever. But. With your bank account. The more you have. The more you make. So now it's improving. It's ten. Then eleven. Then twelve. And so on. So. E. Like. You kind of intuitively know. Oh. It should be E. And not like a. 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. Formally trained. If you've. Taken an algorithm course. You look at. You know. Big O. Complexity. Right. You have. You know. Oh. I can't remember all the. Like. N squared. All these different levels of complexity. For algorithms. And. 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. There are certain algorithms. That do that. And. If you don't understand. You know. The way that those. You know. 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. A simple. Explanation. For something. That you. That confuses. So many people. What is a logarithm? Well. It's. It's the opposite of. Of a. 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. Of a graph. Or. Over the course of inputs. Rather. Oh man. And I need. Every. Little back and forth here. Is great. Because this is. Giving me more. 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. And 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. Hmm. 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. Ah. Yeah. So you can basically. Or like your stock market. Like it went from this. You know. The portfolio went from like. A thousand. To fifteen hundred. Over ten 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 have this sort of analogy. That like logs. Are like time. In a sense. And then. Exponents of the result. Of. What 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. That's good. That's good. Another. So we have this interest rate. So everyday logarithms. Well. Interest rates. Are basically a 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 count 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. Of the deal size. Oh wow. Yeah. Yeah. And 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 of magnitude. Yeah. The scale. Exactly. And the cool thing is. You're able to talk about. A huge difference. Like. Like 50,000. To. I don't know. 50 million. That's a big jump. But I 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 like 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. With 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. 50 to 100. Okay. Three to four. Ooh. Four to five. Hmm. Five to six. Ooh. That's a big jump. Yeah. 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 start. They explode. They. Basically say. The more I have. The more I make. And the more I. You know. The more I make. The more I have. And 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 Tetris. Like Tetris. Exactly. Like in Tetris. The more stuff. That's on the screen. It's even harder. You don't have as much room. And it gets harder. And harder. And harder. So. The 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 brakes on something. You. You. Put a logarithm on it. And suddenly. It's really hard. Like getting page rank 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. 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. It's harder to. It's really hard. So you sort of have this. Scale. And that's like. Oh wow. So. Explained in this way. Oh. It seems natural. It's fun. It's an ally. Versus. And you can see it in your life. Right. Yeah. Exactly. 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. 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. Two hundred pounds. Of body weight. Is. Only what. Point five percent. Of your. Of your body weight. But. A pound. Of. A hundred and fifty pounds. Right. Exactly. Is significantly more. And so. The. 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. From that one over X pattern. Because you're right. Like one pound over. Two hundred. Compared to one pound over. One ninety nine. Then is one pound over one ninety eight. And one. So. You. You. You. You kind of this. One over X pattern. And logs are basically derived from that. Where. As you go. Like. The additional pounds. It's more. More effort. Or. Or it's. It's harder. Also to. To take away. But once. Once you have so little to lose. Getting that last. You know. Five pounds out. Might be really hard. When you're one fifty. Versus when you're at two hundred. 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 two hundred 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. Two fifty or something. Let's say. So that's. You know. Twenty five percent of the time. They're. They're hitting the ball. And then a really good player is three hundred. And then an excellent player is like three fifty. And like an outstanding player is four hundred. And so. Adding fifty extra hits. It gets harder and harder. I don't. Yeah. I'm not sure what the record is. But. You know. If somebody was hitting five hundred. You know. Five hundred or a thousand. Superhuman. Superhuman. It's unheard of. So every extra hit. Gets harder and harder to. Increase your percentage of. 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. 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 things. Something. Something like the Olympics. Very rarely. Will you see somebody. Who's way out in front. Right. The. The slivers between. Superhuman. And. Incredibly good. That sliver is 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 Ferriss. But he was. Speaking with someone. About. Gymnastic training. And. The. The guy is a. He's. Trained a ton of. World champion. Gymnast. Gymnasts. Right. 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. The heavy. The weightlifting champions. Are like. A five pound. Plate. Difference. Or. A two and a half pound. Plate. Difference. And it's. It's so interesting. That we. Get so addicted. To massive changes. And massive progression. When really. At the. You know. At the top. Performing levels. Of most things. It's. It's very small. Differences. Yeah. And this is. This is great. And you know. So my. 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. You know. 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. You're kind of in a rut. You're in a circle. Hey. I'm kind of like. Progressing logarithmically. I would love it. If in the future. People just were that comfortable. Yeah. And that's. You know. My. My goal really. Is to help people. Reach that level of comfort. Where math. It's just a set of ideas. That. In addition to being. Metaphors. You can't actually compute with them. Yeah. Versus things 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 launch 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. Well. I guess I'll have to use the word tangent now. Perfect. Perfect. Okay. So let's. Let's shift into this. The. 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 would be good for. 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 are familiar with. The highway system. So like. You know. The 50 years it was developed. And they. Kind of put it on a grid. And. Unfortunately. Nobody. Nobody told me. Like the. 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 U.S. 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-5. Like in Seattle. There's I-5. 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. 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. Interesting. Going from. 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'll be. You know. 3,000 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-5. From Seattle to San Diego. And then take. I don't know. I-10. I guess. Because it's 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, south, east, 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. Ten. Fifteen. Twenty. So. 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. Two ninety-five. Three ninety-five. Like in Boston. There's one ninety-five. Two ninety-five. Three ninety-five. It's like. Oh. What are those? And so. If there's a three digit number. Those interstates connect to the bigger ones. So. I-95. Will connect to ninety-five. Two ninety-five. Will also connect to ninety-five. Three ninety-five. Will also connect to ninety-five. 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 can. It kind of connects to ninety-five once. So one ninety-five. Will kind of shoot off of ninety-five. But an even number. Like two ninety-five. Will actually loop back. Huh. 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 ninety-five. And then you have sort of a loop. Around the city. And that's kind of a. An even. So like four ninety-five. Or there isn't a six ninety-five. That I know of. But six ninety-five. Would also loop. And so it's like. Oh interesting. So just intuitively. You know. Okay. I'm on ninety-five. And I'm going to take one ninety-five. As my exit. One ninety-five. Is never going to hit ninety-five 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. All these properties. We're communicating 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 is it divisible by any other number? Five. A seven. But not nine. Nine is divisible by three and three. It's like. Oh. Wait a minute. Could we 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. Huh. 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. 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. Huh. So. Yeah. Like 15 is only reachable by three and five. Wow. Like. 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. And maybe. You know. And who knows. Maybe there's other properties. Like I'm going to be sneaky here. Maybe there's other properties. 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. I could go 45. Or 35. Or something. Which takes me down 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. Yeah. You know. Assigning the properties. And like. Programmers use this. With like bits. Right. You have like a. Like a. Eight bit. A number. And each bit. Represents some property. And you say. Okay. Like the color. Or if something is on or off. Is the first bit. And if it's. You know. Left or right. Is the 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. 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. Map data. They could derive. From the number graph. The possible routes. And then eliminate. A bunch of. 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 remeasuring. We're using. It's like. Memoization. Almost. We're. We're memoizing. The fact. That these two roads. Connect. In the number. It's very. That's great. 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. The rope planning. Element of it. But. You've basically. Because you have. The grid system. You don't need to do. This pathfinding. Yeah. Yeah. As a first pass. Anyway. Oh. That's really cool. In particular. If you can get the. The lat and long. Of the two endpoints. And determine. How far are these away. From each other. Then you can say. It's. It's like a 99% likelihood. That you're going to take. An interstate. And so. Exactly. 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. But. But. Discovering this stuff. Is. Is really enlightening. Isn't it? Exactly. And this is the kind of. Exploration that I. That I hope. You know. Programming and math. It's. It's kind of this. What if. It's like. Oh. You know. What if we added. More properties to the numbers. And. What if we. And. Another 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 that mentality. Which I think programming. Gives you that. Oh. I have this information. And what can we fit. And oh. What else can we do. I mean most people. You know. Their familiarity. With systems. Because it might be. The highway system. Or maybe the library. You know. Dewey decimal system. Or something. That's kind of. The extent of it. And I think programming. You learn sort of. The ins and outs. You have a byte. 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 incrementing ID. There's all these things. That you can add to it. And I think. Yeah. That's sort of like. The intuition. That I hope people get. From programming. Versus the specifics. Of like. A for 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 Khaled Azad. Khaled 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 are 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 go to spec.fm. 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.