 Hi, this is Gichu. Welcome to ASMR Math. Now, if you were following the math videos, you'll know that I've said this a lot, but basically mathematics is a language, it's a tool, just like all languages are, and being a unique language, it gives you a certain perspective on things that you might not otherwise have, right? And I've mentioned this before, I guess, I think the first place that I heard this was through Robert Anton Wilson, who was quoting someone else mentioning that you know, some people say it's easier to talk about the concept of relativity, relativity in quantum mechanics in Swahili than it is in English, because Swahili has certain words that really can't be translated well into English that are suited to talk about quantum mechanics, quantum physics, right? Now, I don't know if that's true or not, because I don't speak Swahili, and I don't know anyone who does, so I haven't come across anyone that does, that I can ask them this question if that's true or not. But I know that to be the case through, you know, a couple other languages that I speak and through people that have talked about, and through mathematics. Now, what I want to do in this video is share with you a certain perspective that math gave me on a problem or a life situation that I've always wanted to figure out why this was the case, but I was never able to do that until I looked at it through the lens of mathematics, and all of a sudden it just sort of It was one of those wow moments where I sort of went, you know, did a double take and I looked at it and it was extremely simple, but it blew me away anyway, okay? And the concept I used to understand this concept in life, the concept of mathematics that I used to understand this concept of life, was just simple ratios, okay? Now, this this problem, this situation that has always, or for as long as I can remember, intrigued me, was time, basically trying to get a handle on what time is, and if you've watched one of the previous videos I put out, and we're talking about the speed of light and why we can't travel, the speed of light, and we talked about Einstein's paper of general relativity on the electrodynamics of moving bodies, I guess. I mentioned this, I think towards the end when I guess the credit part was coming off or something like this, where I've been really curious about time, and one thing if you're, you know, I'm not sure how old you are, if you're, you know, in your teen years or if you're much older, this is something that everybody experiences, but everybody, as far as I know, only experiences it during a certain period in life, and the sensation that really triggered this for me, the first place that I remember wanting, you know, trying, wanting to understand this, was when I was in my teens, and in general, when I was sitting in a classroom, because if you're sitting in a classroom, if you're, you know, when you're growing up as a kid, maybe it was preteen, I guess, elementary school, that's when it was really dominant, I believe, in my life, is basically when you're growing up, when you're going to school, as far as I know, everybody's experienced this, where, you know, you're sitting in a classroom and you're looking at the clock and you're bored out of your mind, and five minutes seems like that is taking forever, right? Really, like even now, when I think about those moments, and I remember sitting there going, just watching the seconds tick by, and you're, you're just an awe that five minutes could take so long, right? And as I grew older, what happened was, that experience became less and less, and something associated with that experience is procrastination, where in general for me, anyway, I used to procrastinate a lot when I was younger, because I believe time was moving slower, right? The experience, the sensation of time was slower, hence procrastination. As I, you know, got older, and getting older, hopefully getting a lot older, much, much older, that sensation has diminished, has reduced, has dampened down to a level now that I rarely ever experienced that sensation, where time is moving very, very slow, or or I'm procrastinating, and in general, I don't really procrastinate anymore, right? So the perspective that, that sort of a mathematical perspective that I took towards this, trying to wrap my head around this, okay, was using ratios to look at that time difference, the sensations that I've had when I was younger as compared to the sensations I'm having with time as you know, as of right now, and I'm not sure what it's going to be in the future, but I'm curious to find out, right? And what I did was look at it through the mathematical lens, mathematical perspective, and I used ratios and what I'm about to talk to you about, this is you know, something that's been with me, part of my toolbox of teaching mathematics to almost anyone, right? I usually bring this concept up because it's it's intriguing, it's a wow moment for me, and I love sharing it, and it, you know, it really doesn't matter what level of mathematics it is that you know, okay, because this will make sense to you no matter what, so I use this concept for people who really aren't interested in mathematics, where I want to get them excited about math, okay, and I use it with people who are sort of you know, neither here nor there, and they're just doing it for, you know, the mechanic, you know, just sort of monkey-seeing, monkey-do, that's the that's the education system that we have right now, right? So they're sort of following the procedures and doing what it is that they're doing, you know, sometimes I just want to plant a seed for maybe future if they are interested in this, and I love really deep into this with students that are, you know, have a pretty good grasp of mathematics in there, they're always trying to go more complicated math, and you know, bring this up, and I sort of go, okay, you can start off with a simple concept and build on it, right? So what we're going to do right now in this video with this long-winded introduction is we're going to use ratios to understand time, to have a grasp of time, right, and basically this relates to life, death, and sort of, to me, I took it to the level where try to understand what the concept of borrowed time is, right, living on borrowed time. So let's take a look at this thing. Now, if we're, if we want to see the power of mathematics, right, let's start off with the system, the setup right now as you being a 15-year-old, me being a 45-year-old, and someone else being a 90-year-old, and let's take a look at how the perception of time, how our perception of time will vary depending on how old we are, right? So let's take, let's take, let's use purple. Let's see if the purple is okay. Oh, yeah, this is a nice color. Okay. So let's say we have three people, right, a 15-year-old, a 45-year-old, and a 90-year-old, okay? And let's take one week out of their lives, right? So what we're going to do, instead of taking a look at minutes, seconds, you know, days, right, or months or years, let's narrow our calculations now to one week, right? And I've, you know, I sort of, instead of trying to punch everything into a calculator, what I did is, you know, I did, you know, I created my spreadsheet and did the calculations and everything, in decimal form, and we can definitely do this in fraction form as well. Initially, I was going to do it in fraction form, but, you know, if you want to understand how to use fractions and stuff, we talked a lot about this in the language of mathematics of how to deal with fractions and what's the most important thing you need to know about fractions and stuff like this, right? And we did this in series one, and we did parts of it in future series, and we're going to continue this in series four of the language of mathematics where we're talking about units and ratios, right? And it's an incredibly powerful concept. And, you know, another, I guess, point that I'm going to mention is, coming out of high school, right, the most important thing, you need to have a really good grasp of these fractions, ratios, your units, right, functions, and functions are just an extension of ratios, right? So if you really have a really nice grasp of ratios, what ratios mean, how to deal with ratios, you're basically set for 95, 99% of the mathematics you're going to use in everyday life. Okay, so if you're only interested in math, you need to learn to be able to function in society, to be able to function in a world and almost do anything you want to do, learn your ratios, right? And this is what we're going to do right now. We've talked a lot about this in the language of mathematics already, right? So let's take one week for each one of our subjects or for us, right? So one week from 15 years, one week from 45 years, and one week from 90 years. Now what we should do, because these are in years, these are in weeks, what we should do is convert everything to the same units. That way we can get a direct comparison of things, right? So instead of putting one week here, or 15, 45, and 90 years, I'm going to convert 15, 45, and 90 to years to what they are in weeks, okay? So let's kill the weeks here, right? Because this is a week's roll. What we're going to do is we're going to convert 45, or 15 years into 15 weeks. And all we're going to do is multiply 15 by 52, because there's 52, you know, plus and minus a little bit, 52 weeks in a year, right? So 15 times 52, I did this already in the spreadsheet. So I'm just going to write them down. It's going to be 780 weeks, right? So 780 weeks, 45 years is 2,340 weeks. 2,340 weeks. And 90 years is 4,680 weeks, right? 4,680 weeks, okay? So what we're going to do right now is take one week out of each one of these people, right? So one week gone, one week gone, one week gone, right? So what we can do right now is let's take a look at how this 15-year-old perceives one week to be. Let's take a look at how this 45-year-old takes one week to be and how the 90-year-old takes one week to be, right? Relative to what they've lived, right? So one week out of 780 weeks, because that's what we're doing. We're taking one week out of 780 weeks. It's going to be one divided by 780, right? One divided by 2,340, and one divided by 4,680, okay? Those are our numbers. And all we do is just punch this into a calculator. This is a fraction. One divided by 780 comes out to .00128. So 0.00128, okay? This one comes out to .30, so 0.00043, okay? And the 90 becomes .0000021, okay? That's what one divided by 780 is. That's what one divided by 2,340 is. And that's what one divided by 4,680 is. And we can convert these to percentages, right? So all we do to convert to percent, we go boop boop, move this over to that small places, same with here. So this becomes 0.128%. And what that means is one week out of 780 weeks, one week out of 15 years is .128% of that person's life, right? What they've experienced so far. This is 0.0243%, and this one bring 2 decimal places over, 0.021%, right? So one week out of a 15 year old's life is .128% of their life. One week out of a 45 year old's life is .034% of their life. And one week out of a 90 year old's life is .021% of their life, right? And if we do a comparison between what one week feels like to a 15 year old is compared to what one week feels like to a 45 year old. Well, all we got to do is take this and divide it by this. Or the other way around, you take this and divide it by this. If you take this and divide it by this, you're going to get 3. If you take this divided by this, you're going to get .33, right? And what those numbers mean is if we take .128 divided by .03, 043, that's going to give us 3. That means one week for a 15 year old, relative to what they've lived is 3 times longer than what it feels like for a 45 year old. And it ends up being 6 times longer than what it feels like for a 90 year old, right? Because a 90 year old has lived 6 times more than a 15 year old and a 45 year old has lived twice as long or 3 times as long as a 15 year old, right? So the multiplication factor from here to here is 3, right? And for the 15 year old, it's 3. For the 45 to the 90 year old, it's 2, right? Let's be consistent with this. Let's write it out. So if we go from here to here, we multiply this by 3. If we go from 45 to 90, we multiply this by 2, right? Because it feels it's double the lifespan, right? So one week, if we take this and divide it by that, we're going to get 2. Or, yeah, we're going to get 2, right? So what that means is one week feels twice as long. Or how do we do this? This divided by that is 2. So one week is twice as long, feels like twice as much the experience for a 45 year old as it does for a 90 year old, right? And if we want to go from 15 to 90, we go 3 times 2 is 6. So 15 to 90, we multiply by 6, right? So the ratio of what one week or one amount of time, whatever the unit might be, what it feels like for 15 year olds compared to a 90 year old is 6 times the difference. A 15 year old, whatever the unit of time is right now is weeks, feels 6 times longer or contains 6 times the information of what they've lived, right? Relative to a 90 year old, right? And this should make sense, right? It's pretty intuitive because a 45 year old is 3 times older than a 15 year old, right? So one week that a 45 year old has experienced, well, a 15 year old hasn't lived that long, right? So it feels shorter than a 15 year old, contains, you know, there's more memory with a 45 year old, right? So that sort of feels intuitive, right? That's the first step towards this, right? Now, this assumes to a certain degree, if we want to expand this, that we could take this to the next step and, you know, take it to a multiple of 15, we could take it to 150, we could take it to 100, we could take it to 180, we could take it to any number we want. But us human beings, we don't live that long, right? Not as far as we know. The oldest person is, I think recorded as 120s or 30s or something like this, right? So there's a lifespan associated with us, right? So this makes sense because it's sort of a linear, multi-poligas scale, it keeps on going, right? Now, if we do this comparison, when we put a limit on how old we can be, then the picture changes, right? It becomes a little different. It becomes a little bit more intense, right? So let's erase all this, okay? Let's kill all this and add to how old we can get. Now, for the next sort of analysis, next step, you know, taking a step up in complication, trying to appreciate the power of mathematics and what ratios allows us to do. Instead of looking at the age difference between the 15-year-old, 45-year-old, 90-year-old relative to the life they've had, right? Let's look at this thing relative to the life they have left living, right? So what we're going to do, we're going to add an age limit to this, a maximum lifespan, right? And let's assume that maximum lifespan is 100 years, okay? So we're not going to measure things based on from birth this way. We're going to measure things based on death this way and not how much life they've lived, right? Right, relative from birth to how long they've lived. We're going to measure relative to how long they have left to live, right? We're going to measure it based on a 100-year time limit of how many years, or for our case because we're working in weeks, how many weeks each one of these people has left to live. How many weeks we have left to live, right? So let's take a look at the 15-year-old, 45-year-old and 90-year-old relative to the weeks they have left to live, right? So 15-year-old, they have 85-years-left to live, right? So let's convert this, first of all, 15-year-old to 85-years-left to live, right? A 45-year-old is 55-years-left to live, right? And a 90-year-old is 10-years-left to live. Now let's convert this, these, to weeks-left to live, because we're working in weeks, right? So weeks-left to live, again, I've done, you know, I'm looking at my spreadsheet. So 85-years, right, in weeks becomes 4,420 years, 4,420 weeks, right? 4,420. A 45-year-old is 2860, 2860. And a 90-year-old is 10 weeks or 10 years, which is 10 times 52 is 520 weeks left to live, right? And what we're going to do now is take a look at one week, you know, take one week out of each sets of these, right? So what we're going to do, we're going to go 1 divided by 4,420, 1 divided by 2860, and 1 divided by 520, right? And what that's going to give us, again, it gives us decimals. This is going to be 0.0023, right? But what I'm going to do is I'm just going to convert it directly to percentages, right? Because we already converted decimals, right? Just to save space here because we're running out of space. So that becomes to 0.023% of a 15-year-old's life, right? So if they have, if someone has 85 years to live, if they're 15 years old, they have a lifespan of 100 years, then this person has 85 more years to live. That's a long time to live. And you got 4,420 weeks, right? That you can enjoy yourself. That's 4,420 weekends, if you want to think of it that way. And we're going to take one of those weeks out. That means 0.023% of their life is taken out. Their expected life, right? For a 45-year-old, it becomes 0.035%. Okay? And for a 90-year-old, it's 0.192%. Now, when we did it last time, we did it from birth to what they're expected to live, right? And that was, you know, a multiple of 3, a multiple of 2, and a multiple of 6 from 15 to 90. But the multiples now change, okay? Because there's a limit to how long you're going to live. So, relative to a 15-year-old, one week out of a 15-year-old's life, if we're looking at it from the death perspective, is 0.023% of their life. For a 90-year-old, it's 0.192% of their life. The ratio, the comparison between a 15-year-old and a 90-year-old, this multiple is now 8.5, right? So, it changed. So, the multiple from here to here, right, is going to be 8.5. From the 15-year-old to the 45-year-old. Oh, I can't believe I did this calculation. From a 15-year-old to a 45-year-old, the multiple is only 1.54%. Oh, sorry, 1.54. That's the multiple, right? So, this 0.023 to 0.035, this multiple here is 1.54 times, right? So, I shouldn't really put these down here, because this multiple, let's keep these numbers, these multiples, still at the ratio of birth. This was 6 before, right? This was 3, and this was 2, right? Now, the multiple from here to here is 1.54. The multiple from here to here is 8.5. Now, unfortunately on my spreadsheet, I didn't do the multiple from here to here. Should we do this? Let me check this out. Let me bring out the calculator. So, let's go 0.192 divided by 0.035. This means 5, and the multiple here from here to here becomes 5.5, really. So, the multiple here is, let me make a little bit more room here. This multiple here is 5.5. And if we want to do a check, all we got to do is multiply this times this. And that should come out to about 8.5, right? So, we can go 5.5 times 1.54. Because it wasn't really 5.5, it was a little bit more. So, I'm just rounding. So, if I'm going to round this, this one I should keep to be consistent and make this 1.5 instead of 1.54, if I'm only going to round to 1 decimal place, right? So, times 1.5, right? So, what's happened here is we've gone from a simple intuitive direct connection of just multiples of the originals to something with a limit. And now, this becomes an exponential. Because the closer you get to your age limit of 100 years, right? The growth or the decay, whichever way you're looking at it, right? The difference, the ratio, either goes up exponentially or goes down depending how much time you have left to live relative to what you've lived to vice versa, right? Because ratios, you can always look this one way or another way, right? You can go to a store if you're buying chips, for example, or if you're buying anything that's per gram, right? Some stores have it based on dollars per gram. Some stores have it based on grams per dollar, right? So, it sort of switches over and that's what we're doing right now, sort of giving you the perspective right now as a multiple of what it would be relative to a 15-year-old, right? But if we take this, 100-year-old, and I actually expanded that because we're starting to get curious on this, right? So, if we look at it to someone who has, let's say, where is it, 90-year-old, 95-year-old? If we went to a 95-year-old, a 95-year-old only has 260 weeks to live. So, relative to the amount of time they have left to live, one divided by 260 is 0.00385 and that's 0.385% of their life, right? Which is 17 times the 15-year-olds, right? So, one week for a 95-year-old is 17 times more precious than what it is for a 15-year-old, right? It's, you know, for a 45-year-old one week is only 1.5 times as precious as it is for a 15-year-old, but 8.5 times as precious for a 90-year-old relative to a 15-year-old, right? And for me, when I looked at it from this perspective, when I was trying to wrap my head around the concept of time, what time meant, why time is not absolute, to a certain degree, the way we experience time, our perception of time is not absolute. There are times where, you know, the passage of time seems so, so, so slow. And then there are times where the passage of time, you blink and it's gone. And if there's any bit of advice I can give anyone that I do give advice to people is, if you have friends, have friends from all walks of life and from all ages of life, right? Because as soon as you have friends that are, you know, more than just your age group, which is one of the problems we have in our education system, we're almost grouped together based on age, not based on likes or dislikes or experiences or what they want to do or what they don't want to do, right? But that's going off on a tangent, a different thing, right? But if you ever have the opportunity, right, make sure you interact with people from all walks of life, from all age groups. Because once you do that, you have a better, fuller understanding of time. Because most elderly people or older people you talk to, one of the first things they tell you is, you know, a blink of an eye was over, right? It's done, right? They can't believe that they were, you know, for a 90-year-old, 15 years, when they were 15 years old, seems like only yesterday, right? But for a 15-year-old, when you talk to them, if someone or someone younger, time is going so slow, there's so much procrastination and they could, it's very hard for them to grasp them being 45 years old or 90 years old. You know, some people, you know, when you talk to them when they're teenagers, and I have this perception as well, is 30 years is, you know, when you're 30-year-old, you're old. And then when you turn 45, you look at 30-year-old, you're young, right? And for a 90-year-old, a 45-year-old is a baby. They're just starting their life, right? And this, to a certain degree, shows it, right? Because one week for 45-year-old, there's only one-and-a-half times the life experience left, right? One-and-a-half times more precious than a 15-year-old. But as soon as they get older, the curve actually goes exponential, right? They actually graph this thing, or printouts are in the best, they then, you know, set it up to graph it, but it's an exponential, right? And this curve here, you know, it just keeps on going like this. It becomes, you know, something like this. It just goes up and up. And we talked a little bit about this, because if we set our age, maximum age to be 100 years old, then that's sort of our asymptote, the limit that we've set. And we talked about this when we're talking about division by zero. Because when someone turns 100, right? They don't have any more life to live, right? They got zero years to live. So if you divide by zero, right? Because this would be zero. Someone at 100 years, it's a zero here. They got zero weeks to live, right? So if you're going to take one week out of their life, you got one divided by zero. You can't divide by zero. That's an asymptote, right? That's what we talked about when we talked about limits and asymptotes, right? Infinity and zero, right? They don't have any more life to live, right? That becomes an asymptote. It's an exponential curve, right? So the picture totally changes. If you look at this situation, the scenario, relative to from when you were born, how much life you've lived, as compared to relative to when you're going to die, how much life you have left to live, right? And this is for just humans, right? And keep in mind that life expectancy varies a lot, depending on where you live, what country you're from. And I've looked at, I printed these off. I went to Wikipedia and printed off the life expectancy charts and stuff like this, and it varies a lot. And there is no country in the world that has a life expectancy of 100 years, right? The majority of the country's best one was... The highest ranking one was... Depending on which organization's data you're looking at, some of them, Google was saying Monaco was the highest, which is 89 years old, but maybe that's because that's where a lot of people retire, right? Very, very small place in Bento Monaco, very, very small place, right? But most of the charts had Japan as the highest life expectancy for both sexes being together as 83.7 years, right? For females it was 86.8, for males it was 80.5. And this is life expectancy from birth, right? And then there's another measure in the same charts, which is health-adjusted life expectancy, which is how long are they expected to live a healthy life, right? So for both sexes, life expectancy was 83.7 for Japan, but for health-adjusted life expectancy where they expect to live a healthy life was 75. So the gap there was basically nine years, right? So nine years of an unhealthy life if you're getting older. And these numbers changed according to what country you looked at. Canada for both sexes was 82. Iceland was 82. Well, if you round up 83, Mexico was 87. If you're rounding up, China's 76. The United States was 79. Cuba was 79. The same, right? Iran was 76, right? That's sort of the high and mid ranges. What else do we have here? Brazil was 75. Armenia was 75. And you can go down to, you know, look at the lower ranges. And this one was, you know, there's a ranking of 183 countries. You know, they had Sierra Leone at 50. You know, different countries, South Africa is 63. And these numbers are sort of skewed a little bit, right? Because these are life expectancy from birth, but that data is totally skewed based on infant mortality, right? So you can take a look at this stuff. Life expectancy based on, you know, taking out infant mortality, right? So life expectancy after retaining adulthood. And these numbers get closer together. The ranges don't skew. So life expectancy isn't really the best measure, right? It's skewed by infant mortality, right? But you can take this concept and apply it to the life expectancy to any country you want to compare it to. And beyond that, you can take this same thing, the same type of data, the same ratio comparison and do a comparison based on, you know, life of a corporation, life of a country, life of a tree, of other animals, right? We live a fairly long time when it comes to mammals, right? But we don't live the longest, right? There are sea turtles that live longer than we do. There are parrots that live a very, very long time, right? There are jellyfish that are expected. You know, I believe, I didn't look into this a long time ago. There are jellyfish that scientists are taking a look at because, in essence, those jellyfish are considered to be immortal because they can continuously regenerate their cells, right? I don't know if the five of the scientists are correct or not, but they're expected to live, you know, long in a thousand years or immortal, basically. So there are scientists looking at the genetics of it, right? The traits of these jellyfish try to see what allows them to live a long time, right? So you can do the same comparison for things, you know, outside of the human sphere, right? Compare us to other species, to other cycles, I guess, right? You can compare it to the, you know, how long stars last, how long planets live, the ice age, right? Compare it to anything you want. And it becomes really, really interesting, you know, to the comparison for life, you know, life with the universe and just grow, expand beyond this little experiment we've done for us to grasp what the concept of time is and why time tends to vary, you know, the perception of time tends to vary with age, right? And it's pretty cool, right? And that's one thing I did for me anyway. When I started looking at time in this fashion, from the mathematical lens, it really answered a lot of questions for me. It really made a lot of things come to light and made me procrastinate less, right? And time really didn't grind to a halt anymore, right? It became more and more precious as I keep on getting older and older as we saw here, right? Because as soon as we had a limit, a lifespan for us, because everything has a limit, right? Everything changes. Everything has a lifespan. As soon as we had that, all of a sudden, time became more and more precious, right? So, again, procrastination less and less. And as far as how far you can take this, as far as, you know, the usefulness of this concept of ratios and stuff, this is incredibly powerful. This is really the first step we take when we do ratios on the path for us to do calculus because once we understand time, then we can start doing calculus. Because calculus for me, when people ask me, you know, what's calculus to you? For me, calculus is the introduction of time into mathematics. And as soon as you do that, you're looking at ratios, you're looking at the rate of change, right? Which is really what calculus is and what really this sort of exercise is the first introduction to it. I hope you liked. This was something that I really enjoyed doing. I really enjoyed teaching and I bring up as often as I can of a meaning to do this video for a long time. And I'm glad that we're getting it done now because, you know, some of the other videos we've touched on time a little bit and we've talked about ratios and we will continue to talk about ratios and functions at limits and asymptotes. That's it for now. I'll see you guys in the next video.