Crash Course: Ch. 3 - Exponential Growth & Ch. 4 - The Power of Compounding by Chris Martenson

in the crash course we will learn a few foundational key concepts none, are more important than exponential growth understanding this will greatly enhance our chances to form a better future here's a classic chart displaying exponential growth our chart pattern that is often called a hockey stick we are charting an amount of something overtime the only requirement for a graph to end up looking like this is that the thing being measured grows by some percentage overt each increment of time the slower the percentage rate of growth the greater the length of time we need to chart in order to do visually see this hockey stick shape another thing i want you to take away from this chart is that once an exponential function turns the corner even though the percentage rate of growth might remain constant and possibly quite low the amounts do not day pile up faster and faster in this particular case you were looking at a chart of something that historically grew at less than one percent per year is world population and because it is only growing at roughly one percent per year we need to look at several thousands of years to detect this hockey stick shift the green is history and the red is the most recent UN projection of population growth for just the next 42 years certainly by now math minded folks might be getting a little uncomfortable because they might feel i'm not presenting this information in a classical or even very accurate way where mathematicians have been trained to define exponential growth in terms of the rate of change we're going to focus on the amount of change both are valid it's just that one way is easier to expresses a formula and the other way is easier for most people to intuitively grasped unlike the rate of change the amount of change is not constant it grows larger and larger with every passing unit of time and that's why it's more important for us to appreciate than the rate this is such an important concept that i will dedicate the next chapter to illustrating it. also, mathematicians would say that there's no turned the corner stage of an exponential chart because this is just a artifact of where we draw the left-hand scale that is an exponential chart can nearly always look like a hockey stick in every moment in time as long as we had just left axis properly. but if we know the limits or boundaries of what we are measuring then we can fix the left axis and the turn the corner stages absolutely real and vitally important for example the total carrying capacity of the birth for humans has thought to be somewhere in this own give or take a few billion because of this that turned the corner stage is very real not an artifact of graphical trickery the critical takeaway for exponential functions the one thing i want you to recall relates to the concept of speeding up you can think of the key feature of exponential growth either as the amount that is added growing larger over each additional unit of time or you can think of it as the time shrinking between each additional unit of amount added either way the theme is speeding up to illustrate this using population if we started with one million people and set the growth rate to a measly one percent per year we'd find it would take 694 years before you achieve a billion people but we'd be at two billion people after only a hundred more years while a third billion would require just forty one more years then twenty nine years than twenty-two and then finally only eighteen years to add another to bring us to six billion people that is each additional billion people took a shorter in shorter amount of time to achieve here we can see the theme of speeding up this next chart is a of oil consumption perhaps the most important resource of them all which has been growing at the much faster rate of nearly three percent per year so we can detect the hockey stick shape over the course of just a hundred and fifty years in here too we can fix the left axis with some precision because we know with reasonable accuracy how much will the world can maximally produce so again having turned the corner is an extremely relevant an important event to us and here's the US money supply which has been compounding it incredible rates ranging between five and eighteen percent per year so this chart only needs to be a few decades long see this hockey stick effect and here's worldwide water use species extinction fisheries exploited and forest cover lost each one of these is a finite resource as are many other critical resources and quite a few are approaching their limits and here is the world you live in if it seems like the pace of change is speeding up well .. that's because it is. you happen to live at a time when humans will finally have to confront the fact that our exponential money system and resource use, will ecounter hard physical limits. in behind all of this, driving every bit of every graph - is the number of people on the surface of the planet taken one of the time anyone of these charts could command the full attention of every earnest person on the face of the planet but we need to understand that they are, in fact, all related and interconnected they are all compound graphs and they're all being driven by compounding forces to try and solve one you need to understand how it relates to the other ones that you see as well as others not displayed here because they all intersect and overlap the fact that you live here in the presence of multiple exponential graphs relating to everything from money to population to species extinction has powerful implications for your life and the lives of those who will follow you it deserves you're very highest attention let's move on to an example that will help you better understand these graphs please join me for chapter four compounding's the problem thank you for listening the purpose of this meeting presentations to help you understand the power of compounding it's something such as a population, oil demand, a monry supply, anything steadily increases in size as a proportion of its current size you get a graph that looks like this hockey stick said more simply if something is increasing over time in a percentage basis it's growing exponentially using an example drawn from the magnificent paper by doctor albert bartlett let me illustrate the power of compounding to you. suppose i had a magic eye dropper and I placed a single drop of water in the middle of your left hand the magic part is that this drop of water is going to double in size every minute at first nothing seems to be happening but by the end of the minute that tiny drop is now the size of two tiny drops after another minute you now have a little cool water that is slightly smaller diameter than a dime sitting in your hand after six minutes you now have a blob of water that would just fill a thin bowl suppose we take our magic eye dropper to fenway park and right at twelve o'clock in the afternoon we place a magic drop way down there on the pitcher's mound to make his really interesting suppose that the park is watertight and that you are handcuffed to one of the very highest bleacher seats my question to you is this how long do you have to escape from the handcuffs days ? months ? years ? how long would it take we'll give you a few seconds to think about it the answer if you have until twelve forty nine on that same day to figure out how you get out of those handcuffs in less than 50 minutes are modest little drop of water has managed to completely fill fenway park now let me ask you this at what time of the day would fenway park still be ninety three percent empty space and how many of you would realize the severity of your predicament any guesses ? the answer is twelve forty four if you are squirming in your bleacher seat waiting for help to arrive by the time the field is covered with less than five feet of water you would now have less than five minutes left to get free and that right there illustrates one of the key features a compound growth the one thing that i want you to take away from all of this with exponential functions the action really only heats up in the last few moments we set our seat for forty four minutes nothing much seem to be happening and then in five minutes bang the whole place was full this example is loosely based on a wonderful paper by doctor albert bartlett that clearly and cleanly describes this process of compounding which you can find in our essential reading section doctor bartlett said the greatest shortcoming of the human race is the inability to understand the exponential functions and he's absolutely right with this understanding you'll begin to understand the urgency i feel there's simply not allot of maneuvering room once you hop on the vertical portion of the compound graph time gets short this makes compounding the first key concept of the crash course now what does all of us have to do with money and the economy and your future ha ha i can't wait to tell you let's go find out