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

0 (0 Likes / 0 Dislikes)

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