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    Exponential Growth: Crash Course Chapter 3

    The most important driver of future trends
    by Adam Taggart

    Friday, July 4, 2014, 3:18 PM

Chapter 3 of the Crash Course is now publicly available:


Coming next Friday: Chapter 4: Compounding is the Problem

For those who simply don't want to wait until the end of the year to view the entire new series, you can indulge your binge-watching craving by enrolling to PeakProsperity.com. The entire full new series, all 27 chapters of it, is available — now– to our enrolled users.

Enrolled users can access the new series at www.peakprosperity.com/crashcourse

And for those who have yet to view it, be sure to watch the 'Accelerated' Crash Course — the under-1-hour condensation of the new 4.5-hour series. It's a great vehicle for introducing new eyes to this material.



In the Crash Course we will learn a few foundational Key Concepts. None are more important than exponential growth. 

Understanding exponential growth will greatly enhance our odds of creating a better future.

Here’s a classic chart displaying exponential growth – a chart pattern that is often called a “hockey stick”.   

We are charting an amount of something over time.    

The only requirement for a graph to end up looking like this is that the thing being measured grows by some percentage over each increment of time. 

The slower the percentage rate of growth, the greater the length of time we’d need to chart in order to 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 actual amounts do not. 

They pile up faster and faster. 

In this particular case, you are looking at a chart of something that historically grew at less than 1% per year.   

It is world population. And because it’s only growing at roughly 1% per year, we need to look at several thousands of years to detect this hockey stick shape. 

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 starting to get a little uncomfortable here because they might feel that I am not presenting this information correctly.

Where mathematicians have been trained to define exponential growth in terms of the rate of change, we are going to focus on the amount of change.  

Both are valid, it’s just that one way is easier to express as a formula and the other is easier for most people to intuitively grasp

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 is no  “turn the corner” stage of an exponential chart because this curve is just an artifact of where we draw the left hand scale.

That is, an exponential chart always looks like a hockey stick at every moment in time as long as we adjust the left axis properly.

But if you know the limits or boundaries of what you are measuring, then you can fix the left axis and the “turn the corner” stage is absolutely real and vitally important. 

This is a crucial distinction -- and our future depends on more of us appreciating this.

For example, the total carrying capacity of the earth for humans is thought to be somewhere in this zone, give or take a few billion.

Because of this, the “turn the corner” stage is very real, of immense importance to us, and not an artifact of graphical trickery.

The critical take-away 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 1 million people and set the growth rate to a tiny 1% per year, we’d find that it would take 694 years before we achieved a billion people.

But we’d be at 2 billion people after only 100 more years while the third billion would require just 41 more years.  Then 29 years, then 22, then 18 years to add another, and finally just 15 years for the next billion bringing us to 7 billion people.

That is, each additional billion people took a shorter and shorter amount of time to achieve.  Here we can clearly see the theme of ‘speeding up’.

This next chart is of global consumption of oil, perhaps the most important resource of them all, which has been growing at the much faster rate of nearly 3% per year.

We can easily detect the ‘hockey-stick’ shape over the course of the past one hundred and fifty years since we started powering our economy with petroleum.

And here too we can fix the left axis because we know with reasonable accuracy how much oil the world can maximally produce.  So, again, having  “turned the corner” is extremely relevant and important to us.

And here’s the US money supply, which has been compounding at incredible rates ranging between 5% and 18% per year. 

So this chart only needs to be a few decades long to see the ‘hockey stick’ effect.

And here’s world-wide 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.

This is the world we 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 consumption will encounter hard, physical limits.

And behind all of this, driving every bit of every graph, is the number of people on the surface of the planet.

Which continues to increase – to ‘speed up’ – exponentially.

Taken one at a time, each of these charts should 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 connected.  They are all compound graphs and they are being driven by compounding forces.

To try and solve one, you’d need to understand how it relates to the other ones -- as well as to many others not displayed here -- because they all intersect and overlap.

The fact that you live here, at this moment in history -- 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 your very highest attention.

Let’s move on to an example that will help you understand these graphs a little bit better.

Please join me for the next chapter: Compounding is the Problem.

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  • Fri, Jul 04, 2014 - 8:40pm



    Status: Silver Member

    Joined: Nov 25 2010

    Posts: 199


    This Is The One

    Chris and Adam, 


    Just wanted to let you know this is the section of the Crash Course that sucked me in years ago.  The charts really help explain the exponential function, and they bring it together in a way which forces the viewer to understand these things are happening NOW.  Your use of the charts emphasize how quickly things are changing in a measurable way.  For me, this part of your presentation hooked me in for the rest of it.  It accomplishes what you want it too.



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  • Sat, Jul 05, 2014 - 10:12am



    Status: Silver Member

    Joined: Sep 22 2010

    Posts: 615


    Finally watched the 4 episodes

    Chris and Adam.  A GREAT outcome.  This is the BEST EDUCATIONAL material I have yet seen.  Short, to the point, objective, excellent charts, gradually presented, comments added, etc.  When I first watched The Crash Course when it came out I was hooked back then. I immediately accepted your PERSPECTIVE on the macro-ecopolitical scene, as it was the best THAT MADE SENSE TO ME, after all my studies/research over the years. And since that time I truly believe that The COURSE is still my overarching method of understanding what's happening in the world: the three Es provide the framework for analysis and reasonable conclusions.

    It's difficult to totally express my GRATITUDE for your work/intentions/mission.  Hopefully millions will see all this information presented by the Information SCOUTS supreme!!    Warmest regards,  Ken

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  • Sat, Jul 05, 2014 - 8:59pm



    Status: Member

    Joined: Oct 07 2008

    Posts: 6


    Minor point could imply ignorance

    Your poster image for this chapter (and the video content) shows a hockey stick next to the graph, presumably to say this graph is an example of the "Hockey stick" shape the public have heard about elsewhere. You sadly oriented the hockey stick backwards. While the entire series is good, this immediately grabbed my attention because it might suggest you don't understand the origin of the term. It may seem minor, but I wanted to mention it as it might unsettle others who know you got this backwards.


    "The term "hockey stick graph" was coined by the climatologist Jerry Mahlman, to describe the pattern shown by the Mann, Bradley & Hughes 1999 (MBH99) reconstruction, envisaging a graph that is relatively flat to 1900 as forming an ice hockey stick's "shaft" followed by a sharp, steady increase corresponding to the "blade" portion."

    Minor point. Keep up the good work.

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  • Thu, Jul 10, 2014 - 3:28pm



    Status: Member

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    Posts: 183


    When will this new updated

    When will this new updated version be available on DVD? 

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  • Thu, Jul 10, 2014 - 3:36pm



    Status: Member

    Joined: Apr 18 2009

    Posts: 183


    Hockey Stick Orientation

    I had also imagined the hockey stick the other way around and was surprised to see it illustrated with a vertical orientation as opposed to a horizontal orientation. 


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  • Thu, Jul 10, 2014 - 3:52pm



    Status: Member

    Joined: Apr 18 2009

    Posts: 183


    Feedback on whole series?

    I am an enrolled member, have watched the whole series and have a few comments/ feedback for you, but do not see a comments section in the enrolled section. So I am wondering where to leave those comments? 

    Thanks- you did a fantastic job with it!

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  • Fri, Jul 11, 2014 - 9:53am

    SPAM_Matthew Blain

    SPAM_Matthew Blain

    Status: Member

    Joined: Oct 24 2010

    Posts: 11


    Reply from a Professor Emeritus


    Hi All,


    FWIW, another typical response from a "soul mate" last week. I may sound a little indifferent in my last comment (down page), but perhaps that's because I am. After nearly 10 years writing letters to folk I believed might help steer the Titanic, I'm well and truly in the couldn't-care-less camp these days (I'm the one sitting on the deck chair, watching the sun go down, glass of red in hand; what a beautiful sunset. What a shame...).





    PS. The original black and white video-of-lecture featuring Al Bartlett (not the color staged one) was my lightening-bolt moment!!




    Dear Matthew

    Thanks much for this, also for your earlier email at end of June which I've been getting round to answering.
    About half a dozen responded like you to that xxxxxxxxxxxx broadcast.
    But none were ordinary Joes and Janes I think, ie from the large majority who simply say as you put it “She’ll be right, Mate!”
    “We demand impossible standards of proof when confronted with something we don't want to hear, but will believe any old cobblers if it confirms our prejudices”  George Monbiot, Guardian website, 2011.
    Exponential growth of human numbers times ditto of consumption of resources and of pollution-production (esp of GHGs) - all happening on a finite planet, of which 70% is water, half of rest mountain desert and icecap - it's hardly rocket science that's unsustainable!


    How many wake-up calls (such as these and my own Apology to the future eco-timecapsule project) do our leaders need?!
    everywhere in  the world??
    [By the way I know and treasure Australia, having visited in the last 35 years often more than once every capital city incl Hobart - plus the red Centre]

    Warm regards
    Emeritus Professor of xxxxxxxxxxxxxx
    "We have not inherited the world from our grandparents - we have borrowed it from our grandchildren"



    (My original email to the Professor)


    Hello Professor,

    Thank you for your time this morning on a local television station in Melbourne, Australia (I’ve also just finished watching your TED presentation). I’d be curious to know how many folk from Down Under send an email to you; not “the converted” as such, but rather, my fellow Joes and Janes.

    My following comments are strictly from an Average Joe’s POV, living in mainstream suburbia. They may seem of a skeptical nature, however honesty is my intention...

    The good life

    It seems recent times has given rise to a definite rigidity in the way people plan their future. The thinking that life is generally pretty comfy, that there’ll always be solutions for any problem, large or small. This ultimately suppresses serious thought on future planning; I’d say for the vast majority.

    In other words; people aren’t really thinking about how the world will look fifty years down the track, much less ten years or even five. I’m confident any straw poll would show this. Sure my fellow Joes and Janes realise there’s peaks and troughs, but really, “She’ll be right, Mate!”

    This lack of forward-thinking is exacerbated by the ever increasing cost of living, both globally imposed (rising cost of fossil fuel energy) and self-imposed (more people wanting more). And while we work longer hours to pay for those things we need (and think we need), any notion of problem-solving distant issues will remain locked away in the “to do” box.

    So the meaning of life is fixed: Work, get the money that pays for stuff, for our kids, for our retirement. That’s all she wrote.

    No doubt I’m part of the problem; large house, two cars, energy inefficiency everywhere, on and on. And no doubt I won’t voluntarily give it up... Riding bikes in our hilly, cold and wet suburbia is not an option. Installing expensive, unproven (ROI) solar panels on the roof is not an option. Battery-powered cars that apparently grow on trees is not an option. Asking my neighbours, family or friends to have less children, that’s laughing-stock territory.

    What I’m attempting to illustrate is, that even one who believes change is required is unlikely to do so, for various reasons. And I’m not a lazy person, I work sixty hours a week; it just all seems too hard, too expensive. So what hope is there for the rest? No doubt that is the doomer-way of thinking, but as I see it – living and observing the mainstream way of life where there’s been negligible change – it remains a realistic observation nonetheless.

    The other elephant

    To have more, a couple fundamentals are essential – sustained supply of both energy and basic resources. The primary source of energy, fossil fuel (most particularly, crude oil), has been the driving force for our way of life. Eighty-plus million barrels everyday, energy required to take resources from the earth and use it in mostly ridiculous ways. But long term sustainability of supply (not to mention growth!) is the talk of the ultimate optimist. It can’t possibly be achieved and around the time we top out at a 9B population, peak oil will well and truly be in our mirrors.

    I’ll assume you know more than I do on the subject! 🙂

    I envisage a population reversal on this premise alone. Solar panels, wind farms and the like are not the answer, they are nothing more than a band aid to make a few feel better about themselves. Without copious amounts of cheap portable energy on offer, our way of life – no matter the state-of-play – will fall.

    When the Gulf of Mexico oil disaster was in full swing, why did no-one think to ask, “Why are we drilling for oil in the ocean?” The answer is pretty obvious. Crude is a finite resource.

    What AM I prepared to do?

    I’m quite happy to be governed by wiser heads; heck, I’d embrace it warmly! However, such heads do not seem to exist in any significant numbers and those that might seem driven by factors unrelated to harmonising the planet. Of course, such are the words of anti-establishment, but really they’re not. We need politicians who truly care about the long term future. I cannot think of one that puts the issues on the public table, takes our hand, guides us through such issues as compounding growth (maths that is very basic and easily demonstrated).

    The idea that “growth is good” needs to be reassessed and countered. That alternative forms of (very expensive) energy only kick the can down the road. But the chances of such global debate? Hmmm....

    And it doesn’t help that we, the vast majority of so-called free-thinkers, believe in such stories that belong in a Harry Potter novel, if you get my meaning, and prefer to watch the mish-mash that is mainstream TV (including the program this morning).

    Pessimistic about the future?

    As it stands, I am, yes. Until our leaders begin discussing the basics of un-checked growth on a finite planet in simple terms to my fellow Joes and Janes, I’ll remain that way. I’ll continue to live a care-free life, doing my best to impart a few simple truths to my children. Details are a distraction, I’ll tell them. It’s the big picture that’s important.

    Thank you again for your time.

    Matthew Blain
    Melbourne, Australia
    Father of three great kids




    (My follow-up)


    Hello  again Professor,

    You may have seen this already, certainly worth a  watch...


    The  creators of this are far more optimistic than I, but it’s the nuts and bolts  as far as I’m concerned.


    Matthew Blain




    (My last comment)


    Thank you Professor, for getting back. My 19yo daughter lost the bet! 🙂

    Al Bartlett’s lecture (a roughly shot video) was a lightening-bolt moment for me a few years back, but I fear George Montbiot’s article does little more than reinforce my pessimism for my kids’ futures. It doesn’t surprise me that you received no emails from mainstream Melbourne, other than myself.

    That’s not a self-gratifying comment, BTW. I’m truly saddened by the lack of interest.

    Compounding growth is clearly the nuts and bolts; everything else is mere detail. The only thing that gives me hope is its basic maths which can be simply demonstrated. Indeed, it needs to be demonstrated.

    My wish...

    That learned folk such as yourself organise, head for the barn, grab the pitchforks, demand the politicians listen and understand the basic maths of compounding growth. Have them teach it to the rest of us. ASAP.

    (Shoulder shrug) Pigs might fly...


    PS. As always, I type these letters with little hope of any real outcome. But hope remains nonetheless...



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  • Fri, Aug 01, 2014 - 11:46am


    [email protected]

    Status: Member

    Joined: Aug 01 2014

    Posts: 1


    Great Stuff!

    This really is a most fascinating read, probably the most enlightening thing I have ever read.

    I am very interesting in the environmental and sustainability issues that we face as a species, and am quite good at joining the dots to piece the big picture of events together, however your crash course I watched originally, improved my outlook immensely, could even say so exponentially!  I especially liked how you broke it down into mathematical terms which helped my understanding much easier than with lectures elsewhere I had grown accustomed to.

    It is quite scary to view the problems but enlightening and empowering to know, that by no means is it inevitable for us to be facing the end of the road for as humans, if and optimistically when I believe we will get round to solving our immense problems we will soon have no choice to face head on.

    Your ability to explain the issues matter of factly and impartially is the best part about all your presentations, as none are discussed in the one sided biased views I am most used to reading with.

    I am looking forward to reading your further material.




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