There is no hockey stick

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  • Tue, Apr 06, 2010 - 10:00pm

    #1
    maichem

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    There is no hockey stick

Hi guys/gals,

I may not be a mathematicion by trade, but I don’t believe that the exponential growth CM shows as happening is accurate.   He starts by saying that “amounts” are used in place of “rates” for ease of explanation, but it is a misuse of data to illustrate exponential growth in this way.  The graphs below demonstrate how a simple change in range for the y-axis can change our position on the hockey stick.  I’ve used the same column of data for both graphs with a 5% rate of growth applied; the x-axis remains the same; the y-axis ranges from 0 to 1,000,000 in the first graph and 0 to 10,000,000 in the second graph.  Notice how in the year 60 we are climbing steeply up the hockey stick in graph 1, but barely on an incline in graph 2.

Now, this is not to say that the exponential growth of population is not a problem, or that exponential debt isn’t a problem, but it is to say that the timeline for such cataclysmic doom is unforseeable when looking solely at the “amounts.”

Perhaps this has been discussed, I couldn’t find it anywhere though.

Thoughts?

 

  • Tue, Apr 06, 2010 - 11:43pm

    #2
    Peak Prosperity Admin

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    Re: There is no hockey stick

Chris Martenson DISCUSSES this at the beginning of the relevant chapter.  He explains that the y axis scale is determined by WHEN the impact of what it is that is being charted becomes an issue, so, for example, if the Earth could support 100 billion people, then the y axis would be at least that much, and you are right, there would be no hockey stick on a population chart with a 100 billion y axis….

HOWEVER, the world is ALREADY overpopulated, so a 9 or 10 billion scale is perfectly acceptable, and a hockey stick is detectable…

I suggest you rewatch the chapter on exponential growth.

Mike

  • Wed, Apr 07, 2010 - 01:00am

    #3
    Peak Prosperity Admin

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    Re: There is no hockey stick

Yep. You are right on the money with your interpretation of the exponential function. Is is true *by definition* that there is no inflection point or “elbow” in an exponential curve. However, you will still see people on this site and elsewhere (including Chris) mistakenly talking about the location of the “elbow” or the location of the “point where the curve goes parabolic.” No such point exists as you have shown in your graphs. This supposed/imagined “elbow” point is entirely dependent on what values you choose for x_max and y_max and is different for every set of (x_max, y_max) you choose. 

That academic criticism aside, it turns out that in many cases it doesn’t really matter. As Mike alluded to above, if you fix y_max to the best guess you have as to the real limit imposed by our finite resources then then arguing about the graph looking different when you change the axes becomes a moot point. For example if you are talking about oil production, plot your graph with y_max = total amount of oil estimated in the world. If you are looking at a graph of copper ore, plot the graph with y_max = total amount of estimated copper ore on the planet. This of course, means that you must have an estimate for these limits that you believe. 

A case where this approach does not work is money. The approach outlined above suggests that when we plot things like total credit outstanding or national debt, that we should set y_max to equal the total amount of money in the world. However, in fiat-land there is no hard limit to the amount of $$ in the world and so we cannot  pick a useful upper limit. Therefore take any talk about $$ values “going parabolic” or “passing the elbow” with a big dose of skepticism.

  • Wed, Apr 07, 2010 - 02:09am

    #4
    Peak Prosperity Admin

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    Re: There is no hockey stick

Wow, Taco and Maichem, ya’ll are going to set a new standard for nitpicking while Rome burns.  Just keep telling yourself “There Is No Elbow” and it’ll all work out.

Viva anyway — Sager

  • Wed, Apr 07, 2010 - 02:19am

    #5
    Peak Prosperity Admin

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    Re: There is no hockey stick

 

 nope.. nothing to see here…

 

 

  • Wed, Apr 07, 2010 - 03:03am

    #6
    Peak Prosperity Admin

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    Re: There is no hockey stick

Plato,

I like your graph. And I understand your point that there is *definitely* an elbow in that graph. I do not disagree. However that data set does not depict exponential growth. The growth of BASE up until late 2008 is very close to linear growth (a slightly better fit would be x^2) — *not* exponential growth. After late 2008 an entirely new growth pattern formed one that could be considered discontinuous with the previous pattern. Additionally, this new growth pattern — while too early to make an accurate statement about its nature — conforms best to a linear or x^2 model of growth.

To be clear, I don’t like that graph at all, but I’m not sure it belongs in a discussion about exponential growth.

  • Wed, Apr 07, 2010 - 03:10am

    #7
    Peak Prosperity Admin

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    Re: There is no hockey stick

Oooh Oooh, I have one, it does not show exponential growth, but….

Gross+Federal+Debt+yoy+Change.png

  • Wed, Apr 07, 2010 - 08:54am

    #8
    Peak Prosperity Admin

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    Re: There is no hockey stick

Well said, damnthematrix.

By Maichem’s argument, he might as well have used a y scale that was a factor of 10 more than he did and it would appear as though there is hardly any movement in the consumption of whatever is being measured. Using a meaningful scale for the y axis at least illustrates our problem better than using a scale that shows the graph almost empty. Chris’s baseball stadium analogy is a good one here. Each doubling gives an absolute increment that is accelerating. The stadium might be three quarters empty but it only takes two more doublings to fill it. In each doubling, we consume more, in that increment than all consumption ever beforehand.

The apparent inflection point is needed to try to wake people up. If people were given the impression that the there are, say, a thousand times more resources than has already been used, then that would be a false impression. Consequently, Maichem’s second graph is only useful if the y axis truly gives some idea of the limit. Even then, it would downplay the problem that the future has; at some point, even the second graph will start to look like the first (at which time, some future maichem will point out that choosing a much larger upper value will diminish the problem).

  • Sun, Apr 11, 2010 - 01:13pm

    #9
    Peak Prosperity Admin

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    Re: There is no hockey stick

Ok, help me out here.  It seems that two problems are being conflated here.  There has been recently a huge increase in our nations (sorry, US, for me) debt in the last few decades.  What I think is that some are trying to say that it is the nature of the Fed and how money is intoduced into the economy through debt that is causing this problem.  It seems to me that the bulk of this debt is from deficit spending.  The fact that we have the ability to monetize our debt (via the Fed) certainly is one of the moral hazards that encourages us to increase our debt but it doesn’t necessarily mean that we are doomed to be increasing our debt at our current rate.

Here is where I would like the community to check my math:  Imagine the US electorate finally acquires the political will to have its government spend only what it takes in, in taxes, and no more.  In this scenario, the only new money (and by the nature of how the fed works, debt) that would need to come into the system is the interest on the national debt? Right?  Everything else is paid for with taxes, but the money for the interest has not been created yet and is not out there in the econmy to be collected?

If my second paragraph is correct.  Here is my math:  The current national debt is given a value of 1 (to keep the math easy).  Let us place the interest for the national debt at 3% (higher than what T-bills are paying now but about the rate of historical inflation))  using this compound interest calculator here: http://www.moneychimp.com/calculator/compound_interest_calculator.htm  $1 at 3% compounded yearly for 100 years is $19.22 (or 19.22 x our actual current debt) at 200 years it is 369x, at 300 years 7098.51 times etc.

Scary numbers but won’t the effort of paying the interest on this be about the same as long as the economy grows at the same  rate as the debt interest rate?  The econmy should also be expanding exponentially and thus have more wealth to pay interest.  The debt and its interest payment should still be the same percent of the gdp, or economy as a whole?

If my math is right, the real danger is not that we bring money into the world via debt, but that we take on much, much more debt than is necessary to just pay our interest and keep money coming into the economy.  It would seem that if we balance our budget, inflation and growth will adequately support our creation of money. 

  • Mon, Apr 12, 2010 - 07:05pm

    #10
    Peak Prosperity Admin

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    Re: There is no hockey stick

vieuxcarre,

You need to watch the Crash Course (on this site) to understand why the economy cannot keep growing forever.

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