There is no hockey stick

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maichem's picture
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?

Damnthematrix's picture
Damnthematrix
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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

taco's picture
taco
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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.

SagerXX's picture
SagerXX
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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

plato1965's picture
plato1965
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Re: There is no hockey stick

nope.. nothing to see here...

taco's picture
taco
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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.

Tycer's picture
Tycer
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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

sofistek's picture
sofistek
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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).

vieuxcarre's picture
vieuxcarre
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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. 

sofistek's picture
sofistek
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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.

britinbe's picture
britinbe
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Re: There is no hockey stick

.....maybe also watch the Al Bartlett videos on Youtube (called "the most important video you will ever see"), Al does a great job of addressing these issues nicely and demonstrates man's inability to understand the exponential function

Anyone up for rearranging the deck chairs on the Titanic??

ckessel's picture
ckessel
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Posts: 450
Re: There is no hockey stick

britinbe wrote:

.....maybe also watch the Al Bartlett videos on Youtube (called "the most important video you will ever see"), Al does a great job of addressing these issues nicely and demonstrates man's inability to understand the exponential function

Anyone up for rearranging the deck chairs on the Titanic??

+1 britinbe,

Some of the above comments are a classic demonstration of Albert Bartletts quote you mention. Mathematics is really a tool and can be used as such if it is recognized for what it is. OR   you can pick up  hammer and try and use the claw end to drive a nail .........and claim that the darn tool just won't work no matter how many time you try and strike the nail. 

All I can say is keep swingin!  Sooner or later it will come to you.

Coop

Vanityfox451's picture
Vanityfox451
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The Most Important Video You'll Ever See!

Britnbe, ckessel,

Everyone on this site that are new need to grasp the message in these films. This was the very beginning of my journey of understanding to the importance of the Exponential Function ...

~ VF ~

silvervarg's picture
silvervarg
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Re: There is no hockey stick

Viuxcarre must have already grasped the concept of exponential growth as he clearly stated that as long as the "economy grows" at the same rate or faster than the "current national debt" we are not getting in worse shape.

That would be that the rate of the national debt to GDP would be constant or dropping.

Question is if the "economy" can grow at an exponential rate without taking on more debt and without having exponentially increasing population (that helps expand GDP).

I am not sure I have an answer to that question. At first I was about to answer, but the more I weight into the question the more uncertain I get about the answer. As allways oppinions are welcome.

redpill's picture
redpill
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Re: There is no hockey stick

People seem to miss the important point that the data series used by CM tend to have something in common, because they exist in the real world: they are all bound by real limits.  This is what makes the displayed curves legitimate. 

Were it just theoretical math there would be no basis for displaying the series like they are, because there would be no reason to suggest arbitrary boundaries in the y-axis.  But in the real world, things do have maximums.  There is a maximum amount of debt we can have in relation to our ability to produce, there is a maximum population the planet can hold, there is a maximum amount of oil that can be drilled.  You can argue about the boundaries he chooses for those maximums, but the key point is those maximums exist whether we are able to accurately estimate them or not.

darran's picture
darran
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Re: There is no hockey stick

redpill

ludwig wittgenstien would have a field day   this is nonsense   , as  something cannot be an A and not an A that is a contradiction and not coherant to logic of any sort.

first you state that as things exist in the real world thus they are bound by real limits ( be they absolute or not i presume)

then you say were it just theoretical maths( which it is not )  we would not have to place the axis in or with boundries( so we do )  as there would be no arbirty boundries to suggest( that there are what figures these arbitry boundries are is debatable)

then you suggest that there are boundries ( as you say now contradict the above statement,im  not sure if you count them as arbitry or not ) in the real world and  suggest that as they exist they must have limits or bounries( again contrary to what is suggested before)

so the notion that there is no hockey stick is wrong based on  your contradiction, as if there are limits be that knowable or not or calculatable or not then the rational of compounding is real within the real world

what may be said is that the figures for calculating the graphs are wrong or pessamistic ( mathusian , although he wasnt far wrong an industrial evolution stoped his predictions  )  ( and im not so sure they are )

ps even in theoretic maths there are boundries so again contrary to what is

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VilmaGGerber
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