The 30% figure in the headlne is misleading because of the hydro component. There is no way to grow hydro generation. All the dams that can be built have been built.

Here are a couple of graphs that give a clearer picture of the situation. If you want to predict the future, extrapolate by looking at the graphs. You can somewhat guess at the future that way and it's not what is suggested by the Guardian headline. That headline is aspiration, not reality.

https://www.statista.com/stati...
https://ourworldindata.org/gra...

The picture painted by these graphs is somewhat different. Energy consumption will continue its rapid growth and fossil fuel consumption will grow with it. Wind and solar will also grow dramatically and will somewhat dent the growth of the fossil fuel component.

alt dot org slash nethack

watch the ttyrecs

choose the name that's right for you

dare to compare

The headline is based on the latest IEA (International Energy Agency) forecast called the "2012 World Energy Outlook"

Follow the link to a graph of what is being forecast and to the report in question:

http://earlywarn.blogspot.fr/2012/11/iea-us-to-be-worlds-largest-oil-producer.html

Look at the graph: conventional oil and natgas are in decline.
Note the super optimistic growth assumptions for unconventional gas and oil.
What is the methodology behind this extrapolation? That's the question people should be asking themselves.

Natgas price is at historic lows. Low prices mean small profits mean decreasing investment.
These days the unconventional gas industry is facing something of a bust:

http://www.nytimes.com/2012/10/21/business/energy-environment/in-a-natural-gas-glut-big-winners-and-losers.html?pagewanted=all&_r=0

How well does that fit with the optimistic growth scenario?

Also, the IEA does not exactly have a sterling reputation for balanced impartial forecasts:

http://www.guardian.co.uk/environment/2009/nov/09/peak-oil-international-energy-agency

Just because something is a headline, doesn't mean it's true. Time will tell, of course.

Here is a calculation to illustrate the main idea

Define the function f(x) = (x+2)/(x+1)
a function of this type is called a fractional linear transformation

Set
x0=1
and iterate using f(x)
x1=f(x0) = 3/2=1.5
x2=f(x1)= 7/5=1.4
x3=f(x2) = 17/12 ~ 1.4167
x4=f(x3)=41/29 ~ 1.4138
x5=f(x4)=99/70 ~ 1.4143
x6=f(x5) =239/169 ~ 1.4142

These fractions approximate, indeed converge to the square root of 2

It turns out that in this particular case these fractions are the best possible approximations for sqrt(2)

We know that 1.4142 are the 1st 6 digits of sqrt(2)

sqrt(2) ~ 1+f1 where
f1=0.4142....
1/f1 = 2+f2 where
f2=0.41421...
1/f2 = 2+f3 where
f3=0.41421...

actually f1=f2=f3=.... ad infinitum

This means that
sqrt(2) = 1+ 1/(2+1/(2+1/(2+...))))
The last expression is called a continued fraction

the numbers in it are obtained by subtracting away the whole part taking the reciprocal, subtracting away the whole part, etc

The amazing thing is that for square roots this process isn't random but repeats cyclically. For sqrt(2) the cycle is particularly simple
we start with 1 and after that all the #s we get are 2

The numbers
1
1+1/2=3/2
1+1/(2+1/2) = 7/5
1+1/(2+1/(2+1/2)) = 17/12
are the fractions that result from truncating the continued fractions
These fractions are the best possible approximations for sqrt(2) ("best possible" has a precise meaning that we don't need to get into here)

Now here is the punchline.

Notice how we get the same fractions by iterating f(x) and by doing the continued fraction expansion

This doesn't happen for all square roots.
More interestingly, there can be an infinite overlap in the two sequences of approximations
O'Dorney figured out when this happens

http://www.maa.org/abstracts/mf2010-abstracts.pdf

See page 13

Hamming codes are practical things, while Shannon's analyses of codes were more abstract (though still hugely useful and important)
Consider the checksum bit. It helps to catch errors but there are 2 problems. First, if there is a double error (more likely if the checksum is on a longer string), then the error isn't caught Second, even if we know there is an error, we can't recover, but have to resend.
The easiest error-correcting code is to replace every bit with a triple copy of itself. So
101 becomes 111000111
This way, we can recover from any single error, but the scheme is very inefficient.
Hamming's simplest code takes a 4 bit message and adds 3 very special parity bits (think partial checksums) arranged in a clever way so that any one bit error can be isolated and corrected.
That's the basic idea. The details are many places, such as http://en.wikipedia.org/wiki/Hamming(7,4)