Do renewables decrease global CO2 emissions?

Given the noisy propaganda about the positive impact of renewables, or "clean energy,"  or "green energy" on global emissions of carbon dioxide, one expects there would be some.  Unfortunately, there is none as far as I can tell.  In fact, the situation is even more hopeless than I feared in my darkest dreams.

Here is the data from the International Energy Agency (IEA), plotted originally by P.F. Henshaw, and replotted a little differently by me. You can click on the plots to see them in high resolution.

Above you see a semi-logarithmic plot of the normalized

1. Global Gross Domestic Product (GDP), 
2. Rate of use of energy in the world (Energy), 
3. Rate of global carbon dioxide emissions (CO2), and 
4. Dollars of income generated per unit of energy expanded globally per year ($/Btu).  

All values are relative to those in 1971, and all curves start from 1. All trends are exponential, so they plot as approximately straight lines on the semi-logarithmic scale.  The global GDP grows roughly 1.85 times faster than global energy use and global CO2 emissions, and 3.7 times faster than global efficiency.

By rescaling the slopes of the trends above with the multipliers shown in the inset box, all trends more less overlay.  So here is the really bad news:

1. The rate of energy use and carbon dioxide emissions are virtually identical and have grown exponentially over the last 40 years.  
2. The impact of large dams and nuclear power plants has been barely visible, and disappeared by 2007.
3. The renewable energy sources, wind turbines, biomass cogeneration, and biofuels (photovoltaic panel area is too small to be relevant), are barely keeping up with the deforestation and general paving of the world.
4. Increased efficiency leads to more energy use and the ratio of the slopes has remained constant (3.7) over the last 40 years.  Thus, just as Stanley Javons predicted, higher efficiency leads to more energy use which leads to still higher efficiency.
5. Since the Earth is finite, this trend cannot continue and the current global economy must break down.  There is nothing we can do about it, unless we fundamentally change, and the approach to breakdown is exponential.  I spoke more on this subject here.
6. For example, the expected period of doubling of global energy consumption is 34-37 years.  Since this doubling is impossible, claims to the contrary by the IPCC notwithstanding, the global economy as we know it today will cease to exist within the next 10-20 years.

Now the good news:

1. Something's gotta give! It is quite possible that earthlings can learn and act when faced with an old problem with no old solutions.